High-Energy Emission from Pulsars and their Systems

Astrophysics and Space Science Proceedings

For further volumes: http://www.springer.com/series/7395

High-Energy Emission from Pulsars and their Systems Proceedings of the First Session of the Sant Cugat Forum on Astrophysics Editors

Nanda Rea Diego F. Torres

Editors Nanda Rea Institut de Ciències de l’Espai (IEEC-CSIC) Campus UAB Fac. de Ciències Torre C5, parell, 2a planta 08193 Barcelona Spain [email protected]

Diego F. Torres Institut de Ciències de l’Espai (IEEC-CSIC) Campus UAB Fac. de Ciències Torre C5, parell, 2a planta 08193 Barcelona Spain [email protected]

ISSN 1570-6591 e-ISSN 1570-6605 ISBN 978-3-642-17250-2 e-ISBN 978-3-642-17251-9 DOI 10.1007/978-3-642-17251-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011920988 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

This book is dedicated to the memory of Prof. Okkie de Jager

Preface

The Sant Cugat Forum on Astrophysics1 is a framework meant to host international meetings on violent and energetic phenomena in the Universe happening both at Galactic and extra-Galactic scales. Among the meetings hosted by the Forum, the most recognizable will be the Workshop sessions focusing on a specific aspect of astrophysics, like the one this book is about. These will typically be held every two years, with a typical size of 100 persons, hosting many plenary talks, and having a duration of about four days. The Forum has been established under the auspices of the Sant Cugat City Hall, the Institute for Space Sciences (ICE-CSIC), the Institut d’Estudis Espacials de Catalunya (IEEC), and the Instituci´o Catalana de Recerca i Estudis Avanc¸ats (ICREA). The inaugural meeting of the Forum, which we are pleased to report on with this book, has been about the High-Energy Emission from Pulsars and their Systems. The aim of this meeting was to address, in a global context, the current knowledge and challenges on the high-energy emission from isolated and non-isolated neutron stars, as confronted with observations of both the Fermi satellite (and its main experiment: the Large Area Telescope) and the currently operating groundbased Cherenkov telescopes (like MAGIC, H.E.S.S., and VERITAS). Participants have also discussed the prospects for possible observations with planned instruments across the multi-wavelength spectrum (e.g. SKA, LOFAR, E-VLT, IXO, CTA) and how will they impact on our theoretical understanding of these systems. Following the Forum intentions, this book does not represent only the proceedings of such meeting, but also, a reflection on the state-of-the-art in the topic. The Forum enjoyed an inaugural act presided by the Sant Cugat Major, the Exmo. Sr. LLuis Recoder i Miralles, which was followed by a public talk by Prof. J. BellBurnell. This talk has been simultaneously translated from English to more than 500 attendees, among them, many local high-school students. The organizers warmly thank Prof. J. Bell-Burnell and Mr. Recoder i Miralles for their substantive support 1

Its website is http://www.ice.csic.es/research/forum . ix

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and commitment in giving the Forum such an stellar start. Also a first-timer, this meeting saw the presentation of the initial Sant Cugat Forum on Astrophysics Award given to the best presentation by a Young Scientist. It was given to Mr. Xue-Ning Bai, for his work on Modeling of gamma-ray Pulsar Light Curves from Force-Free Magnetosphere, which is included in this volume. Before putting this volume in the hands of its readers, hoping that it will contribute as a reference work of such an amazingly evolving field, it is then very appropriate, and a pleasure, to warmly thank Prof. J. Bell-Burnell, and the Scientific Organizing Committee (SOC), who have helped us shape the content and direction of the Workshop. The SOC was formed by Jonathan Arons (University of Berkeley, USA) Wlodek Bednarek (Lodz University, Poland) K. S. Cheng (Hong Kong University, China) Okkie de Jager (Potchefstroom, South Africa) Guillaume Dubus (LOAG, France) Alice Harding (NASA / GSFC, USA) Kouichi Hirotani (TIARA, Taiwan) Gianluca Israel (INAF, Italy) Simon Johnston (CSIRO, Australia) Sandro Mereghetti (IASF, Italy) Nanda Rea (IEEC-CSIC, Spain) Olaf Reimer (Innsbruck University, Austria) Diego F. Torres (ICREA / IEEC-CSIC, Spain). The meeting would have been impossible without the help of the local organization, which was formed by Anna Bertolin (IEEC) Andrea Caliandro (IEEC-CSIC) LLu´ıs Campins i Punter (Museu Monastir, Sant Cugat) Ana Castells (Casa de la Cultura, Sant Cugat) Aida Chavarr´ıa (Teatro Auditori, Sant Cugat) Marta de Castro (Oficina de Turismo, Sant Cugat) Elsa de Cea (IEEC-CSIC) Valent´ı Feixas i Sibila (Sant Cugat City Hall, Spain) Daniela Hadasch (IEEC-CSIC) Pilar Montes (IEEC) Delfi Nieto (IEEC) and especially, without the support of our sponsors: the Instituci´o Catalana de Recerca i Estudis Avanc¸ats (ICREA), who presented us with its prestigious Conference Award for the organization of this meeting, the Institut d’Estudis Espacials de Catalunya (IEEC), the Institute for Space Sciences (ICE-CSIC), and the Ag`encia de

Preface

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Gesti´o de Ajuts Universitaris i de Recerca (AGAUR). The Forum logo and artwork were created by Anna Pedescoll and Ignasi Sans, from the Sant Cugat City Hall Communication Department, to whom we are indebted.

Some ideas can never flourish without the far-reaching vision of those extraordinary persons that provide unfading support to projects that otherwise could only be qualified as chimeras. In this case, this person is Valent´ı Feixas i Sibila, Director of Cultural Affairs of the Sant Cugat City Hall.

Sant Cugat September 2010

Nanda Rea Diego F. Torres

Contents

Radio Pulsar Phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simon Johnston and Aris Karastergiou 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Observational Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Integrated profiles and polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Pulse width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Profile shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Linear polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Position angle swing and orthogonal modes . . . . . . . . . . . 3.5 Circular polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Rotating Vector Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Problems and Perils of the RVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Radius-to-Frequency mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Velocity - spin axis alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Beam models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Rankin et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Lyne & Manchester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Karastergiou & Johnston . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Two Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 The radio loud magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Pulsars with notches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Future instruments and the Square Kilometre Array . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radio pulsar populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Duncan R. Lorimer 1 Selection effects in radio pulsar surveys . . . . . . . . . . . . . . . . . . . . . . . 1.1 Flux–distance relationship . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The radio sky background . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Propagation effects in the interstellar medium . . . . . . . . . .

1 1 2 4 5 5 6 7 7 8 10 11 12 12 12 13 14 14 14 15 16 17 18 21 21 22 22 22

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1.4 Finite size of the emission beam . . . . . . . . . . . . . . . . . . . . . 1.5 Pulse nulling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Intermittency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Correcting the biases in the observed sample . . . . . . . . . . . . . . . . . . 3 Recent results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Pulsar space distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Pulsar velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Pulsar luminosities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Magnetic alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Magnetic field decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Final thoughts and future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Rotating radio transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Millisecond pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Pulsars in the Magellanic Clouds . . . . . . . . . . . . . . . . . . . . 4.4 Globular cluster pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23 24 24 24 26 26 28 28 30 31 32 32 32 33 33 34

Pulsar Results with the Fermi Large Area Telescope . . . . . . . . . . . . . . . . . . . . Paul S. Ray and Pablo M. Saz Parkinson for the Fermi LAT Collaboration, the LAT Pulsar Timing Consortium, and the LAT Pulsar Search Consortium 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Gamma-ray Pulsars in the Year 2000 . . . . . . . . . . . . . . . . . 1.2 Fermi and AGILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The EGRET Pulsars in Exquisite Detail . . . . . . . . . . . . . . . . . . . . . . . 3 Young Pulsars Found Using Radio Ephemerides . . . . . . . . . . . . . . . 4 Millisecond Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Radio MSPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Searches of LAT Unassociated Sources . . . . . . . . . . . . . . . 4.3 Globular Cluster MSPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Blind Periodicity Searches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Pulsar Timing with the LAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Multiwavelength Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 The LAT Pulsar Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Future Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Fermi view of the EGRET pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Gargano for the Fermi-LAT collaboration 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Analysis results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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37 37 38 39 42 42 43 44 45 46 48 49 52 54 55

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“Garden-variety” Gamma-ray Pulsars J0248+6021 & J2240+5832 . . . . . . David A. Smith for the Fermi LAT Collaboration 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Two Not-So-Typical Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 About those distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Understanding the Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Extension studies of galactic sources with Fermi . . . . . . . . . . . . . . . . . . . . . . . Francesco Giordano on behalf of the Fermi-LAT Collaboration 1 The simulated cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Galactic extended SNRs: the W51C, the W44 and the IC443 . . . . . 3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Advances in understanding double features in radio pulsar profiles . . . . . . Jarosław Dyks, Bronisław Rudak and Paul Demorest 1 The Double Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Emission from the Polar Cap and Slot Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alice K. Harding and Isabelle A. Grenier 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Polar cap and slot gap electrodynamics . . . . . . . . . . . . . . . . . . . . . . . 2.1 Polar cap pair cascades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The slot gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Geometry of high-energy radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Confronting the Fermi observations . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Population synthesis and light curve fitting . . . . . . . . . . . . 4.3 New insights from the increasing γ-ray MSP Population . 5 Learning from Nature - Future pulsar modeling . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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63 64 64 65 66 67

69 72 73 73

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79 80 81 82 84 85 86 87 94 96 97

Gamma-ray emission and pair creation of outer gap . . . . . . . . . . . . . . . . . . . . 99 K. S. Cheng 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 2 Two dimensional outergap model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 2.1 Gap structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 2.2 Curvature radiation spectrum . . . . . . . . . . . . . . . . . . . . . . . . 103 2.3 Properties of curvature spectra with gap parameters . . . . . 104 2.4 Fitting Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3 Pair creation mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.1 Photon-photon pair-creation process . . . . . . . . . . . . . . . . . . 108

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3.2 New gap closure mechanism . . . . . . . . . . . . . . . . . . . . . . . . 109 3.3 Predictions of new outer gap model . . . . . . . . . . . . . . . . . . 112 4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 What Pulsar High-Energy Emission Model Survives? . . . . . . . . . . . . . . . . . . 117 Kouichi Hirotani 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 2 Basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 2.1 Poisson Equation for Electrostatic Potential . . . . . . . . . . . . 120 2.2 Particle Boltzmann Equations . . . . . . . . . . . . . . . . . . . . . . . 122 2.3 Radiative Transfer Equation . . . . . . . . . . . . . . . . . . . . . . . . . 123 2.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 3 Self-consistent OG solution: the case of the Crab pulsar . . . . . . . . . 125 3.1 Gap geometry and acceleration electric field . . . . . . . . . . . 125 3.2 Photon mapping result and radiation spectrum . . . . . . . . . 125 4 Slot-gap model: the case of the Crab pulsar . . . . . . . . . . . . . . . . . . . . 126 4.1 Formation of a slot gap in the polar-cap region . . . . . . . . . 127 4.2 Lower-altitude slot-gap solution . . . . . . . . . . . . . . . . . . . . . 129 4.3 Higher-altitude slot-gap model . . . . . . . . . . . . . . . . . . . . . . 130 5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Current Models of Pulsar Magnetospheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Anatoly Spitkovsky 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 2 Plasma supply and charge-separated models . . . . . . . . . . . . . . . . . . . 140 3 Force-free models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 4 Implications of the magnetospheric solutions . . . . . . . . . . . . . . . . . . 149 4.1 Consequences for spin down . . . . . . . . . . . . . . . . . . . . . . . . 149 4.2 High energy emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.3 Reconnection and time-dependence . . . . . . . . . . . . . . . . . . 153 4.4 Current structure and origin . . . . . . . . . . . . . . . . . . . . . . . . . 154 4.5 Differential rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Modeling of γ-ray Pulsar Light Curves from Force-Free Magnetosphere . . 159 Xue-Ning Bai & Anatoly Spitkovsky References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 A Tale of Two Current Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Jonathan Arons 1 Follow The Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 2 Follow the Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

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The high-energy emission from the pulsar striped wind . . . . . . . . . . . . . . . . . 181 J´erˆome P´etri 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 2 The striped wind model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 3 Application to γ-ray pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Gamma-rays from millisecond pulsars in Globular Clusters . . . . . . . . . . . . . 185 Włodek Bednarek 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 2 The stellar content of Globular Clusters . . . . . . . . . . . . . . . . . . . . . . . 186 3 Compact objects within Globular Clusters . . . . . . . . . . . . . . . . . . . . . 187 3.1 Millisecond pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 3.2 Cataclysmic Variables and LMXBs . . . . . . . . . . . . . . . . . . . 188 3.3 Intermediate mass black holes ? . . . . . . . . . . . . . . . . . . . . . 188 4 Non-thermal emission from Globular Clusters . . . . . . . . . . . . . . . . . 189 4.1 Low energy radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 4.2 Gamma-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 5 Models for gamma-ray emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 5.1 Interpretation of the observed GeV γ-ray emission . . . . . . 192 5.2 TeV γ-ray emission from MSP winds and shocks . . . . . . . 193 5.3 Constraints on the MSP population . . . . . . . . . . . . . . . . . . . 197 6 Gamma-rays from electrons injected from other sources ? . . . . . . . 200 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 Modelling the Growing Population of γ-ray Millisecond Pulsars . . . . . . . . . 207 C. Venter, A. K. Harding, and T. J. Johnson 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 2 Pulsar Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 4 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 A Joint Radio Gamma-ray Variability Study of the Crab Pulsar . . . . . . . . . 213 Glenn Jones and Ryan Shannon 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 2 Radio Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 2.1 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 3 Gamma-Ray Radio Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

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AGILE observations of PSR B1509-58 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 M. Pilia and A. Pellizzoni for the AGILE Team and Pulsar Working Group 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 2 AGILE Observations, Data Analysis and Results . . . . . . . . . . . . . . . 220 3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Understanding the fundamental parameters of millisecond pulsars . . . . . . 225 Benoit Pancrazi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 2 Observations and data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 3 Discussion and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 Pulsars as gravitational wave detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 George Hobbs 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 2 Using pulsars to search for GWs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 3 Current data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 4 Potential sources of gravitational waves . . . . . . . . . . . . . . . . . . . . . . . 236 4.1 Single sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 4.2 Burst sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 4.3 Stochastic background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 5 Accessing pulsar data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 6 The future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 Magnetar outbursts: an observational review . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Nanda Rea & Paolo Esposito 1 Author’s preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 2 A bit of history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 3 General observational characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 250 4 Multiband view of magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 4.1 Radio emission of magnetars . . . . . . . . . . . . . . . . . . . . . . . . 251 4.2 Optical and infrared emission of magnetars . . . . . . . . . . . . 253 4.3 Soft X-ray emission of magnetars . . . . . . . . . . . . . . . . . . . . 253 4.4 Hard X-ray emission of magnetars . . . . . . . . . . . . . . . . . . . 254 5 Magnetars’ Outbursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 5.1 XTE J1810−197 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 5.2 1E 1547−5408 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 5.3 AX J1844−0258 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 5.4 1E 2259+586 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 5.5 1E 1048.1−5937 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 5.6 CXOU J1647−4552 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 5.7 4U 0142+614 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

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5.8 SGR 1806−20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 5.9 SGR 1627−41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 5.10 SGR 0501+4516 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 5.11 SGR 0418+5729 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 5.12 SGR 1833−0832 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Wide-band X-ray Studies of Magnetars with Suzaku . . . . . . . . . . . . . . . . . . . 275 T. Enoto, K. Makishima, N. Rea, Y. E. Nakagawa, K. Nakazawa, and T. Sakamoto 1 Suzaku Observations of Magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 2 Spectral Evolution of Magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 Bursts and Flares from Highly Magnetic Pulsars . . . . . . . . . . . . . . . . . . . . . . . 279 GianLuca Israel and Simone Dall’Osso 1 MAGnetic NEutron sTARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 2 SGRs Giant Flares and their magnetic fields . . . . . . . . . . . . . . . . . . . 282 2.1 The Cavallo-Fabian-Rees Variability Limit . . . . . . . . . . . . 284 3 SGRs Intermediate Flares in the Swift era . . . . . . . . . . . . . . . . . . . . . 285 3.1 The March 2006 Burst Storm of SGR 1900+14 . . . . . . . . 287 3.2 Further Observations: the case of SGR 0501+4516 and 1E 1547.0-5408 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Activated Magnetospheres of Magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Andrei M. Beloborodov 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 2 Electrodynamics of untwisting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 2.1 Evolution equation for axisymmetric twist . . . . . . . . . . . . . 301 2.2 j-bundle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 3 Transient magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 3.1 Magnetospheric activity or deep crustal heating? . . . . . . . 306 3.2 Individual objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 4 Pair creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 5 Plasma circulation in the magnetosphere . . . . . . . . . . . . . . . . . . . . . . 313 6 Magnetospheric emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

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Suzaku Detection of Hard X-ray Emission in SGR 0501+4516 Short Burst Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Yujin E. Nakagawa, Teruaki Enoto, Kazuo Makishima, Atsumasa Yoshida, Kazutaka Yamaoka, Takanori Sakamoto, Nanda Rea, Kevin Hurley, Suzaku SGR 0501+4516 Team and HETE-2 Team 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 2 Hard X-ray Emission in Burst Spectra . . . . . . . . . . . . . . . . . . . . . . . . 324 3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 The magnetar emission in the IR band: the role of magnetospheric currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Silvia Zane, Luciano Nobili and Roberto Turolla 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 2 Pair production in the inner magnetosphere . . . . . . . . . . . . . . . . . . . . 330 3 IR/Optical emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 4 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 Double features in mean pulsar profiles and the nature of their radio emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 George I. Melikidze and Janusz Gil 1 Frequency dependence of the bifurcation angle . . . . . . . . . . . . . . . . 337 2 Energy considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 Can the magnetic field of long-period X-ray pulsars be supercritical ? . . . . 341 N.R. Ikhsanov and N.G. Beskrovnaya 1 Magnetar hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 2 Feedback hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 X-ray emission from isolated neutron stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 Sandro Mereghetti 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 2 Origin of the X-ray emission in isolated neutron stars . . . . . . . . . . . 347 3 The X-ray Dim Isolated Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . 348 4 Central Compact Objects in Supernova Remnants . . . . . . . . . . . . . . 351 5 The Magnetar candidates: Anomalous X-ray Pulsars and Soft Gamma-ray Repeaters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 6 Rotating Radio Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 7 Rotation-powered pulsars with high magnetic field . . . . . . . . . . . . . 357 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

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X-ray thermal radiation from hot polar cap in pulsars . . . . . . . . . . . . . . . . . . 365 Janusz Gil and George I. Melikidze 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 2 Surface magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 3 Drifting subpulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 Radio polarization of RRAT J1819-1458 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 A. Karastergiou 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 2 Polarization characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 3 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Multiwavelength Observations of Pulsar Wind Nebulae . . . . . . . . . . . . . . . . . 373 Patrick Slane 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 2 Dynamical Evolution of PWNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 3 Spectral Evolution of PWNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 4 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 4.1 3C 58 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 4.2 Vela X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 4.3 G327.1−1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 4.4 HESS J1640−465 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 Multi-wavelength Observations of Composite Supernova Remnants . . . . . . 393 Tea Temim 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 2 G54.1+0.3: Expansion into SN Ejecta . . . . . . . . . . . . . . . . . . . . . . . . 394 3 G327.1-1.1: Interaction with the Reverse Shock . . . . . . . . . . . . . . . . 395 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 Fermi-LAT Results on Pulsar Wind Nebulae after 1.5 year of Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 M.-H. Grondin & M. Lemoine-Goumard for the Fermi-LAT Collaboration and the Pulsar Timing Consortium 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 2 The Crab Nebula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 3 The Vela-X PWN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 4 The PWN in MSH 15−52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 5 PSR J1907+0602 and its TeV PWN . . . . . . . . . . . . . . . . . . . . . . . . . . 404 6 The PWN HESS J1640-465 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

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A plausible pulsar wind nebula candidate powered by PSR J1023-5746 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410

Pulsar Wind Nebulae: The GeV to TeV Connection . . . . . . . . . . . . . . . . . . . . 413 O. C. de Jager 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 2 The Crab Nebula in γ-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 2.1 The acceleration limit for electrons in the Crab Nebula . . 414 2.2 The inverse Compton spectrum of the Crab Nebula towards the spectral tail . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 3 Accelerated PWN Spectra: Observations of the Cooling Effect . . . 417 4 A Single Spectral Component for the GeV to TeV Emission from the PWN of PSR B1509-58 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 5 Calorimetric GeV emission from PWN . . . . . . . . . . . . . . . . . . . . . . . 421 6 Discontinuous GeV and TeV Emission from Two-Component PWN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 6.1 Two-Component Extended Emission from the Vela X PWN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 6.2 Radio and X-Ray Torii of Vela X near the Termination Shock: Discontinuous Spectra . . . . . . . . . . . . . . . . . . . . . . . 422 7 HESS J1640–465: Another Two-Component Candidate? . . . . . . . . 424 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 Extended hard X-ray emission from Vela X . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 Fabio Mattana, R´egis Terrier, Diego G¨otz, Gabriele Ponti, Laurent Bouchet, Maurizio Falanga, Matthieu Renaud, Stephane Schanne 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 2 INTEGRAL identification of extended hard X-ray emission . . . . . . 432 3 Combined IBIS/ISGRI and Suzaku/XIS spectral analysis . . . . . . . . 434 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Cherenkov Telescopes Results on Pulsar Wind Nebulae and Pulsars . . . . . . 435 Emma de O˜na Wilhelmi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 2 IACT Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 3 Observations of pulsars with IACTs . . . . . . . . . . . . . . . . . . . . . . . . . . 440 4 Observations of PWNe with Cherenkov telescopes . . . . . . . . . . . . . 441 4.1 Young/Composite Pulsar Wind Nebula . . . . . . . . . . . . . . . . 444 4.2 ”Relic” Pulsar Wind Nebula . . . . . . . . . . . . . . . . . . . . . . . . . 447 4.3 Other PWNe candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

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Lepton Acceleration in Pulsar Wind Nebulae . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Matthew G. Baring 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 2 Lepton Acceleration at Relativistic Shocks . . . . . . . . . . . . . . . . . . . . 455 2.1 The Monte Carlo Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 2.2 Results for Relativistic Shock Acceleration . . . . . . . . . . . . 458 3 The Quasi-Perpendicular Pulsar Wind Termination Shock . . . . . . . 464 4 Connecting to PWN Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 MHD models of Pulsar Wind Nebulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 Niccol`o Bucciantini 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 2 Jet-Torus structure and Inner flow properties . . . . . . . . . . . . . . . . . . . 475 2.1 Time variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 2.2 Gamma rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 3 Evolution of PWNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 TeV Gamma Ray Survey on the Direction of Fermi-LAT Pulsars with the Tibet Air Shower Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 M. Amenomori, X. J. Bi, D. Chen, S. W. Cui, Danzengluobu, L. K. Ding, X. H. Ding, C. Fan, C. F. Feng, Zhaoyang Feng, Z. Y. Feng, X. Y. Gao, Q. X. Geng, Q. B. Gou, H. W. Guo, H. H. He, M. He, K. Hibino, N. Hotta, Haibing Hu, H. B. Hu, J. Huang, Q. Huang, H. Y. Jia, L. Jiang, F. Kajino, K. Kasahara, Y. Katayose, C. Kato, K. Kawata, Labaciren, G. M. Le, A. F. Li, H. C. Li, J. Y. Li, C. Liu, Y.-Q. Lou, H. Lu, X. R. Meng, K. Mizutani, J. Mu, K. Munakata, H. Nanjo, M. Nishizawa, M. Ohnishi, I. Ohta, S. Ozawa, T. Saito, T. Y. Saito, M. Sakata, T. K. Sako, M. Shibata, A. Shiomi, T. Shirai, H. Sugimoto, M. Takita, Y. H. Tan, N. Tateyama, S. Torii, H. Tsuchiya, S. Udo, B. Wang, H. Wang, Y. Wang, Y. G. Wang, H. R. Wu, L. Xue, Y. Yamamoto, C. T. Yan, X. C. Yang, S. Yasue, Z. H. Ye, G. C. Yu, A. F. Yuan, T. Yuda, H. M. Zhang, J. L. Zhang, N. J. Zhang, X. Y. Zhang, Y. Zhang, Yi Zhang, Ying Zhang, Zhaxisangzhu, and X. X. Zhou (The Tibet ASγ Collaboration) 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 2 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Fermi results on γ-ray binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Adam B. Hill, Richard Dubois, and Diego F Torres for the Fermi-LAT collaboration 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 2 LS I +61 303 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498

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The original discovery, and further TeV observations: flux, spectrum, periodicity . . . . . . . . . . . . . . . . . . . . . . . . . . 498 2.2 TeV and X-ray simultaneous observations . . . . . . . . . . . . . 499 2.3 The Fermi results on LS I +61◦ 303 . . . . . . . . . . . . . . . . . . . 500 3 LS 5039 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502 3.1 The original discovery, and further TeV observations: flux, spectrum, periodicity . . . . . . . . . . . . . . . . . . . . . . . . . . 502 3.2 The Fermi results on LS 5039 . . . . . . . . . . . . . . . . . . . . . . . 503 4 Cygnus X-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 4.1 Historical observations at high energies . . . . . . . . . . . . . . . 503 4.2 The Fermi results on Cygnus X-3 . . . . . . . . . . . . . . . . . . . . 504 5 Cygnus X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 5.1 Reports of high energy and very high energy emission . . . 508 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 Cherenkov Telescope results on gamma-ray binaries . . . . . . . . . . . . . . . . . . . 513 Juan Cortina 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 2 Detected in VHE: PSR B1259-63, LS 5039 and LS I+61◦303 . . . . 514 2.1 PSR B1259-63/SS2833 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 2.2 LS 5039 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 2.3 LS I+61◦ 303 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 3 Uncertain VHE binaries: Cyg X-1 and HESS J0632+057 . . . . . . . . 519 3.1 Cyg X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 3.2 HESS J0632+057 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521 4 Searches for other VHE binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 4.1 Cyg X-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 γ-ray binaries as non-accreting pulsar systems . . . . . . . . . . . . . . . . . . . . . . . . . 531 Diego F. Torres 1 Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 2 Why is a non-accreting pulsar system a tenable alternative? . . . . . . 532 3 Caveats in the search for X-ray spectral lines . . . . . . . . . . . . . . . . . . 538 4 Caveats in the search for pulsations . . . . . . . . . . . . . . . . . . . . . . . . . . 540 5 Notes on the theoretical models based on pulsar systems . . . . . . . . 542 5.1 A perspective on the GeV cutoffs of LS I +61◦ 303 and LS 5039 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 6 Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548

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Relativistic motion and beamed radiation in gamma-ray binaries . . . . . . . . 551 Benoˆıt Cerutti, Guillaume Dubus, and Gilles Henri 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 2 Observational backdrop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552 3 Doppler-boosted emission in LS 5039 and LS I +61 303 . . . . . . . . . 552 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 A leptonic One-Zone model of the X-Ray/VHE correlated emission in LS I +61 303 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 V. Zabalza, J.M. Paredes and V. Bosch-Ramon 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 2 Model description and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 New Optical Results on γ-ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559 J. Casares, J.M. Corral-Santana, A. Herrero, J.C. Morales, T. Mu˜noz-Darias, I. Negueruela, J.M. Paredes, I. Ribas, M. Rib´o, D. Steeghs, L. van Spaandonk and F. Vilardell 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559 2 Revised Orbital Solution in LS 5039 . . . . . . . . . . . . . . . . . . . . . . . . . 560 3 Probing Binarity in MWC 148 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 The International X-ray Observatory and other X-ray missions, expectations for pulsar physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 Yukikatsu Terada and Tadayasu Dotani 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 2 Future X-ray Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565 2.1 Overview of X-ray Missions . . . . . . . . . . . . . . . . . . . . . . . . 565 2.2 The Small Satellite Missions in 2010s . . . . . . . . . . . . . . . . 566 2.3 The ASTRO-H Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568 2.4 The International X-ray Observatory . . . . . . . . . . . . . . . . . 569 3 Pulsar Sciences with Future X-ray Missions . . . . . . . . . . . . . . . . . . . 570 3.1 General relativity under strong gravity . . . . . . . . . . . . . . . . 570 3.2 Equation of State in neutron stars . . . . . . . . . . . . . . . . . . . . 572 3.3 Plasma physics under a strong magnetic field . . . . . . . . . . 573 3.4 Emission mechanism from Magnetars . . . . . . . . . . . . . . . . 575 3.5 Diversity of Pulsar systems: white dwarf pulsars . . . . . . . . 577 4 Synergy with other wavelength observatories . . . . . . . . . . . . . . . . . . 580 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581

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X-ray Polarimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 Marco Feroci and Paolo Soffitta 1 Neutron Stars Science with X-ray Polarimetry . . . . . . . . . . . . . . . . . 585 2 Fundamental Parameters of X-ray Polarimetry . . . . . . . . . . . . . . . . 587 3 Classical Techniques and Observational Status . . . . . . . . . . . . . . . . 588 3.1 Bragg Polarimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588 3.2 Thompson/Compton Polarimeters . . . . . . . . . . . . . . . . . . . . 591 3.3 Observational results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594 4 A jump in sensitivity: the focal plane photoelectric polarimeters for soft X-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 4.1 The Gas Pixel Detector (GPD) solution . . . . . . . . . . . . . . . 597 4.2 The Time Projection Chamber (TPC) polarimeter solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598 5 Observational Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600 5.1 Gravity and Extreme Magnetism SMEX (GEMS) . . . . . . 600 5.2 New Hard X-ray Mission (NHXM) . . . . . . . . . . . . . . . . . . . 601 5.3 International X-ray Observatory (IXO) . . . . . . . . . . . . . . . . 604 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 New results on high energy cosmic ray electrons observed with Fermi LAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 Alexander Moiseev, on behalf of the Fermi LAT Collaboration 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 2 Detection of electrons by LAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612 3 Result and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620 5 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620 Positrons from pulsar winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623 Pasquale Blasi and Elena Amato 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 2 A pulsar wind inside a supernova remnant . . . . . . . . . . . . . . . . . . . . . 626 3 A pulsar wind escaping the parent supernova remnant: bow shock nebulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629 4 The positron flux from pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631 5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640

List of Contributors

Aliu Ester Barnard College / Columbia University Department of Physics and Astronomy Barnard College Columbia University New York NY 10027 USA [email protected] Arons Jonathan University of California Berkeley Astronomy Department 601 Campbell Hall Berkeley CA 94720-3411 [email protected] Bai Xue-Ning Princeton University Dept. of Astrophysical Sciences Peyton Hall Princeton University Princeton NJ 08544 USA [email protected] Baring Matthew Rice University Rice University Department of Physics and Astronomy - MS 108 P. O. Box 1892 Houston Texas 77251-1892 USA [email protected] Bates Samuel University of Manchester 7 Catterick Road Didsbury Manchester M20 6HN UNITED KINGDOM [email protected] Bednarek Wlodek Department of Astrophysics University of Lodz Department of Astrophysics University of Lodz ul. Pomorska 149 / 153 90-236 Lodz Poland [email protected] Bell-Burnell Jocelyn Oxford University Department of Physics Denys Wilkinson Building Keble Road Oxford OX1 3RH [email protected] Beloborodov Andrei Columbia University Physics Department 1013 Pupin Hall MC 5204 Box 04 538 W 120 St New York NY 10027 [email protected]

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List of Contributors

Blasi Pasquale INAF / Aretri Astrophysical Observatory INAF / Osservatorio Astrofisico di Arcetri Largo E. Fermi 5 50125 Firenze Italy [email protected] Bronek Rudak Nicolaus Copernicus Astronomical Center Rabianska 8 87-100 Torun Poland [email protected]

Bucciantini Niccoló NORDITA / Albanova NORDITA Roslagstullsbacken 23 106 91 Stockholm [email protected] Burgay Marta INAF - Cagliari Observatory [email protected] Caliandro G. Andrea Institut de Ciencies de L’Espai Institut de Ciencies de L’Espai (IEEC-CSIC) Campus UAB Fac. de Ciencies Torre C5 parell 2a planta 08193 Barcelona Spain [email protected]

Cañellas i Pagès, Albert Universitat de Barcelona Departament d’Astronomia i Meteorologia Facultat de Fsica 7a planta Universitat de Barcelona Mart i Franqus 1 08028 Barcelona Spain [email protected] Carramiñana Alberto INAOE Instituto Nacional de Astrofsica ptica y Electrnica Lus Enrique Erro 1 Tonantzintla Puebla 72840 Mxico [email protected] Casares Jorge IAC Instituto de Astrofisica de Canarias c / Via Lactea s / n 38200-La Laguna Tenerife [email protected] Celotti Anna Lisa SISSA Head of Astrophysics Sector via Beirut 2-4 34151 Trieste Italy [email protected] Cerutti Benoit Laboratoire d’Astrophysique de Grenoble Laboratoire d’Astrophysique Observatoire de Grenoble BP 53 F-38041 GRENOBLE Cdex 9 FRANCE [email protected] Cheng KS Department of Physics University of Hong Kong 530 Chong Yuet Ming Physics Bldg The University of Hong Kong Pokfulam Road Hong Kong [email protected] Coenen Thijs Universiteit van Amsterdam Plantage Kerklaan 16-II Amsterdam The Netherlands [email protected]

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Cortina Juan IFAE Institut de Fisica d’Altes Energies - IFAE Edifici Cn. UAB 08193 Bellaterra (Barcelona Spain). [email protected] de Cea Elsa Institut de Ciencies de L’Espai Institut de Ciencies de L’Espai (IEEC-CSIC) Campus UAB Fac. de Ciencies Torre C5 parell 2a planta 08193 Barcelona Spain [email protected] de Jager Okkie North-West University Physics Department North-West University Potchefstroom South Africa 2520 [email protected]

de Oña Wilhelmi Emma Max-Planck-Institut fur KernPhysik Max-Planck-Institut fr Kernphysik Saupfercheckweg 1 69117 Heidelberg Germany [email protected] Dhillon Vik University of Sheffield Department of Physics and Astronomy University of Sheffield Sheffield S3 7RH [email protected] Dubois Richard SLAC MS 71 2575 Sandhill Road Menlo Park CA USA 94025 [email protected] Dumora Denis CEN Bordeaux-Gradignan / Universit Bordeaux 1 CENBG chemin du Solarium 33175 Gradignan Cedex [email protected] Dyks Jaroslaw Copernicus Astronomical Center ”Centrum Astronomiczne im. M. Kopernika Rabianska 8 87-100 Torun Poland” [email protected] Enoto Teruaki Tokyo University Department of Physics Graduate School of Science The University of Tokyo Hongo 7-3-1 Bunkyo-ku Tokyo 113-0033 Japan [email protected] Feroci Marco INAF / IASF ”INAF - ISTITUTO DI ASTROFISICA SPAZIALE E FISICA COSMICA Via Fosso del Cavaliere 100 00133 Rome ITALY” [email protected] Freire Paulo MPI Bonn Max-Planck-Institut fr Radioastronomie Auf dem Hgel 69 D-53121 Bonn Germany [email protected] Gargano Fabio INFN-Bari Via Orabona 4 70126 Bari Italy [email protected] Giavitto Gianluca IFAE Institut de Fsica d’Altes Energies Edifici Cn. Facultat Cincies UAB E-08193 Bellaterra Spain [email protected]

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Gil Janusz Institute of Astronomy University of Zielona Gora Institute of Astronomy University of Zielona Gora 65-265 Giordano Francesco Physics Department / INFN / Bari Via Amendola 173 I-70126 Bari - Italy [email protected] Grenier Isabelle AIM University Paris Diderot & CEA Saclay AIM Service d’Astrophysique CEA Saclay 91191 Gif sur Yvette France [email protected] Grondin Marie-Helene CENBG / CNRS-IN2P3 ”Centre d’Etudes Nucleaires de Bordeaux Gradignan Chemin du Solarium 33170 Gradignan France” [email protected] Hadasch Daniela Institut de Ciencies de L’Espai Institut de Ciencies de L’Espai (IEEC-CSIC) Campus UAB Fac. de Ciencies Torre C5 parell 2a planta 08193 Barcelona Spain [email protected] Hermsen Wim SRON Netherlands Insitute for Space Research SRON Sorbonnelaan 2 3584 CA Utrecht [email protected] Hessels Jason ASTRON P.O. Box 2 990AA Dwingeloo The Netherlands” [email protected] Hirotani Kouichi TIARA TIARA 8F General bldg 2 Department of Physics National Tsing Hua University 101 Sec. 2 Kuang Fu Rd. Hsinchu Taiwan 300 [email protected] Hobbs George Australia Telescope National Facility CSIRO Australia Telescope National Facility PO Box 76 Epping NSW 1710 Australia [email protected] Ikhsanov Nazar NASA / Marshall Space Flight Center 320 Sparkman Drive Huntsville AL 35805 nazar [email protected] Israel GianLuca INAF - Roma Astronomical Observatory Via Frascati 33 Monte Porzio Catone (RM) I-00040 ITALY [email protected] Johnston Simon ATNF CSIRO ATNF CSIRO PO Box 76 Epping New South Wales 1710 Australia [email protected] Jones Glenn NRAO / Caltech Caltech MC 136-93 1200 E. California Blvd. Pasadena CA 91125 jones [email protected]

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Karastergiou Aris University of Oxford Oxford Astrophysics Denys Wilkinson Building Keble Road Oxford OX1 3RH UK [email protected] Kawata Kazumasa ICRR University of Tokyo Institute for Cosmic Ray Research University of Tokyo 5-1-5 Kashiwanoha Kashiwa Chiba 277-8582 Japan [email protected] Keane Evan University of Manchester Room 3.224 Alan Turing Building Jodrell Bank Centre for Astrophysics University of Manchester Manchester M13 9PL [email protected] Kirk John Max-Planck-Institut fuer Kernphysik Postfach 103980 69029 Heidelberg Germany [email protected] Klepser Stefan IFAE Spain Institut de Fsica d’Altes Energies Edifici Cn. Facultat Cincies UAB E-08193 Bellaterra Spain [email protected] Kondratiev Vladislav ASTRON ASTRON P.O. Box 2 7990 AA Dwingeloo The Netherlands [email protected] Kuiper Lucien SRON-The Netherlands Sorbonnelaan 2 3584-CA Utrecht The Netherlands [email protected] Lemoine-Goumard Marianne CENBG - CNRS-IN2P3 CENBG Chemin du Solarium BP120 33175 Gradignan Cedex France [email protected] Lorenz Eckart MPI Physics Munich Max Planck Inst. for Physics Foehringer Ring 6 D 80805 MUNICH [email protected] Lorimer Duncan West Virginia University Physics Department 210 Hodges Hall Morgantown WV 26501 [email protected] Mattana Fabio APC (CNRS-Universit Paris 7) Laboratoire APC Btiment Condorcet 10 rue Alice Domon et Lonie Duquet 75205 Paris Cedex 13 France [email protected] Melikidze George Institute of Astronomy University of Zielona Gora ”Institute of Astronomy Lubuska 2 65-265 Zielona Gora Poland” [email protected] Mereghetti Sandro IASF MILANO / INAF IASF via Bassini 15 20133 Milano Italy [email protected]

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Moiseev Alexander NASA / GSFC NASA / GSFC code 661 Greenbelt MD 20771 USA [email protected]

Moldón Javier Universitat de Barcelona Departament d’Astronomia i Meteorologia Facultat de Fsica Planta 7 Universitat de Barcelona Mart i Franqus 08028 Barcelona Spain [email protected] Nakagawa Yujin Institute of Physical and Chemical Research Makishima Cosmic Radiation Laboratory RIBF Bldg. 4F Higashi-Chiku (RIKEN) 2-1 Hirosawa Wako Saitama 351-0198 Japan [email protected] Nobili Luciano University of Padova ”Dip. di Fisica ””G.Galilei”” Via Marzolo 8 35131 Padova Italy” [email protected] Pancrazi Benoit CESR Toulouse 6 rue Duplex 87000 Limoges France [email protected] Paredes Josep Maria Universitat de Barcelona Departament d’Astronomia i Meteorologia Facultat de Fsica Planta 7 Universitat de Barcelona Mart i Franqus 08028 Barcelona Spain [email protected] Pellizzoni Alberto INAF-Osservatorio Astronomico di Cagliari INAF-Osservatorio Astronomico di Cagliari loc. Poggio dei Pini strada 54 I-09012 Capoterra (CA) ITALY [email protected] Pessah Martin Institute for Advanced Study Institute for Advanced Study School of Natural Sciences Bloomberg Hall 253 Princeton NJ 08540 [email protected] P´etri Jerome Observatoire Astronomique de Strasbourg Observatoire Astronomique de Strasbourg 11 rue de l’Universit 67000 Strasbourg [email protected] Pierbattista Marco AIM Sap CEA Saclay AIM Service d’Astrophysique CEA Saclay 91191 Gif / Yvette France [email protected] Pilia Maura Universit degli Studi dell’Insubria INAF c / o Dottorandi di Astrofisica via Valleggio 11 22100 Como ITALY [email protected] Ray Paul Naval Research Laboratory Code 7655.4 4555 Overlook Ave. SW Washington DC 20375-5352 USA [email protected]

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Razzano Massimiliano INFN-Pisa INFN Sezione di Pisa Edificio C - Polo Fibonacci Largo B. Pontecorvo 3 - 56127 Pisa [email protected] Rea Nanda Institut de Ciencies de L’Espai Institut de Ciencies de L’Espai (IEEC-CSIC) Campus UAB Fac. de Ciencies Torre C5 parell 2a planta 08193 Barcelona Spain [email protected] Reichardt Ignasi IFAE Institut de Fsica d’Altes Energies Edifici C7b Campus de la Universitat Autnoma 08193 Bellaterra [email protected] Reimer Olaf Universität Innsbruck Institut fr Astro- und Teilchenphysik LeopoldFranzens-Universität Innsbruck Technikerstr. 25 / 8 6020 Innsbruck Austria [email protected] Reposeur Thierry CENBG / CNRS CENBG Chemin du Solarium - BP 20 F-33175 Gradignan Cedex, France [email protected]

Ribó Marc Universitat de Barcelona Departament d’Astronomia i Meteorologia Facultat de Fsica 7a planta Universitat de Barcelona Mart i Franqus 1 08028 Barcelona Spain [email protected] Saz Parkinson Pablo Santa Cruz Institute for Particle Physics 715 Koshland Way Santa Cruz CA 95064 [email protected] Shannon Ryan Cornell University R.R. 1 S-58 C-9 Oliver BC V0H 1T0 Canada [email protected] Sheidaei Farzaneh North-West University Physics Department North-West University Potchefstroom South Africa 2520 [email protected] Slane Patrick Harvard-Smithsonian Center for Astrophysics 60 Garden Street Cambridge MA 02138 [email protected] Slowikowska Agnieszka Kepler Institute of Astronomy Institute of Astronomy Wieza Braniborska ul. Lubuska 2 65-265 Zielona Gora Poland [email protected] Smith David CNRS / IN2P3 / CENBG CENBG Chemin du Solarium - BP 20 F-33175 Gradignan Cedex [email protected] Soffitta Paolo IASF-Roma / INAF Via Fosso del Cavaliere 100 00133 Rome [email protected]

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Spitkovsky Anatoly Princeton University Department of Astrophysical Sciences. Princeton University. Peyton Hall Ivy Lane. Princeton NJ 08544 [email protected] Stappers Ben University of Manchester Jodrell Bank Centre for Astrophysics The University of Manchester Alan Turing Building Manchester M13 9PL United Kingdom [email protected] Stella Luigi INAF - Roma Astronomical Observatory Via Frascati 33 Monte Porzio Catone (RM) I-00040 ITALY [email protected] Tea Temim Harvard-Smithsonian Center for Astrophysics 60 Garden Street MS 21 Cambridge MA 02138 United States [email protected] Terada Yukikatsu Saitama University Saitama University Department of Science and Technology Physics 255 Simo Ohkubo Sakura-ku Saitama-city Japan 338-8570 [email protected] Terrier Regis APC CNRS / Universit Paris 7 Universit Paris Diderot-Paris 7 Laboratoire APC Btiment Condorcet Case 7020 75205 Paris Cedex 13 France [email protected] Tiengo Andrea INAF-IASF Milano INAF-IASF Milano via Bassini 15 I-20133 Milano Italy [email protected] Torres Diego F. Institut de Ciencies de L’Espai Institut de Ciencies de L’Espai (IEEC-CSIC) Campus UAB Fac. de Ciencies Torre C5 parell 2a planta 08193 Barcelona Spain [email protected] Trepl Ludwig AIU Jena Astrophysikalisches Institut und Universitaets-Sternwarte Schillergaesschen 2-3 07745 Jena [email protected] Treves Aldo Universit degli Studi dell’Insubria Via Valleggio 11 22100 Como Italy [email protected] Turolla Roberto Dept. of Physics University of Padova Department of Physics University of Padova Via Marzolo 8 35131 Padova Italy [email protected] van Leeuwen Joeri ASTRON ASTRON P.O. Box 2 7990 AA Dwingeloo The Netherlands [email protected]

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Venter Christo North-West University Potchefstroom Campus Unit for Space Physics North-West University Potchefstroom Campus Private Bag X6001 Potchefstroom 2520 South Africa [email protected]

Zabalza Víctor Universitat de Barcelona Dpt. Astronomia i Meteorologia Planta 7 Facultat de Fsica C / Marti i Franqus 1 08028 Barcelona [email protected] Zane Silvia MSSL University College London Mullard Space Science Laboratory University College of London Holmbury St Mary Dorking Surrey RH5 6NT UK [email protected] Zanin Roberta IFAE Institut de Fsica d’Altes Energies Edifici Cn. Facultat Cincies UAB E-08193 Bellaterra Spain [email protected] 3671949

Radio Pulsar Phenomenology Simon Johnston and Aris Karastergiou

Abstract Radio pulsars were discovered more than 40 years ago and continue to provide fertile scientific research programs. The vast majority of the nearly 2000 pulsars known are detected only at radio wavelengths. Current research at radio wavelengths includes surveys for pulsars, pulsar timing, pulsars as probes of Galactic structure, understanding the emission process and the study of phenomenlogy of pulsars generally. In this chapter we will concentrate on what can be learned from the integrated pulse profile i.e. the stable profile formed after integrating typically thousands of individual pulses. In particular we will show how to interpret the profiles, how to derive pulsar geometry by using the polarization information and comment on the various beam models developed over the years. We show how integrated profiles of the radio magnetars and pulsars with notches may help our understanding of the physics of the radio emission. Finally, we mention the future of pulsar research with telescopes such as the Square Kilometre Array.

1 Introduction The topic of radio pulsar phenomenology is an extremely large one, and one which cannot be encompassed in this short article. The following broad topics would fall under this remit: • Pulsar Timing • Propagation Effects • Pulsar Populations Simon Johnston ATNF, CSIRO, PO Box 76, Epping, NSW 1718, Australia. e-mail: [email protected] Aris Karastergiou Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_1, © Springer-Verlag Berlin Heidelberg 2011

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• Single Pulses • Integrated Profiles

This chapter will concentrate mainly on the discussion of the integrated profiles of pulsars and the implications of the observations for beam models and will not consider the others in any great detail. However, we give a short outline of each of these other topics below along with references for the interested reader. For a general overview of radio pulsars from an observational perspective, readers are referred to the recent books by Lorimer & Kramer [1] and Lyne & Graham-Smith [2]. Pulsar Timing: After a pulsar has been discovered, a campaign of pulsar timing is required to determine its parameters including the spin period and its derivatives, the dispersion measure and associated derivables including surface magnetic field, spin down energy, radio luminosity and distance. If a pulsar is in a binary orbit, the orbital elements can be determined. Longer-scale timing programs on pulsars can lead to discovery of glitches, to uncovering timing noise and to aiding the discovery of pulsars at the highest energies (e.g. [3, 4]). High precision pulsar timing can yield stringent tests of gravity [5] and general relativity [6] through determination of post-Newtonian parameters and may allow detection of gravitational radiation in the future [7]. Propagation Effects: The radiation from pulsars traverses the magneto-ionic, turbulent plasma that we call the interstellar medium. Determining the dispersion and rotation measure of pulsars allows us to determine the density of free electrons in the Galaxy [8] and gives us an idea of the magnetic field configuration [9]. Observations of scintillation parameters [10, 11] and scatter broadening [12, 13] allow us to probe the turbulence in the medium [14, 15]. Pulsar population research aims to answer questions about the total number of pulsars in the Galaxy [16, 17], the evolution of pulsars from young highly energetic objects to the cessation of emission once the death line is crossed to possible resurrection via spin-up to millisecond pulsars, magnetic field evolution [18, 19], the beaming fraction [10, 21], the velocity distribution [28, 23] and the completeness of pulsar surveys [16]. Single pulses from pulsars have been studied since they first showed up on pen charts more than 40 years ago and is an area ripe in pulsar phenomenology. Manifestations of single pulses in total intensity are for example nulling pulsars [24, 25, 14], giant pulses [27, 28, 29], RRATS [30, 31] and drifting subpulses [32, 33, 34]. The polarization of single pulses yields a further treasure trove [35, 36] especially when studied over a wide frequency range [37, 38].

2 Observational Basics The period-period derivative diagram (P − P˙ diagram) is a useful starting point for understanding the various flavours of pulsars. Figure 1 is the modern version of the diagram with nearly 2000 pulsars currently known. Note that figure 1 shows the

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lines of constant characteristic age, τc , magnetic field strength, B s , and the spin˙ These are given by down energy, E. τc (seconds) =

P 2 P˙

(1)

p B s(gauss) = 3.2 × 1019 P P˙ ˙ ˙ E(erg/s) = 4π I PP 2

3

(2) (3)

The pulsars on the P − P˙ diagram subdivide into four main regions. The majority of sources are the ‘normal’ pulsars with P ∼ 1 s, P˙ ∼ 10−15 and B s ∼ 1012 G. The pulsars near the top right of the diagram have long spin periods and high magnetic fields (B s > 1013 G). These are the anomalous X-ray pulsars, the soft gamma-ray repeaters, the magnetars and some of the RRATs. The pulsars near the bottom left of the diagram are the millisecond pulsars with P < 10 ms and B < 109 G. These have likely been spun-up and suffered magnetic field decay through accretion of material from their companion stars. In between the true millisecond pulsars and the bulk of the population are the mildly recycled pulsars and the double neutron star systems.

Fig. 1 The pulsar P − P˙ diagram. Yellow dots denote the position of known pulsars in the diagram. Dark blue lines are lines of constant magnetic field (Equation 2), green lines show constant characteristic age (Equation 1) and light blue denotes lines of constant E˙ (Equation 3).

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3 Integrated profiles and polarization Generally, the integration of thousands of single pulses from a given pulsar leads to a stable integrated profile. The stability of the integrated profile over many years enables high precision timing to be made and is one of the defining properties of radio pulsars. One surprising aspect is that the millisecond pulsars have integrated profiles which are largely indistinguishable from those of the normal pulsars even though their spin period are three orders of magnitude smaller and their magnetic field strengths four orders of magnitude smaller. Figure 2 shows, as an example of a typical pulsar, the integrated profile of PSR J0536–7543. There are a number of salient points to be taken from the figure which we outline in the subsections below.

Fig. 2 Integrated profile of PSR J0536–7543 at an observing frequency of 1.4 GHz with the Parkes radio telescope. The black trace shows the total intensity, red is the linear polarization and blue the circular polarization. The top panel show the position angle of the linear polarization.

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3.1 Pulse width Typically the width of the profiles of radio pulsars does not exceed 30◦ or some 10% of the pulse period. Although the observed pulse width depends on the often unknown geometry (see equation 6 below), it has been found by a number of authors [39, 40, 41, 42] that the pulse width is proportional to P−1/2 . This is expected if the edge of the active area of the polar cap is set by the last open field lines. This is an important result and implies (see equation 7) that the height at which a pulsar emits is largely independent of its period [42, 43] with typical values of 300 km at 1 GHz. A more recent study of this phenomenon [44] showed that the young, high E˙ pulsars did not always conform to this behaviour (see also [45]). Many of these pulsars have beams which are significantly wider than expected from a simple P−1/2 law. The interpretation that their emission heights are large, close to 1000 km or 10% of the light cylinder radius. There is also the special case of pulsars for which we see emission separated by close to 180◦ in phase which implies the pulsar is an orthogonal rotator and we see emission from both poles [46, 47]. In the case of PSR B1702–19, it appears as if there is some form of communication between the opposite poles because the pulse modulation is phase locked [48]. Recent results [49, 47] have also shown that emission might occur from the closed field lines in some pulsars with interpulses.

3.2 Profile shape Pulse profiles come in what seems to be a bewilderingly variety of shapes and the question of classification of pulse morphology has been addressed since the early days of pulsar research. In normal pulsars, the integrated profiles can be decomposed into a small number of Gaussian components [50, 51] even though the individual single pulses which go into making the integrated profile can be highly complex. We will discuss this further in section 8 below when we consider beam models in more detail.

Fig. 3 Integrated profile of PSR J2048–1616 at frequencies of (from left to right) 243, 320, 660, 1400 and 3100 MHz from data taken with the GMRT and Parkes [52].

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The shape of the profile varies with observing frequency as can be seen in for PSR J2048–1616 in figure 3. At low frequencies, the central component tends to dominate whereas at higher frequencies the outer components are brighter. Also the polarization fraction tends to be higher at lower frequencies, as does the overall pulse width.

3.3 Linear polarization The linear polarization from pulsars is typically 10-30% in older pulsars and in excess of 50% in younger pulsars. Note also from Figure 2 that the structure of the linearly polarized profile appears to follow that in total intensity and that the very edges of the profile are depolarized. This is also typical of many pulsars. 100

80

L [%]

60

40

20

0 29 10

30

10

31

10

32

10

33

10

34

10

10

35

36

10

10

37

10

38

•

E [erg/s]

˙ taken from [44]. The dashed line shows a Fig. 4 Linear polarization fraction as a function of E, linear fit and the solid curve the fit of an arctan function illustrating the step in the degree of linear polarization.

It has been pointed out by several authors that degree of linear polarization is high for high E˙ pulsars [53, 54, 55, 44]. This correlation can clearly be seen in Figure 4. There is a transition from a low to a high degree of linear polarization which happens around E˙ ∼ 1034 −1035 erg s−1 . Virtually all pulsars with E˙ < 5 ×1033 erg s−1 have less than 50% linear polarization and for almost all pulsars with with

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E˙ > 2 × 1035 erg s−1 the percentage exceeds 50%. There appears to be a transition region in between where pulsars can both have low and high degrees of polarization, although the transition is remarkably sharp and there are well defined spaces in the figure which are almost empty.

3.4 Position angle swing and orthogonal modes As the radio emission is tied strongly to the magnetic field lines, the plane of polarization is determined by the angle of the magnetic field as it sweeps past the line of sight. The position angle of the linear polarization as a function of pulse longitude therefore contains geometric information as we shall see in the next section. The emission of pulsars is thought to be a combination of two orthogonally polarized modes (OPM, e.g. [56, 36]). This aspect of the emission can manifest itself in sharp ∼ 90◦ jumps in the position angle over a small pulse longitude range. These jumps are thought to be sudden transitions from the domination of one mode to the other. Jumps in the position angle swing therefore indicate that both modes are present in the emission. The mixing of both modes at a certain longitude will lead to depolarization. It is sometimes the case that orthogonal mode jumps are also accompanied by a change in the sign of the circular polarization [57]. Figure 7 shows an example of a pulsar with orthogonal mode jumps in its position angle swing accompanied by depolarization of the linear emission. However, it is not always the case that the jumps in position angle are exactly 90◦ as expected in the case of purely orthogonal mode superposition. One possible explanation is that the two modes suffer differing amounts of refraction in the magnetosphere [58]. A study of PSR 0329+54 showed the ordinary mode appeared to be affected by refraction and that the circular polarization is a natural by-product of elliptically polarized modes [59].

3.5 Circular polarization Pulsars generally have a reasonable degree of circular polarization in their pulse profiles. The handedness of circular polarization can change as a function of pulse longitude. Indeed, in a number of objects the handedness changes through the symmetrical centre of the pulse profile [60] which not only gives a clue as to the location of the magnetic axis but also has implications for the emission mechanism. This idea was questioned by [61] who in turn claimed evidence for a correlation between the handedness of circular polarization and the sense of swing of the position angle of the linear polarization. In the high E˙ pulsars with double profiles, it was found that the total power and the circular polarization usually dominates in the trailing component [62]. It remains unclear whether the circular polarization is intrinsic to the

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emission mechanism itself (i.e. the modes are naturally elliptically polarized [59]) or a result of the propagation through the magnetosphere [63].

4 Rotating Vector Model In the rotating vector model (RVM; [64]), the position angle (PA) as a function of pulse longitude, φ, can be expressed as ! sinα sin(φ − φ0 ) PA = PA0 + arctan (4) sinζ cosα − cosζ sinα cos(φ − φ0 ) Here, α is the angle between the rotation axis and the magnetic axis and ζ = α + β with β being the angle of closest approach of the line of sight to the magnetic axis. φ0 is the pulse longitude at which the PA is PA0 , which also corresponds to the PA of the rotation axis projected onto the plane of the sky. Figure 5 shows the geometry of the model. We note that RVM fitting does not depend on the total intensity profile, or the location of the profile symmetry points.

Fig. 5 Geometry of the polar cap model for pulsars showing the relevant angles, α, β and ζ as described in the text. Figure taken from [65].

Unfortunately, for most pulsars it is difficult to determine α and β with any degree of accuracy, partly because the longitude over which pulsars emit is rather small and partly because strong deviations from a simple swing of PA are often observed. This makes the determination of the various angles straightforward only in the ∼15 per cent of pulsars for which the RVM works - see the discussion in [66] for details. If the emission occurs at some height above the pulsar surface, the PA swing can be delayed with respect to the total intensity profile by relativistic effects such as aberration and retardation as initially discussed by [67]. The magnitude of the shift

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in longitude, δφ(PA) (in radians), is related to the emission height relative to the centre of the star, hem , via 8 π hem δφ(PA) = (5) Pc where P is the pulsar period and c the speed of light [67]. We note that, at least to first order, the PA swing is not altered by aberration and retardation effects other than the longitude delay [68, 69]. These effects therefore do not affect the measured values of α and β from equation 4. There is also a geometrical method which can be used to compute emission heights if the angles α and β are known. Under the assumption of a dipolar field and a circular emission zone, the half-opening angle of the emission cone, ρe can be expressed as cosρe = cosα cosζ + sinα sinζ cos(W/2) (6) where W is the measured pulse width in longitude [70]. If one assumes that the emission extends to the final open field line then the emission height can be derived through the expression given by [71]. r π hem ρo = 3 (7) 2Pc Here we use ρo to denote the half-opening angle of the cone at the last open field line (see figure 5, and note that unless the emission extends right to the edge of the cone then ρo > ρe . It is possible to compute relative emission heights of the radiation without the polarization information [72]. Imagine the emission which comes from a circularly symmetric region around the magnetic pole. Then, this conal emission arises higher in the magnetosphere than the pole emission, the entire circular structure will be shifted relative to the pole due to aberration and retardation effects and the profile will appear asymmetric. If a given profile contains well defined central and conal emission then the difference in separation between the leading and trailing conal components and the centre, δφ(CC), can be used to compute their relative emission heights, ∆hem . In this case [73] δφ(CC) =

4 π ∆hem Pc

(8)

This equation has been modified to take into account the viewing geometry which can affect the derived emission heights by ∼10 per cent in some cases [74]. It can be useful to compare the emission height with the radius of the light cylinder, rlc = Pc/2π. Generally it is found that the radio emission occurs in regions significantly below about 0.1 rlc . Substantial discussion of the merits and failings of all these methods can be found in recent papers [75, 76, 73, 74, 44].

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5 Problems and Perils of the RVM We have seen in Section 4 that it is possible to determine the geometrical parameters α and β through observations of the sweep of the position angle of linear polarization as a function of pulse longitude. In figure 2 we showed a fairly typical pulsar profile which appears to have smooth swing of position angle and thus amenable to determining geometry through equation 4.

Fig. 6 Left-hand panel: Contours of χ2 in the α-β plane after fitting the RVM equation to the position angle swing of PSR J0536–7543. It can be seen that although β can be constrained to lie between 0◦ and –4◦ , α cannot be constrained. Right-hand panel: Integrated profile of PSR J0536– 7543 showing the entire 360◦ of longitude. Two different RVM fits are shown (blue and green lines) both of which fit the observed position angle swing nicely but differ significantly outside the pulse window.

The top panel of figure 6 shows χ2 contours in the α-β plane after applying the RVM to the data in figure 2. The figure shows a typical ‘banana’ like shape. The implications of this are that α is very poorly constrained, whereas at least an upper bound on β can be obtained. Why is this the case? The main reason is the restricted longitude range over which radio emission is seen. The bottom panel of figure 6 shows the same pulsar as figure 2 but now with the full 360◦ of pulse rotation. Two RVM fits are shown; it can be seen that they fit the data well but clearly diverge outside the pulse window where there are no constraints. Exacerbating the problems of restricted longitude range and effects caused either by propagation through the pulsar magnetosphere or through the interstellar medium which can cause severe distortions of the RVM as seen in the two pulsars shown in figure 7. Clearly the position angle swing in these pulsars cannot be well described by the RVM even when an attempt is made to correct for orthogonal modes.

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Fig. 7 Integrated profiles for PSR J0452–1759 (left) and J1453–6413 (right). The position angle swing in PSR J0452–1759 shows evidence for 4 orthogonal mode jumps, whereas the behaviour of PSR J1453–6413 is not suitable for RVM fitting.

6 Radius-to-Frequency mapping The frequency dependence of radio emission from pulsars is a key aspect of the emission mechanism. In the radio part of the electromagnetic spectrum, pulsars are known to emit from low as 10 MHz [77] to at least 150 GHz [78]. Observations of a large sample of pulsars over a wide frequency range [79, 52] allows a generalization of the behaviour of integrated profiles with frequency: profiles get narrower, the polarization fraction declines and outer components become more prominent as the frequency increases. However, many counterexamples to these rules are also observed, and pulsars with complex profiles are especially prone to rule breaking. The so-called radius to frequency mapping (RFM) idea is that lower frequencies are emitted higher in the magnetosphere than higher frequencies which naturally results in wider observed profiles (see equation 7). This idea was originally formulated [80] in the early 1970s. It was observed that the components of double peaked pulsars move closer together as frequency increases and that this could be interpreted by assuming that the emission takes place at the local plasma frequency. The exact dependence on the emission height with frequency differed between physical models [81, 82]. A width-frequency law was postulated [83] which essentially shows that pulse widening only really occurs at frequencies below ∼1 GHz; above this value the pulse width is constant (see also figure 3). An important paper in this area came from a study of the single pulses in the Vela pulsar by Krishnamohan & Downs [84]. They showed that the properties of the single pulses in Vela could best be explained if the emission components originated from different heights in the magnetosphere at a particular frequency. In recent work, Gangadhara & Gupta [72] showed for PSR B0329+54 that the emission heights at a given frequency vary as a function of pulse longitude with high emission heights seen at the edges of profiles and low emission heights in the central parts of the profile. Furthermore, Mitra & Rankin [43] show that inner cones

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originate from lower in the magnetosphere than outer cones. The combination of these results are a key result which breaks the long-held assumption that emission from a given frequency arises at a uniform height above the pole.

7 Velocity - spin axis alignment The velocities of pulsars are significantly larger than those of their progenitor (highmass) stars (e.g. [28]). This implies that the birth process of pulsars also produces their high velocities and that the supernova or events soon thereafter must be asymmetrical. In the mid 1970s, the so-called rocket mechanism was proposed [85], whereby an offset of the magnetic dipole from the centre of the star causes the star to accelerate along its rotation axis. Observational tests of this model were largely inconclusive [86, 87, 88]. The debate started anew when both [89] and [90] proposed a model in which the same (off-centre) explosion processes that give pulsars their high velocity also produce their fast rotation. In these models, a single short duration impulse would ensure that the velocity and rotation axes were perpendicular whereas multiple, finite duration kicks would align the velocity and rotation axes. Observational evidence for a correlation came from X-ray observations of an equatorial torus and polar jets in a number of young pulsars [91, 92] whose axis of symmetry was consistent with the proper motion direction. The position angle of the axis of rotation of a pulsar can also be determined from polarization observations through two different techniques. In the first, one can determine both φ0 and PA0 directly from equation 4. However, as we have seen, in a large number of cases it is difficult to do unambiguously. In these cases, extra information can be brought to bear, for example a change in the handedness of circular polarization at φ0 [60], profile symmetry [93, 65] and the frequency evolution of the profiles [93, 65, 94]. Pulsar polarization was used to great effect by Johnston et al. [95] who showed strong observational evidence for a relationship between the direction of a pulsar’s motion and its rotation axis and concluded that the velocity vector and the rotation axis of pulsars are aligned at birth.

8 Beam models 8.1 Rankin et al. A hugely influential paper on the morphology and classification of pulsar profiles was published in the early 1980s by Rankin [93] and subsequently in a series of papers over the years [96, 71, 60, 42].

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Her classification scheme of pulsar profiles is best seen in Figure 8. Although the conal structure of pulsar beams had been postulated earlier [97, 98], Rankin proposed that an additional core component played a prominent role. She proposed that the core (central part) of the beam had a different emission process than the conal (outer) parts of the beam. At lower frequencies, core emission dominates, whereas at higher frequencies the conal emission tends to be more prominent. She also suggested that beams were elliptical rather than circular.

Fig. 8 Schematic diagram of the pulsar beam geometry taken from [93]. Different cuts of the line of sight through the beam then produce different pulse profiles as shown, Note also the cones are elliptical and the hatchings show the direction of the polarization vector.

8.2 Lyne & Manchester A seminal paper published in 1988, saw Lyne & Manchester [65] gather together all available data on the integrated pulse profiles. Although they recognised the core and cone structure outlined in [93], they suggested that rather than having two distinct emission processes, there was a gradual change in characteristics from the magnetic axis out to the last open field lines. Their model is sometimes referred to as the ‘patchy-beam model’ because they showed that the distribution of emission zones within the beam was random and patchy (see also [99]). An example of this patchiness was their classification of partial cones, those in which only the leading

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or trailing edge of the beam could be discerned. They further concluded that beams were largely circular and that alignment between the rotation axis and the magnetic axis occurred on a timescale of ∼ 107 yr (see also [10, 21]).

8.3 Karastergiou & Johnston Motivated by the recent results on the location of the radio emission in pulsar magnetospheres, Karastergiou & Johnston [100] developed a model which accounted for the large diversity found in the average profile shapes of pulsars. At the centre of their model lies the idea that radio emission at a particular frequency arises from wide range of altitudes above the surface of the star and that it is confined to a region close to the last open field lines. They showed that the radial height range over which emission occurs is responsible for the complex average pulse shapes rather than the transverse (longitudinal) range proposed in most other models. They claimed that there must be a change in the height range as a function of the pulsar spin down energy with highly energetic pulsars emitting only over a narrow range.

9 Two Case Studies 9.1 The radio loud magnetars An important sub-class of neutron stars are the magnetars which are neutron stars with long spin period (2-12 s) and very high magnetic fileds. Crucially, these stars are not powered by spin-down but rather by magnetic field decay. A growing number of magnetars are known, and three of them have been detected as radio pulsars – PSR J1809–1943 [101], PSR J1550–5418 [102] and PSR J1622–4950 [103]. The integrated profiles of these magnetars, somewhat surprisingly, show common features including [106, 105, 104] • • • • • •

variability in shape on short and long timescales variability in flux density almost complete linear polarization of the profile little variation with frequency emission with a flat spectral index a position angle swing which follows the RVM

The first two of these features (the variability) is very uncommon in other pulsars but yet is seen in all 3 of the magnetars. Furthermore the flat spectral index, which has yielded a detection of PSR J1809–1943 at frequencies up to 150 GHz [78] is also far removed from the relatively steep spectral index of most pulsars. Perhaps most surprisingly of all is the fact that the position angle swing follows the RVM. Why should this be the case, since it seems uncertain that magnetars have

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Fig. 9 Integrated profiles of the magnetars PSR J1550–5418 at 1.4 GHz (left) and J1809–1943 at 8.4 GHz (right) showing the full pulse phase. Figures adapted from references [104] and [105].

regular dipole fields and that their super-strong magnetic fields are not conducive for radio emission in the first place? Although the RVM fits are not conclusive, it appears at least as if there is some evidence that all three of the radio-loud magnetars are close to being aligned rotators. If correct, this must also be an important clue as to their origin, as the probability of having an aligned rotator and small probability of intersecting the beam of an aligned rotator makes it very unlikely to occur by chance.

9.2 Pulsars with notches There are, at present, three pulsars which show “double notches” in their integrated profiles. These were first noted in PSR B1929+10 [107] and described in detail for PSR B0950+08 (as shown in figure 10) by McLaughlin & Rankin [108] who also pointed out that that these features were also present in the millisecond pulsar PSR J0437–4715 [109]. The notches have the appearance of an absorption feature in the profile [110] and in all three pulsars there are common features [111]. • The double notches have a W shape; the two notches have the same width and are relatively broad • The notches occur on the edges of the profile, far from the strongest component • The notches have a high degree of linear polarization • The position angle sweep is largely unaffected by the presence of the notches

It has been argued [111] that these features strongly support the idea that the radio emission from pulsars is maser-like (e.g. [112]). In particular, the seemingly wide-band radio coherency arises from inverse Compton scattering of a narrow band of frequencies by a broad energy distribution of electrons. The decrease in emission seen at the notch then arises either because the emitting region contains a gap or

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Fig. 10 Integrated profile of PSR B0950+08 taken from [108]. The notches can be seen on the rising edge of the main component. The inset shows a blow-up of the region, showing the characteristic W shape of the notches.

their is an absorber high in the magnetosphere which blocks some of the radiation. The double nature of the notches arises naturally from the ‘hollow-cone’ type nature of the maser emission.

10 Summary Understanding the phenomenology of radio pulsars is both a quest to advance general knowledge by addressing a difficult open question in astrophysics, and a specific effort to improve timing models of pulsars to the extent that subtle effects such as gravitational radiation can be identified within pulsar timing residuals. The latter will become particularly interesting in the coming decade, as surveys will discover the populations of millisecond pulsars most suitable for gravitational wave detection through timing, and possibly the exotic pulsar binaries that will help address fundamental questions about gravity. The input of our understanding of pulsar phenomenology into pulsar timing models will be through a precise description of the effects intrinsic to the pulsar and, more specifically here, to the pulsar magnetosphere. We have given an overview in this short chapter of some of the current understanding which arises from a study of the integrated profiles of pulsars. We have seen that the RVM is a powerful tool to obtain the pulsar geometry, crucial for our

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understanding of both the radio and the high energy emission. In practice, however, obtaining constrained geometries remains difficult. We have briefly described some of the main beam models. Finally we looked at two classes of pulsars, the magnetars and the pulsars with notches and seen how detailed examination of their pulse profiles can yield insights into the physical mechanisms.

11 Future instruments and the Square Kilometre Array Progress in understanding the radio phenomenology will be made by advances in specific areas, through targetted surveys with new instruments. The first area involves solving the problem of pulsar polarization, and development of models that separate effects intrinsic to the pulsar from a variety of propagation induced effects. Recovering the intrinsic polarization relies on (i) better modelling of scattering through the interstellar medium (ii) understanding the impact on polarization of the emission height of the various components and (iii) understanding of orthogonal modes of polarization in the magnetosphere. Progress in this field will be achieved by polarimetry of many pulsars at the highest time resolutions, with the next generation of baseband recorders. Instruments like LOFAR [113], MeerKAT and ASKAP [114] will specifically target pulsars to address these questions across a very broad range of frequencies. Understanding the intrinsic polarization is key to understanding the geometric orientation of pulsars. Further to the above, the increased sensitivity across such a broad band of radio frequencies with instruments such as LOFAR, MeerKAT, the ATA and eVLA will be exploited by surveys of knon pulsars to examine the frequency dependence of emission components. Their number, width and intensity will be measured (together with the total pulse width) as a function of frequency over a continuous and unprecedented range. Where possible, this will be attempted through simultaneous or quasi-simultaneous observations, designed to address the question of radius-tofrequency mapping. The broadband total power and polarization measurements will provide 3D tomography of the magnetosphere, which will form the basis for interpretation of timing irregularities of magnetospheric origin. The great advantage of the Square Kilometre Array with respect to the above instruments will be its ability to obtain high signal to noise ratio measurements of individual pulses, illuminating the dynamic nature of the pulsar magnetosphere and permitting further refinements to the radio beam model. This is particularly important given the limited number of pulsars where individual pulses are observable today, particularly at frequencies above a few GHz. Studies of pulsar radio emission essentially require the highest possible sensitivity per time and frequency element, for which the Square Kilometre Array will be by far the best instrument planned [115, 116].

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Acknowledgements We would like to thank the organisers for inviting us to Barcelona and giving us the opening talk slot of the meeting! Thanks also to Patrick Weltevrede for the banana plot in Figure 6 and Mike Keith for comments on the document.

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Radio pulsar populations Duncan R. Lorimer

Abstract The goal of this article is to summarize the current state of play in the field of radio pulsar statistics. Simply put, from the observed sample of objects from a variety of surveys with different telescopes, we wish to infer the properties of the underlying sample and to connect these with other astrophysical populations (for example supernova remnants or X-ray binaries). The main problem we need to tackle is the fact that, like many areas of science, the observed populations are often heavily biased by a variety of selection effects. After a review of the main effects relevant to radio pulsars, I discuss techniques to correct for them and summarize some of the most recent results. Perhaps the main point I would like to make in this article is that current models to describe the population are far from complete and often suffer from strong covariances between input parameters. That said, there are a number of very interesting conclusions that can be made concerning the evolution of neutron stars based on current data. While the focus of this review will be on the population of isolated Galactic pulsars, I will also briefly comment on millisecond and binary pulsars as well as the pulsar content of globular clusters and the Magellanic Clouds.

1 Selection effects in radio pulsar surveys The current sample of radio pulsars is now close to 2000 and is continuously increasing thanks to a wide variety of large-scale and targeted searches being carried out at most of the major radio observatories. The approximate rate of discoveries at the current time is about 100 pulsars per calendar year, and we expect this trend to continue and accelerate over the next decade as more powerful facilities come online (both at radio and non-radio wavelengths). An excellent example of recent progress can be seen in the flurry of radio pulsar counterparts to Fermi gamma-ray sources as reported by Ray and Saz Parkinson elsewhere in these proceedings. It is Department of Physics, West Virginia University, Morgantown, WV 26506, USA, e-mail: Duncan. [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_2, © Springer-Verlag Berlin Heidelberg 2011

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important to note, however, that while this sample represents a great improvement over, say, the situation 20 years ago, it still likely only amounts to a few percent of the underlying population of pulsars whose properties we wish to constrain. The main observational selection effects that cause this are summarized below.

1.1 Flux–distance relationship Like all astronomical sources, observed pulsars of a given luminosity L are strongly selected by their apparent flux density, S . In a classical Euclidean model, for a pulsar a distance d from Earth which beams to a certain fraction f of 4π sr, the flux density S = L/(4πd2 f ). This is known as the inverse square law and is commonly assumed for astrophysical sources. Since all pulsar surveys have some limiting flux density, only those objects bright or close enough will be detectable. Note that in the absence of prior knowledge about beaming, geometrical factors are usually ignored and the resulting ‘pseudoluminosity’ is quoted at some standard observing frequency; e.g., at 1400 MHz, L1400 ≡ S 1400 d2 . Recently, the validity of the inverse square law has been called into question by Singleton et al. [1], and that perhaps the flux scales as 1/d instead. It is important to fully investigate this claim. As Singleton et al. point out, if confirmed, it would have dramatic implications for many of the conclusions presented here. In a search for radio transients in M31 with Westerbork, RubioHerrera [2] has investigated the implications of non-1/d2 scalings on his results and finds that many more transients should have be observable for a 1/d law, and that a 1/d2 law is consistent with the number of candidates seen. For now, we note that any flux–distance relationship will bias the sample towards bright and/or nearby objects.

1.2 The radio sky background A fundamental sensitivity limit on any radio observation is the system noise temperature, normally expressed in Kelvins as T sys . While every effort is made to minimize this at the telescope, synchrotron radiating electrons in the Galactic magnetic field contribute significantly with a ‘sky background’ component, T sky . At observing frequencies ν ∼ 0.4 GHz, T sky dominates T sys for observations along the Galactic plane. Fortunately, T sky ∝ ν−2.8 so this effect is significantly reduced when ν > 0.4 GHz.

1.3 Propagation effects in the interstellar medium Dispersion and scatter-broadening of the pulses in the interstellar medium hamper detection of short period and/or distant objects. The effects of scattering are shown in Fig. 1. Fortunately, like T sky , the scatter-broadening time τscatt has a strong fre-

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Fig. 1 Left: pulse scattering by irregularities in the interstellar medium shown here as an idealized ‘thin screen’ of material lying midway between the pulsar and the observer. Right: a simulation showing the fraction of pulsars undetectable due to scattering as a function of observing frequency.

quency dependence, scaling roughly as ν−4 . Fig. 1 shows that for survey frequencies below 1 GHz, scattering ‘hides’ a large fraction of the population. Additionally, scintillation, the diffractive and refractive modulation of apparent flux densities by turbulences in the interstellar medium [3] affect pulsar detection. For example, two northern sky surveys carried out 20 years apart with comparable sensitivity [4, 5] detected a number of pulsars above and below the nominal search thresholds of one experiment but not the other. Surveying the sky multiple times minimizes the effects of scintillation and enhances the detectability of intrinsically faint pulsars.

1.4 Finite size of the emission beam The fact that pulsars do not beam to 4π sr means that we see only a fraction f of the total active population. For a circular beam, Gunn & Ostriker [6] estimated f ∼ 1/6. A consensus on the precise shape of the emission beam has yet to be reached. Narayan & Vivekanand [7] argued that the beams are elongated in the meridional direction. Lyne & Manchester [14], on the other hand, favour a circular beam. Using the same database, Biggs [9] presented evidence in favour of meridional compression! All these studies do agree that the beam size is period dependent, with shorter period pulsars having larger beaming fractions. A very popular model assumed by current studies derives from the work of Tauris & Manchester [10] who found that   f ≃ 0.09 log(P/s) − 1 2 + 0.03, where P is the period. A complete model for f needs to account for other factors, such as evolution of the inclination angle between the spin and magnetic axes and the beaming of millisecond pulsars.

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1.5 Pulse nulling The abrupt cessation of the pulsed emission for many pulse periods, was first identified by Backer [11]. Ritchings [12] subsequently presented evidence that the incidence of nulling became more frequent in older long-period pulsars, suggesting that it signified the onset of the final stages of the neutron star’s life as an active radio pulsar. Since most pulsar surveys have short (< few min) integration times, there is an obvious selection effect against nulling objects. Means of reducing the impact of this effect are to look for individual pulses in search data [13], survey the sky many times, or use longer integrations. Indeed, the longer dwell times (35-minute pointings) used in the Parkes multibeam survey have been particularly successful in this regard, discovering a number of nulling pulsars [14].

1.6 Intermittency Recently, a new class of “intermittent pulsars” has been found. These provide unique and new insights into neutron star physics and populations [2]. The prototype, PSR B1931+24, shows a quasi-periodic on/off cycle in which the spin-down rate increases by ∼ 50% when the pulsar is in its on state compared to the off state! While the behaviour of this pulsar appears to be linked to the increase in magnetospheric currents when it is on, there is no satisfactory explanation for this effect. Since PSR B1931+24 is only visible for 20% of the time, we can readily estimate that there should be at least five times as many similar objects. We believe this number may be severely underestimated. It is important to establish how many similar objects exist, and what the related timescales of their non-emitting state are. These pulsars, and their cousins the rotating radio transients (discussed in Section 4.1), remain a very exciting area of current research.

2 Correcting the biases in the observed sample How can we account for the effects discussed above and recover the properties of the underlying pulsar populations? While some progress can be made analytically (see, e.g. the early work of Gunn & Ostriker [6]), the non-uniform nature of all the above effects more readily lends itself to a Monte Carlo approach to modeling pulsar populations and their detection. The two main ways to implement such models can be thought of as either a fully dynamical approach or a static “snapshot” model. For the former case, a simulation is created in which a model galaxy of pulsars is seeded according to various prescriptions of birth locations and initial rotational parameters. Each of these synthetic pulsars is then “evolved” both kinematically in a model for the Galactic gravitational potential and rotationally using a model for neutron star spin-down. The properties of the resulting population are then saved.

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Fig. 2 Schematic summarizing a fully dynamical Monte Carlo simulation of the Galactic pulsar population. The main ingredients are the model gravitational potential (Φ), some prescription for the neutron star evolution with time and a model of the interstellar medium. Pulsars whose apparent flux densities exceed those of the main surveys (S min ) are saved and the resulting “model sample” is compared to the actual sample of pulsars detected by those surveys.

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Using detailed models for the pulsar surveys, it is possible to compute whether each synthetic pulsar is actually detectable and the properties of these “observable” pulsars are saved. These samples may then be compared to the real observed sample to asses the validity of the Monte Carlo model. The process is summarized in Fig. 2. The snapshot approach differs from the fully dynamical approach in that the pulsars are seeded at their final positions in the model galaxy without assuming anything about spin-down or kinematic evolution and thus form a picture of the current-day population. To model pulsar detectability, both approaches are based around the well-known pulsar radiometer equation [16] which has been demonstrated to provide an adequate description of the sensitivity of pulsar surveys [17]. The advantage of the snapshot approach over the dynamical one is that it is simpler, requiring fewer assumptions about motion in the galaxy or spindown and can often be optimized to form a model with a unique best solution. Its major downfall, however, is that its simplicity means that it says very little if anything about the progenitor population. Fully dynamical models provide insights into these details, and can for example describe the distribution of pulsars in P and P˙ space about which the snapshot approach is blind to. However, as discussed below, a major point to keep in mind is that there is often no unique model that can describe the data and some care needs to be exercised when interpreting the conclusions.

3 Recent results With these caveats in mind, we now briefly review some of the latest findings of studies which adopt either the snapshot or full dynamical modeling approach.

3.1 Pulsar space distribution Models of the Galactic distribution of pulsars have been constructed from observationally biased samples for many years [18, 19, 20]. These studies typically follow the snapshot approach in which the population can be represented in terms of four independent distribution functions: Galactocentric radius R, vertical dispersion from the Galactic plane z, pulse period P and luminosity L. In a recent approach of this kind [21], we investigated models which accounted for the observed distribution of pulsars seen by the Parkes Multibeam Pulsar Survey [22] which provides the largest uniform sample (over 1000 Galactic pulsars) for such analyses. Using an iterative Monte Carlo approach, we found that it is possible to find a unique model which converges to the same functional form regardless of the initial shape of the distribution functions in R, L, z and P. An example of the model output is shown in Fig. 3 which contrasts the underlying and observed distribution functions for the final model. The L, z and P distributions show the number of pulsars as a function

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of each parameter. For R, the results are shown as the projected surface density of objects on the Galactic plane, ρ(R).

Fig. 3 Observed number distribution from our input sample (upper panels) and derived distributions (lower panels) for the parameters: (a) ρ(R); (b) z; (c) L; (d) P. The solid curves are smooth analytic functions fitted to the data (see [21] for details). The dotted curves show: (a) the assumed radial density function of free electrons (from the NE2001 electron density model); (b) an exponential z distribution with a scale height of 350 pc; (c) a log-normal fit to the optimal pulsar population model derived by [23]; (d) a period distribution derived from studying pulse-width statistics [24].

One important limitation of this approach is that the form of the spatial distributions R and z depends heavily upon the assumed model for the Galactic distribution of free electrons. The model shown in Fig. 3a assumes the commonly used “NE2001” model [25]. An example of this dependence is the R distribution in which the pulsars naturally follow the R distribution of free electrons. While the NE2001 model achieves a high level of sophistication, including electron density enhancements in spiral arms, and can account for a wide variety of observations, it is known to have a number of shortcomings [26, 27] which are currently being addressed in a new model (Cordes, private communication). In Fig 3b, for example, it is seen that the optimal model z distribution is significantly larger than observed — this is a direct result of the NE2001 electron scale height [21]. It is conceivable that future population studies with larger samples of pulsars could be carried out where the distribution of free electrons is allowed to vary. At the current time, however, one

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should be mindful of the fact that any conclusions about the spatial distribution of pulsars are strongly coupled to models of the free electron density.

3.2 Pulsar velocities A number of studies of the birth velocities of pulsars have been carried out over the years and there has been much debate as to whether the distribution for nonrecycled pulsars is unimodal [28] or bimodal [29, 30] Recent studies [31, 23] find no compelling evidence to model the distribution with multiple components and the individual 1-D components of the pulsar’s birth velocity vector follow either a Gaussian [31] or exponential form [23] with a mean value in the range 400–500 km s−1 .

Fig. 4 Normalized 3-D velocity probability density functions obtained from the observed 1-D (left) 2-D (right) distributions using a deconvolution technique [31]. The uncertainties on each histogram bin are calculated as the square root of the number of pulsars in each bin. The dotted curve shows the 3-D distribution favoured by Arzoumanian et al. [30]. The solid curve is the bestfitting Maxwellian distribution to the histogram from the 2-D distribution with σ = 265 km s−1 .

Fig. 4 shows the results of a deconvolution process from Hobbs et al. [31] where the 3-D space velocity distribution may be derived self consistently by appropriately deprojecting either the 1-D or 2-D distributions of young pulsars (defined to be those with characteristic ages less than 1 Myr). As can be seen, a previously suggested two-component model is not implied by these data. While it is found for millisecond and binary pulsars that the velocity distribution is different to the normal pulsars shown here, the main conclusion to take away from current results is that the distribution of velocities for isolated radio pulsars is unimodal.

3.3 Pulsar luminosities Because of the strong connection between distance and luminosity, any uncertainty in the pulsar distance scale propagates through to an uncertainty in the luminosity function [32]. Two critical questions concerning pulsar luminosities we wish to an-

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swer are: (1) what, if any, evolution in luminosity is there with pulsar age? (2) what is the shape of the luminosity function? The idea of a decay in luminosity has been in the literature for some time. Taylor & Manchester [19] have pointed out that the simple fact that the distribution of pulse periods tails off at long periods demands that the luminosity decays with time. If the luminosity were constant, many more pulsars would be observed. This can be readily shown via simulations in which assigning the luminosity to a pulsar at random results in a pile up of pulsars at high P and low P˙ which is not observed in the real sample [23]. The exact form of the luminosity decay remains contentious, however. While the best dynamical models can account for the observed data with a simple power law model in which L ∝ Pα P˙ β , the values of the exponents α and β are neither readily found from fits to the observed population [33] nor are uniquely constrained from the dynamical modeling [34].

Fig. 5 Results from Faucher-Gigu´ere & Kaspi [23] which show the underlying luminosity function (defined to be at a frequency of 1.4 GHz) for their optimal model of the isolated pulsar population. The solid line shows a Gaussian fit to the data where the mean of the distribution in log L is –1.1 and the standard deviation is 0.9.

One result that does appear to be robust is the form of the luminosity distribution. While the snapshot models typically favour some sort of power-law distribution for the number of pulsars N(L) in which d log N/d log L ∼ −1, they remain agnostic about the distribution of luminosities below the minimum value in the observed sample, Lmin . The dynamical approach suggests that the underlying shape of the luminosity function is log-normal in form [23]. The parent luminosity distribution from this simulation is shown in Fig. 5. Simulations with different spin-down models all appear to show the same basic shape [34, 35] Whether this distribution applies to millisecond pulsars is currently unclear.

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3.4 Magnetic alignment Recently, two groups have provided strong evidence that the angles between the magnetic and spin axes of neutron stars are not random and, in fact, appear to decay on a timescale of 107 yr or less. Weltevrede & Johnston [36] provide strong empirical evidence for such magnetic alignment based on the statistics of pulsars which exhibit interpulses. They point out that the fraction of pulsars whose profiles can be described by viewing an orthogonal rotator is strongly linked to the stars’ rotational period, with a much higher interpulse fraction observed at longer periods than would be expected from randomly inclined lighthouse beams. Unless the observational sample is in some way biased, their conclusions appear to be irrefutable. In an independent approach, Young et al. [37] also find evidence for magnetic alignment from an analysis of the pulse width statistics of pulsars. They argue, from graphs of pulse width versus characteristic age (see examples in Fig. 6) which show a turn-up at long periods, that only alignment on a timescale of a few million years can explain the increase in pulse width. The two competing effects which shape these curves are the narrowing of pulse widths with period, and the alignment of the magnetic axis which means that older pulsars are more likely to be seen as aligned objects where the emission occupies a larger fraction of the rotational period.

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Both the above studies suggest that some sort of alignment is taking place in isolated radio pulsars. As pointed out by Ridley & Lorimer [34] however, this observation throws up a conundrum when one attempts to construct a self-consistent model of spin-down evolution. The standard magnetic dipole model, in which the braking torque is proportional to the square of the sine of the inclination angle, does not do a good job of reproducing the P − P˙ diagram if this angle evolves with time in the manner expected above. Furthermore, the hybrid spin-down model of Contopoulos & Spitkovsky [38] which can account for alignment, appears to provide a very poor description of the observed distribution in P − P˙ space. A more sophisticated model for pulsar spindown is needed which can reconcile these differences.

3.5 Magnetic field decay No discussion of pulsar statistics would be complete without a mention of magnetic field decay — a contentious issue that has raged for the past 30 yr. For many years, it was believed that the magnetic fields of isolated pulsars decayed exponentially on a 1/e timescale of 10 Myr or less [20]. Popular opinion switched toward favouring models with essentially no field decay in the 1990s [39, 40].

Fig. 7 Results of simulations by Popov et al. [35] which show how comparable results can be found by modeling the population without field decay (upper panels, following the prescription given by Faucher-Gigu´ere & Kaspi [23]) and with field decay (lower panels, following a magnetothermal model of Popov et al. [35]). Both models give statistically equivalent results. The observed distributions in period and magnetic field strength are shown by the red histograms. KolmogorovSmirnov probabilities that the model and observed data are drawn from the same parent population are shown on the top right hand corner of each histogram. The model distributions are shown with statistical error bars. Both models appear to provide equally viable descriptions of the data.

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Nowadays, the community is split between no significant magnetic field decay [23, 34] and a decaying field [41, 35]. The simulations shown in Fig. 7 present models of the radio pulsar population with and without the effects of magnetic field decay. Is this another example of covariance between model parameters, or fundamental differences in modeling techniques? For me, the answer remains to be found.

4 Final thoughts and future prospects In this review, I have focused on a number of recent results concerning the population of isolated pulsars. While we have come a long way in understanding the distribution of these object in the Galaxy, their initial velocity dispersion and luminosity function, much remains to be understood in terms of their spin-down behaviour. A model which can account for the observed magnetic alignment, nulling, beaming and spin-down evolution is a major goal for any future study. Some further areas that are ripe for research are summarized briefly below.

4.1 Rotating radio transients An even more extreme class of intermittent neutron stars are the so-called rotating radio transients [3]. Their detection was made possible by searching for dispersed radio bursts [43] which often do not show up in conventional Fourier-transform based searches [44]. Since the initial discovery, a significant effort has gone in to searching for and characterizing more RRATs. Over 30 are currently known [45, 46, 47, 48, 49] but only seven have timing solutions, with four of these only recently achieved [49]. Recently, Lyne et al. [50] reported the detection of two glitches in RRAT J1819−1458. While these events are similar in magnitude to the glitches seen in young pulsars and magnetars, they are accompanied by a long-term decrease in the spin-down rate, suggesting that it previously occupied the phase space populated by the magnetars. Further observations are needed to confirm this “exhausted magnetar” hypothesis. The Galactic population of such objects is potentially significant and it remains to be determined whether alternative evolutionary scenarios need to be invoked other than core-collapse supernova [51]. Further work will certainly clarify this issue as known sources are better characterized.

4.2 Millisecond pulsars For many years, studies of the Galactic population of millisecond pulsars have been plagued by small-number statistics [52]. More meaningful results were obtained during the 1990s with the advent of all-sky surveys of the local population [53]

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where it was found that the velocity distribution of millisecond and binary pulsars is significantly lower than that of the normal isolated population discussed above. Presently, with an exponentially growing sample of millisecond pulsars we are in an era where it is possible for the first time to carry out full population syntheses of the Galactic population. Story et al. [54] have carried out much work in this area and have paved the way for future studies, though many questions remain to be answered including: (i) what is the overall Galactic distribution of millisecond pulsars?; (ii) is the millisecond pulsar luminosity function comparable to normal pulsars?; (iii) are all millisecond pulsars produced in low-mass X-ray binary systems?; and (iv) what is the origin of isolated millisecond pulsars?

4.3 Pulsars in the Magellanic Clouds Currently 19 radio pulsars are known in the Large and Small Magellanic Clouds [55]. Ridley & Lorimer [56] recently carried out a snapshot analysis of this population assuming the log-normal luminosity function for Galactic pulsars described above. We found that there are roughly 18,000 and 11,000 normal pulsars in the large and small clouds respectively. After accounting for beaming effects, and the fraction of high-velocity pulsars which escape the clouds, the estimated birth rates in both clouds appear to be comparable and in the range 0.5–1 pulsar per century. Although higher than estimates for the rate of core-collapse supernovae in the clouds, these pulsar birth rates are consistent with historical supernova observations in the past 300 yr. A fully dynamical model incorporating the kinematics and spindown of the pulsars in the Magellanic Clouds would be a logical extension of this work. A substantial population of active radio pulsars (of order a few hundred thousand) have escaped the clouds and populate the local intergalactic medium. For the millisecond pulsar population, the lack of any detections from current surveys leads only upper limits of up to 40,000 sources in the two clouds. A new survey with greatly improved time and frequency resolution currently underway at Parkes could detect a few of these sources (if they exist) and place valuable constraints on the total population. Giant-pulse emitting neutron stars could also be seen by this survey.

4.4 Globular cluster pulsars The first pulsar in a GC was found over 20 years ago [57]. Currently, there are 140 radio pulsars in 26 GCs [58]. Progress towards the current sample has proceeded in two phases. In the late 1980s and early 1990s, searches uncovered about two dozen of the brightest objects [59]. Further progress was only made later, around the year 2000, when a combination of advances in high-frequency broadband receivers, software algorithms, computing power and data storage capabilities led to a resurgence of discoveries [60, 61, 62, 63, 64] and interest from observers and theorists [15].

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While much of the recent focus on the observational results mentioned above has been on revealing unique systems and their applications for fundamental physics, relatively little attention has been paid on understanding the population of GC pulsars as a whole. In fact, the last major study into GC pulsar statistics were carried out in the late 1980s [80]. A major finding of this work was that the birth rate required to sustain the population of ∼ 104 MSPs estimated in all GCs was 100 times higher than the birth rate of their proposed progenitors [68], the LMXBs. Since then, the discovery of large numbers of quiescent LMXBs[81] has decreased this disparity, but another potential problem has emerged. If NSs are formed as in the Galaxy, i.e. in the core collapse supernovae of massive stars, then the large resultant velocities observed among the young pulsars [31] would eject the vast majority of all NSs from GCs. This would result in a very small number of primordial NSs in clusters. How do GCs retain enough NSs to form all the quiescent LMXBs and MSPs we observe? Are there other NS formation mechanisms at work? We anticipate significant progress in many of these areas in the near future.

Acknowledgments My research is funded by the West Virginia Experimental Program to Stimulate Competitive Research, the Research Corporation, the Smithsonian Astrophysical Observatory, the National Radio Astronomy Observatory and the National Science Foundation. I thank the Physics Department, Eberly College of Arts & Sciences and the Senate Research Committee for supporting my travel to this meeting.

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Pulsar Results with the Fermi Large Area Telescope Paul S. Ray and Pablo M. Saz Parkinson for the Fermi LAT Collaboration, the LAT Pulsar Timing Consortium, and the LAT Pulsar Search Consortium

Abstract The launch of the Fermi Gamma-ray Space Telescope has heralded a new era in the study of gamma-ray pulsars. The population of confirmed gamma-ray pulsars has gone from 6–7 to more than 60, and the superb sensitivity of the Large Area Telescope (LAT) on Fermi has allowed the detailed study of their spectra and light curves. Twenty-four of these pulsars were discovered in blind searches of the gamma-ray data, and twenty-one of these are, at present, radio quiet, despite deep radio follow-up observations. In addition, millisecond pulsars have been confirmed as a class of gamma-ray emitters, both individually and collectively in globular clusters. Recently, radio searches in the direction of LAT sources with no likely counterparts have been highly productive, leading to the discovery of a large number of new millisecond pulsars. Taken together, these discoveries promise a great improvement in the understanding of the gamma-ray emission properties and Galactic population of pulsars. We summarize some of the results stemming from these newly-detected pulsars and their timing and multi-wavelength follow-up observations.

1 Introduction 1.1 Gamma-ray Pulsars in the Year 2000 Ten years ago, on 4 June 2000, the Compton Gamma Ray Observatory (CGRO) was de-orbited, ending nine years of operation, during which it revolutionized Paul S. Ray Naval Research Laboratory, 4555 Overlook Ave., SW, Washington DC 20375-5352 USA e-mail: [email protected] Pablo M. Saz Parkinson Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 95064 USA e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_3, © Springer-Verlag Berlin Heidelberg 2011

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gamma-ray astronomy. In particular, the Energetic Gamma Ray Experiment Telescope (EGRET) surveyed the sky at energies > 100 MeV with much better sensitivity than previous experiments. The landmark Third EGRET (3EG) Catalog [35] reported the characteristics of 271 gamma-ray sources. The largest class of identified sources were blazars, with 66 sources, followed by 5 pulsars (Crab, Vela, Geminga, PSR B1055−52, and PSR B1706−44), 1 solar flare, the Large Magellenic Cloud, and one probable radio galaxy (Centaurus A). Interestingly, the majority of the 3EG sources (170 of them) were not associated with any known classes of gamma-ray emitting objects. It was widely believed that a large number of the unidentified EGRET sources, particularly along the Galactic plane, could be pulsars [e.g. 63], and several radio pulsars were, in fact, discovered by searching the error circles of EGRET unidentified sources [e.g. 32, 54]. Further work on EGRET data revealed one more high-confidence pulsar (PSR B1951+32) and several candidates, including one millisecond pulsar [46]. An excellent observational summary of what was known about gamma-ray pulsars at the end of the EGRET era was presented by Thompson [59]. It is also worth noting that a 7th gamma-ray pulsar (PSR B1509−58) was detected by the COMPTEL experiment up to 10 MeV [45], though it was never seen with EGRET. Pre-launch predictions of the number of gamma-ray pulsars that Fermi LAT would detect (as well as the fraction of those that would be radio quiet) are highly dependent on the assumed gamma-ray emission model, ranging from a few tens to many hundreds [e.g. 50], with the larger number (and fraction of radio-quiet pulsars) usually predicted by outer-magnetosphere models, where the gamma-ray beam is expected to be broader [39, 34]. It should be noted that the detection of a gamma-ray pulsar, in this context, does not necessarily imply the detection of its pulsations; most models, for example, “predict” that EGRET detected far more than the 6 gamma-ray pulsars for which high-confidence pulsations were actually observed, a view that is supported by the subsequent detection of pulsations from many formerly unidentified EGRET sources by the LAT.

1.2 Fermi and AGILE After almost a decade without an orbiting GeV telescope, two new satellites were launched in 2007–2008, ushering in a new era of gamma-ray astronomy. AGILE (an Italian acronym for Astro-rivelatore Gamma a Immagini LEggero) was launched on 23 April 2007 and the Fermi Gamma-ray Space Telescope (formerly GLAST) was launched on 11 June 2008. The prime instruments on both spacecraft are pair production gamma-ray telsecopes, like EGRET. However, instead of a gas spark chamber, they employ more modern solid-state silicon strip detectors to track the gamma-ray and particle events. While AGILE had a 14-month head start on Fermi, and has made many important contributions, it represents a modest improvement in sensitivity compared to EGRET. In this paper we focus on the pulsar results made possible by the enormous leap in sensitivity afforded by Fermi.

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The primary instrument on Fermi is called the Large Area Telescope (LAT) [24]. The LAT is a pair conversion gamma-ray telescope where incoming gamma rays are converted to electron-positron pairs in a set of tungsten foils. The resulting electronpositron pair and shower of secondary particles are tracked by a stack of silicon strip detectors to determine the incident direction of the photon before the energy of the shower is recorded in a CsI calorimeter. The instrument is wrapped in a segmented anti-coincidence detector that aids in the separation of events due to charged particles from those resulting from photons. This is critical because charged particle events outnumber photon events by a factor of 104 . The LAT is sensitive to photons in the energy range 30 MeV to > 300 GeV, with an effective area of ∼ 8000 cm2 at 1 GeV. The point spread function is ∼ 0.8◦ at 1 GeV and is a strong function of energy, scaling like E −0.8 until the resolution becomes limited by position resolution in the tracker at about 0.07◦1 . Compared to EGRET, the LAT represents a major improvement in effective area, field of view, and angular resolution. In addition, it operates in a sky survey mode which avoids loss of observing efficiency from Earth occultations and covers the sky nearly uniformly every two orbits (∼ 3 hours). These characteristics give the LAT unprecedented sensitivity for discovery and study of gamma-ray pulsars. The First Fermi LAT catalog [1FGL; 16] of 1451 gamma-ray sources detected during the first 11 months of science operations contains 56 sources that have been firmly identified as pulsars through their gamma-ray pulsations. Several additional gamma-ray pulsars have been identified since the release of the catalog, bringing the total number to more than 60. In the following sections, we describe the various populations of gamma-ray pulsars being explored by the LAT, and the different techniques employed in their detection, as well as some of the new insights being gained through these new findings. We end with a brief summary and some thoughts on the future goals and expectations for pulsar astrophysics with the LAT in the coming years.

2 The EGRET Pulsars in Exquisite Detail The EGRET experiment represented a major improvement relative to previous gamma-ray missions (e.g. SAS-2 and COS-B). In addition to increasing the number of high-confidence gamma-ray pulsars from 2 to 6, the higher sensitivity of EGRET led to a better understanding of the known gamma-ray pulsars (at the time, only the Crab and Vela). Similarly, the LAT, with its improved sensitivity and broader energy range is not only enabling the discovery of a large number of new gamma-ray pulsars, but is also greatly expanding our knowledge of the previously known EGRETdetected pulsars. Because these pulsars are among the brightest known gamma-ray sources, the LAT is able to accumulate enough statistics to allow for detailed (and phase-resolved) spectral analyses, in many cases answering some questions left over 1

This is the individual photon angular resolution. Bright sources can be localized more precisely via centroiding.

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from the EGRET era, or challenging some of the previous EGRET results which in most cases were based on limited statistics. Early LAT observations of Vela, the brightest steady gamma-ray source, confirmed some of the basic features of this pulsar: It has two asymmetric peaks that evolve differently with energy, and a phase-averaged spectrum well modeled by a hard power-law with an exponential cutoff in the 2–4 GeV energy range. In addition, the much better statistics and time resolution of the LAT data reveal pulse structures as fine as 0.3 ms, and a hitherto unknown third peak in the light curve, which evolves with energy (see Figure 1). Spectral fits to the LAT data suggest that a simple exponential cutoff is preferred over a super-exponential one, indicating that outer-magnetosphere emission models are favored over polar cap type models [6]. More recent results on Vela, using 11 months of observations, show detailed phaseresolved features which confirm the EGRET results on the spectral evolution of the two main peaks. In addition, while the first peak is seen to fade at higher energies, the newly-discovered third peak, along with the second peak, are present up to the highest detected pulsed energies [21]. LAT results on the Crab pulsar confirm that it shares many of the properties of Vela, with two asymmetric peaks evolving differently with energy. The Crab pulsar spectrum is also best modeled with a power law with an exponential cutoff, but the cut-off energy in this case is much higher than Vela (∼6 GeV), with pulsed gammaray photons being detected at least up to ∼20 GeV [18]. One of the new features uncovered by the LAT is an apparent phase shift between the main radio peak and the first gamma-ray peak. Previously, it was thought that these two were aligned, but the fine time resolution of the LAT allows us to determine that the first gamma-ray peak leads the main radio pulse by (281 ± 12 ± 21) µs (see Figure 1). In addition to being the second brightest non-variable source in the GeV sky, Geminga was the first known radio-quiet gamma-ray pulsar. As such, it cannot be timed in radio and until now, a good timing solution relied on X-ray observations. Using ∼1 year of observations, consisting of over 60,000 photons, a timing solution was obtained based solely on gamma rays [11]. Geminga shows many similarities to Vela and the Crab. The phase-averaged spectrum is also well represented by a

Fig. 1 Pulse profile of the Vela pulsar, as a function of energy. The different behavior of the two main peaks is evident. A third peak is seen to appear at higher energies, with its position shifting in phase, as a function of energy [from 21, reproduced by permission of the AAS].

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power law with exponential cutoff, with a hard spectral index and a cutoff energy between 2–3 GeV, leading to pulsed gamma rays being detected up to at least 18 GeV [11]. Detailed phase-resolved spectroscopy shows an evolution of the spectral parameters with phase and appears to indicate that there is emission coming from the pulsar at all rotational phases, favoring, once again, outer-magnetospheric emission models [11]. The remaining EGRET pulsars, J1057−5226, J1709−4429, and J1952+3252, while still bright, were not as bright as Vela, the Crab, and Geminga. LAT observations of these pulsars shed light on some of the key questions left over from the EGRET era. All three pulsars, once again, can be fit with a power law with a simple exponential cutoff. This contradicts earlier EGRET results that indicated that PSR J1709−4429 could be fit with a broken power law and PSR J1952+3252 showed no signs of a cutoff below 30 GeV [12]. It is interesting to note that the conclusion about the EGRET spectrum of PSR J1952+3252 was based on the detection of 2 photons above 10 GeV. Finally, although not detected by EGRET, PSR B1509−58 was seen by the COMPTEL instrument, and is therefore one of the 7 gamma-ray pulsars detected by CGRO. More recently, its detection has also been reported by the AGILE collaboration [10]. Using 1 year of data, the LAT was able to detect pulsations from PSR B1509−58 up to 1 GeV, and confirmed that, unlike the EGRET-detected pulsars, PSR B1509−58 has an energy spectrum that breaks at a few tens of MeV [14]. The high precision phase-resolved spectral measurements made possible with the LAT will be critical for theoretical modeling efforts, which must confront these new data. With the simple question of polar cap vs. outer magnetosphere origin now largely resolved, the important questions become more subtle: Where exactly in the outer magnetosphere is the acceleration occurring? Which magnetosphere geometry is appropriate (e.g. vacuum dipole or force-free magnetosphere)? Fig. 2 Folded light curve of the Crab pulsar [from 18, reproduced by permission of the AAS]. The statistics provided by the LAT allow us to observe structure in the light curve with incredible precision. For example, it is now clear that the main radio pulse (red) and the gammaray pulse (black) do not line up, and in fact are separated by approximately 0.3 ms.

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3 Young Pulsars Found Using Radio Ephemerides In addition to the 7 young (or middle-aged) gamma-ray pulsars previously detected by CGRO, the LAT has also detected gamma-ray emission from an additional dozen or more “young” (non-millisecond) radio-selected pulsars. PSR J2021+3651 holds the distinction of being the first new gamma-ray pulsar in the post-EGRET era. The pulsations were detected with the LAT during the commissioning phase of the instrument [9], although the original discovery of the gamma-ray pulsar was independently reported using AGILE data [33]. Other pulsars detected early in the mission include PSR J1028−5819, shown to be at least partly responsible for the EGRET source 3EG J1027−5817, the single-peaked PSR J2229+6114 in the “Boomerang” pulsar wind nebula (PWN) [5], and the very energetic PSR J0205+6449, in SNR 3C 58 [4]. Several of the newly-detected gamma-ray pulsars were already proposed as marginal EGRET detections, including PSRs J1048−5832 and J0659+1414. Figure 3, for example, shows the folded light curves of PSR J1048−5832, including that generated with EGRET data. While the significance of the EGRET pulsation is clearly limited by the much lower statistics, the perfect alignment of the peaks with the LAT profile confirms that this was, indeed, a real detection, as originally reported by Kaspi et al. [40]. Other young pulsars now seen by the LAT were originally discovered in radio searches of EGRET unidentified sources, and thus proposed as the energetic radio counterparts of the known gamma-ray sources (e.g. PSRs J2021+3651 and J2229+6114). Many, however, had no previous gammaray associations. While the brightest new gamma-ray pulsars (particularly those coincident with formerly-unidentified EGRET sources) could have been detected in blind searches of LAT data (or searching around the extrapolation of the original radio timing solution), the detection of pulsations from fainter gamma-ray pulsars (e.g. PSR J0205+6449) requires contemporaneous phase-connected timing solutions spanning the entire LAT data set. In anticipation of such needs, a comprehensive pulsar monitoring campaign (known as the Pulsar Timing Consortium) was set up, prior to launch, between the LAT collaboration and the major radio telescopes, to ensure periodic monitoring of hundreds of pulsars with large spin-down energies, with the goal of providing the necessary ephemerides [57].

4 Millisecond Pulsars At first glance, millisecond pulsars (MSPs) might not seem like great candidates for gamma-ray emission. After all, they are several orders of magnitude older than the gamma-ray bright young pulsars and their surface magnetic fields are about four orders of magnitude weaker. On the other hand, their very rapid rotation rates give them open field line voltages that are competitive with the young pulsars and their magnetic fields at the light cylinder (BLC) are at about the median value for the young gamma-ray pulsars. This, plus the marginal detection of PSR J0218+4232 with EGRET [46], gave some reason to be optimistic. One particularly prescient pa-

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Fig. 3 Folded light curves of the young energetic pulsar PSR J1048−5832 [from 5, reproduced by permission of the AAS]. The second panel from the bottom shows the EGRET light curve. The Fermi LAT data allow us not only to confirm the marginal EGRET detection (note that the peaks line up), but also to study much finer time scales, as well as the energy evolution of the light curve.

per [58] used a detailed population study based on the pair-starved polar cap model to predict that the LAT should be sensitive enough to detect tens of gamma-ray millisecond pulsars, most of which should be radio quiet and thus form a high-latitude population of unidentified gamma-ray pulsars. They also pointed out that, since the high latitude regions have been very poorly covered by millisecond pulsar surveys so far, radio searches of LAT point sources with pulsar-like spectra should be an efficient way to find new MSPs. Over the first 18 months of the Fermi mission, it has become abundantly clear that millisecond pulsars are a significant contributor to the population of high latitude gamma-ray sources being detected with the LAT. Figure 4 shows the distribution, in Galactic coordinates, of all the MSPs detected to date with Fermi LAT. We describe these discoveries in the following subsections.

4.1 Radio MSPs The first LAT results on MSPs came from folding the gamma-ray data using radio ephemerides for the ∼ 72 field MSPs (i.e. P < 30 ms and outside of the globular cluster system). Within the first 8 months of data taking, significant gamma-ray pulsations were discovered from 8 MSPs, including confirmation of the EGRET detection of PSR J0218+4232 [10, 1]. In addition to the 8 pulsed detections, it was

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noted that there were significant LAT point sources positionally coincident with 5 other MSPs [1]. With continued exposure accumulating, 3 of those 5 now have reported pulsation detections above the 5 σ significance level: PSR J0034−0534 [15], PSR B1937+21 and PSR B1957+20 [42], bringing the total number of radiotimed millisecond gamma-ray pulsars to 11. The initial 8 MSP discoveries tended to resemble the normal pulsar population in most of their characteristics, including the peak separations, fraction that showed single vs. double peaks, and radio lags. This led to the conclusion that MSPs had essentially the same gamma-ray emission mechanism operating in the outer magnetosphere as the young pulsars, as suggested by the similar values of BLC. Interestingly, the three latest discoveries all have gamma-ray light curves that appear to have peaks that are aligned in phase with the radio pulses. This characteristic is very rare among the normal pulsars, with the primary counter-example being the Crab pulsar (where the radio peaks overlap the gamma-ray ones, even though they aren’t perfectly aligned, as described above). It has been suggested that these are cases where the gamma-ray and radio emission are coming from nearly co-located regions of the magnetosphere and that both result from caustic formation [15].

4.2 Searches of LAT Unassociated Sources As mentioned earlier, a promising technique for discovering new MSPs is to perform radio searches in the direction of gamma-ray point sources that have pulsar-like characteristics (e.g. lack of variability and exponentially cutoff spectra). This technique was used, with modest success, on many of the EGRET unidentified sources [29, 27, 41, for example]. These searches were challenging because the EGRET error boxes were many times larger than a typical radio telescope beam, requiring many pointings to cover the source region. With the LAT, the unassociated source localizations are a much better match to radio telescope beam sizes and can generally be searched in a single pointing. The Fermi Pulsar Search Consortium (PSC) was conceived to organize search observations of LAT-discovered pulsars and unassociated sources using several large radio telescopes around the world. Thus far, over 100 LAT unassociated sources, mostly at high Galactic latitudes (See Figure 4), have been searched at 350, 820, or 1400 MHz resulting in the discovery of 18 new millisecond pulsars [51]. These searches are ongoing, and there is no apparent strong correlation between the gamma-ray and radio fluxes of these pulsars, so more discoveries can be expected as fainter LAT unassociated sources2 are searched. These discoveries represent a ∼25% increase in the number of known millisecond pulsars outside of the globular clusters, which is an impressive achievement considering the enormous effort that has gone into radio MSP searches over the last three decades. The new pulsars include several highly interesting sources. Five of 2

The 1FGL catalog, compiled with 11 months of data, lists 630 unassociated sources and many more are expected as the LAT pushes down in sensitivity. Note, however, that AGN (which represent about half of the current associations) will likely comprise a significant fraction of these.

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them are so-called “Black Widow” pulsars, with minimum companion masses of 0.01–0.05 M⊙ and one other has a more typical mass companion, but exhibits radio eclipses. These more than double the known population of such pulsars in the field of the Galaxy and will be important systems for understanding the formation and evolution of millisecond pulsars as well as excellent systems to look for unpulsed gamma-ray emission from intra-binary shocks. Several others are very bright with sharp radio profiles that have the potential to be important additions to pulsar timing array projects that seek to detect nanoHertz gravitational waves via their effect on pulse arrival times [18]. Since all of these pulsars are positionally coincident with LAT gamma-ray sources, it is expected that once sufficiently accurate timing models are available, they will all be found to be gamma-ray pulsars. Indeed, LAT pulsations have already been discovered for the first 3 of the new MSPs [51].

4.3 Globular Cluster MSPs Although there are some 140 pulsars known in globular clusters3 , most of which are MSPs, there have been no reported gamma-ray pulsations from individual millisecond pulsars in globular clusters with the LAT. However, in at least 8 cases, there are point-like gamma-ray sources spatially coincident with globular clusters [3, 43, 13].

J1231-14

J1302-32 J0751+1807 J1745+10

J1614-2230

J1810+17 J1744-1134

J1514-49

J1103-53

B1937+21 J2215+51 J0340+41 J0218+4232

J1658-53 J0613-0200

J2302+44

B1957+20

J1747-40

J2214+30

J0614-33

J2017+06 J1902-51 J2124-3358

J0437-4715 J2241-52

J0023+09

J0100-64

J0030+0451 J0034-0534

Fig. 4 Sky map, in Galactic coordinates, showing millisecond pulsars detected with the Fermi LAT. The background image is made from 16 months of LAT data (2008-08-04 through 2009-1202) with E > 100 MeV. The white crosses mark the 11 previously known radio pulsars found to be gamma-ray pulsars with the LAT. The yellow circles indicate the 18 new radio MSPs discovered in searches of pulsar-like LAT unassociated sources.

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In general, these 8 LAT sources are consistent with being the combined emission of a population of millisecond pulsars in each cluster. Most have spectra that show an exponential cutoff in the few GeV range, as seen with MSPs, but for a couple the significance of the cutoff is too low for it to be considered evidence for an association of the gamma-ray source with the cluster. The fluxes are largely consistent, within the substantial uncertainties, with estimates of the total number of MSPs in each from from radio and X-ray observations. However, in three cases, there are no known MSPs in clusters with associated LAT sources, providing a strong motivation for deeper radio pulsar searches of those clusters. It is worth noting that the AGILE collaboration reported the detection of pulsations from PSR J1824−2452, in the globular cluster M28 [10], but the detection was marginal and appeared in only one subset of the AGILE data. Thus far, this result has not been confirmed by Fermi. In general, the detection of individual gamma-ray pulsars in globular clusters will likely be difficult because of the typically large distances to the clusters (4–12 kpc for the likely LAT-detected clusters) and because of the background provided by the rest of the pulsars in the cluster. However, in ˙ it cases where there is one pulsar (like PSR J1824−2452) that has a very large E, may outshine the rest of the pulsars in the cluster and be detectable individually. Searches with the LAT are ongoing, using radio timing models for a large number of individual pulsars in globular clusters.

5 Blind Periodicity Searches As described in previous sections, it was long thought that many of the EGRET unidentified sources could, in fact, be pulsars—in particular radio-quiet pulsars like Geminga. Previous attempts to carry out blind searches on EGRET data using coherent FFT techniques were unsuccessful [e.g. 28]. The sparse data sets and sensitivity to timing irregularities make such searches incredibly challenging. A new technique was developed to try and ameliorate the problem, by calculating the FFT of the time differences (instead of times of arrival) of events. Time differences are calculated between all events in the time series with respect to events lying within a relatively short sliding window (∼weeks). The lower frequency resolution of the resulting FFTs make these searches less sensitivite to frequency shifts (such as those caused by the spindown of the pulsar), while at the same time resulting in great savings in computational time [23]. This new time-differencing technique was shown to work with EGRET data [64], and has since proven extremely successful with the LAT data, leading to the discovery, so far, of 24 pulsars found in blind searches [2, 56]. Figure 5 shows an example of the output from a successful blind search of a formerly unassociated LAT source, now identified as PSR J1957+5033 [56]. After determining that the highly significant peak at 2.668 Hz is promising, standard pulsar

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packages such as PRESTO4 , and tempo2 [38], are used to refine the result and obtain a final timing solution for the pulsar. Most of the initial 16 pulsars found in blind searches of LAT data were associated with formerly unidentified EGRET sources. In fact, only 3 of the 16 had no EGRET counterpart [2]. Many of these sources were long-suspected of hosting pulsars, including 3EG J1835+5918, the brightest unidentified EGRET source off the Galactic plane, which was even dubbed the ‘Next Geminga’ [31]. Six out of the sixteen pulsars were discovered by assuming a counterpart position derived from observations at other wavelengths (mostly X-ray), instead of the less precise LAT position. A prime example is the discovery of PSR J1836+5925 powering 3EG J1835+5918 [17]. More recently, the last 8 pulsars found in blind searches have mostly been found from newly-discovered LAT sources, with no corresponding EGRET counterpart, except in some cases where the EGRET source might have been confused and is now being resolved into multiple separate gamma-ray sources by the LAT [56]. Although radio beaming fractions for MSPs appear to be large [44], there are still expected to be radio quiet millisecond pulsars detected as point sources with the LAT. A discovery of a radio-quiet MSP in a blind search would be an important result. Unfortunately, the parameter space that needs to be searched is vast. For the case of binary MSPs the problem may be essentially intractable. However, about 25% of MSPs are isolated, including at least two of the LAT-detected radio MSP. For these pulsars the search is daunting, but not impossible. On the plus side, MSPs have low period derivatives and are extremely stable rotators, so the pulse will remain

Fig. 5 Results from a blind search on a formerly unassociated LAT source [now PSR J1957+5033; 56], indicating the presence of a highly significant pulsation at 2.668 Hz. The FFT has been computed using the differences between binned photon arrival times up to a maximum difference of 262,144 s, and the power at each frequency has been normalized to represent the inverse of the probability that it could be due to a random fluctuation, as described in Ziegler et al. [64]. Note that the logarithmic scale results in the majority of the 33,554,432 FFT bins not showing up in the figure. 4

http://www.cv.nrao.edu/∼sransom/presto/, [49]

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phase coherent for a long integration time. Counteracting this is the fact that the fast spin rates require that the pulsar position be known very precisely (∼ 0.1 arcsec). For a typical LAT point source position uncertainty of 3 arcmin, this requires 3.2 × 106 trial positions to cover the region, and each trial position requires a search over frequency and frequency derivative. Current efforts on blind searches of LAT data are concentrating on both searching deeper for young and middle aged pulsars as well as expanding the search parameter space to include isolated MSPs.

6 Pulsar Timing with the LAT Pulsar timing is a powerful technique that involves fitting a model to measured pulse arrival times that can account for every rotation of the neutron star over a time span of years [47, chap. 8]. Of course, such timing yields extremely precise measurements of the spin period and spindown rate of the neutron star, quantities from which estimates of the magnetic field, age, and energy loss rate of the pulsar can be derived. In addition, because of the motion of the Earth around the solar system barycenter, the pulse arrival times are highly sensitive to the pulsar position on the sky. Once those major effects are accounted for, timing is sensitive to a host of other parameters of the system including binary orbital parameters, timing noise, glitches, and even proper motion and parallax in some cases. Traditionally, pulsars have been discovered and timed using radio telescopes. Working in the gamma-ray band, EGRET was not very effective for pulsar timing both because of its limited sensitivity and because of its pointed viewing plan that meant that most pulsars were only observed for a few 2-week observations scattered over the mission. The situation is completely different with Fermi, which now has both the sensitivity to detect a large number of pulsars and a sky survey viewing plan that allows observations of every pulsar in the sky continuously. For most of the 24 blind search pulsars, timing using the LAT data is the only option since they are undetectable or extremely faint at radio wavelengths. In addition there are some very faint radio pulsars, such as PSR J1124−5916 where the observation time required to do radio timing is prohibitive, but which can be readily timed with the LAT. There are several key differences between pulsar timing with the LAT and radio pulsar timing. First, the satellite is not affixed to the Earth, like a ground-based radio telescope. Second, the data are very sparse, with often fewer than 100 photons being used to make a pulse time-of-arrival (TOA) measurement. The first issue is dealt with by transforming the photon arrival times as observed at the satellite to a fictional observatory at the geocenter, thus removing the effects of the spacecraft motion on the measurement. The second difference drives one to adopt a TOA measurement technique different than the traditional radio method of cross correlating a folded pulse profile with a high signal to noise binned template. Instead, TOAs are

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determined by a maximum likelihood fit to the offset between the measured photon times and an analytic template profile [53]. What is impressive is that even with so few photons, timing models can be determined for most detectable LAT pulsars with RMS residuals of order a millisecond using TOAs spaced by a few weeks. This enables arcsecond position determinations as shown in Figures 6 and 8 (right panel). In addition to these precise positions that enable multiwavelength counterpart identifications, pulsar timing with the LAT has provided spindown measurements for the gamma-ray selected pulsars, detection and measurement of glitches, and studies of the timing noise observed in these systems. The precise long-term timing models are also critical for other studies such as blanking a pulsar to remove confusion in the study of a nearby source, as was required for Cygnus X-3 [8] or searches for off-pulse emission, such as from an SNR or PWN [30]. Fig. 6 Comparison of position determinations of PSR J1836+5925. The large ellipse (0.45 arcmin semimajor axis) is the 95% confidence region from positional analysis of 18 months of LAT data (M. Kerr, private communication). The small ellipse (0.8 × 0.4 arcsec) is from the pulsar timing model fit over the same interval [53]. The background image is a Chandra X-ray image showing the point source at the location of the pulsar.

7 Multiwavelength Connections The 24 blind-search pulsars were all discovered in gamma-ray searches and thus are gamma-ray selected pulsars, but targeted radio observations are required to determine if they are also radio quiet, or could have been discovered in radio surveys independently. Radio detections also yield distance estimates from dispersion measure, information on the emission region from radio to gamma-ray offset, and geometry from radio polarization studies. In addition, the population statistics of radio quiet vs. radio loud gamma-ray pulsars have important implications for gamma-ray emission models. Deep radio searches have now resulted in the detection of radio pulsations from three of the 24 blind search pulsars, with strong upper limits on the others [53, 56]. The pulsations from J1741−2054 were found in archival Parkes Multibeam survey data and confirmed using the Green Bank Telescope (GBT) [26]. For J2032+4127,

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Fig. 7 Pseudo-luminosities of the gamma-ray selected pulsars that have since been detected as radio pulsars (red stars), compared to the general population of radio pulsars (blue dots).

the pulsations were discovered using the GBT [26]. The third radio pulsation discovered was from PSR J1907+0602 [19] using a very deep observation with the 305-m Arecibo telescope. The detections provide distance estimates from the dispersion measure, which allow conversion of the radio fluxes into pseudo-luminosities. As shown in Figure 7, two of these pulsars are exceptionally faint, with luminosities about an order of magnitude lower than the faintest radio-discovered young pulsars. This is forcing a reevaluation of what is meant by a ‘radio quiet’ pulsar. Observations of PWNe at TeV energies go back to the very first firm detection of emission from the Crab nebula [62]. Since then, over 100 TeV sources have been detected5 and more than half of these have associated LAT sources [16], which is perhaps not altogether surprising given that the energy ranges of the LAT and groundbased Cerenkov detectors overlap. PWNe represent the largest class of Galactic TeV sources. In fact, the first unidentified TeV source, discovered by the HEGRA telescope in the Cygnus OB2 region, is associated with PSR J2032+4127, one of the pulsars found in blind searches of LAT data [2, 26]. HESS observations of the Galactic plane uncovered a large number of unidentified TeV sources, and many of these are thought to be associated with PWNe. In some cases, the discovery of new LAT pulsars coincident with known TeV sources can put into question previous interpretations of the TeV emission. Figure 8, for example, shows the positional coincidence of the highly energetic pulsar PSR J1023−5746 [56] with the bright TeV source, HESS J1023-575. Located in the vicinity of the young stellar cluster Westerlund 2, the TeV emission from this source was previously thought to be due mainly to the wind interaction from massive stars [22]. The presence of such a pulsar, however, must lead to a re-examination of such conclusions. Furthermore, the identification of the counterpart (right panel in Figure 8) shows that the association with the Westerlund 2 cluster is highly questionable. 5

For an up-to-date catalog of TeV sources, see http://tevcat.uchicago.edu/

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Fig. 8 Left – Fermi LAT counts map of the region around PSR J1023−5746. The green contours represent the HESS significance. Right – Chandra X-ray image of the Westerlund 2 cluster. The X-ray counterpart of PSR J1023−5746 is approximately 8 arcminutes away from the core of the cluster. Inset: Zoomed-in image of a 1 square arcminute region around the location of the pulsar. Note that the 95% (statistical) error ellipse obtained from pulsar timing (shown in white) overlaps with the X-ray source. Figures from Saz Parkinson et al. [56], reproduced by permission of the AAS.

At higher energies still, the Milagro observatory detected significant (> 5σ) TeV emission at a median energy of 35 TeV from the location of 6 gamma-ray pulsars detected by the LAT, and evidence for emission (3 − 5σ) from the location of an additional 8 sources from the Bright Source List [7]. Four of those sources are gamma-ray pulsars, and two more are associated with supernova remnants. This strong connection between young energetic GeV pulsars and their TeV PWNe can play an important role not only in understanding the nature of the emission from such sources, but also as a means to identify likely candidates for gammaray pulsars, ultimately leading to the identification of both TeV and GeV sources. X-ray observations of gamma-ray pulsars and pulsar candidates are particularly important. First, the precise positions of neutron star candidates allow for more sensitive blind searches to take place (as in the case of PSR J0007+7303 or PSR J1836+5925). Secondly, for those pulsar candidates found using the less precise LAT position, X-ray positions can serve to refine the candidate and determine whether it is a real detection. In 4 out of the original 16 pulsars discovered in blind searches, a short observation with the Swift satellite was enough to identify a plausible X-ray counterpart which resulted in a much higher significance of the pulsation [2]. In several other cases (e.g. Gamma Cygni SNR, Cygnus OB2 association), archival observations could be analysed in search of the best possible counterpart.

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10 39 erg 10 38 s -1 erg 10 37 s -1 erg 10 36 s -1 erg 10 35 s -1 erg 10 34 s -1 erg s-

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Fig. 9 Period-Period Derivative diagram showing the LAT-detected pulsars. Included are 24 young or middle-aged radio-timed pulsars (green circles), 25 gamma-ray selected pulsars (blue squares), where all but Geminga were discovered in LAT blind searches, and 14 millisecond pulsars (red triangles), for a total of 63 gamma-ray pulsars. Note that this does not include 15 of the radio millisecond pulsars discovered in searches of LAT unassociated sources, essentially all of which can be expected to be detected as gamma-ray pulsars once their timing models are well determined.

8 The LAT Pulsar Population A Period-Period Derivative diagram showing all 63 gamma-ray pulsar detections made with the LAT to date is shown in Figure 1. This is an update of Figure 2 from the Fermi LAT First Pulsar Catalog [20], which summarizes the characteristics of the 46 gamma-ray pulsars detected with the LAT in the first 6 months of the Fermi mission. The LAT-detected pulsars generally have high values for the detectability metric E˙ 1/2 /D2 and large E˙ and BLC . Which one of these is really telling us about the gamma-ray emission physics at work in these sources remains to be seen. With a large number of detections spanning a range of E˙ from 1033.5 to > 1038 erg s−1 , we can start to address the evolution of gamma-ray luminosity (i.e. efficiency) with ˙ Unfortunately, the large distance uncertainties for most pulsars combined with E. the model-dependent uncertainty in the beaming factor (see below) prevent strong conclusions from being drawn at present [20].

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The spectra of LAT pulsars are well characterized by exponentially cutoff power laws with photon indices near 1.5. The cutoff energies are in the 1–4 GeV range with a small number of outliers on the high and low side. The observed pulse profiles frequently evolve with energy, but generally fall into one of three categories: two peaks separated by ∼ 0.4 − 0.5 in phase, two overlapping peaks separated by ∼ 0.2 in phase, and single peaked profiles. Most of the LAT pulsars are consistent with being 100% pulsed in the gamma-ray band. However, a few (e.g. Geminga and PSR J1836+5925) seem to show magnetospheric emission across all rotational phases. In other cases, an analysis of the ‘off-pulse’ region of pulse phase reveals GeV emission from a pulsar wind nebula, typically with a much harder spectrum than that of the pulsar itself. A review of LAT observations of PWNe is presented elsewhere in this volume [30]. The large number of radio and gamma-ray selected pulsars found with the LAT, combined with deep radio searches of the new gamma-ray selected population will enable population studies that will help shed light on the beaming fractions in the two bands and test predictions of the various models for the emission region geometries. One such early study [52] finds that the radio beaming fraction is near unity for the the highest E˙ pulsars and decreases to ∼ 0.5 for the lower E˙ gamma-ray pulsars, implying that very high- E˙ pulsars may produce their radio emission in the outer magnetosphere. If confirmed, this would have major implications. The current challenge is to use the abundance of well-measured light curves to constrain the geometry of the emitting region and the relevant magnetospheric physics. The favored approach is to choose an emission region location (e.g. polar cap (PC), outer gap (OG), or two-pole caustic (TPC)), combine it with an assumed magnetic field geometry and compute an ‘atlas’ of predicted gamma-ray light curves that can be compared with observations. This has been done for vacuum dipole field geometries [61], as well as for numerically-modeled ‘force-free’ geometries [25]. Other groups have specifically targeted millisecond pulsars [60]. The predicted light curve morphologies are sensitively dependent on both the misalignment between the spin and magnetic axes of the neutron star (α) and the viewing angle (ζ) between the spin axis and the line of sight. Without a priori knowledge of these angles, it can be hard to discriminate among models based on light curve fits. However, if the angles can be constrained by other methods, such as radio polarization measurements or Xray PWN geometry, the degeneracies can be broken. An important output of these model fits is the ‘flux correction factor’ fΩ , defined such that the true gamma-ray luminosity, Lγ of a pulsar is Lγ = 4π fΩ F obs D2 ,

(1)

where F obs is the observed gamma-ray flux and D is the distance. In the EGRET era it was commonly assumed that fΩ ∼ 1/4π, but current models predict values much closer to 1. This parameter is crucial for understanding the energetics of these systems and the efficiency (η) with which they convert rotational energy into gammarays. Recent model comparisons with a few LAT pulsar light curves [55] suggest that OG models with alternate field geometries are preferred in these cases. How-

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ever, other objects may be consistent with lower altitude emission, and additional comparisons are needed to see if the data are consistent with emission beyond the light cylinder, as suggested by the force-free models. With many more high quality light curves being collected by the LAT, it should be possible to make powerful tests of these models, especially if when angle constraints from radio and X-ray observations are available.

9 Future Expectations The next few years promise a continued stream of exciting pulsar results from the LAT. With the very reasonable assumption that the 18 new millisecond pulsars found in radio searches of LAT unassociated sources will all turn out to be gamma-ray pulsars, there will soon be more than 75 solid gamma-ray pulsar detections. This number is not totally unexpected, according to several pre-launch predictions. What is more surprising is that the population is divided into three essentially equal groups: young or middle-aged radio-selected pulsars, young or middle-aged gamma-ray selected pulsars, and millisecond pulsars. Modeling the spectra, light curves, and population statistics of the LAT pulsars will be extremely important over the next few years to turn the powerful observations into improved understanding of the physical mechanism for pulsar gamma-ray emission. But, since this is a primarily observational review, we close with a few of the important observational questions that we expect to be addressed in the coming years. • Are there radio quiet millisecond pulsars? This is both a great challenge for the observers and has very important implications for the emission mechanisms and geometry. • If the ‘gamma-ray binaries’ LS I +61 303 and LS 5039 (see review in this volume Hill et al. [36]) are powered by energetic pulsars, can we detect the gamma-ray pulsations with the LAT? • What are the non-detections of known pulsars telling us? While the new pulsar discoveries have grabbed most of the attention, it may be that one or more key non-detections will tell us something important about what drives gamma-ray pulsars. However, these studies are critically reliant on accurate distance determinations, so this is really a reminder that improved VLBA or timing parallax measurements for as many pulsars as possible will be of great value in increasing the science return from LAT pulsar studies. Acknowledgements The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat a` l’Energie Atomique and the Centre National de la Recherche Scientifique / Institut National de Physique Nucl´eaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto

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Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged ´ from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Etudes Spatiales in France. Pablo Saz Parkinson acknowledges support from the American Astronomical Society and the National Science Foundation in the form of an International Travel Grant, which enabled him to attend this conference. Basic research in astronomy at the Naval Research Laboratory is supported by 6.1 base funding.

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Fermi view of the EGRET pulsars F. Gargano for the Fermi-LAT collaboration

Abstract The six EGRET gamma ray pulsars are among the most interesting objects in the sky observed by Fermi: they are bright galactic gamma ray sources and they have good and updated timing solutions. EGRET has studied these pulsars up to an energy of 10 GeV, and at least for the brightest three it has analyzed the evolution of the emission with phase. The Large Area Telescope (LAT) on Fermi, thanks to its excellent sensitivity, has collected, in only one year, more photons then EGRET in its entire lifetime. The increased photon statistic and the outstanding timing capability, has allowed us to build detailed pulse profiles of all these six pulsars and to deeply study the changes of the emission spectrum with phase. Moreover we have obtained an excellent timing solution for Geminga using only gamma rays, and for all these pulsars we have observed that the emission spectrum is consistent with a power law with simple exponential cut-off. The study of the six EGRET pulsars with Fermi is therefore very important to improve our understanding of the pulsed gamma ray emission from neutron stars and, thanks to the very rich details of the analysis, it is a good test bench for different emission models.

1 Introduction Before Fermi only six pulsars were known as high-confidence gamma-rays emitters above 100 MeV. After the launch of the Fermi Gamma-ray Space Telescope on 11 June 2008 our view of the gamma-ray pulsar-sky is dramatically changed, since we now know more then 60 pulsars that emit above 100 MeV. EGRET data has allowed to build the gamma-ray light curves and the spectral emission spectra up to 10 GeV, but with only a handful of photons above 5 GeV the high energy emission wasn’t well studied and understood. Compared with its predecessor, the Fermi-LAT [1] has a larger effective area (8000 cm2 on-axis, 1GeV) and an improved angular resoluIstituto Nazionale di Fisica Nucleare, sez. Bari, Via Orabona 4, 70126 Bari, Italy e-mail: fabio. [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_4, © Springer-Verlag Berlin Heidelberg 2011

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tion (θ68 =0.6◦ at 1 GeV for events in the front section of the tracker). The large field of view (2.4 sr) allows the LAT to observe the full sky in survey mode every 3 hours. This excellent sensistivity has allowd, after only one year of survay mode observations of these six pulsars, to collect over an order of magnitude photons more than EGRET in its nine year lifetime. This unprecedented high statistics (more then 150000 photons for Vela) allowed us to construct high-quality pulse profiles and study their evolution with energy. Moreover, we have constructed detailed phase-resolved spectra of these pulsars revealing a complex evolution of the spectral parameters with phase. As a result, the study of the six EGRET pulsars has improved our understanding of pulsed emission and is allowing us to test the predictions of the current high-energy pulsed emission models.

2 Analysis results The analysis for the different pulsars have been done using different datasets ranging from 8 to 13 months, and for all of them photons from the Diffuse class are selected, i.e. the highest quality photon data, having the most stringent background rejection. In addition, we exclude the events with zenith angles greater than 105◦ due to the Earth bright γ-ray albedo. All the results shown in this review come from the following papers, where it is possible to find all the details of the analysis: [2] for Vela, [3] for Crab, [4] and [5] for Geminga and [6] for PSR J1057−5226, PSR J1709−4429, and PSR J1952+3252 The light curves are a powerful tool to study the mechanism hidden behind the pulsed emission, at all wavelengths. For this reason a great effort has been put in building good and accurate timing solution, that completely cover the observational periods of the six pulsars. For Crab, PSR J1057−5226 and PSR J1952+3252 the timing solution has been built from radio observations, while for Vela, Geminga and PSR J1709−4429 we have used a timing solution based on Fermi data. Before Fermi-LAT the ephemeris for Geminga, the fist known gamma-selected pulsar, were maintained by RXTE, but since the Fermi-LAT operates in sky-survey mode, it observes Geminga on a daily base and it can provide very accurate and updated timing solutions. For Vela we have chosen to use γ-ray data because it has been demonstrated that they give a more accurate solution than the radio observations. For PSR J1709−4429 the situation is slightly different, since a glitch has occurred around 2008 August 14, and so all the previous timing solution were not valid any more: we have then built a valid timing solution using only LAT data. The complete timing solutions are available at the Fermi Science Support Center (FSSC) website1 . In Table 1 are summarized the main parameters of the light curves and in Fig. 1 are shown the light curves for PSR J1057−5226, J1709−4429 and J1952+3253. With the exception of PSR J1057−5226, all the pulsars show well defined light 1

http://fermi.gsfc.nasa.gov/ssc/data/access/lat/ephems/

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curves with two main peaks, well described by lorentzian functions both symmetric or asymmetric. The ratio between the two peaks tends to change with energy, and in particular there is always a peak that almost disappears at high energy. Instead PSR J1057−5226 is different, since its light curve is very complex and we can barely point out the two peaks. For this pulsar a longer observation period is needed to study the details of the pulsed emission. All the pulsars show light curves in agreement with the one observed by EGRET [7]. For all the radio-selected pulsars it’s evident that there is a shift in phase between the radio and the gamma pulsation, and this could be explained if we assume a different location for the two different kind of emission. Pulsar Name

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0.13128±0.00016 0.095±0.002 — 0.31±0.03 0.242±0.002 0.154±0.001

0.4332±0.0002 0.398±0.003 0.497±0.004 0.28±0.03 0.250±0.004 0.485±0.017

Table 1 The main contributor to the timing solution is in the 2nd column, the post-fit RMS of the timing solution is in the 3rd one. The parameters derived from the fits to the pulse profile, the peak separation and phase lag between the radio and the first γ-ray pulse, are listed in the 4th and 5th columns.

The high statistic and the excellent performance of the LAT, has allowed to study in great details the γ-ray emission of all the six pulsars from 100 MeV to 100 GeV. For all the pulsars we can now safely reject the hypotesis of a phase averaged emission modeled by a power-law or a broken power-law, in favor of a power-law with simple exponential cutoff. The spectral parameters are summarized in Table 2. Pulsar Name

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1.51±0.01 1.97±0.02 1.30±0.01 1.20±0.05 1.71±0.02 1.57±0.31

2.857±0.089 5.8±0.5 2.46±0.04 1.50±0.09 4.45±0.23 2.80±0.37

95.0±7.1 20.9±0.3 41.4±0.2 3.36±0.10 15.97±024 1.89±0.12

49.10±2.05 8.17±0.12 25.7±0.12 1.77±0.01 6.698±0.08 0.92±0.03

Table 2 Spectral parameters obtained from fitting the energy spectra with a power-law with expo−Γ e(−E/E cutoff ) The last two parameters are the integrated photon flux nential cutoff dN/dE = KE GeV and the integrated energy flux above 100 MeV. Only the statistical errors are reported, for the systematics please refer to the papers of the single pulsars.

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It is worth pointing out that for almost all the pulsars we get a better fit if we use a power law with super-exponential cutoff, with the super-exponent value ranging from almost 1 for PSR J1057−5226 to almost 0.5 for PSR J1709−4429: in any case lower then 1. In our opinion this is due to the fact that the phase averaged spectrum can be a combination of several spectra exhibiting simple-exponentialcutoff shape with different cutoff energies. This has been verified performing for all the six pulsars a phase resolved spectral analysis that for all of them has shown a trend of both spectral index and energy cutoff with phase. For the details please refer to the single pulsar papers.

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3 Conclusion Fermi has confirmed and extended all the results of EGRET, both for the light curves and the spectral shapes, moreover it has given an answer to some of the question left open by EGRET, especially related to the high energy emission. It is interesting to point out that while Vela, Crab and Geminga are among the brightest sources in the γ-ray sky, the other three pulsars aren’t so bright, so an interesting question could be why these three pulsars have been the only ones observed by EGRET. Now we know ([10] and [11]) that they have nothing of really peculiar with respect to all the others known γ-ray pulsars: a possible reason to account for their detection could be that they were the ones with the best timing solution at the EGRET time and this has allowed to clearly detect the γ pulsation. The observation of these 6 well known gamma-ray pulsars has provided a great improvement in our knowledge of the highenergy emission mechanism. We now have an answer to some of the questions left open by EGRET: the gamma-rays are produced in the high magnetosphere of the neutron star and the radio and gamma emission are loacted in different region around the pulsar. For a detailed analysis on the implication of the observed light curves and the spectral behavior of these pulsars on the validation of different emission models please refer to the cited papers. Acknowledgements The Fermi LAT Collaboration acknowledges support from a number of agencies and institutes for both development and the operation of the LAT as well as scientific data analysis. These include NASA and DOE in the United States, CEA/Irfu and IN2P3/CNRS in France, ASI and INFN in Italy, MEXT, KEK, and JAXA in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the National Space Board in Sweden. Additional support from INAF in Italy and CNES in France for science analysis during the operations phase is also gratefully acknowledged. The Parkes radio telescope is part of the Australia Telescope which is funded by the Commonwealth Government for operation as a National Facility managed by CSIRO. The Nanc¸ay Radio Observatory is operated by the Paris Observatory, associated with the French Centre National de la Recherche Scientifique (CNRS). We thank our colleagues for their assistance with the radio timing observations.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Atwood, W. B., et al. 2009, ApJ, 697, 1071 Abdo A. A. et al. 2010, accepted for publication in ApJ. arXiv:1002.4050 Abdo, A. A. et al. 2010, ApJ, 708, 1254 Abdo A. A. et al. 2010 submitted to ApJ. Razzano, M., Dumora, D. & Gargano, F. 2009, arXiv:0912.5442 Abdo, A. A. et al. 2010, submitted to ApJ. Kanbach, G. 1998 Adv Space res, Vol 21 N◦ .1/2 pp. 227-235 G. Theureau, N. Coudreau, N. Hallet, M. Hanski, L. Alsac, et al., 2005, A&A 430, 373 R.N. Manchester, 2008, AIP Conf. Ser. 983, 584 Ray, P. these proceedings Abdo, A. A. et al. 2010, ApJS, 187, 460

“Garden-variety” Gamma-ray Pulsars J0248+6021 & J2240+5832 David A. Smith for the Fermi LAT Collaboration

Abstract PSRs J0248+6021 & J2240+5832 are “typical” young, radio-loud pulsars detected in GeV gamma rays using the Large Area Telescope (LAT) on the Fermi satellite. “Typical” because their P, P˙ lie mid-range of those of the new gamma-ray pulsars, but also because of some nagging little observational problems. This paper focusses on the observables available to help interpret the wave of new gamma-ray pulsar findings, and some of their limitations.

1 Introduction We did it! Ray & Saz Parkinson (these proceedings) describe the ten-fold increase in the number of known gamma-ray pulsars, over a broad range of radio-loud to radio-quiet, of young and old, of fast and slow, of isolated pulsars and of pulsars grouped in globular clusters or in binary systems. Many power pulsar wind nebulae (PWN, Grondin & Lemoine-Goumard, these proceedings). In the lean years between EGRET and Fermi it was said these discoveries would enable us to understand pulsar emission and to explain the role of pulsars in a variety of Galactic processes. So, how do we actually go about it? The LAT’s “First Pulsar Catalog” [3] is a good start: it tabulates a series of gamma-ray observables for the first 46 gamma-ray pulsars seen with Fermi as uniformly as possible, and makes some simple, global comparisons with model predictions. The LAT team aspires to a more ambitious “Second Pulsar Catalog” in 2011, with not only more gamma-ray pulsars but also considering good gamma-ray candidates not seen, and comparing with expectations David A. Smith Centre d’Etudes Nucl´eaires de Bordeaux-Gradignan, CNRS-IN2P3, Universit´e Bordeaux I, BP 120, 33175 Gradignan, France. e-mail: [email protected] Co-workers (please see Acknowledgements section) N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_5, © Springer-Verlag Berlin Heidelberg 2011

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of population models updated using the insights acquired since the Fermi and AGILE [10] discoveries. Conducted in parallel is the also necessary approach of detailed study of single objects: our second paper on Vela [1] and our paper on the 9th millisecond pulsar, PSR J0034-0534 [2], are just two examples. This article highlights some observables to illustrate some recurring issues. A detailed article on these two pulsars is [16].

2 Two Not-So-Typical Pulsars Pulsars PSR J0248+6021 and PSR J2240+5832 were discovered in 1998 with the Nanc¸ay radiotelescope [5] in a northern Galactic plane survey [12]. Figure 1 shows the radio pulse profile for PSR J0248+6021, along with the polarization and position angle. Like > 80% of radio pulsars, it has a single, narrow radio pulse. The radio profile of PSR J2240+5832 is similar except for the absence of scatter broadening seen in the trailing edge of J0248’s pulse. Both pulsars have the same large spindown power, E˙ = 2.1 × 1035 erg/s, similar rotation periods (217 ms and 140 ms, respectively), and comparable surface magnetic fields (∼ 1012 G) and characteristic ages (∼ 100 kyr). They both have large Dispersion Measures (DM): 370 pc cm−3 for J0248+6021 and 263 pc cm−3 for J2240+5832. For these DMs, the NE2001 model [6] places J2240 very far from the Sun (> 7 kpc), and places J0248 even farther (beyond the Galaxy’s edge, > 9 kpc). Figure 1 also shows the pulse profiles for PSR J0248+6021 in different gammaray energy bands. Only a single peak is prominent, offset from the radio peak by δ = 0.4 in phase, unusual for gamma-ray pulsars, > 80 % of which have two peaks. Here too, the two pulsars are strikingly similar: J2240 also has only one peak, with a larger offset, δ = 0.6. The six gamma-ray pulsars discussed in [18] all have a single gamma-ray peak. As in that paper, we exploit radio polarization data to try to unravel the pulsar geometry. PSR J0248+6021 is in the “First Pulsar Catalog”, whereas PSR J2240+5832 had not yet been detected. Why should the nearer of these two similar pulsars be fainter in gamma rays? Both are at low latitude (|b| < 0.7◦), but in fact the background from diffuse Galactic emission and neighboring sources is much higher for J0248. Might beam geometry be a key difference? Is it “just” the distance? Something else?

3 About those distances DM’s provide a valuable first estimate of a pulsar’s distance. But NE2001’s assumptions about the electron densities in and between the Galaxy’s spiral arms and in a small number of tabulated clouds are easily overwhelmed by the complexity of the star-forming regions hosting massive stars and ,often, their pulsar progeny. For J0248 it is easy to see what’s fooling NE2001: it lies in one of the thickest parts of

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the “Soul” nebula, the giant HII region W5, 0.8◦ west of the center of the open cluster IC 1848 in the Galaxy’s Perseus arm (see the beautifully detailed WISE infrared photograph1.) NE2001 predicts DM = 61 cm−3 pc for 2 kpc for that direction. The excess needed to make up the difference is a quite plausible 18 electrons cm−3 . Twelve years of pulsar timing provides more distance constraints. One example is the proper motion: including uncertainties, PSR J0248+6021 has µ > 48 mas/yr. The largest neutron star velocities due to supernova “birth kicks” are ∼ 1000 km s−1 [7], implying d < 4.4 kpc. But if it is in W5 at 2 kpc then it has a typical transverse velocity vT ∼ 500 km/s. Another example is that the DM of PSR J0248+6021 increased by 0.3 cm−3 pc per year for three years, and then decreased at the same rate for another two years: the pulsar is indeed moving through a cloud. Both pulsars are noisy (J0248 had five glitches in 12 years). The long lever-arm helps constrain degenerate parameters in the timing model. Radio polarization data give a Rotation Measure RM = −158 ± 6 rad m−2 from which the parallel component of the magnetic field along the line-of-sight is Bk = 1.23RM/DM = 0.5µG. This matches nicely the expectation from Figure 6 of [8] and therefore the pulsar is most likely within the Perseus arm. We assign to PSR J0248+6021 the distance of IC 1848, d = 2.0±0.2 kpc. VLBI parallax measurements for all Fermi pulsars are being undertaken and will let us check these arguments in the years to come2 . Turning to PSR J2240+5832, no clouds are obvious in archival images and the NE2001 average electron distribution may be fine. The proper motion measurement gives half the apparent speed and < 1000 km s−1 jives with the Galaxy’s Outer arm. An average vT ∼ 400 km/s would place the pulsar in the Perseus arm. We have RM = 24 ± 4 rad m−2 , but the magnetic fields are poorly known in this direction, so that it only weakly supports the pulsar being so distant. The beautiful “anatomically correct” drawing of the Milky Way in [13] shows that the Outer arm is somewhat closer ( < 8.3 kpc in this direction) than what was known when NE2001 was created. Neutron stars are likely born within arms and, since vT τc < 0.1 kpc, the pulsars should still be there. We conclude with two hypotheses for the distance to PSR J2240+5832: Outer arm (d = 7.7 ± 0.7 kpc) versus the Perseus arm (d = 3.8 ± 0.8 kpc). The gamma-ray luminosity Lγ is plausible in both cases.

4 Understanding the Beams Theorists approach pulsar beam modeling in two steps. First is to think deeply about the underlying physics, to choose simplifying assumptions about the essentially intractable 3-D problem that will lead to realistic, feasible calculations. The next is to distill these meditations such that an observer can compare his data with pre1 2

2010 June 1 NASA APOD (“Astrophysical Picture of the Day”) Fermi Cycle 3 proposal, S. Chatterjee et al.

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dictions. One hopes for an iterative process converging to a clearer, truer vision of neutron star magnetospheres. The “Atlas” approach of [14] is exemplary in this regard: different models are treated uniformly, large numbers of pulse profiles are generated, and a “recipe” guides comparison between data and theory. Spitkovsky & Bai (these proceedings) and Harding & Grenier (these proceedings) have similarly begun to provide Atlas-like tools. See also [17]. It is hoped that alternative theoretical approaches (e.g. Petri ; Arons ; Cheng ; Hirotani, these proceedings) will also lead to direct comparison with the data as we approach 100 varied gamma-ray pulsars. The existing theories mainly address pulse profile shapes. We observers would love to test predictions of how, for example, the photon spectral index Γ or the energy cut-off Ec depend on other measurable parameters. The gamma-ray luminosity ˙ via the beam-correction factor fΩ , albeit with limited discrimLγ is linked to (P, P) inating power at this time (in part due to the huge uncertainties imposed by the distance problem). Self-consistent treatment of radio beams, including polarization, may come in the near future. For PSRs J2240+5832 and J0248+6021, we fit the radio linear polarization Position Angle (PA) versus rotation phase to the Rotating Vector Model [RVM, 11]. The goal is to obtain independent constraints on the inclination ζ of the neutron star rotation axis to the line-of-sight to Earth, and the angle α between the rotation axis and the magnetic axis. The narrow, single radio pulses make RVM fits difficult, and the scattering tail on J0248 makes it even harder. Nevertheless, the magnetic impact parameter β = ζ − α is constrained to β ≈ 5◦ for J0248 and to β ≈ 16◦ for J2240. The “Atlas” approach is to find the (α, ζ) combination for which the predicted gammaray pulse profile (including absolute phase relative to a radio pulse assumed to be centered on the magnetic axis) best matches the observed profile. The (α, ζ) ranges favored by RVM overlap those preferred by “Atlas”, with some difficulties detailed in [16]. Detailed X-ray images of PWN can constrain ζ [9], which is one of several motivations for finding new PWN (Slane, these proceedings). Neither J0248 nor J2240 show evidence for off-pulse gamma-ray emission in the Fermi data. For J0248, nearby radio and optical structures led us to look a bit harder. Mostly to no avail, although see [16], which do give some upper limits and TeV speculations that will interest some readers.

5 Conclusions Pulsars lie at the crossroads of varied domains of astrophysics. Comparing observed properties with model predictions for individual pulsars over as wide a range of parameter space as possible allows theorists to more accurately describe these cosmic particle accelerators. One can then improve the fidelity of neutron star population syntheses, integrating reliable predictions for gamma-ray and electron emissions. The stakes may be high – an example is whether the cosmic electron spectrum

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(Moiseev, these proceedings) has a partial Dark Matter origin, or is instead totally dominated by pulsars. The long-term aim of the ongoing multi-disciplinary work on gamma-ray pulsars, illustrated here with PSRs J0248+6021 and J2240+5832, is to better fit pulsars into the Galactic puzzle. Acknowledgements The authors of the full paper describing this work [16] are members of the LAT Collaboration [4] and/or the Fermi Pulsar Timing Consortium [15]. The immense groundwork laid by the full team made these results possible. The paper authors are: G. Theureau, D. Parent, I. Cognard, G. Desvignes, D. A. Smith, R. W. Romani, J. M. Casandjian, C. C. Cheung, H. A. Craig, D. Donato, L. Guillemot, A. K. Harding, J.-F. Lestrade, P. S. Ray, D. J. Thompson, W. W. Tian, K. Watters. We thank Simon Johnston for useful discussions about the radio polarization data.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Abdo, A. A. et al. 2010a, ApJ, 713, 154 Abdo, A. A. et al. 2010b, ApJ, 712, 957 Abdo, A. A. et al. 2010c, ApJS, 187, 460 Atwood, W. B. et al. 2009, ApJ, 697, 1071 Cognard, I., Theureau, G., Desvignes, G., & Ferdman, R. 2009, ArXiv e-prints Cordes, J. M., & Lazio, T. J. W. 2002, ArXiv e-prints, (arXiv:astro-ph/0207156) Hobbs, G., Lorimer, D. R., Lyne, A. G., & Kramer, M. 2005, MNRAS, 360, 974 Mitra, D., Wielebinski, R., Kramer, M., & Jessner, A. 2003, A&A, 398, 993 Ng, C.-Y., & Romani, R. W. 2008, ApJ, 673, 411 Pellizzoni, A. et al. 2009, ApJ, 695, L115 Radhakrishnan, V., & Cooke, D. J. 1969, ApJ, 3, 225 Ray, P. S., Cadwell, B. J., Lazio, T. J. W., Foster, R. S., Backer, D. C., Cognard, I., & Lestrade, J.-F. 1999, in BAAS, Vol. 31, Bulletin of the American Astronomical Society, 903 Reid, M. J. et al. 2009, ApJ, 700, 137 Romani, R. W., & Watters, K. P. 2010, ApJ, 714, 810 Smith, D. A. et al. 2008, A&A, 492, 923 Theureau, G., Parent, D., Cognard, I., & Smith, D. A. 2010, A&A, submitted Venter, C., Harding, A. K., & Guillemot, L. 2009, ApJ, 707, 800 Weltevrede, P. et al. 2010, ApJ, 708, 1426

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Fig. 1 Phase-aligned γ-ray and radio profiles for PSR J0248+6021 obtained with the Fermi Large Area Telescope and the Nanc¸ay Radio Telescope. The bottom panels show three radio frequencies, as well as the linear (red dashed) and circular polarizations (blue dotted) and the position angle sweep with an RVM fit. Other panels show phase-folded γ-ray data in different energy bands. The black histogram in the > 1GeV panel shows photons with > 3 GeV. Two rotations are shown. For details see [16].

Extension studies of galactic sources with Fermi Francesco Giordano on behalf of the Fermi-LAT Collaboration

Abstract The Fermi data analysis tools have been developed on maximum likelihood minimization routine. This analysis technique is extensively used to determine the spectral parameters as the flux and the spectral index of a gamma-ray source, crucial aspects in determining how particles are accelerated, but it may also be used to measure the extension of not pointlike emission regions obtaining precious information about the sites where the acceleration takes place. The capability of the analysis presented here has been deeply studied with simulations varying the source flux, the spectral index, and the position within the galactic plane. This analysis procedure has been applied for determining the extension of the Vela X [1] and the MS H 1552 [2] [3] PWNe, as well as the extension of the W51C [4], W44 [5] and the IC443 [6] SNRs.

1 The simulated cases A simulation based on the Fermi Science Tool gtobssim has been run to investigate the extension determination of gamma-ray galactic sources. Two different cases have been studied. The first concerned the study of the extensions of galactic sources located in very crowded region like the ridge or in less noisy regions like the anticenter. The second test case was a simulation of an extended source emitting underneath a bright pulsar located in the Vela region. The aim is to study the effect of the Nebula on the pulsar spectrum and to test the capability of detecting the Nebula selecting the off-pulse phase of the pulsar as done in the detection of VelaX and MS H1552[3]. Extended Sources analysis. The detection of a possible extension of a galactic source is a crucial aspect in those cases where the gamma-rays emission is suspected to come from the shell of a SNR rather than from a compact object within Francesco Giordano Dipartimento Interateneo di Fisica dell’Universita’ e del Politecninco di Bari and INFN Sez. Bari, Via Amendola 173, I-70126 Bari (Italy); e-mail: francesco.giordano.ba.infn.it N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_6, © Springer-Verlag Berlin Heidelberg 2011

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the SNR. Some examples of these pulsar-SNRs complex are the two middle aged W44 and W51 SNRs as well as the IC443 SNR. A simulation has been developed in order to study the effect on the extension determination depending on the brightness, the hardness and the background contamination. Three different integral fluxes (10−8 cm−2 s−1 , 10−7 cm−2 s−1 and 10−6 cm−2 s−1 for E>100MeV) and two different spectral indexes (-1.5, -2.5) have been simulated, locating the sources both in the very dense galactic ridge and in the lower noisy MilkyWay anticenter. The analysis is based on the binned gtlike [7] Fermi Science Tool. A region of 10◦ around the source has been selected and a cut at 100MeV has been applied, extending the energy range up to 100GeV. For each test case it was assumed a pointlike hypothesis and different extended gaussian templates with a width ranging from 0.1◦ to 1.5◦ and a maximum likelihood fit was done. For each different template hypothesis the Test Statistic (TS), which is an estimator of the significance of the detection, is evaluated from the fit and the trend versus the template extension is reconstructed. The extension is then quoted as the dimension of the template which maximizes the TS value if significantly higher than the pointlike hypothesis (TSext -TS ptlike > 5σ) and the uncertainty is estimated looking at the width of the curve around the maximum according to TSle f t =TSright =TSext -25. As a general behaviour (Table1), the detection of the extension of weak and soft sources especially in very crowded regions (like the galactic ridge) was found to be very hard. However, due to the spectral shape of the galactic diffuse emission, and mostly due to the Fermi PSF which improves at high energy (∼0.5◦ at 1GeV), hard sources are easier to be detected even at low longitude. Table 1 Measured extension as a function of background, spectral index Γ, integral flux F above 100MeV (ph cm−2 s−1 ) and extension σext . Low Background High Background Γ=-1.5 Γ=-2.5 Γ=-1.5 Γ=-2.5 σext F=10−6 F=10−7 F=10−8 F=10−6 F=10−7 F=10−6 F=10−7 F=10−6 0.25◦ 0.25±0.002 0.25±0.03 0.25±0.15 0.25±0.03 0.25±0.2 0.25±0.004 0.25±0.05 0.2±0.1 0.5◦ 0.5±0.005 0.5±0.04 0.5±0.2 0.5±0.04 0.5±0.3 0.5±0.007 0.5±0.1 0.4±0.15 1.0◦ 1.±0.01 1±0.05 0.8±0.4 1±0.08 0.8±0.4 1±0.01 1±0.3 1.3±0.4

An extended source behind a pulsar. The second simulation was developed to study the capability of detecting an extended emission behind the pulsation of a bright pulsar and at the same time to study possible effects on the pulsar spectrum if the contribution from the Nebula is neglected. A Vela-like pulsar (Fig.1 left) has been simulated assuming for the spectral shape a power law with an exponential cutoff with an integral flux for E>100MeV of 9×10−6 cm−2 s−1 , index equal to −1.62 and energy break at 8GeV. For the Nebula was assumed an isotropic extended source of 0.8◦ centered at the pulsar location with a power law emission with a flux of 10−7 cm−2 s−1 and an index of -2.1. Fig.1 shows the timing solution and the spectra results. It is worth to note that the fits of the pulsar obtained including the Nebula in the model (solid line) or neglecting its diffuse contribution (dashed line) are different. The integral flux of

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Fig. 1 Top: Pulsar phasogram. Bottom: The pulsar spectrum and the off-pulse detection.

the pulsar fitted neglecting the Nebula is higher than the flux measured considering its contribution (8.7 ± 0.3 ×10−6 cm−2 s−1 vs 9.4 ± 0.1×10−6cm−2 s−1 ). Concerning the break and the index, the values obtained including the Nebula are 8.6 ± 0.3 GeV and -1.63 ± 0.01 closer to the simulation if compared to 10.5 ± 0.3 GeV and -1.72 ± 0.05 obtained fitting the pulsar alone. A possible explanation of these differences may be that lower energy photons have the responsibility to make the spectrum softer, higher energy gamma-ray photons, especially those above the pulsar break, clearly belong to the Nebula but if the extended source is not taken into account, the fitting procedure force them to be attributed to the pulsar, resulting in a spectral

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function with a higher break. In the same figure is also shown what has been detected in the narrow Off-Pulse window (from 0.4 to 0.6): an extended emission has been detected at 6σ level, with an integral flux 0.2 times lower than the simulated value and a spectral index of approximately -2.1.

2 Galactic extended SNRs: the W51C, the W44 and the IC443 Two galactic classes of objects are expected to be extended: the SNRs and PWNe. The Fermi detection of the extension of the VelaX and the MSH1552 PWNe are deeply presented in [3]. Concerning the SNRs, fermi has detected the extension of three SNRs: the W51C, the W44 and the IC443. The W51C is a middle-aged supernova remnant (∼104 yr) with intense radio synchrotron emission in its shell. It is well known that the W51C is interacting with a surrounding molecular cloud. For running binned gtlike it was assumed a two-dimensional gaussian template [4], detecting an extension of σext = 0.22◦±0.02◦ . The extension of the source support the idea of precluding gamma ray radiation from the CXOJ192318.5+143035 pulsar as a dominant component of the observed spectrum. The W44 is another middle aged SNR known to be interacting with a molecular cloud. The analysis for extended sources has been applied and it has revealed that the GeV emission is significantly extended. It was also applied a deconvolution technique [5] for determining a precise morphology of the acceleration site. According to these considerations, the hypothesis that the gamma-rays may come from the radio pulsar PSR B1853+01 or from its small PWN (1′ − 2′ in X-rays and radio) is disfavoured. A hadronic scenario with the molecular cloud acting as an active dump for pion production seems to be more plausible. The last case of an extended SNR is the IC 443. This SNR located in the outer Galactic plane, has an angular extent of ∼ 45′ in the radio with an age still uncertain (3-4 ky ÷ 20-30 ky). In the IC443 complex it is well known to be the CXOU J061705.3+222127 compact object and also a PWN. A blind frequency search has been performed but also in this case no pulsation has been discovered. EGRET first (3EGJ0617+2238) and MAGIC (MAGIC J0616+225) and VERITAS (VER J0616.9+2230) later have all found a gamma-ray emission from the IC443 SNR and the centroids of the three sources are all displaced from that of the PWN. The extension of the IC443 measured with the Fermi LAT is 0.27◦ ± 0.03◦ and it overlaps almost completely with the VERITAS detection. For all these reasons the GeV-TeV data points have been fitted together favouring a hadronic scenario, even though a possible contribution from the PWN at low energy (E<100MeV) is not excluded.

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3 Conclusions A method for determining the spatial extension of Fermi galactic sources has been described and applied to simulated cases and to real extended sources. The discovery of a possible source extension is crucial for determining accurately the spectral feature of the gamma ray emission and also for discerning the place where the accelerations take place. Moreover, in pulsar-PWN systems or in pulsar-SNR complexes, the capability of disentangling the pulsar emission from the environment is among the most exciting results of the next Fermi Galactic analysis. Acknowledgements The Fermi LAT Collaboration acknowledges support from a number of agencies and institutes for both development and the operation of the LAT as well as scientific data analysis. These include NASA and DOE in the United States, CEA/Irfu and IN2P3/CNRS in France, ASI and INFN in Italy, MEXT, KEK, and JAXA in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the National Space Board in Sweden. Additional support from INAF in Italy and CNES in France for science analysis during the operations phase is also gratefully acknowledged.

References 1. 2. 3. 4. 5. 6. 7.

Abdo et al., The Astrophysical Journal 713, 2010 Abdo et al., The Astrophysical Journal 714, 2010 M.H. Grondin: These proceedings Abdo et al., The Astrophysical Journal 706, 2009 Abdo et al., Science 1182787 (2010) Abdo et al., The Astrophysical Journal 712, 2010 Fermi Science Support Center, http://fermi.gsfc.nasa.gov/ssc/.

Advances in understanding double features in radio pulsar profiles Jarosław Dyks, Bronisław Rudak and Paul Demorest

Abstract High-quality integrated radio profiles of some pulsars exhibit double, highly symmetric features both in emission and absorption. It is shown that both types of features are produced by a split-fan beam of extraordinary-mode curvature radiation (CR) that is emitted/absorbed by radially extended streams of magnetospheric plasma. With no emissivity in the plane of the stream, such a beam produces bifurcated emission components (BFCs) when our line of sight passes through the plane. This interpretation explains several observed properties of double features, such as their symmetry, shape, convergence rate and their high polarization degree. The stream-cut geometry also explains the lack of radius-to-frequency mapping in the millisecond pulsars.

1 The Double Features Double absorption features in radio-pulse profiles were first indentified independently by Rankin & Rathnasree (1997; B1929+10) and Navarro, Manchester, Sandhu, et al. (1997; J0437−4715; in Fig. 1a they are visible at φ = 71◦ ). McLaughlin & Rankin (2004) discovered the double notches in the leading wing of the main pulse of B0950+08. These papers established the key properties of double notches: 1) They have the ‘W’ shape with relative depth reaching the large value of ∼ 25% (B1929+10, Perry & Lyne 1985) or possibly even ∼ 50% (J0437−4715). 2) They occur in highly polarised emission (Π ∼ 70 − 100%). 3) They approach each other at increasing frequency ν.

Jarosław Dyks, Bronisław Rudak Nicolaus Coprnicus Astronomical Centre, Rabia´nska 8, 87-100, Toru´n e-mail: jinx@ncac. torun.pl,[email protected] Paul Demorest Department of Astronomy, University of California, Berkeley, CA 94720-3411 N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_7, © Springer-Verlag Berlin Heidelberg 2011

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Fig. 1 Pulse profiles of two millisecond pulsars at different frequencies. The profile of J0437−4715 (left) contains double notches at φ = 71◦ , and a bifurcated component at φ = 51◦ . In the right-hand side profiles a strong BFC is visible at φ = 70◦ and a weak one at 245◦ . The double features make it possible to align the profiles in absolute way. Note the lack of radius-to-frequency mapping. Zero levels and flux units are arbitrary and different for each profile.

2 The interpretation The notches have been interpreted as a direct imprint of the microscopic beam intrinsic to a specific radiation mechanism (Dyks, Rudak & Rankin 2007, hereafter DRR07) . This implied the possibility to observe the microbeam in emission, as a bifurcated emission component (BFC). Examples of such features are visible in Fig. 1a (J0437−4715, at φ ≃ 51◦ ) and Fig. 1b (J1012+5307, at φ ≃ 71◦ ). Numerical simulations have shown that to produce deep double notches, the microbeam needs to have a double-lobe shape, with the radio emission mostly occurring at two small angles with respect to the plane of electron trajectory (Dyks, Rudak & Demorest 2009, hereafter DRD09). This split-fan topology also provides a natural way to observe BFCs (Fig. 2). According to this interpretation, the outer (“conal”) components of J0437−4715 result from a sightline cut through a spoke-like shaped emission pattern (emitting streams spreading away from the dipole axis). Regardless of the observation frequency, the radio emission can be detected only when the line of sight passes through the plane of the emitting stream (Fig. 2). This explains the lack of radiusto-frequency mapping in J0437 and other millisecond pulsars (Kramer et al. 1999). Thanks to this ν-independent location of double features, pulsar profiles observed at different ν can be aligned in the absolute way (see Fig. 1a and b). The inferred microbeam is the one of curvature radiation (CR) in orthogonal mode, i.e. polarised perpendicularly to the plane of electron trajectory. The beam is mirror-symmetric with respect to this plane. The beam’s bifurcation angle 2ψmax decreases with increasing frequency ν at a rate that depends on the location of ν in the curvature spectrum. At low frequencies, i.e., for ν < νcr , where νcr is the characteristic (peak) frequency of CR, we have ψmax ∝ ν−a with a = 1/3; for ν > νcr we have a = 1/2 (Jackson 1975). Therefore, the merging index a is likely to corre-

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Fig. 2 The origin of bifurcated components in radio pulse profiles. The double-lobe shape of instantaneous microbeam of curvature-radiation is shown at three positions along electron trajectory. The outward motion of electrons smears out the radiation pattern into a split-fan beam. Fig. 3 Merging rate index a in the relations ∆ ∝ ν−a , where ∆ is the observed separation of maxima/minima in double features. ‘DN’ stands for double notches, whereas ‘BFC’ for bifurcated emission components. The range of a expected for the CR is marked with vertical dashed lines. The errors are statistical 1σ.

late with the spectral index α, defined through Fν ∝ ν−α (a is expected to decrease with decreasing ν and α). Evidence for this is provided by the data: the BFC of J1012+5307, with the smallest merging index measured so far, has a very flat (hard) radio spectrum, with α ≃ 0.8. Within the errors, most of the measured values of a are consistent with the range of (0.33 − 0.5), appropriate for CR (Fig. 3). The unimodal nature of the beam is consistent with the observed high polarisation degree of the emission that contains double features. The BFC of J1012 is expected to have the shape of the ⊥-mode CR beam (eq. 4 in DRD09), convolved with the profile of stream density, and geometric effects, and with some contribution of the second (k) mode. Fig. 4 shows that a frequencyintegrated CR beam can imitate these factors fairly well. The BFC of J1012+5307 is ten times wider than the intrinsic bifurcation angle of CR, 2ψmax = 0.8◦(ρ7 ν9 )−1/3 , calculated for dipolar radii of curvature ρ7 = ρ/(107 cm) ∼ 1, and ν9 = ν/(1 GHz). The BFC might have been enlarged by geometrical viewing effects (cutting the stream at a small angle δcut or a near alignment of sightline with the rotation axis). In a forthcoming paper we show that in the case of the non-orthogonal cut, the BFC is near symmetrical only at a single ‘frequency of symmetry’ νsym . For ν , νsym the BFC becomes asymmetric, because

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Fig. 4 Best fit of the νintegrated and ⊥-modedominated curvature beam to the BFC of J1012+5307 at 0.82 GHz. The fit has χ2 /dof ≃ 3.6. Dashed verticals mark the phase interval of the fit.

of residual radius-to-frequency mapping. Peaks of such a BFC dominate alternatingly below/above νsym , which agrees with the observations (see fig. 5 in Kramer et al. 1999). We do not expect the double features to be visible in single pulses. This can be understood from Fig. 2: before the line of sight moves from the left to the righthand-side lobe of the microbeam, the electrons observed through the left lobe (contributing to the leading peak of the BFC) are ‘gone’. Radiation of the trailing peak of the BFC comes from different (new) electrons, which in the meantime have approached the line of sight. If the electrons are being ejected in the form of random sparks, the instantaneous flux in the two peaks of BFC will not be the same. It will resemble the normal noisy single-pulse signal of pulsars. Acknowledgements This work has been supported by the grant N203 387737 of the Ministry of Science and Higher Education.

References 1. 2. 3. 4. 5. 6. 7. 8.

Dyks J., Rudak B., & Rankin J. M., 2007, A&A, 465, 981 (DRR07) Dyks J., Rudak B., & Demorest P., 2009, MNRAS, 401, 1781 (DRD09) Jackson J.D., 1975, “Classical Electrodynamics”, John Wiley & Sons Inc, New York Kramer M., Lange C., Lorimer D., Backer D.C., Xilouris K. M., et al., 1999, ApJ, 526, 957 McLaughlin M. A., & Rankin J. M., 2004, MNRAS, 351, 808 Navarro J., Manchester R. N., Sandhu J. S., Kulkarni S.R., Bailes M., 1997, ApJ, 486, 1019 Perry, T.E., & Lyne, A. G. 1985, MNRAS, 212, 489 Rankin J.M., & Rathnasree N., 1997, J. Astrophys. Astron., 18, 91

Emission from the Polar Cap and Slot Gap Confronting Fermi Pulsar Observations Alice K. Harding and Isabelle A. Grenier

Abstract High-energy emission from pulsar polar caps is expected to occur in connection with electron-positron pair cascades close to the neutron star surface in rotation-powered pulsars. The abundant new results from Fermi, however, strongly suggest that the observed emission from pulsars originates in the outer magnetosphere and we have yet to observe any significant component of emission coming from the polar cap. The polar cap model also predicted a high-altitude emission component from electrons undergoing continuous acceleration from the polar cap to near the light cylinder in the slot gap. Emission from the slot gap will form caustics due to aberration and time delays that bunch the radiation on the trailing field lines of both magnetic poles. While the resulting light curves can account for the variety and distribution of observed Fermi light curves, the slot gap model falls short of accounting for the total luminosity implied by observations, requiring either a larger current of accelerated particles or a larger electric field in the gap. Population synthesis and phase-resolved spectral modeling can help us build improved emission models and constrain global magnetosphere structure.

1 Introduction Rotation-powered pulsars are one of the major source classes detected by the Fermi Large Area Telescope (LAT) and they dominate the identified source population in the Galactic Plane at low latitudes [3]. Since launch in 2008, the rate of discovery of new gamma-ray pulsars has exceeded expectations and the discovery of new pulsars Alice K. Harding Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, e-mail: [email protected] Isabelle A. Grenier AIM, Service d’Astrophysique, CEA Saclay, 91191 Gif Sur Yvette, France e-mail: Isabelle. [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_8, © Springer-Verlag Berlin Heidelberg 2011

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through blind frequency searches of γ-ray data alone has been a huge success [1]. Radio-quiet or radio-weak pulsars may in fact dominate the γ-ray pulsar population, which would suggest that the space density of pulsars could be substantially larger than was implied by radio pulsars alone. Another new γ-ray source population discovered by Fermi in its first six months of operation are the millisecond pulsars (MSPs) [4]. All of these have been discovered through their radio pulsations, as the fact that 80% of MSPs are in binary systems makes blind period searches in γ rays very difficult if not impossible. However, many new radio MSPs have been recently discovered in Fermi unidentified sources (Ransom et al. 2010). These new Fermi-assisted searches have so far netted 18 new MSPs, increasing the number in the Galactic Field by nearly a third in a few months. The majority of these are very nearby (< 1 kpc), at high Galactic latitude, and in binary systems, including four “black-widow” MSPs that are interacting with and ablating their companions. The combined population of gamma-ray pulsars presently numbers about 68, a factor of ten larger than before Fermi. With the tremendous increase in new data, the time has never been better for uncovering the secrets of pulsars: the global current circulation in their magnetosphere, where they accelerate particles, how they radiate, the shape of their magnetospheres and their energetics. For more than forty years, the development of a variety of pulsar emission models has progressed slowly, in the absence of enough data to rule any out or distinguish among them. The emission developed along two major paths. Polar cap models [57, 19] assume that acceleration takes place near the neutron star surface at the magnetic polar caps, where large electric fields are induced. Acceleration also takes place in a slot gap along the last open field line up to high altitudes. The high-energy radiation occurs within a few stellar radii of the surface since the particles lose their energy rapidly, and also in the slot gap from the neutron star surface up to the light cylinder. Outer gap models [54, 18] assume that particle acceleration and high-energy emission take place in vacuum gaps that develop along the last open field lines above the null charge surface to very high altitude. A subset of models assume emission from below the null surface. In this review, we will discuss the the polar cap and slot gap model for high-energy radiation, and its predictions in light of the new Fermi data. Complementary reviews of the outer gap model by Hirotani [40] and Cheng [17] also appear in these proceedings.

2 Polar cap and slot gap electrodynamics Polar cap accelerators are based on the concept of “starvation” electric fields, where the space charge above the polar cap is not sufficient to maintain force-free (E · B = 0) conditions. The force-free charge density was first introduced by Goldreich & Julian (1969), and can be derived from −∇ ·

(Ω × r) × B = ∇ · E = 4πρGJ , c

(1)

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where Ω is the pulsar rotation rate. For a dipole field and r ≪ Rlc , where Rlc = c/Ω is the light cylinder radius, Ω·B ρGJ = − . (2) 2πec Even for a current density, ρGJ , of electrons or ions extracted from the neutron star surface, the space charge ρ < ρGJ above the surface since a continuous current density falls off faster with r than ρGJ in a dipole field due to field line curvature. Therefore, an electric field develops parallel to the magnetic field, E k , in the absence of any other sources of charge [14] ∇2 Φ = ∇ · Ek = −4π(ρ − ρGJ)

(3)

A plausible source of charge is electron-positron pair production by single photons in the strong magnetic field of the neutron star [27, 20]. However, the photons must have energies and angles above threshold E γ sin θkB > 2mc2 to pair produce and for the surface fields around 1012 − 1013 G the cross section is proportional to exp (−4/3χ), where χ = ǫB′ sin θkB /2, where ǫ is the photon energy E γ in units of mc2 , B′ ≡ B/4.4 × 1013 G and θkB is the angle of photon propagation to the field. Since the photons are initially emitted nearly parallel to the magnetic field so that > 0.1, thus requires that the photons sin θkB ≪ 1, the condition for pair production, χ ∼ have very high energies ǫ > 100 MeV. Such high energies require particle acceleration to Lorentz factors of at least γ ∼ 105 − 107 .

2.1 Polar cap pair cascades The two main types of polar cap accelerator are vacuum gaps [57, 62] and spacecharge limited flow (SCLF) gaps [14, 35]. Which of these form in a particular pulsar depends on whether the neutron star surface temperature is high enough to overcome the binding (or cohesive) forces on charged particles due to the lattice structure in a strong magnetic field [43]. If the surface temperature is not high enough, vacuum gaps can form above the surface [62]. The surface temperatures of most pulsars are thought to be high enough that charges are “boiled off” the surface layers and can flow along the open field lines in SCLF. The E k in SCLF accelerators is computed using Eqn(3) assuming that ρ(R) = ρGJ (R) at the neutron star surface. Since ρGJ (r) is modified by inertial frame-dragging [49], Ek is significantly larger than it is for flat space. Acceleration will be self-limited by the development of pair cascades, at altitudes where the particles reach high enough Lorentz factors to radiate γ-ray photons. The pair cascades can be initiated either by curvature radiation (CR) [19] or by resonant or non-resonant inverse-Compton scattering (ICS) of stellar thermal X-rays by primary electrons [59]. The polarization of pairs above the pair formation front (PFF) may short out the Ek by reversing a small fraction of the positrons, halting any further acceleration at higher altitude. These accelerators can thus maintain a steady

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current of upwardly accelerating electrons, at j−k ≃ cρGJ , and a downward current of positrons, at j+k ≪ cρGJ , which heat the polar cap. It was found that in dipole field geometry, the E k is screened above the PFF very effectively by CR-initiated pair cascades but the ICS-initiated pair cascades produce multiplicities too low to completely screen Ek [36]. Pulsars older than ∼ 107 yr and most of the millisecond pulsars cannot produce pair cascades through CR since the E k does not grow fast enough to accelerate particles as the dipole field falls. These pulsars are “pairstarved” and since their Ek is unscreened, particles continue to accelerate on all open field lines to high altitude. The stability of SCLF accelerators has not yet been verified through time-dependent models, and some simplified studies [41] have in fact shown that some oscillations in the pair creation rate could exist. This is certainly an issue that needs further investigation. Stability of vacuum gaps has also been studied by Gil et al. [31] and more recently time-dependent vacuum gaps have been modeled by Timokhin [61]. The pairs are produced in excited Landau states that decay through emission of synchrotron/cyclotron photons, many of which will produce more pairs in excited states. The pairs can also produce ICS photons, through scattering surface thermal X-rays, which may produce pairs [70]. Radiated spectra from CR-initiated [19] and ICS-initiated [59] cascades are very hard (roughly power laws with indices 1.5 2.0) [33] with cutoffs due to magnetic pair production attenuation at energies around several GeV [34]. Since the pair production attenuation coefficient is exponential in photon energy, the spectral cutoffs have a very sharp,“super-exponential” shape and are therefore a distinguishable prediction of polar cap models. The polar cap cascade radiation produces a hollow cone of emission around the magnetic pole, with opening angle determined by the polar cap half-angle, θPC , at the radius of emission r. The characteristics of emission from this type of polar cap model [21] could reproduce some features of γ-ray pulsars, including the wide double-peaked pulses observed from γ-ray pulsars like the Crab, Vela and Geminga, and the phase-revolved spectra. However, the polar cap opening angle is very small (a few degrees) unless the emission occurs more than a few stellar radii above the surface [23]. Daugherty & Harding[21] had to assume extended acceleration to 3 stellar radii and an artificial enhancement of primary particle flux near the polar cap rim in order to reproduce the Vela pulsar spectrum and pulse profile.

2.2 The slot gap Due to the geometry of the field lines and the assumed boundary conditions of the accelerator, the altitude of the PFF varies with magnetic colatitude across the polar cap [13, 35]. Near the polar cap rim, which is assumed to be a perfectly conducting boundary, the electric field is decreasing and a larger distance is required for the electrons to accelerate to the Lorentz factor needed to radiate photons energetic enough to produce pairs. The PFF thus curves upward as the boundary is approached, forming a narrow slot gap near the last open field line [13]. Since Ek

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is unscreened in the slot gap, particles continue to accelerate and radiate to high altitude along the last open field lines. The accelerating E k in the slot gap can be determined by solving Poission’s Equation in the narrow flux tube bounded on the inner edge by the PFF and on the outer edge by the fully-conducting last open field line. Muslimov & Harding have found solutions for the SG E k , including inertial frame-dragging, both near the neutron star surface [46] in dipole field geometry " # 3 κ θ0 2 E ||,low ≃ − B0θ04 ∆ξSG cos α + sin α cos ϕ [1 − ξ∗2 ] (4) 4 η4 2η1/2 and at large altitudes [47]. In Eqn (4), α is the angle of the magnetic axis to the rotation axis, ϕ is the magnetic azimuth, B0 is the surface magnetic field strength, ξ∗ is the magnetic colatitude in the SG, where ξ∗ = 0 at the gap center, and κ = 0.15I45/R36 , where I45 = I/1045 g cm2 is the neutron star (NS) moment of inertia and R6 is the neutron star radius in units of 106 cm. The luminosity of the SG from each magnetic pole is LSγ G

= εγ c

Z

2π 0

dϕ

Z

θ0 θ0 (1−∆ξSG )

ρ(η)Φ(η)r2 sin θdθ

(5)

where ρ(η) and Φ(η) are the primary charge density and potential as a function of radius η ≡ r/R, in units of NS radius and εγ is the radiation efficiency. The width of the slot gap, ∆ξSG , is a function of pulsar period, P, and surface magnetic field, B12 ≡ B0 /1012 G [46], and can be expressed as a fraction in colatitude ξ ≡ θ/θ0 of the polar cap opening angle, θ0 ≃ (ΩR/c)1/2. Young Crab-like and Vela-like pulsars have widths ∆ξSG ≈ 0.05 − 0.1 which increase with age as P B−4/7 approximately. 12 Using the expressions for the low-altitude SG in Eqn (12) for Φ and Eqn (4) for ρ from [46], we have ∆ξSG 1 )[κ(1 − κ)(1 − 3 ) cos2 α + 2 η s    9 2 ∆ξSG 2  H(η) f (η) θ0 (1 − )H (1)  η − 1 sin2 α] 8 2 H(1) f (1)

3 LSγ G,low = εγ E˙ sd ∆ξSG (1 −

(6)

where E˙ sd = Ω4 B20 R6 /6c3 f (1)2 is the spin-down power, and H(η), f (η) are functions given in Muslimov & Tsygan [49] (see also [35]). The high-altitude SG luminosity from each pole can also be determined from Eqn (5) using Eqn (52) for Φ and Eqn (21) for ρ from [47], ( ∆ξSG 1 η 3 LSγ G,high = εγ E˙ sd ∆ξSG β(1 − ) [κ(β − κ)(1 − 3 ) + 1 − β](1 + ) cos2 α 2 ηlc ηc  s      H(ηc )   9 f (1)  + θ2 H 2 (1)  ηc − β sin2 α (7)   8 H(1) f (ηc ) 

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where β = (1 − 3η/4ηlc)1/2 and ηlc = rlc /R = c/ΩR. The electrons that accelerate in the slot gap will radiate curvature, inverse Compton and synchrotron radiation at high altitudes. Initially, their Lorentz factors will be limited by curvature-radiation reaction, to γCRR = ((3/2)E ||ρ2c /e)1/4 ∼ 3 × 107 and 3 /ρ ≈ 3 GeV. Musthe peak energy of their CR spectrum will be εCR = 2λC γCRR c peak limov & Harding[46] found that pair cascades on the inner edge of the slot gap occur at altitudes of 3-4 stellar radii and have higher multiplicities M+ ∼ 104 − 105 than the polar cap cascades. As the electrons reach higher altitude, where the local magnetic field has dropped to B ∼ 106 − 108 G, they may be able to resonantly absorb radio photons of energy ε0,GHz that are at the cyclotron resonance in their rest frame [42]. The condition for resonant absorption is γR = 3 × 105 B8 ε0,GHz /(1 − βµ0) where B8 ≡ B/108 G and µ0 is the cosine of the angle between the radio photon and the electron momentum. The electrons are then excited to higher Landau states and radiate synchrotron emission. Petrova [50] concluded that this process could be a significant source of radiation for young pulsars [39]. It could also be significant for millisecond pulsars with high radio luminosities like PSR J0218+4232 [38].

3 Geometry of high-energy radiation The geometry of emission at high altitude is strongly influenced by special relativistic effects of aberration, time-of-flight and retardation of the magnetic field. Aberration and time-of-flight each produce phase shifts of comparable magnitudes ∆φ ∼ −r/Rlc in radiation emitted at different altitudes rem to the light cylinder radius Rlc . Morini [45] first noted that the combined phase shifts from aberration and timeof-flight, of photons radiated tangent to a magnetic dipole field from the polar cap to the light cylinder, nearly cancel those due to field line curvature on the trailing edge of the open-field region. Radiation along such trailing field lines bunches in phase, forming a sharp emission peak or caustic in the pulse profile. On the leading side, these phase shifts add up to spread photons emitted at various altitudes over a large range of phases. The effect is most pronounced for large α and emission between altitudes rem ∼ 0.2 − 0.8 R LC . Sweepback of the magnetic dipole field due to retardation [22, 68] affects photon emission directions near the light cylinder, and also distorts the polar cap and open field volume [12, 24], even at the stellar surface. Most observer angles sweep across caustics from both magnetic poles, resulting in a double-peaked pulse profile where the peaks generally have phase separation less than 180◦ [26]. Furthermore, emission occurs at all phases in the profile. Such profiles are very similar to those of the bright γ-ray pulsars, Crab and Vela. The predicted polarization characteristics of such a “two-pole caustic” (TPC) model in a retarded vacuum dipole [22] geometry can also explain the observed optical polarization of the Crab pulsar [25]. Radiation from the slot gap has a geometry very similar to that of the “twopole caustic” model and thus displays caustics in the intensity phase plots as well as Crab-like pulse profiles [47]. The high-altitude slot gap thus may be a viable

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model for high-energy emission from young pulsars. However particle acceleration in the slot gap, as derived for dipole fields, may not operate at all inclination angles. The low altitude E k , shown in Eqn (4), is a function of both α and ϕ. For large α and cos ϕ < 0 (field lines curving away from the rotation axis), the second term in Eqn (4) can become large and negative at large r, causing the E k to reverse sign. This would cause a buildup of charge at that location, and would clearly be an unstable situation. The charge flow along those field lines might then be either time-dependent or nonexistent. The solution for E k at high-altitude in the slot gap [47] may moderate > 70◦ the E reverses sign at low this effect somewhat, but for fast rotators and α ∼ k altitude. A possible resolution to this problem may require opposite signs of charge being accelerated in different parts of the polar cap (see Section 5). Until recently, the retarded vacuum dipole was the only geometry used to model high-energy pulsar light curves. Although it was obvious that the Deutsch solution was not a realistic model for pulsar magnetospheres filled with currents and charge, it was relatively simple and easily implemented. In the last few years, solutions for the force-free magnetosphere have been computed for oblique rotators [58, 60]. Since such geometries assume that E · B = 0 everywhere and there is no particle acceleration, they are still not realistic. Yet they are thought to be closer to the magnetospheric geometry of a young pulsar in which pair cascades screen the Ek throughout most of the open field volume except in small or narrow charge-depleted regions. The first light curve models using force-free geometry [15] show that the caustic patterns are somewhat different from those in in vacuum dipole geometry. Since the force-free field lines at large radii are straighter than dipole field lines, due to distortion by the toroidal currents, the footpoints of the open field lines define a wider polar cap. The caustics of the TPC and OG emission are less sharp and stronger caustics appear near or across the light cylinder. The light curves resulting from this “separatrix layer” (SL) model, emission in a narrow gap between ξ = 0.9 or 0.95 and 1.0 very similar to the SG except extended beyond the light cylinder, produce similar double-peaked shapes to those of the SG. Pair starved polar cap models (PSPC) produce very different emission patterns, with radiation concentrated near the polar caps but extending to high altitude [26]. The predicted light curves will consist of narrow peaks in phase with the radio pulse if the viewing angle crosses near the magnetic axis, but will consist of a single broad peak leading the radio pulse if the viewing angle to the magnetic axis is large, since the high-altitude emission will be shifted to earlier phase by aberration [26].

4 Confronting the Fermi observations Since its launch in 2008, Fermi has discovered many new gamma-ray pulsars, increasing the known population by a factor of ten [53]. Several classes have emerged: young and energetic radio-loud gamma-ray pulsars, young radio-quiet or radioweak gamma-ray pulsars, and old gamma-ray millisecond pulsars. Surprisingly, each of these classes comprises about a third of the population. With its increased

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sensitivity, Fermi has also measured the spectra and light curves of the known and bright pulsars with much greater detail. We now have the prospect of discriminating between emission models and magnetospheric geometry as was never before possible.

4.1 Spectra One of the most important measurements that Fermi was anticipated to make early in the mission was of the spectral cutoff shape of Vela and other bright pulsars. Determining whether the cutoff fit better with a simple or a super-exponential could confirm or rule out gamma-ray emission in the strong near-surface magnetic fields predicted by PC models. Within the first few months of data collection, Fermi measurement of the spectra cutoff of Vela [2] was able to rule out the super-exponential fit with a significance of 16σ. The cutoffs of other bright pulsar spectra such as Geminga [7] and the Crab [8] also fit a simple exponential shape, indicating that the gamma rays are emitted far above the neutron star surface. In fact, the fits even prefer a shape that is more gradual than a simple exponential. Measurements of the pulsar spectra across the profile in small phase bins is revealing new details about the emission. Both the photon index and particularly the cutoff energy vary with phase. The cutoff energy undergoes rapid changes in the peaks and in the interpeak region, in the case of Vela [5], by factors of 2 - 3. Such changes in cutoff energy can account for the gradual shape of the phase-average spectra and also indicate rapid changes in characteristics affecting the radiation, such as altitude or magnetic field line curvature. In most outer magnetosphere (OM) models, the accelerating particles are radiation-reaction limited (i.e. their rate of energy gain from acceleration is balanced by their curvature radiation losses), so that the steady-state Lorentz factor is γCR =

"

3 Ek ρ2c 2 e

#1/4

,

(8)

where ρc is the local field line radius of curvature, and the expected spectral cutoff energy is ! E k 3/4 1/2 3λ –c 3 ECR = γ = 0.32 λc ρc . (9) 2 ρc CR e

where λc = 2πλ–c is the electron Compton wavelength. The cutoff values roughly agree with those predicted for curvature radiation in the outer magnetosphere since the Ek is similar for SG and OG models. So, the variation in E c with phase would reflect variations in radius of curvature, E k or both. It opens the possibility of testing emission models and magnetospheric geometry, in particular force-free versus vacuum field geometries, by comparing their prediction of E c phase variations with the data.

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4.2 Population synthesis and light curve fitting With the much larger population of detected gamma-ray pulsars, both radio-loud and radio-weak, population synthesis becomes a more powerful tool for comparing the distributions of various properties with those predicted by models. If the different emission models such as SG, OG, PC or SL models predict distinct distributions of measurable gamma-ray pulsar properties, such as age, spin-down luminosity, gamma-ray vs. spin-down luminosity, light curve peak separations and radio lags, then observed distributions will distinguish between these models or constrain their parameters. Pierbattista et al. [52] have simulated a population of normal isolated pulsars using a Gaussian distribution for the initial period and a log-normal distribution for the initial magnetic field. The neutron star motions have been evolved in the Galactic potential. Geometrical and luminosity models of the core and cone components of the radio beam have been implemented to compare with the observed properties of the radio pulsars in the ATNF11 catalogue. We discuss here the case of neutron star evolution with magnetic field decay. Details of the population synthesis are given in Gonthier et al. 2010 [30], while details of the light curve simulations and early results are given by [51] and [52]. We have modeled the gamma-ray emission from the simulated pulsars for four cases: • PC: low-altitude pair cascade radiation from the slot gap above the polar cap • SG: radiation from particles accelerating in the slot gap to 95 % of the light cylinder radius • OG: radiation from the outer gap, following Zhang et al. [69] • OPC: radiation from the one-pole caustic outer-gap geometry, from the null surface up to the light cylinder, following Watters et al. [67] The main difference between the OG and OPC cases is twofold: 1) the gammaray luminosity scales as Lγ = w3OG E˙ sd for the OG and Lγ = wOPC E˙ sd in the OPC case; 2) the gap width in the OG case is computed according to the physical model of Zhang et al. [69] whereas it is simply the gamma-ray efficiency wOPC = (1033erg s−1 / E˙ sd )1/2 in the OPC case. The actual OG width changes with magnetic obliquity α and it varies with altitude, so we compute its average along the last closed field line. To locate the PFF that defines the inside gap boundary, the calculation uses the E|| (r) structure and the radiation-reaction limited Lorentz factor of the primary CR gamma rays, as well as the angle dependence of the 2-photon pair production cross-section. The assumed geometry is simple (the X rays leave radially the heated polar cap and the gamma rays are produced tangent to the last closed field line), but it captures the evolution of the gap width with P, B, and α. To determine the gap width in the SG case we find the value of ξ where the PFF at location zPFF (ξ), in units of stellar radius, begins to rise sharply,

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Fig. 1 Slot gap phaseplots for different choices of gap widths, 0.1 (left panels) and 0.5 (right panels) and magnetic obliquities (α = 20◦ , 50◦ and 80◦ from top to bottom).

dzPFF dξ

!

=λ

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where λ ∼ 0.1 − 0.3 is a free parameter [46]. We find that a value λ = 0.2 provides the best match to the Lγ vs. E˙ sd seen in the Fermi pulsars. For the PC case, we use an emission distribution on the low-altitude field lines that approximates that of simulated pair cascades [46]. A simple radiative efficiency has been used to convert particle power into gamma-ray luminosity (100%, 400%, 30%, and 20% for the PC, SG, OG, and OPC models, respectively, to match the Fermi luminosity constraints). The need for an efficiency in excess of 1 is discussed below. To describe the radiation pattern across the sky resulting from the sweeping of each beam, we have computed 2D phaseplots or skymaps in the (ζ, φ) plane of the observer viewing angle ζ and rotational phase φ (Figures 1 and 2 show examples). The calculation includes field retardation assuming the vacuum solution [22], light travel delays, and relativistic aberration [25]. The sharp peaks seen from the OG profiles in Figure 2 result from the assumption of a very thin radiative layer along the gap inner edge (away from the last closed field line). The SG peaks in Figure 1 appear more smeared because we have assumed a broader photon distribution across the gap width. Their density profile perpendicular to the field lines peaks in the middle of the gap and falls to zero along the last closed line and along the gap inner edge. A grid of phaseplots has been produced to fully sample the magnetic obliquities and pulsar characteristics relevant to each radio and gamma-ray beam model (period and its derivative, magnetic field, gap width, radio frequency). The phaseplot of a particular pulsar has been obtained by careful interpolation within the

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Fig. 2 Outer gap phaseplots for different gap widths and magnetic obliquities.as in Fig. 1.

grid, preserving the continuous transformation of pattern shapes from one choice of parameter to the next. The phaseplot has then been normalized to twice the total luminosity per pole that the pulsar can sustain for a given model. Light curves, at the viewing angle of the simulated star, have been integrated to compare the average point-source gamma-ray flux with the 6-month sensitivity map given in the Fermi pulsar catalogue [9]. The population synthesis results can be used to probe both the energetics of the gamma-ray emission, by comparing simulated and observed distributions of gamma-ray vs. spin-down luminosity, and the geometry of the gamma-ray emission, by comparing simulated and observed light curve characteristics. One important quantity we can determine (and in fact requires a particular emission model to determine) is the beam correction factor fΩ [67], which allows us to derive the total luminosity radiated by a pulsar Lγ = 4π fΩ Fγ d2 , from its measured phase-averaged energy flux Fγ . Figure 3 shows the computed beam correction factors for the simulated pulsars in the PC, SG, OG and OPC models as a function of spin-down luminosity. The PC model has very small values of fΩ because all of the visible emission is concentrated in a small region near the magnetic poles. The SG, OG and OPC models have larger values of fΩ since emission is distributed over a large part of the sky. In the SG case, fΩ ∼ 1, and can even be larger than 1, with small dispersion and a very small trend decreasing fΩ with E˙ sd . As the SG ages and the gap widens, the centroid of emission moves toward the magnetic pole but the emission pattern on the sky remains extended because emission comes from all altitudes. In the OG and OPC cases, fΩ has a larger range from around 1 down to 0.01, with a distinct trend of smaller fΩ with decreasing E˙ sd . This trend results from the widening of the gap with age, which in OG models moves the emission towards the magnetic axis, and

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collapses the emission in the skymap onto the spin equator (ζ = 90◦ ). This has an effect similar to the PC model and thus produces small fΩ values (but the emission is at very high altitude). The smaller values of fΩ in the outer models allows smaller gamma-ray efficiencies in older pulsars, but the large dispersion can severely impact the derivation of a pulsar luminosity from the observations. The large spread in fΩ values that we find for the OPC model is purely due to the radiation pattern of the pulsed emission since there is no dispersion in the modelled luminosity. 1

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Fig. 3 Beam correction factor fΩ vs. E˙ sd for simulated pulsars in PC, SG, OP and OPC models.

The derived values of fΩ can be used to determine the Lγ for the observed pulsars from their Fγ and we may examine their gamma-ray efficiencies with age. The Fermi pulsars cover five decades of spin-down power and four decades of gamma1/2 > 1034 − 1035 erg s−1 which at E˙ sd ∼ ray luminosity, showing a general trend Lγ ∝ E˙ sd ˙ ˙ breaks to Lγ ∝ Esd at lower Esd . Both PC and SG models predict such a break, since pair screening at high E˙ sd limits the acceleration voltage to about V = 1013 Volt independent of P and B [35]. In that case, the gamma-ray luminosity Lγ = V n˙ p is 1/2 simply proportional to the primary current, n˙ p = ρGJ APC c ∝ E˙ sd [32]. For pulsars ˙ with lower Esd , pairs are not produced efficiently enough to screen the Ek and the 1/2 voltage grows to the entire open field value VPC ∝ E˙ sd . Both the normalization of the Lγ vs. E˙ sd and the position of the break constrain the gap acceleration and the width of the SG as a function of pulsar age. Figure 4 shows the different model predictions plotted with the Lγ of the Fermi pulsars. The OG model also generally 1/2 predicts a trend of Lγ ∝ E˙ sd at high E˙ sd , since the voltage of the OG is limited by pair screening in a similar way to that of the PC and SG. In the simulated pulsar populations, the SG model predicts a slightly higher proportion of young and energetic pulsars than the OG model, so that the SG is in better agreement with

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the data in this respect. As mentioned above, the predicted break can be adjusted to fit the data by varying the parameter λ that determines how the SG widens with age and we find that a relatively large value of λ, giving relatively narrow gaps, produces the best break location. Narrower gaps also produce narrower gamma-ray peaks that provide better fits to gamma-ray pulsar light curves. So both the Fermi lightcurve shapes and the Lγ vs. E˙ sd trend point to narrow gaps. However, smaller gap widths give lower predicted Lγ for the SG that are too low compared to those of the observed pulsars by about a factor of five. This indicates that either the current of radiating particles or the voltage in the SG is higher than currently expected. 29

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Fig. 4 Plots of Lγ vs. E˙ sd for PC, SG, OG and OPC models with the Fermi pulsars. The dotted line is Lγ = E˙ sd

Another measure that can discriminate between emission models is the distribution of viewing angle ζ and magnetic inclination angle α. Figure 5 shows the ζ and α of the simulated pulsars for each model. The results are strikingly model dependent, with PC models favoring very small or very large ζ, SG models allowing visible emission at all ζ across the sky, and OG models favoring a small range near the equator ζ ∼ 90◦ . An interesting correlation is that in SG models, the range of ζ decreases with increasing α while in OG and OPC models the range of ζ increases with α. These trends are again due to the different sky patterns in the SG and OG models, with the outer-gap models at smaller α being restricted to small bands near ζ = 90◦, while the SG patterns are not so restricted. The total number of pulsars detectable by Fermi after 6 months, as well as the ratio of radio loud (RL) to radio quiet/weak (RQ), are also shown in Figure 5 for each model. Compared with the number of 38 detected non-millisecond pulsars reported in the Fermi pulsar catalog [9], the number of visible simulated pulsars for the SG is only a few short but the PC, OG and OPC are significantly below the observed number. The mean ages of the

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simulated visible pulsars in all models, however, are greater than for the observed pulsars, as can be seen in Figure 7. PC : 5.1 RL/RQ 2.6

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The Fermi pulsar light curves show a fair degree of diversity, but there are several distinctive patterns that have emerged. About 75% have two peaks and a majority of these have a wide separation between 0.4 and 0.5 of pulse phase. The pulses are very narrow in most cases, with widths of less than 0.1 in phase. The light curve shapes of the simulated pulsars have been analyzed for several key characteristics that can be compared with those of the data. We have built an automated classification scheme based on the number of maxima, minima, and inversion points in the profile. The light curves were first smoothed to keep only the bulk features, i.e. a single peak, two well-separated peaks, a closer double peak, triple peaks, shoulders, etc. that are displayed in Figure 6. The light curves have then been fitted with a combination of Gaussians (for the PC) or of Gaussians and Lorentzians (for the SG, OG, and OPC) in order to locate the peak positions in phase and to derive their intensity and width. The closest magnetic pole is set at phase zero. We have divided the different light curve types into different classes for each model. Figure 6 shows the classes for PC, SG, OG and OPC models and their frequency of occurrence in both the simulated parent population and in the population that would be visible to Fermi as point source after 6 months of sky survey. It is apparent by the similarity of the parent and visible population distributions that there is little loss of morphology information in the visible sample.

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Fig. 6 Typical examples of light curve shapes found for each model. The histograms give the recurrence of each class in the parent sample that shines towards us (in black) and in the visible gamma-ray sample that passes the Fermi detection threshold (in gray).

Since there are many parameters with which to explore the light curve diversity (peak multiplicity and separation, sharpness, skewness, radio-gamma peak lags, etc.) in this multivariate space (E˙ sd , gap width, age, obliquity, orientation, etc.), we present and comment on only a few snapshots taken from two samples, the total parent population of neutron stars with non-zero light curve, and the visible gamma-ray sample with an integrated point-source flux that is larger than the 6-month Fermi sensitivity threshold in the pulsar direction. The comparison between the parent and visible samples is less sensitive to orientation effects than to flux thresholding since the pulsars from both samples do shine in our direction. Figure 7 shows the distribution of peak spacing with characteristic age. It is apparent that all of the models lack widely-spaced peaks. This may tell us that the assumed magnetospheric geometry needs to be revisited [55], but it also reflects the lack of young pulsars that can match the Fermi sensitivity threshold in all the simulated models. The problem is more pronounced for the OG models because the peak separation rapidly shrinks with age as the gap widens. Such a correlation results from the one-pole origin of both peaks of the OG models, where the peak spacing narrows as the inner edge of the gap moves closer to the magnetic axis as the gap width grows with age. The OG peak separation is also very sensitive to α. The SG model predicts more pulsars with peak separations of 0.4 - 0.5 than the PC or OG models and it exhibits little evolution of peak spacing with age, since the two peaks originate from opposite magnetic poles and even as the gap widens with age the peak spacing remains roughly the same for a given inclination and viewing angle. The Fermi pulsars do not seem to show a strong correlation of peak spacing with age, as predicted by the OG and OPC models. The data thus favor two-pole emission models such as the SG, TPC or SL models.

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4.3 New insights from the increasing γ-ray MSP Population The discovery of gamma-ray pulsations from millisecond pulsars (MSPs) and the extraordinary increase in their number in the last year or two opens up the opportunity for improved understanding of this ancient population of neutron stars. By the same token, the latest results reveal more complicated and varied characteristics than previously imagined. Continued observations will add more MSP members to the high-energy source catalogs of space missions such as Fermi and AGILE, while the non-detection of VHE gamma rays from MSPs to date by ground-based instruments such as H.E.S.S. and MAGIC tentatively rule out spectral components beyond 100 GeV, such as those expected from ICS emission. Pre-Fermi Expectations: PSPC Models MSPs occupy the lower left corner of the ˙ therefore low magnetic fields. PP˙ diagram due to their relatively short P and low P, This region falls below the predicted curvature radiation (CR) pair death line [37], so that MSPs were not expected to have copious pair production in their magnetospheres. Rather, it was believed that most MSPs should have unscreened magnetospheres [38], as is evidenced by modeling of MSPs assuming pair-starved electric fields in the so-called pair-starved polar cap (PSPC) scenario [48, 38], and prediction of single gamma-ray pulses roughly in phase with the radio [63, 28]. In the PSPC model, the low pair multiplicity allows charges to be continually accelerated up to high altitudes over the full open-field-line region. Furthermore, the formation of a PSPC gap is seen as the relaxation of an SG accelerator to a PSPC structure with increasing pulsar age.

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Post-Fermi MSP modeling: OGs, TPCs / SGs, and PSPCs Recent results [26] of 3D emission modeling of 8 Fermi-LAT MSPs [4] led to the surprising conclusion that the radiation of most of the MSPs originate in the outer magnetosphere. A large number of light curves were generated for the standard PC, PSPC, OG, and TPC geometries, for nearly the full range of inclination and observer angles, as well as various periods and gap widths. While PC models do not provide good fits for MSP light curves with a nonzero phase lag between radio and gamma-ray peaks, most of the light curves are best fit by TPC and OG models. This indicates that narrow accelerating gaps limited by robust pair production exist even in MSPs with very low spin-down luminosities. The gamma-ray light curve lags the radio for six MSPs (PSR J0030+0451, PSR J1614−2230, PSR J0218+4232, PSR J0437−4715, PSR J1613−0200, and PSR J0751+1807), and are well fit by TPC and OG models. The very thin TPC / OG gaps needed to model the Fermi-LAT MSP light curves indicate that new pair creation mechanisms (or different magnetospheric conditions) are needed for low-E˙ sd pulsars. For two other MSPs (PSR J1744−1134 and PSR J2124−3358) the gammaray curves lead the radio by 0.15 in phase, and these two cases are exclusively fit by the PSPC model, where we are viewing the high-altitude emission. Lastly, several new MSPs now exhibit phase-aligned radio and gamma-ray light curves (see next section), so that three mutually exclusive gamma-ray MSP subclasses are now emerging. The gamma-ray spectra of MSP detected by Fermi are also similar to those of the younger gamma-ray pulsars: hard power laws with simple (not super-) exponential cutoffs around several GeV [4]. This finding is consistent with emission from the outer magnetosphere although, because MSP surface fields are so low, one does not expect magnetic pair production to cut off the spectrum below the CR cutoff at least for the low- E˙ sd sources [38]. The fact that the magnetic field strength at the light cylinder is similar for MSP and young gamma-ray pulsars though lends support to the outer magnetosphere emission hypothesis. Phase-aligned MSP light curves The discovery of three MSPs (PSR J0034−0534, PSR J1939+2134, and PSR J1959+2048) with phase-aligned radio and gamma-ray light curves [6, 4] argues for co-located emission regions for the radio and gammaray radiation. While these light curves may be reproduced by (faded) PC models (low-altitude geometric models with modulated gamma-ray emissivities which mimic results from pair cascade modeling; see section 4.2) [25], there are also very reasonable fits provided by so-called ‘altitude-limited TPC / OG’ models [66]. In the latter models, we limit the minimum, rmin , and maximum, rmax , radius of emission of the TPC and OG gaps which provides a greater variety of pulse shapes. The extended radio emission ( rmin = 0.6Rlc, rmax = 0.8Rlc ) is enveloped by the gamma-ray emission regions ( rmin = R, rmax = 0.9Rlc) for the case of PSR J0034−0534, and is typically situated very close to the light cylinder, which is relatively near the stellar surface when compared with of younger pulsars (e.g., a 2 ms MSP’s light cylinder occurs at ∼10 stellar radii).

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VHE Expectations Since the observed CR spectral cutoffs occur around a few GeV (section 4.1), it is very unlikely that these GeV components will be seen by Cherenkov detectors. Rather, it is hoped that ICS components due to the scattering of thermal X-ray photons by relativistic electrons may be visible in the upper GeV to TeV range. However, modeling of ICS components for MSPs using PSPC electric fields [16, 38] reveal that these components are expected to be at a much lower level than the CR radiation, although such ICS calculations should be redone using SG / OG electric fields in the light of the the new results described above. Still, the order-of-magnitude sensitivity increase of the CTA and AGIS over the current ground-based observatories might lead to the detection of VHE emission from MSPs [56].

5 Learning from Nature - Future pulsar modeling In the two years since the launch of Fermi, we have learned much about pulsar emission. Predictions of a number of different models have now confronted the data and, although some have provided encouraging fits to observed light curves, all have failed in some aspects. Polar cap models where emission originates near the NS surface do not seem to be producing the main gamma-ray pulsations from any detected Fermi pulsars. This result does not, however, imply that near-surface acceleration and pair cascades are not occurring. Such cascades are in fact thought to be necessary for observed radio emission, to establish force-free conditions over most of the open magnetosphere in young pulsars and to create narrow accelerator and radiation gaps. We just need to understand why the gamma-ray emission that accompanies the pair cascades is not yet seen. If it is a matter of viewing geometry, the PC emission should cross our line-of-sight eventually. If the luminosity is simply below present sensitivity levels, detecting the PC emission may require deeper observation of faint off-pulse bumps. If PC emission remains invisible, population modeling will be able to give interesting limits of PC cascade activity. The observed gamma-ray pulse shapes and phase lags with respect to the radio pulses point to high-altitude emission from narrow gaps being dominant for all geometries. In general though, the SG/TPC and OG models that seem to provide reasonably good fits to Fermi pulsar light curves do not provide enough power through the thin gaps required for good light curve fits. Does this tell us that these models have the right geometry of emission but the wrong energetics? The population studies also show that none of the models (PC, SG, OG or OPC) produce enough young pulsars compared to observations, and therefore do not produce the numbers of visible gamma-ray pulsars that Fermi is detecting. This problem may be a result the simulated neutron stars evolving too fast toward longer periods (possibly due to the wrong initial period or magnetic field distribution), or result from the SG or OG widths growing too fast with age. In addition, the model fits to MSP light curves seem to also require narrow gap widths. But the standard models predict that

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MSPs should not be producing the high-multiplicity pair cascades necessary to form narrow accelerator gaps. However, all of the acceleration and radiation models developed to date assume dipole magnetic fields and do not incorporate current closure. Perhaps the failure of the models to confront many properties of the data is linked to these approximations and understanding the Fermi observations will require models to include more realistic field geometry and energetics. In the last few years, the “pulsar equation” [44] has finally been solved numerically to produce oblique pulsar magnetosphere models [58] with current closure. The current in these models has a strong effect on the magnetic field geometry, producing currents sheets and large distortions from the vacuum geometry in the outer magnetosphere. Although these models are force-free (E · B = 0) so that there is no particle acceleration, in the case of young pulsars with (apparently) very thin accelerator gaps, the force-free models may provide a more realistic zeroth-order geometry for pulsar acceleration models. It is likely that the accelerating electric fields that exist in the gaps in force-free geometry are quite different from those in vacuum geometry. The force-free magnetospheres have larger polar caps and currents of both sign across the polar cap [15]. The existence and form of slot gaps and outer gaps in force-free magnetospheres will depend on how pair cascades can function and whether they can provide the high pair multiplicity and currents that are required. The next few years will present new challenges for pulsar modeling but also an unprecedented opportunity to make use of a growing data set from Fermi that will provide us with more challenges for years to come. We would like to thank our collaborators, Christo Venter, Marco Pierbattista and Peter Gonthier, for all their help in generating the results for this review.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 4. 12. 13. 14. 15. 16. 17. 18.

Abdo, A. A. et al. 2009, Science, 325, 840 Abdo, A. A. et al. 2009, ApJ, 696, 1084 Abdo, A. A. et al. 2010, ApJS, 188, 405 Adbo, A. A. et al. 2009, Science, 325 848–852 Abdo, A. A. et al. 2010, ApJ, 713, 154 Abdo, A.A. et al., ApJ 712, 957–963 (2010) Abdo, A. A. et al. 2010, ApJ, submitted. Abdo, A. A. et al. 2010, ApJ, 708, 1254 Abdo, A. A. et al. 2010, ApJS, 187, 460 Abdo, A.A. et al., A. & A., submitted (2010) Abdo, A.A. et al., in preparation. Arendt, P. N. & Eilek, J. A., ApJ, submitted, (astro-ph/98011257) (1998) Arons, J. ApJ, 266, 215 (1983) Arons, J. & Scharlemann, E. T. ApJ, 231, 854 (1979) Bai,, X. & Spitkovsky, A. 2010, Apj, 715, 1282 Bulik, T., Rudak, B., & Dyks, J. MNRAS, 317, 97 (2000) Cheng, K. S.: these proceedings (2010) Cheng, K. S., Ruderman, M. A. & Zhang, L. 2000, ApJ, 537, 964

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Alice K. Harding and Isabelle A. Grenier Daugherty, J. K. & A. K. Harding, ApJ, 252 337 (1982) Daugherty, J. K. & Harding, A. K. ApJ 273 761 (1983) Daugherty, J. K. & A. K. Harding, ApJ, 458, 278 (1996) Deutsch, A., Annales d’Astrophysique, 18, 1 (1955) Dyks, J. & Rudak, B.: A & A, 393, 511 (2002) Dyks, J. & Harding, A. K., ApJ, 614, 869 (2004) Dyks, J., A. K. Harding & B. Rudak, ApJ, 606, 1125 (2004) Dyks, J. & B. Rudak, ApJ, 598, 1201 (2003) Erber, T. 1966, Rev. Mod. Phys., 38, 626 Fra¸ckowiak, M., Rudak, B., Adv. Space Res., 35 1152 (2005) Goldreich, P. & Julian, W. H. ApJ, 157, 869 (1969) Gonthier, P. L., Nagelkirk, E., Stam, M., Harding, A. K., 2010, Proc. of 2009 Fermi symposium, eConf C091122 Gil, J.; Melikidze, G.; Zhang, B.: A & A, 457, 5 (2006) Harding, A. K. 1981, ApJ, 245, 267 Harding, A. K. & Daugherty, J. K.: Adv. Space Res., 21, 251 (1998) Harding, A. K., Baring, M. G. & Gonthier, P. L. ApJ 476 246 (1997) Harding, A. K. & Muslimov, A. G., ApJ, 508, 328 (1998) Harding, A. K. & Muslimov, A. G. ApJ 568 862 (2002) Harding, A. K., Muslimov, A. & Zhang, B. ApJ 576 366 (2002) Harding, A. K., Usov, V. V. & Muslimov, A. G.: ApJ, 622, 531 (2005) Harding, A. K., Stern, J. V., Dyks, J. & Frackowiak, M. 2008, ApJ, 680, 1378 Hirotani, K. 2010, these proceedings (2010) Levinson, A., Melrose, D., A. Judge & Q. Luo: ApJ, 631, 456 (2005) Lyubarskii, Y. E., & Petrova, S. A. A&A, 337, 433 (1998) Medin, Z. & Lai, Dong 2007, MNRAS, 382, 1833 Michel, F. C. ApJ, 180, 207 (1973) Morini, M. MNRAS, 303, 495 (1983) Muslimov, A. G. & Harding, A. K. ApJ, 588, 430 (2003) Muslimov, A. G. & Harding, A. K. ApJ, 606, 1143 (2004a) Muslimov, A. G. & Harding, A. K.: ApJ, 617, 471 (2004b) Muslimov, A. G. & Tsygan, A. I., MNRAS, 255, 61 (1992) Petrova, S. A. A&A, 408, 1057 (2003) Pierbattista, M., Grenier, I. A., Harding, A. K. & Gonthier, P. L. 2010, A & A, in prep. Pierbattista, M., Grenier, I. A., Harding, A. K. & Gonthier, P. L. 2010, Proc. of 2009 Fermi symposium, eConf C091122 Ray, P. & Saz-Parkinson, P. 2010, these proceedings Romani, R. W.; Yadigaroglu, I.-A. 1995, ApJ, 438, 314 Romani, R. W., & Watters, K. P., ApJ, 714, 810 (2010) Rudak, B., these proceedings. Ruderman, M.A. & Sutherland, P. G. ApJ, 196, 51 (1975) Spitkovsky, A. ApJ, 648, L51 (2006) Sturner, S. J.; Dermer, C. D.; Michel, F. C. ApJ, 445, 736 (1995) Timokhin, A. MNRAS, 36, 1055 (2006) Timokhin, A., 2009 Fermi Symposium eConf Proceedings C091122 Usov, V. V. & Melrose, D. B. Aust. J. Phys., 48, 571 (1995) Venter, C., De Jager, O.C, ApJ 619 L167 (2005) Venter, C., Harding, A.K., Guillemot, L., ApJ 707 800–822 (2009) Venter, C., Harding, A.K., in preparation. Venter, C., Harding, A.K., Johnson, T.J., these proceedings. Watters, K. P.; Romani, R. W.; Weltevrede, P.; Johnston, S. 2009, ApJ, 695, 1289 Yadigaroglu, I. A., Ph.D. Thesis, Stanford University (1997) Zhang, L.; Cheng, K. S.; Jiang, Z. J.; Leung, P. 2004, ApJ, 604, 317 Zhang, B. & Harding, A. K. ApJ 532, 1150 (2000)

Gamma-ray emission and pair creation of outer gap K. S. Cheng

Abstract In this talk we use a simple two dimensional outer gap model, which consists of a primary acceleration region plus a screening region, to calculate the theoretical curvature radiation spectrum. We find that the observed spectra of all mature pulsars detected by Fermi can be explained in terms of three independent gap parameters,i.e. the gap current in the primary accelerator, the outer gap size and the gap ratio between the primary region and the total gap size. The fitting results indicate that (1)the current in primary region is only 10% of Goldreich-Julian current, which ensures the production of multi-GeV photons from the gap and (2)the gamma-ray power of pulsars is a broken power law of spin-down power, which suggests that there are two gap closure mechanisms. We next examine two possible pair creation processes, i.e. photon-photon pair creation and magnetic pair creation, we find that the former should be dominated for Lsd > 1036erg/s and the latter is more important for Lsd < 1036 erg/s. If the magnetic pair creation is the gap closure mechanism we predict that the gamma-ray luminosity (Lγ ) and the cut-off energy of 1/4 the spectrum (Ec ) are given by Lγ ∝ L5/8 sd and Ec ∝ L sd respectively.

1 Introduction Pulsars are rapidly spinning and strongly magnetized neutron stars. They act like monopolar generators. The potential drops for young pulsars can be much higher than 1015 V. It is generally believed that the pulsar magnetosphere should fill with charge separated plasma, which corotates with the star with angular velocity (Ω) up to the light cylinder radius (rL = c/Ω), where the corotation speed equals the speed of light. In equilibrium the Lorentz force of a test charged particle in the magnetosphere should be zero, i.e. E + Ω×r×B = 0. The charge density (ρ) of the pulsar c K. S. Cheng Department of Physics, University of Hong Kong, China, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_9, © Springer-Verlag Berlin Heidelberg 2011

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magnetosphere can be obtained by ∇ · E = 4πρ, which gives ρGJ = Ω·B 2πc and this solution is called the Goldreich-Julian solution (Goldreich and Julian 1969). There is an interesting region called null charge surface, where Ω is perpendicular to B and hence ρGJ = 0. Since the charge carriers in the opposite side of this region is opposite, therefore when the current passes through this surface charges are removed from this region and hence a vacuum region is created. Since this vacuum region deviates from equilibrium situation hence the electric field along the magnetic field lines exist and it is called ”Gap”. The question is ”Would this gap continue to grow when the current continue to across the null charge surface?”. The answer is ”No” because the electric field along magnetic field increases when the vacuum region becomes bigger. Furthermore when charged particles accelerate in this region they emit curvature photons, whose characteristic energy depends on the strength of the electric field. When the vacuum region grows the characteristic energy of curvature photon also increases. Eventually the energy of curvature photons, typically a few GeV, becomes high enough to become electron/positron pairs when they collide with the background soft photons, e.g. soft X-rays emitted from the stellar surface. These pairs can stop the further growth of the ”Gap”. It has been first shown that two slab-like stable outermagnetospheric gaps can exist in the pulsar magnetopshere (cf. Fig. 7 of Cheng, Ho and Ruderman 1986a). Mathematically stable static outergap can exist by adding two boundary surface charge layers on the top and bottom boundary of the gap. Realistically the top boundary of the outergap should be a current layer, which gradually screen out the gap electric field to recover the Goldreich-Julian solution outside the gap (cf. Fig.12c of Cheng, Ho and Ruderman 1986a). Therefore in general the gap should consist of two regions, a primary acceleration region, where the current flow is much lower than the Goldreich-Julian current, and the screening region, where most of gap current is flowing and the current density can exceed the Goldreich-Julian value in order to screen the gap electric field from outside.

2 Two dimensional outergap model Although the detailed observed spectrum, e.g. the phase resolved spectrum, is determined by a three dimensional models (e.g. Tang et. al. 2008, Harding et al. 2008, Hirotani 2008, Bai & Spitkovsky 2010), the phase average spectrum can be determined by two dimensional models. By fitting the phase average spectrum of pulsars we can obtain some very useful key parameters of the gap including the current distribution, size of the gap etc. These information can let us know how the gap evolves. In this section we use a simple two dimensional outergap model to explain all fermi detected gamma-ray pulsars except 4 very young Crab-like pulsars, whose radiation is expected to be synchrotron-self-Compton process because the hot surface and the small light cylinder make the optical depth of curvature photon larger than unity. We believe that high energy photons from most Fermi pulsars are curvature photons except these four young pulsars, whose age is less than 104 yr old.

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2.1 Gap structure Fig.1 illustrates our two-dimensional gap structure. We express the potential in the gap as Φ = Φ′ + Φ0 , where Φ0 is the co-rotating potential, which satisfies ▽2 Φ0 = −4πρGJ with ρGJ being the Goldreich-Julain charge density. In addition, the potential Φ′ is the so called non co-rotating potential, which represents the deviation from co-rotating potential and generates the accelerating electric field. Using the Poisson equation ▽2 Φ = −4πρ, and assuming the derivative of the potential field in the azimuthal direction is much smaller than those in the poloidal plane, we express the Poisson equation of Φ′ in the simple 2-dimensional geometry as ! ∂2 ∂2 + Φ′ = −4π(ρ − ρGJ ), (1) ∂x2 ∂z2 where the coordinates x and z are distance along and the perpendicular to the magnetic field lines, respectively. In the present simple two-dimensional geometry, we ΩBx express the Goldreich-Julain charge density as ρGJ (x) ≈ − 2πcs (cf. Eqs. 3.2 and 3.3 of CHRa), where Ω is the angular velocity, B ≈ B(Rlc) is the magnetic field strength in the outer magnetosphere, Rlc = c/Ω is the light cylinder radius and s ≈ Rlc is the curvature radius of the magnetic field lines.

Fig. 1 Schematic view of the gap structure. (a)The structure of the two-dimensional outer gap. The regions I and II are the primary region and the screening region respectively. (b)The distribution of the charge density in the trans-field (z) direction in the gap. (c)The distribution of the g(z) in z-direction in the gap. (d)The distribution of the potential Φ′ (z), and the accelerating electric field E⊥ ∝ Φ′ (z).

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Since we are interested in the distribution of the accelerating field in the transfield direction (z-direction), we approximately express the deviation of the charge density from the Goldreich-Julian charge density as ρ−ρGJ ∼ g(z)ρGJ (x), where g(z) expresses the deviation from the Goldreich-Julian charge density averaged along the magnetic field line between the inner and outer boundaries. By assuming that the derivative of the potential field in the trans-field direction is larger than that along the magnetic field line and ignoring the variation of the Goldreich-Julian charge density in the trans-field direction, we rewrite the Poisson equation (1) as, ∂2 ′ Φ (x, z) = −4πρGJ (x)g(z). ∂z2 By defining Φ′ (x, z) = ρGJ (x)Φ′ (z), the Poisson equation becomes ∂2 ′ Φ (z) = −4πg(z). ∂z2

(2)

The accelerating electric field is calculated from E || (z) = −∂Φ′ (x, z)/∂x. To solve the equation (2) we impose the boundary conditions on the lower and upper boundaries. We put the lower boundary at the last-open field line, where the condition Φ(z = 0) = 0 (3) is imposed. On the upper boundary, we impose the gap closure conditions that Φ(z = h2 ) = 0 and E ⊥ (z = h2 ) = 0,

(4)

which ensure that the total potential (co-rotational potential + non co-rotational potential) field in the gap is continuously connected to the co-rotational potential field outside the gap. The location of the upper boundary can not be arbitrary chosen, because both Dirichlet-type and Neumann-type conditions are imposed on the upper boundary. We divide the gap into two regions, i.e. the primary acceleration region and the screening region. The main acceleration region is expanding between the last-open field line and the height z = h1 (region I in Fig.1a), and the screening region is expanding between z = h1 and z = h2 (region II in Fig.1a). We note that the averaged charge density must be less than the Goldreich-Julian value, that is |ρ| < |ρGJ |, in the primary acceleration region, while |ρ| > |ρGJ | in the screening region. To simplify the problem, we treat the distribution of the number density and therefore of the charge density in the trans-field direction (z-direction) as a step function (Fig.1b). Because we consider the case that the inclination angle is smaller than α < 90◦ and because the primary acceleration region extends between the null charge surface and the light cylinder, we describe the deviation of the charge density from the Goldreich-Julian charge density as * + ( ρ − ρGJ −g1 , if 0 ≤ z ≤ h1 = g(z) = , (5) g2 , if h1 < z ≤ h2 ρGJ

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where g1 > 0 and g2 > 0 (cf. Fig.1c). Using the boundary conditions that Φ′z (z = 0) = 0 and Φ′z (z = h2 ) = 0 and imposing the continuity of the potential field Φ′z and ∂Φ′z /∂z at the height h1 , we obtain the solution of the Poisson equation (2)analytically, which is function of four gap parameters, i.e. h1 , h2 , g1 and g2 . However, the gap closure condition E ⊥ = 0 on the upper boundary implies the relation that h2 h1

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2.2 Curvature radiation spectrum The charged particles are accelerated by the electric field along the magnetic field lines in the gap, and emit γ-rays via the curvature radiation. The accelerating electric field is approximately computed from E || (z) = −

∂ ′ ∂ρGJ (x) ΩB(Rlc ) ′ Φ (x, z) ∼ −Φ′z (z) ∼ Φz (z), ∂x ∂x 2πsc

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implying ∆A = 2πRlch2 (Rlc ) and ΩB(Rlc )R2lc (1 + g(z)) dN = 2πR2lc n(z) = . dz ec

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2.3 Properties of curvature spectra with gap parameters Basically we have three independent fitting parameters, i.e the fractional gap size defined by f ≡ h2 (Rlc )/Rlc , the number density (current) in the primary region (1 − g1) and the ratio between the thicknesses of primary region and total gap size h1 /h2 . In Fig. 2 we show how these gap parameters affect the radiation spectrum. We can see that. (i)When the gap size increases both the radiation power and the electric field increases, hence the cut-off energy of the spectra increases. (ii)Basically the spectrum consists of two components, i.e. the primary region radiates high energy gamma-rays and the screening region radiate softer gamma-rays. When the current in the primary region increases but all other parameters fixed, the flux in the high energy component increases and the spectrum becomes harder. (iii)When the size of the primary region increases but the currents in both acceleration regions are fixed, the charge density in the primary decreases and hence the electric field in this region increases. This make the cut-off energy higher. At the same time the charge density in the screening increases and hence the electric field in this region decreases. The characteristic photon energy in this region becomes even lower. The combined effects make the high energy component and low energy component separate wider and hence the overall spectrum becomes flatter.

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2.4 Fitting Results We fit the spectra of the 42 γ-ray pulsars measured by the EGRET and Fermi telescopes with the present model. For the observed spectra, we use information reported in the first Fermi catalogue (Abdo et al. 2010), in which the observed data were fit with a single power law plus exponential cut-off form. In our fitting, we do not include the Crab-like young pulsars (e.g. the Crab pulsar, PSR J11245916) because the radiation mechanism of the Crab-like pulsars are synchrotronself-Compton process instead of curvature radiation process (Cheng, Ruderman & Zhang 2000; Takata & Chang 2007). In the Crab-like pulsars their soft photon density is sufficiently high so that most curvature photons from the outer gap will be converted into pairs within the light cylinder and the observed gamma-rays resulting from the inverse Compton scattering of the synchrotron photons of secondary pairs. This radiation process differs from what we have considered in this paper and therefore we will not consider them. As discussed in section 2.3, our fitting parameters are the fractional gap thickness f , the charge density in the primary region, 1 − g1 , and the ratio h1 /h2 . In fact, given observed phase-averaged spectrum can be uniquely fit with one set of ( f, 1 − g1 , h1 /h2 ) with a small uncertainty. The model fitting was proceeded as following. First, we deduced the typical fractional gap thickness, f , from the observed intensity and the cut-off energy, because the fractional gap thickness f greatly affects the intensity and the cut-off energy. For the next step, we fit the spectral slope

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E (MeV)

Fig. 4 This figure shows the model results for 6 canonical pulsars. The solid lines represent the best fitting model spectra with the fitting parameters listed in each panel. The circles are the observed data from Fermi LAT, which are taken from Abdo et al. (2009) for the Vela pulsar and Trep et al. (2010) for J2021+4026. The boxes are the observed data from EGERT (Fierro 1995). The dotted lines in the panels of the Geminga and the Vela pulsars are results for the fractional gap thickness (f = 0.7 for the Geminga and 0.145 for the Vela) about 10 % less than the best fitting fractional gap thickness, while the dashed-dotted lines are results for 1-g1 (0.13 for the Geminga and 0.1 for the Vela) and h1/h2 (0.867 for the Geminga and 0.967 for the Vela) about 10-20 % less than the best fitting parameters.

3

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Canonical Pulsar MSP 2

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L

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Fig. 5 The predicted gammaray luminosity as a function of the spin down power. The circle and triangle represent for the canonical and millisecond pulsars. The solid and dashed lines represent the models by Zhang & Cheng (1997) and Takata et al. (2010), respectively.

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below the cut-off energy with the charge density in the primary region, 1 − g1 , which mainly controls the slope of the calculated spectrum. Finally, we determined h1 /h2 , which controls the spectral width between the cut-off energy in several GeV and the spectral break energy in lower energy bands. In Fig. 3 we summarize the fitting results of the gap parameters for 42 Fermi detected gamma-ray pulsars. In Fig. 3a we can see that the primary region occupies 92% to 97% of the entire gap with a mean roughly about 95%. In Fig. 3b the fitted gap current in the primary region is only 10% of the Goldreich-Julian value. It indicates that most the outergap region is still quite empty. This is very important

Gamma-ray emission and pair creation of outer gap

107

because if the gap current is large it reduces the gap electric field substantially. Consequently multi-GeV photons, which collide with soft photons to make pairs, cannot be produced. The fitting results are consistent with this requirement. In Fig. 3c the gap size increases with age. This is easily to be understood because when the pulsars age, the gap electric field reduces. In order to maintain multi-GeV production, the gap needs to grow larger to compensate the weakening of the gap. In Fig.3d the total gap current is quite constant and close to 55% of the Goldreich-Julian value. First it tells us that the gap electric field is guaranteed non-zero and secondly it may suggest a dynamic gap. We can speculate that the gap may begin with quite empty and once the pair creation occurs, the gap will fill with full Goldreich-Julian current. Since all particles, i.e. photons and charged particles, in the gap are moving with speed of light and hence after the time average the mean current in the gap may close to 55%. Fig.4 presents the fitting results with the observed data for the 6 canonical pulsars. The data points are taken from the EGRET observations (Fierro, 1995) for the Geminga, PSRs J057-5226,J1709-4229 and J1952+3252, and from the Fermi observations for the Vela (Abdo et al. 2009 and 2010) and PSR J2021+4206 (Trep et al. 2010). The grey strips represent the errors of the photon index, cut-off energy and intensity measured by the Fermi observations. The solid lines represent the best fit spectra with the fitting parameters listed in each panel and in Table 1. We use the dashed and dashed-dotted lines in the panels of the Gemiga and Vela pulsars to preset how the best fit parameters include the uncertainties. The dotted lines are results for the fractional gap thickness ( f = 0.7 for the Geminga and 0.145 for the Vela) about 10 % less than the best fitting values, while the dashed-dotted lines are results for 1 − g1 (0.13 for the Geminga and 0.1 for the Vela) and h1 /h2 (0.867 for the Geminga and 0.967 for the Vela) about 10-20 % less than the best fitting values. It is obvious that both dashed and dashed-dotted lines can not explain the observed data, implying the fitting parameters include uncertainties of about 10 % for the Geminga and Vela pulsars. The fitting results of the remaining Fermi pulsars including 8 millisecond pulsars can be found in Yu, Takata and Cheng (2010). In general our model can fit the observed phase average spectrum of all Fermi extremely well. The theoretical gamma-ray power can also be obtained numerically in fitting. In Fig. 5 we plot the the fitting gamma-ray power (Lγ ) versus the spin-down power of pulsars (L sd ). There appears some indication in this figure that the gamma-ray power seems insensitive to the spin-down power for L sd > 1036 erg/s whereas the gammaray power satisfies a simple power law for L sd < 1036 erg/s, which may imply the gap controlling mechanism may be different in these two regions. In next section we will introduce a new gap closure mechanism.

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3 Pair creation mechanisms 3.1 Photon-photon pair-creation process The outer gap accelerator model was proposed by Cheng, Ho and Ruderman (1986a,b), who argued that a large global current flow through the outer magnetosphere causes a charge depletion region around the null charge surface. In the charge depletion region, the non-corotational electric field along the magnetic field accelerates the charged particles, which can emit γ-ray photons. This non-corotational electric field could be screened out by the discharge of the copious electron and positron pairs produced by the pair-creation process of the γ-ray photons. The outer gap would be completely screened out in the trans-field direction, where the noncorotational electric field perpendicular to the magnetic field, En,⊥ , in the poloidal plane is equal to zero. This condition implies that the total potential (corotational + non-corotational) field is continuously connected to the corotational field outside the outer gap. Fig. 6 Schematic view of the outer gap accelerator. In the outer magnetosphere, the photon-photon pair-creation process produce the pairs in the gap uniformly. The pairs created by the magnetic pair-creation process close the outer gap in the outer magnetosphere. The favorable magnetic structure near the stellar surface is depicted in Figure 7.

Ω

µ + e-

+ e+ e- e

X-ray

e-e+

γ-ray

Co-

rota

ting

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e+ ma

gne

tosp

her

e

Zhang & Cheng (1997) discussed the gap closure mechanism by the photonphoton pair-creation process between the high-energy γ-rays emitted in the gap and the X-ray photons coming from the stellar surface. They estimated the typical gap thickness from the pair-creation condition Eγ E x ∼ (2me c2 ), where Eγ is the energy of the emitted γ-ray photons in the outer gap and E X is the energy of the soft-photons from the stellar surface, and they obtained the fractional gap thickness as fZC ≡ h⊥ (Rlc /2)/Rlc ∼ 5.5P26/21 B−4/7 , d,12

(13)

where Rlc is the light cylinder radius, h⊥ (Rlc /2) is the gap thickness in poloidal plane at r = Rlc /2 and Bd,12 is the global stellar magnetic field in units of 1012 Gauss. The outer gap closure mechanism with the photon-photon pair-creation process in the trans-field direction have also been discussed by solving the electrodynamics in the outer gap with 2-dimensional and 3-dimensional geometry (Takata, Shibata and Hirotani 2004; Hirotani 2006a,b; Hirotani 2008). For example, Hirotani (2006a)

Gamma-ray emission and pair creation of outer gap

109 Global field e-

Curvature photons (~100MeV)

Fig. 7 Schematic view of the favorable magnetic structure near the stellar surface.

gne to

γ(

ma ing ot a t

∼5 M

h ,m

co-r

Local field

e+ −

γ(

e+ − α>π/2

eV )

γ

e+ −

sph

∼1 00 M

ere

eV )

Synchrotron photons (~5MeV)

γ

γ

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e-

e+ −

Stellar surface

demonstrated that the outer gap for the young pulsar, the Crab pulsar, is almost screened out in the trans-field direction at the fractional gap thickness of f ∼ 0.2 (figure 6 in Hirotani 2006a). For mature pulsars such like Gemiga, on the other hand, Takata and Chang (2009) argued that the photon-photon pair-creation process will be insufficient in the outer magnetosphere and the outer gap could occupy entire region between the last-open field lines and the critical field lines that have the null charge point at the light cylinder.

3.2 New gap closure mechanism Recently Takata, Wang and Cheng (2010) proposed a possible gap closure mechanism, in which the magnetic par-creation process near the stellar surface supplies the electron and positron pairs to close the outer gap in the trans-field direction. It has been proposed that the magnetic field near the stellar surface is enhanced by the strong multiple magnetic field, although the global magnetic field is well described by the dipole field (Blandford et al. 1983; Romani 1990; Ruderman 1991). The neutron star magnetic field will be produced by a current flowing the crust, which has a thickness of δr ∼ 1 − 3 × 105 cm ≪ R s . It was suggested that the magnetic structure near the stellar surface is super position of clumps resolved into multiples of characteristic of the order of R s /δr (Arons 1993). If the clumps cover whole stellar surface, the strength of the stellar magnetic field is order of B s ∼ (R s /δr)n Bd , where Bd is the strength of dipole magnetic field determined by the observed rotation period P and ˙ and n = 1 and 2 represent coherent and incoherent superpothe period derivative P, sition of the magnetic momentum of the clump, respectively. This model indicates the strength of the stellar magnetic field can take easily B s ∼ 10 − 100Bd. Therefore, even in the millisecond pulsar, the magnetic field near the star surface will be close

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to B s ∼ 1011 Gauss, and the magnetic pair-creation process will take place close to the stellar surface. We argue that the γ-rays emitted near the stellar surface is converted into the pairs via the magnetic pair-creation process above the height (h⊥,m ) measured from the last-open field line. In equation (16), we will estimate the height, h⊥,m , above which the pair-creation process takes place. The important conditions for closing the gap by the pairs produced by the magnetic pair-creation process are as follows; (1) the gap was not closed by the photon-photon pair-creation process below the height h⊥,m , (2) the local magnetic field lines near the stellar surface is bending away from the last-open field lines (see Fig.7 below) due to the strong multiple fields, and (3) some of magnetic pairs migrate into outer magnetosphere. The second condition is required to produce outflows of the magnetic pairs. Fig.6 and Fig.7 represents the schematic view of the outer magnetosphere and of the magnetic structure near the stellar surface, which is favored in this study, respectively. In the outer magnetosphere, the photon-photon pair-production process creates pairs, which are separated by the accelerating electric field. Inward propagating particles will emit the γ-ray photons toward the strong magnetic field region near the stellar surface. As demonstrated by the electrodynamic study (e.g. Hirotani 2006a), the electric field below null charge surface are significantly reduced by the pairs and arises with a very weak field. Below the null charge surface, therefore, the curvature energy loss will not be able to be compensated by the acceleration of the electric field in the gap, and the incoming particles loose their energy by the curvature radiation. Takata et al. show that there is a minimum energy of the curvature photons, which does not depend on any pulsar parameters and the curvature 2 radius of the local magnetic field, and it is given by Emin ∼ mαe cf ∼ 100 MeV, where α f is the fine structure constant. Before hitting the stellar surface each gap particle can emit ∼ 104 100MeV curvature photons. Most of these curvature photons can be converted into e± pairs by the strong magnetic field. The mean free path of the magnetic pair-creation process of the photon with the energy Eγ is described as (Erber 1966;Ruderman & Surtherland 1975) ! 4.4 h¯ Bq 4 lm = exp , (14) α f m e c B⊥ 3χ where χ = Eγ B⊥ /2me c2 Bq , α f is the fine structure constant, Bq = 4.4 × 1013 Gauss and B⊥ = B sin θa with θa is the angle between the direction of the propagating for the photon and the magnetic field. The exponential dependency of the mean-free path on the photon energy Eγ and the angle θa implies that most of emitted photons will be converted into pairs if the condition that Eγ B⊥ /(2me c2 Bq ) ∼ χ is satisfied. Using the magnetic pair-creation condition, we can estimate height measured from the last open field line, above which the magnetic pair-creation process of the photons with Emin ∼ 100 MeV becomes important with the dipole magnetic field geometry. The collision angle θa between the trajectory of the curvature photons and the magnetic field line is approximately described as

Gamma-ray emission and pair creation of outer gap

sin θa ∼

ℓ ∼ s

111

r

2h⊥ , s

(15)

√ where ℓ ∼ 2h⊥ s is the propagating distance of a photon from the emission point, and h⊥ is the thickness of the gap near the inner boundary. The magnetic paircreation condition implies that the curvature photons with an energy ∼ 100 MeV will be converted into the pairs above the height h⊥,m (Ri ) ∼ 104 χ2−1 B−2 m,12 s7 cm,

(16)

where Ri expresses the critical radial distance below which the magnetic paircreation process becomes to be important and it will be Ri ∼ 2 − 3R s for the canonical pulsars and Ri ∼ R s for the millisecond pulsars. In addition, χ−1 = χ/0.1, Bm,12 is the strength of the magnetic field at the pair-creation position in units of 1012 Gauss, and we used E min = 100 MeV. Rescaling the thickness at the stellar radius using the magnetic flux conservation, we obtain h⊥ (R s , m) ∼ (R s /Ri )3/2 h⊥,m (Ri ) with R s being the stellar radius. As we have discussed above, the incoming particles will create pairs above the height h⊥,m , which is described by equation (16), via the magnetic pair-creation process near the stellar surface, and the multiplicity could acquire Me± ∼ 104 − 105 for the canonical pulsars and ∼ 104 for the millisecond pulsars. Although it is expected most of the created pairs have inward momentum and migrate toward the star, it may be possible that a tiny fraction of the created pairs are produced with outward momentum and migrate into outer magnetosphere, as discussed below. In fact, only an extremely small fraction of pairs out of Me± ∼ 104 − 105 will be enough to close the outer gap accelerator in the trans-field direction everywhere in the outer magnetosphere. The magnetic pairs would be produced with an outward momentum if the magnetic structure near the stellar surface is affected by the strong multiple field, as illustrated in Fig.7, which shows how some pairs can acquire the outgoing momentum due to the geometry of the local magnetic field lines. Near the stellar surface, the magnetic field lines (dashed lines) can be bending away from the last-open field line due to a strong multiple field (solid-dashed line). The solid curved lines represent the global field which are not affected by the local magnetic field, and thin dashed-line represent the geometry without the multiple field. The 100 MeV curvature photons (solid arrows) emitted by the incoming particles, which were accelerated inside the outer gap, are converted into the pairs via the magnetic pair-creation above height, h⊥,m described by equation (16). For the canonical pulsars, the synchrotron radiation of the created pairs will produces 10 MeV photons (dashed arrows), which could be converted into new pairs by a strong magnetic field near the stellar surface. If the direction of the magnetic field at the pair-creation positions is bending away from the last-open field line, it is possible that the collision angle (denoted as α in the Fig.7 between the photons and the magnetic field line becomes larger than α ≥ 90◦ , implying the created pair has the outward momentum.

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K. S. Cheng 103

Lγ/Ec2 (1033 erg/s/GeV2)

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Radio-selected Gamma-ray selected Millisecond Model

101

10

0

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Fig. 8 Plot of Lγ /Ec2 as a −1/2 function of B1/2 d,12 P−1 .

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101

We note that (1) because the position of the pair-creation point is determined by the value B sin α, and (2) because the collision angle changes from a smaller value to a larger value as the photon propagate toward the stellar surface, the position with the collision angle smaller than 90◦ is preferentially chosen as the pair-creation point, although sin α gives the same values with, for example, α = 80◦ and 110◦ . However, the magnetic field also increases as the photons propagate toward the stellar surface, implying the strength of the magnetic field is bigger for the position with α = 110◦ than that with α = 80◦ . As a result, it will be possible that some photons do not have enough energy to produce the pairs with the magnetic field at the position with α = 80◦ , but do to produce the pairs at the position with α = 110◦ . On these ground, some created pairs will be able to have the outward momentum, if the local magnetic field is bending away from the last-open field line. If all field lines in the polar cap region are bending toward the last-open field line, it is not expected outgoing pairs because the collision angle is always α < 90◦ . In such a case, all pairs created by the magnetic pair-creation process will have an inward momentum, implying the photon-photon pair-creation process will be only possible mechanism to close the outer gap.

3.3 Predictions of new outer gap model Our gap closure process is summarized as follows; 1. the incoming particles emit ∼100 MeV photon below the null charge surface, 2. the ∼100MeV photons emitted toward the stellar surface will produce the pairs via the magnetic pair-creation process (Me± ∼ 104 − 105 ) above the height h⊥,m estimated by equation (16), and 3. if some fraction of the created pairs will be produced with an outward momentum due to the geometry of the local magnetic field, and the returning pairs completely close the outer gap in the trans-field direction everywhere in the outer magnetosphere.

Ec; Cut-off energy (GeV)

Gamma-ray emission and pair creation of outer gap

Fig. 9 Plot of the cut-off energy as a fucntion of the spin down power. The line is the model prediction, Ec ∼ 1/4 0.22K 3/2 B1/4 d,12 L sd,34 GeV with

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104

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Applying equation (16) as the typical gap thickness of the gap we define the fractional gap thickness as fm ≡

h⊥,m (R s ) ∼ 0.25K(χ, Bm, s)P1/2 , −1 rp

with K = χ2−1 B−2 m,12 s7

Rs Ri

!3/2

.

(17)

(18)

By assuming a simple localized dipole field on the surface of neutron star, Takata et al. (2010) have estimated that K ∼ 1 for canonical pulsars and K ∼ 10 for millisecond pulsars. Applying the fractional gap thickness to the acceleration and curvature emission process beyond the null charge surface, we discuss the expected properties of the γray radiation from the outer gap closed by the magnetic pair-creation process. The typical magnitude of the electric field in the gap beyond the null charge surface is given by f 2 Va E|| (K, Bd , P) ∼ m ∼ 8.3 × 104 K 2 Bd,12 P−2 (19) −1 Volt/cm. Rlc which can accelerate the electrons and positrons up to γ(K, Bd ) ∼

3s2 E|| 2e

!1/4

∼ 2.1 × 107 K 1/2 B1/4 , d,12

(20)

where we used s = Rlc in the outer magnetosphere. We find that the maximum Lorentz factor does not depend on the rotational period. The typical energy of the curvature radiation by the accelerated particles in the outer magnetosphere is Ec (K, Bd , P) =

3 hcγ3 ∼ 0.55K 3/2 B3/4 P−1 GeV. d,12 −1 4π s

(21)

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Fig. 10 Plot of the γ-ray luminosity as a function of the spin down power. The line is the model prediction, Lγ ∼ 5/8 2 × 1032 K 3 B3/4 d,12 L sd,34 erg/s with <

K 3 B3/4 d,12

Lγ ; Gamma-ray luminosity (1033 erg/s)

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Because the efficiency of the emission is significantly reduced above the energy E c , we expect that the γ-ray spectrum has the cut-off energy of Ec . The total current flowing in the gap is order of Igap ∼ fm IGJ , where IGJ = πBd R s /PRlc is the Goldreich-Julain current. Using the total potential drop in the gap of Vgap ∼ fm2 Va , we can estimate the γ-ray luminosity as Lγ (K, Bd , P) ∼ Igap Vgap ∼ 2 × 1033 K 3 B2d,12 P−5/2 erg/s. −1

(22)

3.3.1 Switching between two gap closure processes We have emphasized that both photon-photon pair creation and magnetic pair creation occur in different regions of pulsar magnetosphere. But there is only one of them will be the dominant gap closure mechanism. The simplest criterion is which mechanism makes the gap smaller. Therefore from the condition fZC = fm , we can determine the switching of gap closure processes taking place at L sd ∼ 2.5 × 1036(K/2)−168/31 B−34/31 erg/s. d,12

(23)

The above equation is consistent with our 2D model fitting results shown in section 2. 3.3.2 Comparison with Fermi observations Takata et al. (2010) have made a detailed comparison between model predictions and the data of Fermi. Here we just discuss three of them. Again we would like to emphasize that K is an unknown parameter, which depends on the surface magnetic field structure of neutron stars. In order to avoid this unknown parameter we can consider −1 2 Lγ /E c2 = 6.6 × 1034 B1/2 (24) d,12 P−1 erg/s GeV ,

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115

this ratio only depends on the observed pulsar parameters. Fig. 8 shows reasonable linear relation as predicted in above equation. If we recast the cut-off energy Ec (21) and the γ-ray luminosity Lγ (22) as a function of the spin down power L sd = (2π)2 B2d R6s /6c3 P4 , we obtain

and

Ec ∼ 0.22K 3/2 B1/4 L1/4 GeV d,12 sd,34

(25)

Lγ ∼ 2 × 1032 K 3 B3/4 L5/8 , erg/s d,12 sd,34

(26)

respectively. Takata et al. (2010) show that although K and the average mangetic field between canonical pulsars and millisecond pulsars are very much different, it turns 3 3/4 out that the proportionality coefficients K 3/2 B1/4 d,12 in equation (25) and K Bd,12 in equation (26) have less dependency on the pulsar populations. The model predicted values of these two combined coefficients for canonical pulsars and millisecond pulsars only differ by a factor less than 2. Consequently in Fig. 9 and Fig. 10 we can see that both populations can form simple relation with the spin-down power of pulsars.

4 Summary We find that a 2D outergap model with a primary region plus a screening region can explain the phase average spectrum of all mature pulsars detected by Fermi very well.The fitting results indicate that the primary region consists of 10% GJ current and the screening region contains 40%. The low current in primary region ensures the production of multi-GeV photons and hence pair creation can take place. The total current in the gap is 50% of the Goldreich-Julian current may suggest a dynamic gap. The size of the gap increases with age. By plotting the fitted gamma-ray power versus the spin-down power of pulsars suggest that there may be two possible pair creation processes controlling the gap closure, i.e. photon-photon pair creation and magnetic pair creation. The transition takes place erg/s. If the magnetic pair creation is the at L sd ∼ 2.5 × 1036(K/2)−168/31 B−34/31 d,12

respectively. More and Ec ∝ L1/4 gap closure mechanism we predict that Lγ ∝ L5/8 sd sd predictions can be found in Takata, Wang and Cheng (2010). Acknowledgements This work is in collaboration with J. Takata and Y.Wang and is supported by a GRF grant of Hong Kong SAR Government under HKU700908P.

References 22. Abdo A.A. et al., 2009, ApJ, 696, 1084 22. Abdo A.A. et al., 2010, ApJS, 187, 460

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Arons J., 1993, ApJ, 408, 160 Bai, Xue-Ning & Spitkovsky, A. 2010, ApJ, in press Blandford R.D., Applegate J.H. & Hernquist, L., 1983, MNRAS, 204, 1025 Cheng K.S., Ruderman M. & Zhang L. 2000, ApJ, 537, 964 Cheng K.S., Ho C. & Ruderman M. 1986a, ApJ, 300, 500 Cheng K.S., Ho C. & Ruderman M. 1986b, ApJ, 300, 522 Erber T., 1966, RvMP, 38, 626 Fierro J.M., 1995, PhD thesis, Stanford Univ Goldreich P. & Julian W.H. 1969, ApJ, 157, 869 Harding, A. K., Stern, J. V., Dyks, J., & Frackowiak, M. 2008, ApJ, 680. 1378 Hirotani, K. 2008, ApJ, 688, 25 Hirotani K., 2006a, ApJ, 652, 1475 Hirotani K., 2006b, Mod. Phys. Lett. A, 21, 1319 Romani R.W, 1990, Nature, 347, 741 Ruderman M., 1991, ApJ, 366, 261 Ruderman M.A. & Sutherland P.G., 1975, ApJ, 196, 51 Takata J., Shibata S. & Hirotani K. 2004, MNRAS, 354, 1120 Takata J. & Chang H.-K., 2007 ApJ, 670, 677 Takata, J., Wang, Y. & Cheng, K.S. 2010, ApJ in press Tang, Anisia P. S., Takata, J., Jia, J. J. & Cheng, K. S. 2008, ApJ, 676, 562 Trepl, L., Hui, C. Y., Cheng, K. S., Takata, J., Wang, Y., Liu, Z. Y. & Wang, N., MNRAS, 2010 in press 22. Wang, Y., Takata, J. & Cheng, K.S. 2010, ApJ submitted 22. Zhang L. & Cheng K.S., 1997, ApJ, 487, 370

What Pulsar High-Energy Emission Model Survives? Electrodynamical Considerations Kouichi Hirotani

Abstract We explore particle accelerator electrodynamics in the magnetosphere of a rapidly rotating neutron star (NS). We address the importance of a self-consistent treatment of pair production, solving the Maxwell and Boltzmann equations simultaneously. It is demonstrated that the accelerator solution is obtained if we specify only the following four parameters: the NS spin period, magnetic dipole moment, magnetic inclination angle with respect to the rotation axis, and the NS surface temperature. Applying the scheme to the Crab pulsar, we show that the solution reproduces the gamma-ray observations at least qualitatively and that the solution corresponds to a quantitative extension of phenomenological outer-gap models. We also apply it to the slot-gap model, a geometrically thin version of the pair-starved polarcap (PSPC) model, to show that this alternative model predicts too small photon flux compared to observations. It is discussed that the PSPC model is electrodynamically vulnerable to pair production.

1 Introduction Rotation-powered pulsars are excellent laboratories for testing particle acceleration theories. The major advantage of studying pulsars is that we know that they are powered by rotational energy loss. It is generally accepted that the rotating magnetic field works as a unipolar inductor to exert a large electro-motive force on the spinning neutron star (NS) surface and that the resulting potential drop in the rotating magnetosphere leads to the acceleration of charged particles to ultra-relativistic energies. The challenge is then to investigate where and how they convert this energy into radiation that we observe. Kouichi Hirotani Academia Sinica, Institute of Astronomy and Astrophysics (ASIAA) / Theoretical Institute for Advanced Research in Astrophysics (TIARA), P. O. Box 23-141, Taipei, Taiwan, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_10, © Springer-Verlag Berlin Heidelberg 2011

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Kouichi Hirotani

The pulsar magnetosphere can be divided into two zones (fig. 1). The closed zone is filled with a dense plasma co-rotating with the star, whereas the open zone allows plasmas to flow along the open field lines, escaping to large distances through the light cylinder (LC). Here, the LC is located at the so-called ‘light cylinder radius’, ̟LC = c/Ω, from the rotation axis, where Ω denotes the NS rotational angular frequency and c the speed of light. The last-open field lines, which become parallel to the rotation axis at the LC, form the border of the open magnetic field line bundle. In all the pulsar emission models, particle acceleration and the resulting photon emissions take place within the open zone. Fig. 1 Schematic figure (side view) of the pulsar magnetosphere. The slot gap extends from the stellar surface to the light cylinder on the last-open field line (in the open zone) with trans-field thickness much less than the outer gap. The outer gap is traditionally assumed to be located between the null charge surface and the light cylinder. For middle-aged pulsars, the OG trans-field thickness becomes greater than depicted.

magnetic dipole axis

null surface magnetic field lines

outer gap NS

slot gap polar gap

last-open field line

closed zone

pulsed γ-rays

light cylinder

light cylinder radius

ϖLC= 3 108(Ω /102 rad s-1) cm

Attempts to model pulsar high-energy emissions concentrate on a few scenarios: (i) polar-cap (PC) models with emission above a PC surface [23, 16, 18, 58], (ii) outer-gap (OG) models with emission near LC [10, 11, 14, 15, 55, 56, 68, 13], (iii) emission models from a striped wind [4, 5, 51, 54]. In scenarios (i) and (ii), both PC and OG models predict that e± ’s are accelerated in a charge depletion region, a potential drop, by the magnetic-field-aligned electric field, Ek , to radiate high-energy gamma-rays via the curvature and inverse-Compton processes. Thus, their electrodynamics is more or less common. However, the physical processes taking place in scenario (iii) are quite different from those in scenarios (i) and (ii). Thus, in this chapter, we will focus on scenarios (i) and (ii), and first solve both models from the same set of basic equations under different boundary conditions. It is widely accepted from phenomenological studies that coherent radio photons are emitted from the PC accelerator (or equivalently ‘inner gap’ as depicted in fig. 1). It should be noted that the PC model predicts the so-called ‘pencil beam’ emission with a small solid angle along the magnetic axis, because the emission takes place in the lower altitudes (i.e., near the NS surface). Since the radio pulsation generally exhibits a single sharp peak in each rotational period, we can reproduce the pulse profiles if the observer’s viewing angle, ζobs , with respect to the rotation axis, is close to the magnetic inclination angle, α, with respect to the rotation axis. However, to explain the emissions of incoherent high-energy photons, which generally exhibit

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widely separated double peaks, one has to invoke a very small α and ζobs . Thus, to explain the γ-ray pulsations detected from several brightest pulsars [50, 21, 35, 21, 42, 64, 41, 53, 37], a high-altitude emission, which results in the so-called ‘fan beam’ emission with a large solid angle (∼ 1 ster), drew attention as an alternative possibility. The possibility of a high-altitude extension of the PC accelerator was originally introduced by [2]. Developing this electrodynamical model, and incorporating general relativistic effects [47], [48] began discussing high-energy emission from the pulsar slot gap (SG), a narrow region on the last-open field line where Ek is decreasing and accelerating particles cannot create pairs. Then [49] extended this loweraltitude solution (within a few stellar radii) to higher altitudes (near the LC) and found that curvature radiation of the primary particles forms caustic patterns, as suggested in the two-pole caustic model [19]. Subsequently, [13] examined polarization characteristics and found that fast swings of the position angle and minima of polarization degree can be qualitatively reproduced within their two-pole caustic model. This type of emission, SG emission, fills the whole sky and all phases in a light curve. That is, most observers catch emission from the two poles, if ζobs is in a reasonable range (e.g., 45◦ < ζobs < 125◦ for α > 30◦ ). More recently, [24] investigated the SG emission, adding synchrotron radiation of the gap-accelerated primaries and higher-generation pairs produced at lower-altitude PC region. They applied the model to the Crab pulsar and predicted the pulse profiles and the phaseresolved spectra, which are consistent with the observations from 0.3 keV to 10 GeV. An alternative way to consider a high-altitude emission is the OG model. To examine the OG quantitatively, [28, 29] first solved the set of Maxwell and Boltzmann equations in a pulsar magnetosphere, extending the method originally proposed for a pair-production cascade in a rotating black-hole magnetosphere [6, 27]. Before [28], the accelerator position, strength of E k , and even the existence of the OG itself, have been hypothesized. However, in their one-dimensional analysis of a pair-production cascade along the magnetic field lines, [28] demonstrated that the OG does exist as the solution of the set of the Maxwell and Boltzmann equations. After that, a number of papers appeared in the same context (for one-dimensional solution along the magnetic field lines, see, [30]; for two-dimensional solutions, see [60, 31, 32, 62, 33]), confirming that the traditional OG models give qualitatively good agreement with these self-consistent solutions. In the present chapter, we extend the method presented in [31], which analyzes the OG electrodynamics in the 2-D poloidal plane, into the 3-D magnetosphere. We demonstrate that the OG solution is uniquely obtained if we specify the NS rotational period, P, magnetic dipole moment, µ, surface temperature, kT , and α, without introducing any artificial assumptions. Phase-resolved spectra and pulse profiles can be predicted, if we additionally specify ζobs and the distance to the pulsar, d. In § 2 we present basic equations. Then in § 3, we demonstrate that the OG solution is quantitatively obtained from the set of Maxwell-Boltzmann equations. In § 4, we apply the same method to the SG model and point out its difficulties. We finally discuss another electrodynamical difficulty of PSPC in § 5.

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2 Basic equations Around a rotating neutron star with angular frequency Ω, mass M and moment of inertia I, the background space-time geometry is given by [39] ds2 = gtt dt2 + 2gtϕ dtdϕ + grr dr2 + gθθ dθ2 + gϕϕ dϕ2 , where

 rg  2 rg gtt ≡ 1 − c , gtϕ ≡ ac sin2 θ, r r  rg −1 grr ≡ − 1 − , gθθ ≡ −r2 , gϕϕ ≡ −r2 sin2 θ; r

(1) (2) (3)

rg ≡ 2GM/c2 indicates the Schwarzschild radius, and a ≡ IΩ/(Mc) parameterizes the stellar angular momentum. At radial coordinate r, the inertial frame is dragged at angular frequency ω ≡ −gtϕ /gϕϕ = 0.15ΩI45r6 −3 , where I45 ≡ I/(1045g cm2 ), r6 ≡ r/10 km, and r∗ represents the stellar radius.

2.1 Poisson Equation for Electrostatic Potential First, we consider the Poisson equation for the electrostatic potential, which is given by the Gauss’s law as "√ # −g µν 1 4π tµ ∇µ F = √ ∂µ g (−gϕϕ Ftν + gtϕ F ϕν ) = 2 (ρe + ρion ), (4) 2 −g c ρw √ where ∇ denotes the covariant derivative, the Greek indices run over t, r, θ, ϕ; −g = q grr gθθ ρ2w = cr2 sin θ and ρ2w ≡ g2tϕ − gtt gϕϕ = c2 (1 − rg /r)r2 sin2 θ. In the right-hand side, ρe denotes the sum of positronic and electronic charge densities, and ρion the ionic one. The six independent components of the field-strength tensor F µν give the electromagnetic fields observed by a distant static observer [8, 9]. Assuming that the electromagnetic fields are unchanged in the corotating frame, we can introduce the non-corotational potential Ψ such that Fµt + ΩF µϕ = −∂µ Ψ (r, θ, ϕ − Ωt),

(5)

where µ = t, r, θ, ϕ. If F At + ΩF Aϕ = 0 holds for A = r, θ, the angular frequency Ω of a magnetic field is conserved along the field line. On the neutron-star surface, we impose Fθt + ΩF θϕ = 0 (perfect conductor) to find that the surface is equi-potential, that is, ∂θ Ψ = ∂t Ψ + Ω∂ϕ Ψ = 0 holds. However, in a particle acceleration region, F At + ΩF Aϕ deviates from 0 and the magnetic field does not rigidly rotate (even though the deviation from the uniform rotation is small when the potential drop in the gap is much less than the EMF exerted on the spinning neutron star surface). The deviation is expressed in terms of Ψ , which gives the strength of the acceleration

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electric field that is measured by a distant static observer as Ek ≡

B Bi Bi · E = (Fit + ΩF iϕ ) = (−∇i Ψ), B B B

(6)

where the Latin index i runs over spatial coordinates r, θ, ϕ, and an identity Br F rϕ + Bθ F θϕ = 0 is used. If Ψ varies along the magnetic field line, charged particles are accelerated along the field line; we call such a gap of electro-static potential a ‘gap’. If the potential variation is large enough, we can expect enough high-energy emissions from the gap. Substituting equation (5) into (4), we obtain the Poisson equation for the noncorotational potential, ! √ −g µν c2 − √ ∂µ g gϕϕ ∂ν Ψ = 4π(ρ − ρGJ), (7) −g ρ2w where the general relativistic Goldreich-Julian (GJ) charge density is defined as "√ # −g µν c2 ρGJ ≡ g gϕϕ (Ω − ω)F ϕν , (8) √ ∂µ 4π −g ρ2w which reduces to the ordinary, special-relativistic expression of the GJ charge density [25, 43] in the limit r ≫ rg . Instead of (r,θ,ϕ), we adopt in this chapter the magnetic coordinates (s,θ∗ ,ϕ∗ ) such that s denotes the distance along a magnetic field line, θ∗ and ϕ∗ represents the magnetic colatitude and the magnetic azimuth, respectively, of the point where the field line intersects the neutron star (NS) surface (fig 2). For explicit expressions of the Poisson equation (7) in the magnetic coordinates (s,θ∗ ,ϕ∗ ), see [31].

θ* sinϕ*

Fig. 2 Magnetic coordinates (θ∗ ,ϕ∗ ) that specify individual magnetic field lines on the polar-cap surface. The dots denote the footpoints of the magnetic field lines along which the simulation is performed; 40 grids are taken in θ∗ direction, and 96 grids in ϕ∗ direction (even though only 8 points are depicted at each ϕ∗ ). The rotation axis resides at ϕ∗ = π. Both axes are in radian unit.

last-open fieldline, h =0

θ*

θ

max

* ϕ *

magnetic axis, h =1

ϕ*=0

θ* cosϕ*

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2.2 Particle Boltzmann Equations Second, we consider the Boltzmann equations for particles. At time t, position r, and momentum p, the distribution function N+ of positrons (or N− of electrons) obeys the following Boltzmann equation,   ∂N ∂N± v ± + vi · ∇i N± + qE + × B · = S ± (t, r, p), ∂t c ∂p

(9)

where v ≡p/(me γ); mp e refers to the rest mass of the electron, q the charge on the positron, and γ ≡ 1/ 1 − (|v|/c)2 the Lorentz factor. In a pulsar magnetosphere, the collision term S + (or S − ) consists of the terms representing the appearing and disappearing rates of positrons (or electrons) at r and p per unit time per unit phasespace volume due to pair creation, pair annihilation, and the energy transfer due to IC scatterings and synchro-curvature process. Imposing a stationary condition ∂/∂t + Ω∂/∂φ = 0, utilizing ∇ · B = 0, and introducing dimensionless particle densities per unit magnetic flux tube such that n± = hN± i/(ΩB/2πce), where hi denotes the quantity averaged in a gyration, we can reduce the particle Boltzmann equations as c cos χ

 ∂n± ∂n± ∂n± 2πce  + p˙ + χ˙ = S IC + S p , ∂s ∂p ∂χ ΩB

(10)

where the upper and lower signs correspond to the positrons p (with charge q = +e) and electrons (q = −e), respectively, and p ≡ |p| = me c γ2 − 1. In the right-hand side, S IC represents the difference between the disappearing and appearing rates of e± ’s at Lorentz factor γ due to the inverse-Compton scatterings (ICS), whereas S p denotes the particle production rate due to photon absorption. The characteristics of equation (10) in the phase space are given by p˙ ≡ qE k cos χ −

PSC , c

χ˙ ≡ −

qEk sin χ ∂(ln B1/2 ) +c sin χ, p ∂s

(11)

where the particle position s is related with time t by s˙ = ds/dt = c cos χ. For outward- (or inward-) migrating particles, cos χ > 0 (or cos χ < 0). The radiationreaction force [12, 68], PSC /c, is introduced as a friction term to compute p˙ [31]. If we integrate n± over p and χ, and multiply the local GJ number density, ΩB/2πce, we obtain the spatial number density of particles. Therefore, we can express ρe as ZZ   ΩB ρe = n+ (s, θ∗ , ϕ∗ , γ, χ) − n−(s, θ∗ , ϕ∗ , γ, χ) dγdχ. (12) 2πc In equation (10), collision terms are expressed as

What Pulsar Emission Model Survives?

S IC ≡ − +

ǫn−1 X<γ n

X

123

γ ηIC (hǫn i, γ, µc )

ηeIC (γi , γ, µc )

i

Sp ≡

Z

ZZZ

ZZZ

N± (s, θ∗ , ϕ∗ , γi , χ)d 3 p

N± (s, θ∗ , ϕ∗ , γi , χ)d 3 p,

(αγB + αγγ )

Z

Iν dωdν, hν

(13)

(14)

where hǫn i = (ǫn−1 + ǫn )/2 represents the typical photon energy within the interval [me c2 ǫn−1 ,me c2 ǫn ], µc the cosine of the collision angle between the particles and the soft photons, Iν the specific intensity of the radiation field, ω the solid angle into which the photons are R propagating. To compute S p at each point, the differential photon number flux Iν /(hν)dω should be calculated by summing up Iν /(hν) from all the directions. The absorption coefficient due to one-photon and two-photon pair production processes are given by ! e2 /¯hc me c ′ 8 1 αγB = B ⊥ exp − δ(γ − γ0)δ(χ − χ0), (15) 4.4 h¯ 3 ǫγ B′ ⊥ Z 1 − cosθc ∞ dFs ∂2 σγγ αγγ = dǫs . (16) 2 dǫs dγdχ ǫth In equation (15), θc denotes the collision angle between the photon and the magnetic field; B′ ⊥ ≡ B sin θc /Bcr . In equation (16), θc does that between the two photons. The γ IC redistribution function ηIC (ǫγ , γ, µc ) represents the probability that a particle with Lorentz factor γ upscatters photons into energies between me c2 ǫγ and me c2 (ǫγ +dǫγ ) per unit time when the collision angle is cos−1 µc , where ǫγ = hν/(me c2 ) refers to the dimensionless photon energy. On the other hand, ηeIC (γi , γ f , µc ) describes the probability that a particle changes Lorentz factor from γi to γ f in a scattering. We γ γ thus obtain ηeIC (γi , γ f , µc ) = ηIC (γi − γ f , γi , µc ). See [30] for explicit expression of ηIC and ∂2 σγγ /dγdχ. Using the dimensionless number densities, n± , we can express the spatial number densities of e± ’s as ZZZ ZZ ΩB 3 N± d p = n± dγdχ. (17) 2πce

2.3 Radiative Transfer Equation Third, we consider the radiative transfer equation. The specific intensity, Iν , varies with distance l along the ray by [31] dIν = −αν Iν + jν , dl

(18)

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where αν and jν refer to the absorption and emission coefficients, respectively. Both αν and jν are a function of position l, photon energy E γ , and propagation direction (kθ ,kϕ ), where kµ denotes the photon momentum four vector (µ = t, r, θ, ϕ). To solve equation (18) along the ray, we have to solve the photon propagation in the curved spacetime. The evolution of momentum and position of a photon is described by the Hamilton-Jacobi equations, c

dkr ∂kt =− , dl ∂r

c

dkθ ∂kt =− , dl ∂θ

c

dr ∂kt = , dl ∂kr

c

dθ ∂kt = . dl ∂kθ

(19)

The photon energy at infinity kt and the azimuthal wave number −kϕ are conserved along the ray in a stationary and axisymmetric spacetime (e.g., described by eqs. [1]–[3]). When a photon is emitted with energy Elocal by a particle with angular velocity ϕ, ˙ it is related to kt and −kϕ by the redshift relation, Elocal = (dt/dτ)(kt + kϕ ϕ), ˙ where dt/dτ is solved from the definition of the proper time, (dt/dτ)2 (gtt + 2gtϕ ϕ˙ + gϕϕ ϕ˙ 2 ) = 1. Hamiltonian kt can be expressed in terms of kr , kθ , kϕ , r, θ from the dispersion relation kµ kµ = 0, a quadratic equation of kµ (µ = t, r, θ, ϕ). Thus, we have to solve the set of four ordinary differential equations (19) for kr , kθ , r, and θ. The photons are emitted along the direction of the instantaneous particle velocity [44, 8, 9] measured by a distant static observer.

2.4 Boundary Conditions First, consider the elliptic type equation (7). To consider the magnetosphere from the PC region to the outer magnetosphere, we define that the inner boundary coincides with the NS surface, on which we put Ψ = 0 for convenience. We assume that the gap lower boundary, θ∗ = θ∗max (ϕ∗ ), coincides with the last open field line, √ √ which is defined by the condition that −grr Br sin θ + −gθθ Bθ cos θ = 0 is satisfied at the LC for each ϕ∗ . We parameterize the trans-field height with hm and put Ψ = 0 at θ∗ < (1 − hm)θ∗max . If hm ≪ 1, the gap becomes latitudinally thin, whereas hm ∼ 1 indicates that the gap occupies most of the open-field region. In this chapter, we define hm (s, ϕ∗ ) such that E k at (s,θ∗ = (1 − hm)θ∗max ,ϕ∗ ) becomes less than 0.01Ψmax /̟LC , where Ψmax denotes the maximum potential drop realized in the entire gap. We parameterize magnetic co-latitudes with h ≡ 1 − θ∗ /θ∗max

(20)

and solve the gap in 0 < h < hm ; here, h = 0 gives the last-open field line. The outer boundary is defined as the place where Ek changes sign near the LC and found to appear near the place where ∂(ρGJ /B)/∂s vanishes due to the flaring up of the field lines towards the rotation axis (eq. [67] of [31]). Second, consider the hyperbolic type equations (10). In § 3, to incorporate OG boundary conditions, we assume that e± ’s and photons do not penetrate into the gap across either the inner or the outer boundaries. However, if the created current

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becomes greater than the GJ value, a resultant positive E k at the NS surface extracts ions from the surface as a space-charge-limited flow (SCLF) so that E k may vanish at the surface; the ionic density is incorporated in equation (4) as ρion (see § 2.5 of [31] for SCLF in OG). In § 4, to incorporate PC model boundary conditions, we put ρion = 0 and evaluate ρe by its GJ value at the NS surface, because e− ’s are ejected from the surface as a SCLF.

3 Self-consistent OG solution: the case of the Crab pulsar Throughout this chapter, we consider a parallel rotator in the sense Ω · B > 0, which leads to ρGJ < 0 in p the PC region. It is reasonable to evaluate µ with its vacuum2 = 1.012I 1/2 P1/2 P ˙ ˙ −15 1/2 , where P = 2π/Ω dedipole value, µd = 3c3 IP P/8π 45 −15 −1 ˙ ˙ notes the NS spin rate, P is its temporal derivative, and P˙ −15 = P/(10 s s ). We obtain the self-consistent solution by specifying only the three parameters, α, kT , and µ, in addition to an observable, P. For an OG, we adopt α = 60◦ in this section.

3.1 Gap geometry and acceleration electric field Let us begin by presenting the solved gap geometry in the 3-D pulsar magnetosphere. In figure 3 (left panel), the gap trans-field thickness, hm , is plotted as a function of the position (s,ϕ∗ ) on the last-open field line surface. At each point (s,ϕ∗ ), Ek maximizes near the central height, h ∼ hm /2. We present such maximum values of Ek (s, ϕ∗ ) in figure 3 (right panel). It follows that E k is screened substantially in the lower altitudes because of the discharge of produced pairs, forming a striking contrast with previous OG models.

3.2 Photon mapping result and radiation spectrum We plot the photon intensity on the pulse phase Φ versus ζobs plane in figure 4. The photons emitted from the north magnetic pole would appear at Φ = 0 and ζobs = α(= 60◦ ). The left panel shows that the OG connected to the north pole emits outward-propagating photons into the southern hemisphere, ζobs > 90◦ , and into the rotation phase −140◦ < Φ < 40◦ , while inward ones into ζobs < 90◦ and 130◦ < Φ < 300◦(= −60◦). On the contrary, from the south-pole OG, inwardpropagating photons appear in ζobs > 90◦ and −50◦ < Φ < 120◦ . Thus, the intensity around ζobs ∼ 120◦ and Φ ∼ 0◦ consists of both the outward emission from the northpole OG and the inward emission from the south-pole OG (right panel). This result is consistent with phenomenological 3-D OG models [59] and self-consistent 2-D

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OG solution [61]. If we specify ζobs , we obtain the photon count as a function of the rotational phase. In figure 5, we present such light curves for three discrete ζobs . Figure 6 depicts the phase-resolved spectrum for ζobs = 105◦ , indicating that the present scheme reproduces the observations at least qualitatively. The first peak (P1) shows softer spectrum than the second peak (P2), because E k becomes small due to the flaring-up field-line geometry near the LC, because collision angles become greater between the primary γ-rays and the secondary X-rays due to the deformation of the field lines near the LC, and because E k is efficiently screened in the middle altitudes of the leading side (LS) due to the propagation of inward γ-rays towards the LS and their subsequent materialization as pairs. The tendency of soft P1 spectrum is, in fact, commonly predicted for other rotation-powered pulsars. The flux correction factor [57] becomes 3.2, 1.8, 0.88, 0.57 at ζobs = 100◦ , 105◦ , 110◦ , and 115◦ , respectively. Note that the ICS photons are emitted by the primary e+ ’s; however, they are totally absorbed by the magnetospheric IR photons to appear as the secondary synchrotron component between 100 MeV and 10 GeV. The present method (coincidentally) corresponds to a quantitative extension of previous phenomenological OG models, which assumes Ek distribution in the 3-D magnetosphere.

Fig. 3 Left: Gap trans-field thickness hm on the 2-D last-open field line surface (s,ϕ∗ ) in the selfconsistent OG solution. The white curve denotes the intersection of the null surface where ρGJ vanishes with the last-open field line surface. Right: Distribution of the maximum value of Ek [V m−1 ] near the gap center (in the meridional direction) on the last-open field line surface.

4 Slot-gap model: the case of the Crab pulsar We apply the same scheme described in previous sections to the SG model, a geometric thin version of the pair-starved polar-cap (PSPC) model. We briefly review the SG formation in section 4.1, then in 4.2-4.3, we first re-examine the SG model

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Fig. 4 Phase plot of the photons having energies above 90 MeV in the self-consistent OG solution. Left: Emission from the north-pole OG alone. Right: Emission from the both poles.

Fig. 5 Pulse profile for ζobs = 95◦ , 105◦ , and 115◦ for the Crab pulsar with α = 60◦ in the self-consistent OG solution. The ordinate denotes the photon energy flux per rotational phase in MeV s−1 cm−2 deg−1 unit.

[48, 49, 24] by our code, which can be commonly applied to both OG and SG models. To compare the results with [24], we adopt α = 45◦ for the SG model.

4.1 Formation of a slot gap in the polar-cap region For a parallel rotator, in a PC SCLF model, e− ’s are extracted at a slightly smaller rate (in an absolute value sense) than the GJ rate, cρ∗GJ , where ∗ denotes a quantity evaluated at the NS surface. Provided that the particle motion is stationary in the co-rotating frame and that pair production does not take place, we find that the real charge density per magnetic flux tube, j/B ∝ ρe /(ΩB/2πc), conserves along the field line; the situation is depicted by the thin green dashed line in figure 7. How about the GJ charge density per magnetic tube, ρGJ /(ΩB/2πc)? Along the magnetic field

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Fig. 6 Phase-resolved spectrum of the pulsed emission from the Crab pulsar in the self-consistent OG solution. The thin solid curves denote the primary photon fluxes, while the thick red solid ones include absorption and subsequent reprocesses. Interstellar absorption is not considered. The filled circles (LECS), open circles (MECS), filled triangles (PDS) denote the Boppo SAX observations, while the open triangle the Gamma-ray Imaging Spectrometer (GRIS), and inverse filled triangles (OSSE), diamonds (COMPTEL), and filled squares (EGRET) denotes the CGRO observations. Data points are from [38] [http://www.sron.nl/divisions/hea/kuiper/data.html].

lines curving away from the rotation axis, its Newtonian GJ value, −Bζ /B, where Bζ denotes the magnetic field component projected along the rotation axis, increases outwards, as indicated by the thin black dotted line. As a result, at the altitude much less than the stellar radius, ρeff ≡ ρGJ − ρe changes sign from negative to positive outwards, leading to a sign reversal of Ek from negative to positive, thereby terminating the gap. (Exactly speaking, the place where Ek changes sign depends not only on the sign of ρeff but also on the trans-field structure; nevertheless, this argument of gap termination is qualitatively correct in any case.) Thus, it had been considered that a PC accelerator is not active along the polar field lines curving away from the rotation axis because of its localized geometry in the vicinity of the NS surface [2]. Subsequently, [47] pointed out that an energetic PC accelerator can exist along such away-curvature field lines due to general relativistic (GR) effects, because ρGJ /B deviates from the Newtonian value due to the Ω − ω factor (instead of Ω) in the right-hand side of equation (8), as indicated by the thin black solid curve in figure 7, where P = 33 ms, r∗ = 10 km, and α = 60◦ are assumed. Since the SCLF has ρe /(ΩB/2πc) as indicated by the thick green solid line for this revised PC model, a negative-definite ρeff , which ensures a negative-definite Ek , extends up to a greater altitude than the Newtonian case. Thus, a PC accelerator exists within the altitude comparable to the NS radius around a rapidly rotating NS. The resulting potential drop is found be enough to reproduce high energy emissions (for details, see [48] and references therein). In spite of these attractive features on energetics, the GR-PC accelerator is still localized within a few stellar radii even for millisecond pulsars. Thus, the emission solid angle is too small to reproduce the wide pulsed profiles that are observed. They were, therefore, motivated by the need to contrive a higher altitude emission model.

Fig. 7 Charge density per magnetic flux tube along the last-open field line that crosses the NS surface at ϕ∗ = 0, thereby curves away from the rotation axis. The black solid curve denotes the GJ charge density (eq. [8]) for a dipole magnetic field with GR corrections, while the black dotted one the Newtonian value. In the PSPC model, the GJ charge distribution is assumed to change from the actual value (black solid line) to the red solid line.

charge density / (ΩB/2πc)

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c) / 2π B /(Ω

-0.28 -0.32

ρ GJ ual act

GR PC accelerator

assume

ρ /(ΩB/2πc)

ρGJ /(ΩB/2πc) in PSPC model

-0.36 -0.40

Newtonian PC accelerator

1 2 3 distance along fieldline / NS radius

4.2 Lower-altitude slot-gap solution

Fig. 8 PFF height, hm , on the last-open field line surface in the lower-altitude SG model. Note that the abscissa is normalized by NS radius, not by ̟LC . The minimum value is 0.01250. In the reddened region, PFF becomes parallel to the NS surface; thus, the gap exists over the entire PC surface.

magnetic azimuth ϕ* [rad]

We re-examine the SG model of [48] by applying the same numerical code as we used in § 3. [48] demonstrated that the pair-formation front (PFF) becomes almost parallel to the NS surface in the central part of the PC (i.e., near the magnetic axis) and that the PFF rapidly curves up to become almost parallel to the last-open field line above several per cent of r∗ for a rapidly rotating, highly magnetized NS. We confirmed their results by our code as indicated by figure 8, which presents the height, hm , of the PFF measured in meridional direction from the last-open field line as a function of s and ϕ∗ . Close to the star, the SG structure is found to be almost independent of ϕ∗ . It is also confirmed that the potential drop, which attains ∼ 1.5 ×1012 V along the field lines threading the higher-altitude SG (e.g., at h = 0.02, see next subsection for details on the high-altitude SG), is consistent with [48] (their eq. [47]). The electrons are accelerated up to the Lorentz factor of ∼ 3 × 106 at s ∼ 0.08r∗ . 0.017 0.0165 0.01251

distance along field line / NS radius

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4.3 Higher-altitude slot-gap model The SG solution described just above exists only within the region in which ρeff = ρGJ − ρe < 0 holds to guarantee a negative-definite E k throughout the gap. The pair-free SG extends, therefore, only up to the altitude rc ∼ 1.2r∗ in the case of the Crab pulsar, because ρe /B is conserved along the field line, as indicated by the thick green dashed line in figure 7. However, if the SG extends only up to such an altitude, the problem of the small emission solid angle occurs in the same way as in PC models. Thus, [49] examined the possibility of an extension of the SG into the higher altitudes, which corresponds to an hybrid scenario of PC and OG geometrical models. However, unlike the OG solution (§ 3), or unlike the lower-altitude SG solution (§ 4.2), the higher-altitude SG model cannot be constructed without additional assumptions. We thus describe them in sections 4.3.1 and 4.3.2, then turn to a re-examination of the high-altitude SG model of [49, 24] in sections 4.3.3 and 4.3.4. 4.3.1 Additional assumption: GJ charge density To extend the SG into the higher altitudes, [49] assumed that ρGJ /B remains constant with s at higher altitudes, as indicated by the red solid curve in figure 7. Their rationale is that the cross-field toroidal motion of e− ’s would effectively screen out the excessive GJ charges and would maintain ρGJ /B at some constant value in the higher altitudes. However, it is not easy to understand why ρGJ , which is purely defined by the magnetic-field and space-time geometries (eq. [8]), can be modified due to the cross-field motion of charges, or to the surface charges on the last-open field lines. For example, if charges are supplied into the gap or if electrons escape from the SG by cross-field motion, they only change the ρe in the right-hand side of equation (8). The surface charges do result in a jump of E ⊥ across the last-open field lines; however, it does not modify the right-hand side of equation (8) at all in the gap. Nevertheless, it is true that a SG could not be extended into the higher altitudes without assuming a negative-definite effective charge density, ρeff = ρGJ − ρe , from the NS surface to the outer magnetosphere. Thus, we follow the assumption proposed by [49] (their eqs. [28]-[30]), as depicted by the red solid curve in figure 7. In our notation, it is equivalent with adopting (eq.[38] in [49]) (" ! # r3 ρeff Ω =− κ β − ∗3 + 1 − β cos α B 2πc rc  s      H(rc ) rc f (r∗ )   3  + H(r∗ )θ∗max  − β sin α cos ϕ∗  , (21)   2 H(r∗ ) r∗ f (rc )  where rc ∼ 1.2r∗ , κ ∼ 0.15 describes the space-time dragging effect, β, H, f are close to unity, β = (1 − 3r/4̟LC)1/2 , H(r) ∼ 1 − 0.1x − 0.026x2 − 0.075x3 + 0.019x4 , f (r) ∼ 1 + 0.3x + 0.096x2, with x = r∗ /r. Note that equation (21), and hence equation

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(38) in [49], is not derived from any basic equations. It is purely derived by assuming that ρGJ has a spatial dependence as equation (20) in [49], which is valid only near the PC surface, and that ρeff nearly saturates at some negative value above r = rc (see the description just above eq. [37] in [49]). In § 5, we will discuss that the same problem arises in the geometrically thick version of PSPC [66], which was recent proposed. 4.3.2 Additional assumption: trans-field thickness We assume that the co-latitudinal thickness is constant at hm = 0.04 in the higheraltitude SG, in the same manner as in [49, 24]. If e− ’s are extracted and accelerated in the lower-altitude SG, it may be natural to suppose such a small hm is realized in the higher altitudes, because the pairs produced outwardly in the PFF will migrate outwards to efficiently screen Ek in the higher altitudes. For instance, in the lower altitudes, hm < 0.017 is obtained in figure 8, or hm ≪ 0.01 is obtained by [48] (their fig. 2). 4.3.3 Acceleration electric field Let us now turn to the discussion of the results of higher-altitude SG model (or equivalently geometrically thin version of PSPC model), adopting the assumption described in the foregoing two sections, and applying the numerical code used for the OG and the lower-altitude SG models also to the higher-altitude SG model. We present Ek distribution for the Crab pulsar with µ = 4 × 1030G cm3 in figure 9. It follows that |Ek | increases with increasing altitude, because |Ek | given by equation (4) in [24] contains a term that increases with the altitude. Note that the Ek in the PSPC model is directly derived from the assumed ρeff (i.e., eq. [21]), instead of solving it from the particle Boltzmann equations. 4.3.4 Insufficient luminosity from the SG Using both the lower- and higher-altitude SG solutions, we map the photon intensity as a function of the pulse phase Φ and ζobs in figure 10. Only the photons having energies greater than 90 MeV are plotted. The yellow rings around the north pole (at ζobs = α = 45◦ and Φ = 0◦ ) and the south pole (at ζobs = π − α = 135◦ and Φ = 180◦) indicate the photons emitted from the lower altitudes. Because |Ek | increases with increasing altitude, caustic is formed by the emission from the middle and higher altitudes. The photon mapping result is consistent with figure 5 of [24]. If we specify ζobs , we obtain the photon count as a function of Φ. In figure 11, we present the pulse profiles for ζobs = 90◦, 100◦ , and 110◦. It follows that the observed double-peak pulse profile can be reproduced if we adopt ζobs ∼ 95◦ .

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We present the phase-averaged spectra for ζobs = 95◦ , 105◦ , 115◦ , and 125◦ in figure 12. The lower-altitude SG emission that is due to the synchrotron process from the cascaded pairs above the polar-cap PFF and becomes important below 10 MeV, is not depicted to clarify the primary SG emissions. It follows that the SG reproduces only several per cent of the observed flux for a moderate of ζobs. The lack of flux is solely because the SG thickness, hm , is much less than unity. This numerical conclusion is consistent with the analytical one [34]. The same difficulty of insufficient luminosity arises for other pulsars, if we adopt the SG model. This is because the analytic expression (eq. [10] in [34]) can be applied to arbitrary pulsars. In general, a gap having such a thin trans-field thickness as h < 0.05, irrespective of whether it is an OG or a SG, cannot reproduce enough γ-ray flux that is observed, unless the particle number density greatly exceeds the GJ value. The only exception could be nearby, young pulsars, which may emit detectable γ-ray flux from a geometrically thin (hm < 0.05) gap.

-1 16

-2 -1 8

-8 0

Fig. 10 Gamma-ray phase plot in the SG model. The abscissa denotes the NS rotation phase Φ, whereas the ordinate the observer’s viewing angle, ζobs . The red ring around Φ ∼ 0 and ζ ∼ α represents the north-pole, lower-altitude SG emissions, whereas the red caustics do the higher-altitude SG emissions.

[10 MeV s cm deg ]

Fig. 9 Acceleration field E k [V m−1 ] distribution, which is computed by equation (21), in the higher-altitude SG model. The maximum value of Ek in the (meridional) transfield direction is plotted on the last-open field line surface (s,ϕ∗ ). The white solid curve represents the null surface position.

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Fig. 11 Pulse profile for three different viewing angles, ζobs , in the higher-altitude SG model. Only the photons having energies greater than 90 MeV are taken into account. The ordinate denotes the photon energy flux per rotational phase in MeV s−1 cm−2 deg−1 unit.

Fig. 12 Phase-averaged spectrum of the Crab pulsar in the higher-altitude SG model at four discrete observer’s viewing angles, ζobs = 95◦ (black solid), 105◦ (red dashed), 115◦ (blue dotted), and 125◦ (green dash-dotted). The ordinate denotes the photon energy flux in MeV s−1 cm−2 unit.

5 Discussion It is demonstrated in § 4.3.1 that a negative Ek in the higher-altitude SG model is derived under the assumption of a constant ρGJ /B (fig. 7), which is inconsistent with the Maxwell eq. (4). The same problem, in fact, arises in the geometrically thick version of PSPC [66], because they adopt the same Ek . It might be possible to argue that ρe /B (instead of ρGJ /B) changes along field line so that |ρeff /B| ≪ |(ρGJ /B)∗| holds, leading to a weak Ek from lower to higher altitudes, as a small deviation from the force-free magnetosphere. However, if Ek is negative as required in the PSPC model, a small amount of pair production leads to the increase of ρeff /B = (ρGJ − ρe )/B outwards (from a negative value), resulting in the reversal of the sign of Ek . This is because e+ ’s return inwards while e− ’s migrate outwards when the produced pairs discharge, leading to a decrease of ρe /B outwards. The same difficulty of outwardly decreasing ρe /B arises, if positive, negative, or both charges are somehow injected into the PSPC accelerator (e.g., by cross-field motion). Note that such a difficulty does not arise in the OG model. Pairs are produced when inward γ-rays collide with outward X-rays in an OG. Due to the discharge in a positive Ek , e+ ’s return outwards while e− ’s migrate inwards, leading to an outwardly increasing ρe /B, which is self-adjusted so that a small-amplitude, posi-

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tive ρeff /B, and hence Ek , is maintained in the inner part of an OG (as solved and demonstrated in fig. 5 of [31]). Thus, Ek sign does not change in an OG, leading to an extended OG from the vicinity of the NS to the outer magnetosphere. In short, it is a positive Ek that is naturally maintained when ρGJ /B is increasing outwards (as commonly assumed in OG and PSPC models). The PSPC model, which requires Ek < 0, is vulnerable to pair production, or to any injection of charges into the gap. Acknowledgements The author is grateful to Drs. D. F. Torres and N. Rea for support and hospitality. He is also indebted to Drs. K. S. Cheng and A. K. Harding for valuable comments and constructive criticisms. This work is supported by the Theoretical Institute for Advanced Research in Astrophysics (TIARA) operated under Academia Sinica and the National Science Council Excellence Projects program in Taiwan administered through grant number NSC 98-2752-M-007006-PAE.

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Current Models of Pulsar Magnetospheres Anatoly Spitkovsky

1 Introduction Pulsar magnetospheres are filled with plasma, and the presence of plasma affects all macroscopic and microscopic properties of the magnetosphere. Although this simple fact was well known since the early days of pulsar research, the ability to quantitatively model plasma effects has emerged mainly in the last decade. This review highlights the main properties and consequences of the current models of pulsar magnetospheres (or, rather, of “magnetospheric models with currents”). The first part concentrates on the influence of plasma currents on the magnetospheric structure, while the second part discusses the emerging picture of pulsar high-energy emission in which strong magnetospheric currents make a surprising contribution. Generally speaking, the models of pulsar magnetospheres can be classified according to the amount of plasma supply they assume. At one extreme is the vacuum magnetosphere, which is modeled with the magnetic field of a spinning dipole in vacuum [10]. Of course, as this solution has no plasma, it has no possibility of producing any pulsar-like emission. However, the fact that this field is described by an analytic formula, has made it the most widely used framework for calculating pulsar properties. For example, the characteristic spin-down energy loss which yielded the fiducial pulsar field strength of 1012G or the polarization sweep of the rotatingvector model are guided by the vacuum field shape. The next order of approximation are models that allow plasma emission from the surface of the star. These include the original charge-separated model of Goldreich and Julian ([18], hereafter GJ), and the space charge-limited models with pair formation (e.g., [1]). These models have both regions that are filled with plasma that shorts out accelerating electric fields and regions where acceleration is present (so-called “gaps”). This approach allows for more realism in studying plasma creation and acceleration, but at the price of being decoupled from the global structure of the magnetosphere. Finally, the class of Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_11, © Springer-Verlag Berlin Heidelberg 2011

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models that concentrate on the global magnetospheric properties assume that abundant plasma exists throughout the magnetosphere and in the wind. This plasma can short out accelerating electric fields and provide corotation of field lines with the star. These models include relativistic MHD description of the magnetosphere and its limit for magnetically-dominated plasmas, the “force-free” models. Which of these different regimes is applicable for real pulsars may ultimately depend on the way plasma is introduced in the magnetosphere, and we turn to this question first.

2 Plasma supply and charge-separated models The first attempt at solving the magnetospheric structure and the problem of plasma supply was made by Goldreich and Julian (GJ) [18], who noticed that the unipolar induction electric fields on a rotating magnetized star are going to pull particles off the surface and fill the magnetosphere with plasma that has net charge density ηGJ = ∇ · E/4π = Ω · B/2πc. This charge density is needed to maintain corotation of the magnetic field lines with the star by forcing the accelerating fields E|| = E · B/B to zero. The GJ model is charge-separated, meaning the plasma density is assumed equal to the GJ charge density everywhere. If the plasma is moving at c, the associated current density ηGJ c is of the right order to cause the toroidal magnetic field at the light cylinder to be equal to the poloidal field. The corotation induces poloidal electric field E p ∼ (Ωr/c)B p, and the resulting outward Poynting flux E˙ rot = cE × B/4π is dominated by the poloidal electric and toroidal magnetic field and leads to the net energy loss from the system. Thus, even an aligned rotator, which has no time-dependent magnetic or electric fields that are needed for vacuum energy loss, can spin down in the presence of plasma. The magnetospheric structure of GJ model is shown in fig. 1a. The GJ magnetosphere consists of closed and open field lines. The last closed field line touches the light cylinder. The plasma on the closed field lines corotates with the star, and streams away on the open field lines, which are asymptotically straight in the poloidal direction. The open field lines also carry the toroidal field and the current needed for the spin down. These gross properties of the magnetosphere make physical sense, and were held to be true for years, even though the actual self-consistent solution escaped many analytical and numerical attempts. One should note that the GJ density nGJ = ηGJ /e is only the minimum plasma density required for corotation; the magnetosphere most likely is populated by much denser plasma. This plasma is generated from pair creation cascades, initialized by curvature and inverse compton gamma rays emitted by particles that accelerate from the surface [57, 1]. The typical “multiplicity” of such pair cascades can raise the plasma density to 104 nGJ in young pulsars. This is corroborated observationally by the requirement that the particle injection into pulsar wind nebulae exceed the GJ flux by a similar factor [10]. Thus, considerable attention has been devoted to magnetospheres filled with dense plasma. Despite being the foundation of the magnetospheric research, the GJ picture may not be viable, at least in the charge-separated regime. Consider the following setup:

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a)

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b)

Fig. 1 a) Schematic shape of the magnetosphere from the Goldreich-Julian model [18]; b) Chargeseparated electrosphere with domes of electrons and a differentially rotating disk of positrons/ions [52].

given a conducting rotating sphere with a dipole magnetic field and free escape of particles from the surface, can this system generate currents and spin down? At first sight this is the setup for the original GJ model, where a charge-separated outflow is expected to form. The problem, as seen from fig. 1a, is that on some field lines the charge separated flow of electrons should turn into protons (or positrons) at the null surface [27]. Thus the GJ flow without pair formation cannot be in a steady state. Indeed, several simulations [31, 51, 52] found that instead of forming an outflow, the rotating sphere is surrounded by electron “domes” near the poles and an equatorial ion “disk” (fig. 1b). These structures extend out to a few stellar radii, and are separated by vacuum regions. This external charge density compensates the vacuum accelerating field on the surface, and particles are not accelerated to the gamma-ray emitting energies. This solution is also stable to artificially induced bursts of pair formation[51]. The charge-separted plasma is not in complete corotation with the star, and the equatorial disk undergoes a diocotoron (nonneutral Kelvin-Helmholtz) instability because of the differential rotation [52, 43, 44, 45]. Over tens of rotational periods, the equatorial plasma drifts in radius, diminishing the differential rotation. This mechanism forms a way of filling the magnetosphere with GJ-like charge density, even though some of the regions are not directly accessible by appropriately charged field lines from the star. There is even a radial current flow, associated with this transport, although it is not enough to be responsible for pulsar action. Moreover, when the particles reach the light cylinder, the electrostatic diocotron instability switches to the electromagnetic magnetron mode, with smaller growth rates [46, 47]. Where such electrospheres fit into the grand scheme of things is not yet clear. They may represent what happens to neutron stars beyond the death line, or may be the intermittent process for establishing corotation in the closed zone of an active pulsar. The time scale of the instability is also interesting in the context of drifting subpulse phenomena. So far, however, the electrospheres have not been

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demonstrated to drive interesting spin down currents. Perhaps this will change with more realistic simulations, in particular 3D simulations with pair formation. One important property of the GJ magnetosphere is that the energy of the magnetospheric plasma is much smaller than the energy in the magnetic field. Even at the light cylinder, the plasma contribution is one part in 104 for young pulsars. The bending of the field lines at the light cylinder is thus not due to the inertial contribution of the plasma, but rather due to the “inertia” of the field. Magnetic domination allows a simplification of the MHD equations to the low-inertia, or “force-free” limit, described below1 .

3 Force-free models In the presence of dense plasma, all accelerating fields are quickly shorted out so that the ideal MHD condition E · B = 0 holds everywhere. The structure of the magnetosphere is then determined by the equilibrium of forces acting on the plasma. In the limit of small plasma inertia and temperature, the right hand side of the momentum equation becomes ρE + 1c j × B = 0, or “force-free”. Significant effort was directed over the years to finding a steady-state axisymmetric solution for the mgnetospheric structure of an aligned rotator subject to these constraints. Introducing flux function ˆ c and writing the corotation electric field Ψ such that poloidal field is Bp = ∇Ψ × φ/r ˆ the force-free constraint can be reduced to as E = rc Ωc−1 Bp × φ, # ∂2 Ψ ∂2 Ψ 1 + x2 ∂Ψ (1 − x ) + − = −I(Ψ)I ′ (Ψ). x ∂x ∂x2 ∂z2 2

"

(1)

Here, x ≡ rc /R L and z ≡ zc /R L are scaled cylindrical coordinates, and I(Ψ ) is the unknown function proportional to the polodial current enclosed by the flux surface Ψ. Known as the “pulsar equation” [38, 50], eq. (1) is a nonlinear second order elliptic equation with a regular singularity at the light cylinder x = 1. The current distribution I(Ψ ) is a priori unknown and should be determined as part of the self-consistent solution. This nonlinearity makes it a very difficult problem. Analytic solutions for the pulsar equation are known only for a monopolar magnetic field [38], and for a corotating dipole magnetosphere without a current [39]. A great advance was made in 1999 by Contopoulos, Kazanas & Fendt ([15], hereafter CKF) who solved the pulsar equation numerically for a dipole magnetic field. They used an elliptic solver to solve eq. (1) both inside and outside the light cylinder for a trial current distribution. In general, such a solution has an unphysical kink in the magnetic field at the light cylinder. A clever iterative algorithm that adjusted the current function to minimize the discontinuity allowed CKF to find a solution that passed smoothly through the light cylinder. This solution, shown in fig. 2, has a corotating closed zone and an open wind zone, with poloidal fieldlines asymptotically becoming monopolar, and toroidal field dominating at infinity. There are no distributed dissipative regions 1

The following chapter follows closely the discussion in [63]

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where E>B beyond the light cylinder, as was expected when early analytic solutions failed [37]. The last open field line corresponds to Ψopen = 1.36Ψ pc where Ψ pc ≡ µ/RL is the flux through the polar cap for the unperturbed vacuum dipole field. a)

b)

Fig. 2 a) Numerical solution of the steady-state pulsar equation using CKF method [15]. Figure from [20]; b) Steady-state poloidal magnetic field lines from a time-dependent aligned rotator simulation [55]. Toroidal field is marked in shades.

The magnetosphere supports an active current system: current is flowing along the open field lines to infinity, and the bulk of return current flows in the equatorial current sheet and on the boundary of closed and open zones, although a 5% fraction is distributed along a set of open field lines near equator (1.08Ψ pc < Ψ < 1.36Ψ pc). The CKF solution was later studied at finer resolution by Gruzinov [20], who calculated the open flux to be 1.27Ψ pc and the energy loss for the aligned rotator to be (1 ± 0.1)µ2Ω4 /c3 . He also obtained analytical expressions for the opening angle of the tip of the closed zone, where the current sheet splits into two (the Ypoint). The Y-point in these solutions is fixed to be at the light cylinder from the outset. However, this does not have to be the case. In fact, Timokhin [58] numerically found a family of solutions where the Y-point could be anywhere inside the light cylinder. Such magnetospheres spin down faster (according to eq. [??]), but otherwise seem accessible and physical. Besides the expectation that the magnetosphere should choose the lowest energy solution, it was not obvious which of these possibilities would exist in nature. The best way to address this was to solve an evolutionary, rather than a boundary value problem. This was done with the advent of time-dependent simulations. The MHD condition E · B = 0 and Maxwell equations can be combined with the force-free constraint to yield an evolutionary system of equations [40, 19, 6]:

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1 ∂E 4π 1 ∂B = ∇ × B − j; = −∇ × E; c ∂t c c ∂t c E × B c (B · ∇ × B − E · ∇ × E)B j = (∇ · E) 2 + . 4π 4π B B2

(2) (3)

This system has been called “force-free electrodynamics,” “magnetodynamics” [29], or “force-free relativistic MHD.” The philosophy behind the equations is very simple: the evolution is driven by the strong electromagnetic fields; however, the plasma, while having negligible inertia, does affect the fields through charges and currents. Unlike the full MHD equations, the small terms associated with the plasma inertia do not enter, and thus the system is not stiff in the highly magnetized regions. The plasma is assumed to move with the E × B velocity perpendicular to the fields; the velocity along the magnetic field is not defined. Eq. 3 serves as the prescription for the plasma current, and has the contributions from charge advection normal to the field and conduction current along the field. Unlike in the pulsar equation, there are no critical points in the system (2-3); yet the evolution from quite regular initial conditions can form discontinuities, or current sheets, and regions where E > B. The most difficult current sheets are the ones where magnetic field goes through zero. In those cases, the fundamental assumption of magnetic domination implicit in the derivation is invalid, and formally one has to resort back to the full MHD equations. In practice, one can deal with current sheets numerically by adding resistivity [29, 55], although there is some freedom in selecting a viable resistive formulation. Time-dependent magnetospheric simulations of the axisymmetric rotator have now been done by several groups [29, 36, 55, 28]. Typical initial conditions are a rotating conducting sphere with dipole magnetic field immersed in a force-free plasma. All groups generally agree on the outcome, although the details depend on the diffusivity of the codes. The time-dependent evolution settles into CKF-like state after a transient. This transient is interesting because in the ideal force-free formulation the topology of the field lines cannot change, so in order to transition from closed to open geometry, the field lines have to be stretched so that they close at infinity. The initial evolution does try to propagate a pulse that stretches the field lines (in the poloidal plane) and after a quarter of a turn an equatorial current sheet forms, because the field drops to zero in the equator (see ref. [54], fig. 1). After the transient, the Y-point settles very close to the light cylinder (fig. 2b). The spin down power measured in simulations for a star with magnetic moment µ is µ2 Ω4 /c3 . Komissarov [29] addressed the same problem with a full relativistic MHD code. That simulation produced the same gross magnetospheric shape and the Y-point near the light cylinder as the force-free simulations, although the conditions in the inner magnetosphere had to be artificially constrained to be numerically tractable. Simulation by Bucciantini et al. [9] also found similar results in the MHD regime at large magnetizations of thermally driven MHD winds from neutron stars. As a result of many numerical experiments, it appears that all signs point to the CKFtype solution being the natural steady state for an aligned rotator. The consequences of this will be investigated in the next section. Since pulsars must necessarily have finite obliqueness angle between the rotation and magnetic axes in order to pulse, the most general case of interest is that of the

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oblique rotator. The time-dependent force-free formulation allows one to solve the 3D problem as well. The difficulties are again associated with the formation of current sheets. For the oblique rotator, the current sheets are not aligned with the grid, and the numerical method has to be able to capture such structures. In [55] this was done on a 7003 cartesian grid for a range of inclination angles. The resulting magnetospheric shape is shown in fig. 3 for a 60◦ inclined rotator after 1.2 turns of the star. After this time the solution becomes nearly steady in the corotating frame 2 . Although the magnetospheric structure is intrinsically 3D, some insight can be gained from considering the shape of the field lines in the corotating frame in the plane defined by µ and Ω vectors. In this plane the field lines are reminiscent of the CKF solution with a closed and open zone and a current sheet. The main difference is that the current sheet oscillates about the rotational equator in a wedge with the opening angle of 2α and the wavelength of 2πRL . The field lines in this plane become straight beyond the light cylinder, corresponding to the inclined split-monopole solution found by Bogovalov [5]. For comparison, the fieldlines of a rotating dipole in vacuum look dipolar in µ-Ω plane out to two light cylinder radii, with no open zone or a current sheet. In the force-free solution the current sheet starts at the intersection of the light cylinder with the closed zone even in the oblique case. In the perpendicular plane the field is increasingly toroidal, reversing the sign in the current sheet (fig. 3b).

a)

b)

Fig. 3 Oblique pulsar magnetosphere with magnetic inclination α = 60◦ in the corotating frame: a) Magnetic fieldlines traced in the µ-Ω plane. Color is the magnetic field perpendicular to the plane; b) Slices through the 60◦ magnetosphere. Shown are fieldlines in the horizontal and vertical plane, color on the vertical plane is the perpendicular field, on the horizontal plane – toroidal field. Sample 3D flux tube is traced in white. From [55].

Having the global 3D solution, one can numerically integrate the escaping Poynting flux and measure the spin down energy loss as a function of inclination angle. The measured values are well fit by the formula [55]: 2

Kalapotharakos & Contopoulos (2010) tested this assumption with much longer simulations with radiating boundary conditions and converged on essentially the same solution

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a)

b)

Fig. 4 Oblique pulsar magnetosphere with magnetic inclination α = 60◦ in the corotating frame: a) Conduction current parameter λ [21] as color on a plane and on the star, with field lines traced in the µ − Ω plane, demonstrating the structure of the current sheet; b) Several slices through the magnetosphere, showing the λ parameter as color, with traced last closed field lines (white).

Lpulsar = k1

µ2 Ω4 (1 + k2 sin2 α), c3

(4)

with coefficients k1 = 1 ± 0.05 and k2 = 1 ± 0.1, or roughly L ≈ µ2 Ω4 /c3 (1 + sin2 α). This formula is a fit to a numerical result, not an analytically derived formula. The errors come from uncertainties associated with the current sheet, which causes some energy to disappear from the simulation as a function of radius. The angular dependence of the spin down should be compared to the commonly used vacuum result, which scales as 2/3 sin2 α. Obviously, eq. 4 gives the right limit for the aligned rotator, consistent with the axisymmetric simulations, and predicts that the 90◦ rotator loses twice as much energy as the aligned one. In-depth study of the 3D magnetosphere is complicated by difficulties in unambiguously identifying flux surfaces in 3D. While individual field lines can be easily traced, meaningful association of different field lines as belonging to a “flux tube” is more involved. An interesting development on this front was made by Gruzinov [21], who derived an invariant of the 3D analog to the pulsar equation: ∇ × (B + V × (V × B)) = λB,

(5)

where V = Ω × r. The quantity λ is conserved along field lines, B · ∇λ = 0. In the axisymmetric case, λ reduces to the integrated current enclosed by a flux tube, I(Ψ ). In 3D, λ is also related to the conduction current: the quantity λB is the field-aligned conduction current density in the corotating frame. Indeed, in the corotating frame, the electric field vanishes, and the force-free condition reduces to the non-relativistic j × B = 0, so the current flows along B in that frame. Isosurfaces of λ can be used to define flux surfaces in 3D, although these flux surfaces do not correspond to open or closed field line bundles. The quantity λ is very useful in marking the location

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of the current sheets and Y-points in 3D. In Fig. 4a, we plot the values of λ in a plane containing µ and Ω. It is clear that λ is conserved along the field lines and large current appears near the edge of the closed field lines and in the oscillating current sheet beyond the light cylinder. In Fig. 4b I plot several slices through the magnetosphere together with the tracing of the last closed field lines to give the impression of the 3D shape of the current sheet.

Fig. 5 Structure of the current (parameter λ) of the force-free magnetosphere in the Ω − µ plane for magnetic inclination angles α = 0◦ , 30◦ , 60◦ and 90◦ respectively. Arrows show the direction of the projected magnetic field in this plane [3].

Fig. 6 The shape of the polar caps in force-free field (solid lines) and the Deutsch field (dashdotted lines) for magnetic inclination angles α = 0◦ , 30◦ , 60◦ and 90◦ (left to right). Overlaid are the color plots of the current to flux ratio λ on the pulsar surface. To better visualize λ, the size of the pulsar is set to be 0.25RLC [3].

In [3], we analyzed the properties of the force-free solution as a function of inclination of the magnetic axis. The main findings can be illustrated in Figs. 5 and 6, where we show the structure of the current in the µ − Ω plane and the current distribution on the polar cap for different inclinations. The transition of current structure is smooth as inclination angle α increases from 0◦ to 90◦ . In Fig. 5, we see that

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at small inclination angle, α = 30◦, the pattern of λ is similar to the axisymmetric case, and the current sheet inside the LC appears slightly wider and weaker. As the inclination angle increases, the distribution of current becomes very asymmetric, and more current is returned to the polar cap through the distributed flow rather than the current sheet. The current flow in the polar cap is predominantly of one sign (e.g., ingoing) for the aligned rotator, bounded by a strong current sheet of opposite sign (e.g., outgoing), and is symmetric with respect to the equatorial plane. In contrast, when α = 90◦ , the current flow has different signs in the northern and southern halves of the polar cap (better seen in Fig. 6), and the current distribution is anti-symmetric with respect to the equatorial plane. On the periphery of the polar cap there are thin current layers, as shown in red (upper) and blue (lower) oval structures in the right panel of Fig. 5. The current in these current layers forms loops connecting the two poles through the closed zone. Integrating over the polar cap, we find that the amount of current flowing to the other pole is about 20% of the current flowing on open field lines. Such closed current loops for orthogonal rotators are qualitatively consistent with predictions of the model by [24], although we find the amount of current shunting to the other pole to be smaller in our simulations. The total current on the open field lines (integrated by magnitude) is just 20% smaller for the orthogonal rotator than for the aligned rotator, suggesting that the current density for the orthogonal rotator exceeds the simple expectation of the speed of light times local GJ density on the polar cap. This current cannot be provided by charge-separated flow alone and requires abundant pair formation. The details of the current adjustment in such polar caps are still uncertain [35]. A thin current sheet outside the LC exists for all inclination angles; its structure asymptotically approaches the rotating split monopole solution outlined by Bogovalov [5]. If the current sheet outside the LC is connected to the star, it must be connected through a current sheet inside the LC, because the current flow in the corotating frame cannot cross magnetic field lines. In fact, the amount of current in the current sheet outside the LC that is connected to the star monotonically decreases with inclination angle (see Appendix B in [3]). This is related to the degradation of the current sheet inside the LC and the thickening of the Y-region for oblique rotators shown in Fig. 5. These features are unlikely to be caused by numerical resistivity, and we have tested that the thickness of the Y-region and the strong current layers inside the LC is not sensitive to numerical resolution. For the orthogonal rotator, the current sheet outside the LC is totally disconnected from the star. Therefore, the oval structures in the right panel of Fig. 5 are most likely the current loops that connect the two poles, rather than current sheets connecting to the outer magnetosphere. This strongly contrasts with the case of the aligned rotator, where the current sheet inside the LC unambiguously exists and connects to the equatorial current sheet outside the LC. While there are definitely strong currents flowing on the periphery of the open field lines for all other inclinations seen from Fig. 5, determining whether their thickness is finite or infinitesimal would require further study, so calling them “strong current layers” rather than “current sheets” is probably more correct.

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From Fig. 6 we see that the polar cap of the FF field encloses the current flowing into and out of the pulsar. For simplicity we defined the polar cap as the locus of field lines that extend to the light cylinder, although more precisely it should be the field lines that extend out to the Y-point. The polar current switches from flowing into the NS at α = 0◦ , to equal halves of oppositely-directed current at α = 90◦ . The peak of the current density slightly lags the zero phase (i.e., the phase of the magnetic pole) due to pulsar rotation. For aligned rotator, the rim of the polar cap corresponds to the footprint of the current sheet, as expected. As α increases, the strong current thickens on one side (lower side in Fig. 6), and weakens on the other side. The thickened part may no longer count as a current sheet, as it gradually occupies half of the polar cap to become the main contributor of the polar current at α = 90◦ . The weakened side gradually shifts to the outside of the polar cap (at α = 90◦ ), and forms the current loop in the closed field lines as seen in the rightmost panel of Fig. 5. The current sheet covers a circle on the polar cap for the aligned rotator. For oblique rotators, the region covered by the current sheet on the polar cap reduces to an arc covering the upper part of the polar cap in Figure 6. The extent of the arc-like region shrinks with inclination angle α, consistent with the reduction of star-connecting current in the current sheet outside the LC. In the mean time, some current in the arc-like region on the polar cap becomes connected to the other pole, forming current loops. This is associated with the thickening of the Y-region discussed in the previous subsection. The loop current is zero for the aligned rotator, and increases to about 20% of the total polar current for the orthogonal rotator. As can be seen, the 3D magnetospheric solution is extremely rich in physics that may have potential observational signatures. Extracting useful information from intrinsically 3D data sets is nontrivial, but this work is currently underway.

4 Implications of the magnetospheric solutions With force-free solutions of the magnetosphere available, we can start asking questions about the assumptions that went into the model, and begin adding extra physics that may have consequences for explaining the observations. In a sense, the forcefree solution provides the scaffold onto which the fully functioning and radiating magnetospheric machine has to be attached.

4.1 Consequences for spin down Having a reliable spin down formula allows better estimation of the magnetic field ˙ 1/2 (1 + sin2 α)−1/2 G. When compared to the strength of pulsars: B0 = 2.6 × 1019(PP) p canonical vacuum perdiction of Bvac = 3.2 × 1019 (P P˙ G the maximal difference is up to a factor of 1.7, which seems relatively unimportant. However, in some cases where the inclination angle of a pulsar is constrained, one could be tempted to use

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the vacuum formula including the angular factor Bvac1 = Bvac sin−1 α. In this case one can infer fields much larger than is warranted, especially for small inclination angles. Another immediate consequence of the spin down formula is that pulsars with large inclination angles should lose more energy than nearly aligned rotators. Therefore, we would expect oblique rotators to spin down faster, and be first to cross the death line in the P − P˙ diagram [13]. That would leave more aligned than oblique pulsars near the death line 3 . To the extent that the inclination angle can be inferred from calculating the pulsed fraction of the radio beam, observationally there indeed seems to be an excess of pulsars which have smaller inclination angles near the death line [34].

4.2 High energy emission Significant amount of research has been invested in explaining the high energy emission from pulsars (e.g., [11, 48, 17, 26]). The models that seem to work best in obtaining widely separated double emission peaks invoke the production of gamma rays in the region associated with the boundary between the closed and open field lines. This works on geometrical grounds, because the photons from different heights and rotation phases can arrive to the observer in phase due to relativistic aberration and light travel time effects (caustics). Most models attribute the production mechanism to an accelerating structure (“a gap”) that exists in the same region. Depending on the range of heights involved in the accelerator, the gaps are called the “slot gap” or the “outer gap” (polar gap may also be important for observations of primary gamma rays in the polar cap cascade). The physics of the gaps as proposed now relies on charge starvation, either because the pairs are underproduced in slot gap region due to geometry of the pair formation front, or because the sign of GJ density reverses with distance (the “null surface”). In force-free solutions the plasma is assumed abundant and there are no special points that would appear to cause violent acceleration. In particular, the “null surface” has no particular significance, as the net charge can change sign in a dense plasma rather easily. What is striking, however, is that the region at the boundary with last closed field lines, is exactly the region where strong current sheets flow in the magnetosphere (fig. 4). Therefore, it is tempting to suggest that we are dealing with the physics of the current sheet; however, whether this interpretation can work in practice requires additional study. In [2, 3] we studied the geometry of the emission zone in the force-free magnetosphere that could lead to the formation of double-peaked light curves4 . The differences in the geometry of the force-free field and the vacuum Deutsch field are not important close to the star, but increase further out, particularly near and beyond the light cylinder. However, as the shape of the polar cap is determined by the be3

The effect discussed in [13] also took into account the modification of the spin down due to the growth of vacuum gaps with age. 4 Also see chapter by X. Bai in this volume.

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havior of the field lines near the LC, even the emission close to the star is likely to be significantly affected by the new field geometry (e.g., compare vacuum polar cap and force-free polar cap in Fig. 6). In order to keep the investigation more general, in [2, 3] the emission was assigned uniformly per unit length of the field line along the whole field line, so that the peaks of the emission are associated with caustics rather than a particular region that is selected to emit more. The photons were emitted parallel to the field lines in the corotating frame and then binned on the sky map accounting for the relativistic effects, such as light aberration and time delay. The resulting sky maps showed that the same magnetospheric locations as invoked for the vacuum field geometry, namely the slot gap and the outer gap regions, did not seem to produce reliable double peaks in the force-free field. This was attributed to the larger polar cap shape in the force-free field and to the different geometry of the field lines near the LC, which affected the geometry of the null charge surface in the outer gap model. The slot gap model in vacuum geometry assigns the emission to an annulus congruent to the last open field lines that extends in radius from the stellar surface to ∼ 0.7RL. The outer gap model extends out from the intersection of the null charge surface with a similar annulus, so the height of the emission depends on the field line. In working with force-free field, we chose to include emission from all field lines in an annulus (since there is no special meaning to the null charge surface) tracing the field lines beyond the light cylinder (typically out to 1.5 RL ).

Fig. 7 Geometry of the emitting flux tube in force-free field for α = 60◦ . a) and b) 3D view of the flux tube. The rings mark intervals of 0.25 RL along each field line; c) location of field lines from the northern hemisphere on the sky map; d) same from both poles; e) sky map intensity.

The geometry of the emitting flux tube and the resulting sky map is shown in Fig. 7. The sky map in 7e shows the intensity of the emission as a function of pulsar phase for different observer viewing angles ξobs . The light curve for a given observer is then a horizontal cut through this plot. Two peaks are generally obtained and their separation can vary up to half a rotation period. This is in agreement with

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the properties of gamma-ray pulsars observed by Fermi. The high intensity regions on the sky map are formed by caustics, as can be seen from the overlap of emission from different heights along field lines in 7c,d. Most of the caustic formation occurs in the outer magnetosphere, at and beyond RL . This can be understood from the fact that force-free field lines start to resemble the rotating split monopole solution beyond the light cylinder, and the shape of the field line in the form of Archemedean spiral is highly conducive to the formation of caustics. Indeed, a relativistic particle rotating with the star and sliding along such a spiral would move on a straight line in the inertial space. Its emission from different radii will thus arrive at the observer simultaneously, and cause a strong caustic. In the vacuum field, particularly in the slot gap (or “two-pole caustic”) model, the caustics are formed due to very different chance overlaps of the emission from different field lines (e.g., see [2]).

a)

b)

Fig. 8 Geometry of the preferred flux tube that produces double-peaked emission in the forcefree magnetosphere with magnetic inclination α = 60◦ . Overplotted is the volume rendering of the strength of the current, dominated by the equatorial current sheet. Two phases of rotation are shown in panels a) and b).

To better illustrate the emitting region preferred in the force-free field, consider the 3D view of the magnetosphere in Fig. 8. White lines mark the preferred field line bundle that gives the double-peaked profiles. We also overplot the volume rendering of the current density, which peaks in the current sheet beyond the light cylinder. It is clear the the white lines trace very well the shape of the current sheet. Incidentally, the bulk of the emission that results in caustics is also accumulated beyond the light cylinder. The reason why these field lines give double peaks is relatively simple: any flux tube that becomes split-monpolar will produce caustics on the sky map that would look like rings surrounding each pole. The caustics from the field lines that start at the north and south magnetic poles merge only for the field lines that meet and follow each other near the current sheet. Thus, the force-free magnetosphere prefers the emission near the last open field lines close to the edge of the polar cap. The actual emission on these lines arises near and beyond the light cylinder close to

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the current sheet. Due to its association with the current sheet, we called this model the ”Separatrix Layer” model. The process responsible for high-energy emission in the force-free magnetosphere is still unclear. In the vacuum field, accelerating gaps filled with vacuum electric fields are postulated near the edge of the polar flux tube, and the emission is typically attributed to radiation-reaction limited curvature radiation of highly relativistic beams. The acceleration and radiation process in the force-free field requires a different approach. Based on geometry, the emission seems to be associated with the current sheet, so it is natural to invoke reconnection in the sheet as a means of both heating and accelerating the plasma. Since the plasma in the current sheet is likely to be much denser than the GJ density typically assumed in gaps, radiationreaction limited curvature radiation may be replaced by synchrotron radiation from the hot streaming plasma in the sheet. Recently, Gruzinov [22] suggested that there are regions in the magnetosphere where the current is necessarily “spacelike,” i.e., there is no frame where the current can be represented as the advection of charge density. This means that the current must be provided by the relative drift between the species, which may result in streaming instabilities and dissipation. The current sheet outside R L is indeed spacelike. Further advances in this modeling require improved force-free or MHD models that can accommodate finite resistivity 5 . This is now being pursued.

4.3 Reconnection and time-dependence Reconnection must be an integral part of the way magnetosphere works. This is clear just from the fact that as the pulsar slows down and the light cylinder recedes, the Y point probably moves out as well. In order to do this, some open field lines have to get converted into closed ones [12, 13], so reconnection must proceed at least on the spindown time scale [14]. Most likely, reconnection proceeds much faster, and the magnetosphere is constantly adjusting to the stresses at the light cylinder. This is evidenced in time-dependent force-free [55] and MHD [9] simulations, where the Y-point can oscillate near the light cylinder, resulting in periodic emission of small plasmoids. The amplitude and frequency of these oscillations depends on resistivity, which is not faithfully modeled in the simulations; however, the dynamical response of the magnetosphere is realistic. This implies that there could be quasiperiodic behavior of the magnetosphere controlled by the magnetospheric crossing time and the reconnection rate. It is natural to suggest that such breathing is ultimately responsible for the drifting subpulse phenomena, although no comprehensive model based on this currently exists. Another consequence of magnetospheric reconnection is the modification of the pulsar braking index. Note, that all force-free models ultimately yield spin down ¨ Ω) ˙ 2 = 3. Most of the reliably power going as Ω4 , so a braking index is n ≡ ΩΩ/( 5

For a particularly promising prescription for resistive force-free model see [22, 23].

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measured braking indexes are below 3 [33]. If the Y point and the light cylinder are allowed to move not in unison, then from n = 3 + 2∂ ln(1 + RY /R L )/∂Ω [9, 13] we get n < 3 for cases where the Y-point does not recede as fast as the light cylinder. Alternative explanations for n < 3 involve inertial effects or the evolution of the magnetic field with pulsar age [7, 49].

4.4 Current structure and origin A large area of research that is now open to reinvestigation concerns the origin and mechanics of current and plasma production in the magnetosphere. The force-free models provide the strength and shape of the conduction current that the magnetospheric plasma has to carry in order to support the stresses at the light cylinder and provide the spin down. How these currents are actually produced and extracted is a question that force-free theory cannot address. To zeroth order, the shape of the current as a function of flux surface coordinate for an aligned rotator is well approximated by the Michel’s split-monopole current [39]: I(Ψ) = R−1 L Ψ(2 − Ψ/Ψopen ) (up to ∼ 20% corrections due to the distributed return current at the edge of the polar cap), or in terms of the GJ current density, j = jGJ (1 − Ψ/Ψopen ), where Ψopen is the flux through the polar cap. This implies that the current significantly varies over the polar cap. On the other hand, most models of the electrostatics of polar accelerating gaps, which create a space-charge limited flow, approach typical values of j = ηGJ c, which are constant over the size of the polar cap. This is because ηGJ does not vary significantly over a small polar cap size, and relativistic outflows are readily produced in the large starvation electric fields near the surface. Herein lies a problem, because the gap seems to be unable to produce the current that is needed by the magnetosphere. This will lead to time dependence as the magnetosphere adjusts to the wrong current, and sends Alfven waves back to the gap. This contradiction probably is a consequence of overdetermining the structure of the gap by only considering the local electrostatics, without the influence of charges in the return current layer. Allowing more freedom to the flow such as counterstreaming electron distributions or time-dependent virtual cathode oscillations [32] could help as well. Another outcome was also entertained [59], where a force-free magnetospheric solution was found that corresponded to the constant current over the pole. The price was to relax the angular velocity of field lines, so the magnetosphere rotated differentially. Another alternative is to question the assumption that the charges are necessarily moving relativistically. Beloborodov [3] found that a space charge limited flow with j < jGJ could be generated in a 1D model of the polar cap, when a current is imposed (presumably by the magnetosphere) and in this case the charges move nonrelativistically. This solution, if it can also work in 2D, has an interesting consequence: the aligned rotator (which has j ≤ jGJ ) everywhere on the polar cap, will not accelerate plasma to high enough energy to radiate gamma rays and spark pair formation. This would be inconsistent with the force-free dense plasma picture, and, more importantly, is unlikely to lead to a viable current outflow higher up in the

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magnetosphere, where the flow has to cross the null surface. More work is clearly needed to understand the “chicken and the egg” question of the plasma supply. In contrast, the force-free current in the oblique rotator is larger than the local GJ current. For finite inclinations, the local GJ density and current drop as cos α. Yet, the current required by the oblique force-free models is of the same order as the GJ current of the aligned rotator. Although in principle, if the plasma is dense enough, super-GJ currents should not difficult to set up, one wonders if this is a generic configuration, or there would be some pulsars that are charge-starved and therefore, would spin down differently. The issue of the magnitude of the current is the fundamental difference between the time-dependent force-free solutions[55], and the analytic solutions of 3D force-free equations constructed by Beskin, Gurevich and Istomin [24, 5, 25], who explicitly require the conduction current in the oblique rotator to be limited by the local GJ current density. This leads to the suppression of the spindown power with inclination as cos2 α, quite the opposite result from eq. (4)! Which one is closer to the truth may depend on what can be produced in the polar gap. Also, since the oblique analytic solutions in [24] cannot be continued beyond the light cylinder, it is not clear whether they can be directly compared with the force-free simulations, which have no significant issues on the light cylinder.

4.5 Differential rotation The force-free models are a good first approximation if the potential drops in the various gaps are small compared to the available vacuum polar cap potential. Even if the gap potential is significant but there is a pair formation front beyond some height above the polar cap, the gaps can still be accommodated into the force-free formalism. The field lines above the gap are equipotentials, and hence rotate with the same angular velocity; however, this angular velocity is different from the stellar rotation Ω, because of the potential drop in the gap. Assuming a small vertical extent of the gap, such configurations can then be simulated by specifying different angular velocities on the surface of the star corresponding to open and closed lines. The effect on the spin down is to reduce the power of the aligned rotator as Laligned = µ2 Ω4 /c3 (1 − Ωdeath /Ω), where Ωdeath is the frequency of the star where the available potential can no longer generate the pairs [13]. So, if a nearly aligned pulsar approaches the death line, its trajectory on the P− P˙ diagram will curve downward, which can help to explain the shape of the P − P˙ diagram without requiring magnetic field decay. One can attempt to heuristically generalize this formula to the oblique rotator as L = µ2 Ω4 /c3 [(1 − Ωdeath /Ω) + ξ(Ωdeath /Ω) sin2 (α)]. Here, the first term in brackets is responsible for the aligned part, and ξ(Ωdeath /Ω) is a slowly varying function that goes from 1 for the healthy young pulsars (Ω ≫ Ωdeath ), to 2/3 for the “dead” pulsars, that have no plasma and must spin down as vacuum rotators. Such modification of the spin down law can help to explain recent observations of transient pulsars [30]. In PSR B1931+24, the torque in the “on” state, when the pulsar is shining and can be interpreted as filled with plasma, exceeds the torque in the

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“off” state by a factor of 1.5. It is clear that if one compares the original plasma spin down expression (4) with the vacuum spin down, the prediction is that the torque ratio has to be larger than 3 for any inclination angle, contradicting the observations. The modified law above does find solutions, but an extra parameter (Ωdeath ) is introduced. One has to also question whether the pulsar really turns off to a complete vacuum, or some residual plasma, perhaps in the closed zone, modifies the vacuum spin down. This can be studied with an oblique force-free simulation with a gap. Alternatively, if the research on polar current production finds that the current is limited to local GJ current, one would have to reconsider the spin down law [25]. Overall, the discovery of transient pulsars holds great promise in constraining the physics of the magnetosphere. For the first time, we have an actual handle on the bulk of the energy flow, and the evolution of the currents in the magnetosphere when the plasma supply is varied6 .

4.6 Conclusion The field of pulsar magnetospheres is now undergoing an exciting transformation, where a calculable standard model is being formulated. The shape and general properties of the plasma-filled magnetosphere are now known, and this opens the possibility of addressing old questions of plasma supply and current formation in a globally self-consistent way. Particularly exciting is the indication of connection between the high energy emission and the strong equatorial current sheet at and beyond the light cylinder. The fact that this region may be active makes energetic sense, as this is the ”wire” that carries most of the return current associated with the spin down energy loss. In order to dissipate large fractions of spin down energy (10-20% are inferred for older gamma-ray emitting pulsars by Fermi observations), a “resistor” in the circuit is needed, and the current sheet is well positioned to act as such a resistor. The actual physics of this resistivity and the ensuing particle energization and acceleration are currently uncertain, but modeling the phase-resolved gamma-ray spectra provided by Fermi will provide good handles on these processes. Important advances are also poised to happen on the theoretical front, with more elaborate relativistic MHD simulations and kinetic studies of the physics of relativistic reconnection coming online soon.

References 1. 2. 3. 3. 6

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A huge unanswered question is what actually triggers the state transition in the transient pulsars!

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Modeling of γ-ray Pulsar Light Curves from Force-Free Magnetosphere Xue-Ning Bai & Anatoly Spitkovsky

Abstract The Fermi LAT has recently discovered dozens of new gamma-ray pulsars, and is destined to revolutionize our knowledge of pulsar science. The gammaray pulsar light curves carry important information about pulsar magnetospheric structure, which has commonly been modeled as a vacuum dipole. We briefly review theoretical models of gamma-ray pulsar light curves and point out their uncertainties due to the usage of vacuum field. We present the first results of pulsar high-energy light curve modeling using the more realistic force-free (FF) field taken from timedependent FF simulations. With the FF field, we find the conventional slot-gap (twopole caustic) and outer-gap models are no longer able to produce the commonly observed double-peak light curves. The most geometrically favored gamma-ray emission zone lies in a thin layer near the edge of the open flux tube. Emission from this “separatrix layer” generally produces two sharp peaks in the light curve, which are formed near and beyond the light cylinder. We show that most features and statistics from the currently available gamma-ray pulsar light curves can be well reproduced and explained in this framework. The location of this emission zone strongly suggests its association with the current sheet, thus calling for more detailed study of current sheet physics and particle acceleration.

Gamma-ray pulsars (GRPs) are the most energetic objects in the pulsar population. Their high-energy emission carries important information about pulsar magnetospheric structure, particle acceleration mechanisms, and plasma physics in strong magnetic fields. Seven GRPs were known before the launch of the Fermi Gammaray Space Telescope (Fermi). With unprecedented sensitivity, Fermi has recently discovered more than 40 new GRPs, including 16 previously unknown pulsars from blind search (see [1] and references therein). The GRP population contains both normal and millisecond pulsars (MSPs). Despite the large diversity in surface magnetic Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ-08544, USA. e-mail: [email protected],[email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_12, © Springer-Verlag Berlin Heidelberg 2011

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field strength and rotation period, all these GRPs possess strong magnetic field at the light cylinder (LC) radius RLC ≡ c/Ω, where Ω is the pulsar’s angular frequency. The gamma-ray light curves from GRPs also show large diversity, but the majority of them are double-peaked with wide separation and have substantial bridge emission between the two peaks. When radio emission is detected, the first gamma-ray peak typically lags the radio pulse by a small fraction (δ) of the rotation period. Gamma-ray emission from GRPs are believed to originate from “gap” regions in the pulsar magnetosphere. Particles are accelerated in the gaps due to strong parallel electric field and produce curvature, synchrotron and inverse Compton radiation. Conventional models for pulsar gamma-ray emission include the polar cap model [8], the slot-gap model (SG, or two-pole caustic model, TPC) [2, 9, 12], the outergap model (OG) [16, 16, 7], and the annular gap model [15]. These models largely work on geometric grounds and differ in the assumed location of the emission zones (i.e., gaps). In particular, the TPC model assumes the emission zone to be located in a thin layer in the periphery of the last open field lines (LOFLs) extending from the neutron star (NS) surface to some cutoff radius inside the LC, while the emission zone in the OG model resides in the open field line region near the LOFLs extending from the null charge surface (NCS) to the LC. These two models are generally more favored because they have more extended emission zones and have been very successful in reproducing double-peak light curves. Most calculations of the GRP light curves from these models approximate the pulsar magnetosphere by a vacuum dipole field (either static or retarded dipole). However, pulsar magnetosphere is filled with plasma [10]. The plasma is essentially force-free (FF), with ρE + j × B/c = 0, where ρ and j are charge and current densities. Recently, [17] obtained the full 3D magnetospheric structure using timedependent FF simulations. The simulations self-consistently take into account the effect of conducting plasma, and provide more realistic approximations to the pulsar magnetosphere. The resulting FF field structure differs substantially from the vacuum field structure due to the strong poloidal current and the returning current sheet (see the Chapter by Spitkovsky). Such deviation raises the question of the robustness of the GRP light curve modeling using the vacuum dipole field. The basic procedure for light curve calculation can be summarized as follows. 1. Trace magnetic field lines to find the LOFLs (which are field lines that touch the LC tangentially), and record the locus of the LOFLs on the polar cap. 2. Define the open volume coordinate (rov , φm ) on the polar cap, where φm is the LOFL is the magnetic colatitude normalized to magnetic azimuth and rov = θm /θm that of the LOFLs. Each (rov , φm ) combination specifies one field line. 3. Assign the emission zone with prescribed range of rov and (inner and outer) spatial cutoff radii. Uniform emissivity along field line is commonly assumed. 4. Trace magnetic field lines in the emission zone, assume photons are emitted along the direction of the field lines in the corotating frame, and project the emitted photons to the sky with correction for aberration and time delay effects.1 1

The treatment of aberration in much of the literature was not self-consistent, see [3] for detailed discussion and correction.

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5. Bin the photons on the sky map (φ, ξobs ), where φ and ξobs correspond to rotation phase and observer’s viewing angle respectively. The light curve is obtained by cutting the sky map at fixed ξobs . Typical sky maps produced by the vacuum TPC and OG models contain sharp and bright arc regions which lead to peaks in the model light curves (see [3]). These arcs are called “caustics”, whose formation is due to the fortuitous overlap of radiation on the sky map from different regions of the magnetosphere. Mathematically, it means that the Jacobian determinant of the map from the emission zone to the sky coordinates approaches zero. Therefore, the formation of caustics (hence the peaks in the light curves) is very sensitive to the magnetic field geometry and the location of the emission zone. Indeed, by considering two types of vacuum fields (static and retarded dipole fields), and two different shapes of the polar caps (circular and polar cap obtained by tracing LOFLs), [3] found that the appearance of the sky maps are very different in the four combinations. Such differences reflect large uncertainties in the light curve modeling using the vacuum field, calling for re-investigation of the GRP emission models using the more realistic FF field. Bai & Spitkovsky [4] presented the first results of GRP light curve modeling using the FF field from simulations by [17]. They found that the TPC model fails to produce the double-peak pulse profiles, mostly because the size of the polar cap in FF magnetosphere is larger than the vacuum field polar cap, which suppresses caustic formation in the inner magnetosphere. The OG model can produce only one peak in most magnetic and viewing geometries, because a large fraction of open field lines do not cross the NCS. By exploring a wide range of different emission zone locations, they found that the most geometrically favored emission zone lies in a thin layer on the open field lines just inside the separatrix that bounds the open flux tube. Based on the geometric location, this emission zone is termed as the “separatrix layer” (SL), which generally corresponds to rov = 0.9 − 0.95. Figure 1 demonstrates how the SL model works in FF field geometry. Clearly, two bright and narrow caustics are formed on the sky map, which can naturally produce widely-separated double-peak pulse profiles under a wide range of viewing angles, as illustrated in panels (d) and (e). The origin of the caustics can be traced from panel (b): there is strong clustering of rings (mapped from panel (a), see the Figure caption) at the position of the caustics. Therefore, beyond a certain distance s0 along these field lines from the NS, emission from a single field line arrives to the observer simultaneously, which strongly enhances the local sky map brightness. Comparing with panel (a) suggests that s0 ≈ 0.75 − 1.0RLC. Therefore, caustics form in the outer magnetosphere, near and beyond the LC. The father the emission zone extends, the stronger the caustics are (hence the sharper the gamma-ray peaks are). This effect is termed as “sky map stagnation” (SMS). SMS is closely related to the fact that the FF field asymptotically approaches the split monopole solution [5], and is a robust effect for all open field lines (rov < 1). Nevertheless, only field lines with rov close to 1 produce sky maps similar to Figure 1. Field lines from smaller rov tend to produce four rather than two peaks. This fact strongly constrains the geometrically favored location of the emission zone to be in the SL.

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Fig. 1 Illustration of the SL model using FF field with magnetic inclination angle α = 60◦ . Panel (a) shows the emission zone geometry plotted as individual field lines (from the north magnetic pole) traced from the NS surface to cylindrical radius R = 1.2RLC . These field lines are projected to the sky map in panel (b). To guide the eye, different symbols are plotted along four field lines in both panels which clarify the line correspondence between the two panels. Furthermore, six rings (in black dots) are plotted across the field lines in panel (a) (the innermost ring is hardly visible) together with their projections in panel (b). Points on each ring are located at fixed distance, s, from the NS surface, measured along the field lines. Different rings are evenly separated, with ∆s = 0.25RLC . Panel (c) shows the brightness of the sky map (from both magnetic poles). Color scale is linear, and black arcs indicate strong caustics. Two sample light curves from ξobs = 45◦ and ξobs = 80◦ are shown in panels (d) and (e) respectively.

An atlas of GRP light curves from the SL model is presented in [4] (see their Figure 9), from which robust predictions on the temporal locations of the two peaks can be made regardless of input physics. The phase lag of the first peak relative to the radio peak ranges from δ = 0.14 to 0.4, and the separation between the two peaks ranges from zero (i.e., one peak) to ∆ = 0.5. Smaller phase lag typically corresponds to larger peak separation, and vice versa (which is also apparent in Figure 1). Statistically, the SL model predicts that majority of the light curves should have widely-separated double peaks, pulsars with smaller peak separation are less common, and pulsars with only one peak are possible but rare. Another consequence of the SL model is that smaller peak separation usually indicates stronger bridge emission between the peaks. All these predictions are consistent with the Fermi GRP sample [1]. Moreover, the fact that a large fraction of MSPs detected by Fermi are single peaked (and double-peaked with small separation) suggests that MSPs tend to have small magnetic inclination angle, based on the SL model. Being a geometric model, the physical origin of the SL emission remains to be explored. However, the location of the SL closely traces the Y-point (or “Y-ring” in 3D) and the equatorial current sheet beyond the LC. Strong dissipation and reconnection is expected in such regions [11], leading to particle acceleration and gamma-ray emission [14]. It may also be related to the stripped wind model by [13].

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Detailed theory on the physics of the Y-ring and current sheet has to be constructed to test these scenarios and uncover the origin of the SL emission.

References 1. 2. 3. 4. 5. 16. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

Abdo, A. A., for the Fermi LAT collaboration, 2010, ApJS, 187, 460 Arons, J., 1983 ApJ, 266, 215 Bai, X.-N., Spitkovsky, A., 2010a, ApJ, 715, 1270 Bai, X.-N., Spitkovsky, A., 2010b, ApJ, 715, 1282 Bogovalov, X.V., 1999, A&A, 349, 1017 Cheng, K.S., Ho, C., Ruderman, M., 1986, ApJ, 300, 500 and 522 Cheng, K.S., Ruderman, M., Zhang, L., 2000, ApJ, 537, 96 Daugherty, J.K., Harding, A.K., 1996, ApJ, 458, 278 Dyks, J., Harding, A.K., Rudak, B., 2004, ApJ, 606, 1125 Goldreich, P., Julian, W.H., 1969, ApJ, 157, 869 Gruzinov, A., 2007, ApJ, 667, L69 Harding, A.K., Stern, J.V., Dyks, J., Frackowiak, M., 2008, ApJ, 680, 1378 Kirk, J.G., Skjæraasen, O., Gallant, Y.A., 2002, A&A, 388, L29 Lyubarskii, Y.E., 1996, A&A, 311, 172 Qiao, G.J., Lee, K.J., Wang, H.G., Xu, R.X., Han, J.L. 2004, ApJ, 606, L49 Romani, R.W., Yadigaroglu, I.-A., 1995, ApJ, 438, 314 Spitkovsky, A., 2006, ApJ, 648, L51

A Tale of Two Current Sheets Jonathan Arons

Abstract I outline a new model of particle acceleration in the current sheet separating the closed from the open field lines in the force-free model of pulsar magnetospheres, based on reconnection at the light cylinder and “auroral” acceleration occurring in the return current channel that connects the light cylinder to the neutron star surface. I discuss recent studies of Pulsar Wind Nebulae, which find that pair outflow rates in excess of those predicted by existing theories of pair creation occur, and use those results to point out that dissipation of the magnetic field in a pulsar’s wind upstream of the termination shock is restored to life as a viable model for the solution of the “σ” problem as a consequence of the lower wind 4-velocity implied by the larger mass loading. †

1 Follow The Energy Rotation Powered Pulsars (RPPs) provide the first and most definitive example of compact astrophysical systems which draw the power for their observed emissions from the extraction of rotational energy from gravitationally bound objects through the action of macroscopic electromagnetic fields. They have motivated models for similar energy extraction from disks around other gravitating bodies, such as black holes (e.g. Rees [46], Begelman et al. [10]). As objects of study, the RPPs have a virtue lacking in the black hole systems: timing of the precisely measured pulse periods, uniquely interpretable as the rotation periods of the underlying neutron stars, Jonathan Arons Department of Astronomy, Department of Physics, Space Sciences Laboratory and Theoretical Astrophysics Center, University of California, Berkeley e-mail: [email protected] (The title goes with apologies to Charles Dickens) †

Collaborators, none of whom should be held responsible for the content of this paper: D. Alsop, E. Amato, D. Backer, P. Chang, N. Bucciantini, B. Gaensler, Y. Gallant, V. Kaspi, A.B. Langdon, C. Max, E. Quataert, A. Spitkovsky, M. Tavani, A. Timokhin N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_13, © Springer-Verlag Berlin Heidelberg 2011

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provide measurements of the total energy budget free of all astrophysical uncertainties, other than the factor of ∼ 2 uncertainty in neutron stars’ moments of inertia, arising from the unecertainties in the equation of state of dense matter. The measured rate of rotational energy loss, P˙ E˙ R = −IΩ∗ Ω˙ ∗ = 4πI 3 , (1) P tells us the total energy budget for these systems, without our having to understand anything about the photon emissions from these systems - which is both a blessing and a curse - a blessing, because in contrast to other relativstic astrophysical systems, we know the energy budget, without having to unravel the partition between flow kinetic energy, large scale Poynting flux, thermal energy and radiative losses - a curse, since the energy loss is radiatively silent, thus supplying little information as to the details of the energy outflow, leaving the mechanics of the machine mysterious. Nevertheless, progress has been made. The Pulsar Wind Nebulae (PWNe) act as catch basins for the rotational energy lost. Observations of these systems Gaensler & Slane [24], using radio (including millimeter), X-ray, gamma ray and occasionally infrared telescopes1 , have made clear that RPPs deliver their energy to the outside world in the form of highly relativistic, magnetized outflows - stellar winds that are exaggerated versions of the solar wind - which must be electromagnetically driven by the magnetic pressure of the wound up magnetic field. The strength of that field is estimated by using the theory of magnetic braking of the neutron stars’ spin, which suggests Ω˙ = −KΩn , Ω = 2π/P,

(2)

P = rotation period, applied to the observed rotations periods and spindown rates ˙ 2. P˙ = −2πΩ/Ω The earliest model applied vacuum electrodynamics to a rotating sphere endowed with a magnetic dipole moment µ centered at the stars’ centers and tipped with respect to the rotation axis by an angle i. That theory yields the spindown luminosity E˙ R = KΩ4 , K = (2/3)µ2 sin2 i/c3 [e.g. [41, 43]] thus n = 3 in this model. Vacuum theory was motivated by the large gravitational forces at the surfaces, suggesting no plasma more than a meter or so above the star, but immediately Deutsch’s much earlier observation [[22]], made in the context of magnetic A stars, that in vacuum large electric fields parallel to B would overwhelm gravity and pull charged particles out from the star until the vacuum electric field would be altered, reducing E · B down to zero, was recovered [25] and extended with the suggestion that the charged particles would feed a curious charge separated wind, p with a total electric current I = cΦmag , Φmag = total magnetospheric potential = E˙ R /c. That wind could carry 1

Most PWNe lie in the galactic plane, therefore are relatively inaccessible to optical techniques, and are even less accessible to UV telescopes. Near and far infrared observations are extremely useful in unraveling the physics of the relativistic outflows [16], but have been much less in evidence than the high energy studies.

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away the rotational energy of even the aligned rotator, in a Poynting flux dominated flow - the electromagnetic energy density would vastly exceed the kinetic energy density (and pressure) of the outflow, in the initially conceived model - the particle flux in that scheme is only cΦ/e = 2.3 × 1030(I45 P˙ 15 /P3 )1/2 elementary charges/s, −15 , the “Goldreich-Julian” current. ˙ I45 = I/1045 cgs, P˙ 15 = P/10

Fig. 1 Observed RPP periods and period derivatives, from [33]. The line bounding the pulsar population corresponds to the magnetospheric voltage Φ = 1012 V, clearly marks a boundary beyond which pulsar emission is unlikely. Simple estimates of pair creation suggests this source of plasma should occur only for voltage larger than this value, which underpins the idea that pair creation is esential for radio emission [[51]]. The change in slope of this “death line” al short period, small P˙ indicates more sophistication in the pair creation physics, and/or in the association of pairs with radio emission, than is incorporated in the simplest models, a conclusion also apparent from the variety of quantitative problems with this widely accepted hypothesis [31, 39].

The charge separated model has several really serious theoretical difficulties, but perhaps of greater importance is that the observations of young PWNe have made clear that the particle outflows are many orders of magnitude larger than the Goldreich-Julian current, thus motivating MHD models, where E · B = 0 is assumed from the start. Pair creation occurring somewhere within the magnetospheres (first suggested by [51]) is thought to be the origin of the required dense plasma, although a quantitative model that yields the high mass loss rates observed is still

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lacking [Bucciantini et al. [16] and references therein]. In recent years, solutions for the MHD structure of the magnetosphere in the appropriate force-free limit have been obtained (numerically - the attempts of analytically minded theorists to guess the answer to the rather formidable free boundary/eigenfunction problem posed by the steady state version of the model, uniformly failed over 30 years of attempts), first for the aligned rotator [[19, 26, 35, 52]], then for the full 3D oblique rotator [[50, 32]]. As far as the P, P˙ diagram goes, the main result from these investigations is the innocuous looking conclusion in expression (3). K = k(1 + sin2 i)

Ω3 µ2 , k = 1 ± 0.1. c3

(3)

Physically, the most important result has been the identification of the current sheets separating the closed from the open regions of the magnetosphere, extending into the wind beyond the magnetosphere, whose last closed flux surface ends just touching the light cylinder whose cylindrical radius is ̟ = c/Ω. That such a current sheet should be present has been suspected from the early days of RPP research [e.g., [40]]. The error in k reflects the uncertainties in the numerical treatment of the problem, many of which are associated with how the current sheet is represented in the numerical schemes. Figure 2 shows a slice through the 3d force-free magnetosphere of the 60◦ rotator, from Spitkovsky’s (2006) results. Observationally, expression (3) shows that the vacuum rotator’s “braking index” n = 3 is preserved in full force-free MHD, which contradicts the observed values in the small number of stars where n has been determined [37], a contradiction which has led to a variety of suggestions ranging from evolution of the magnetic moment µ or the obliquity i [12] to effects of reconnection on the rate of conversion of open magnetic flux to closed [20], as the star spins down and the closed zone expands at the expense of the amount of open magnetic flux. That reconnection might affect the braking index is readily derived from the fact that the torque really depends on the magnitude of the open magnetic flux.The amount of open flux depends on the size of the closed zone, which ends at RY . If RY /R L < 1, the torque increases because of more open field lines and larger Poynting flux than is the case for a magnetosphere closing at r = R L . [15] show that the braking index is   ∂ ln 1 + RRYL ΩΩ¨ n≡ = 3+2 ; (4) ˙2 ∂ ln Ω Ω thus, If RY /R L decreases with decreasing Ω, then n < 3. Reconnection usually is unsteady - figure 3 shows the blobs (“plasmoids”) ejected from the Y-line at the base of the current sheet in the relativistic wind of the aligned rotator. The speculation is that spindown slightly biases these reconnection events so that on the much longer spindown timescale, the net open flux slowly converts to closed. These current fluctuations might be associated with the timing “noise” [2, 18] identified long ago with torque fluctuations (e.g., Helfand et al. [30], Scott et al. [47]), although recent analysis of longer data sets [38] in long period pulsars has called the noise interpretation into question.

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Fig. 2 Field lines and current density of the oblique force-free rotator, i = 60◦ , from Spitkovsky (2006), seen in a cut in the Ω, µ plane. The last closed field lines end at a Y-point (a Y-line, in 3D) at distance RY from the neutron star. The current sheet encloses and separates the closed from the open field regions of the magnetosphere, and the separate branches merge in the wind zone, where the folded sheet continues to separate the oppositely directed fields of the striped wind. The arrows and “Gap” labels locate sites where vacuum gaps have been postulated, in test particle models of accelerators that lead to gamma ray emission and pair creation. None of these gaps appear in a current sheet accelerator based on the force-free magnetosphere model.

In itself, the force-free model does not provide mechanisms for photon emission. But it has a variety of implications, which are slowly being addressed. • The model specifies the polar flux tube size and shape - it is noncircular with a polar cap center displaced from the magnetic axis, even when the magnetic field is the simplest, that of a star centered, point dipole [9]. This has consequences for radio polarization structure, and for polar cap areas and dipole offsets inferred from soft X-ray emission from polar caps [13], thought to be heated by magnetospheric particle bombardment [3, 53, 29]. These theoretical improvements of the polar cap model have yet to be noticed and incorporated in phenomenological models of the observations used by data analysts; such incorporation might yield interesting tests of the force-free model. • The force free model quantitatively specifies the return currents required to prevent the star from charging up, as the polar flow extracts charge from the star.

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Fig. 3 Plasmoids formed at the base of the current sheet of the relativistic aligned rotator, where the sheet crosses the light cylinder, from a relativistic MHD simulation of a newly born neutron star’s magnetosphere [15]. The dissipation that allows reconnection to occur is numerical. They move out radially at the local Alfven speed vA ≈ c, and recur on the magnetospheric Alfven transit time ∼ P/π

The results for the oblique rotator are partly in accord with long held expectations, that return current exists in a thin (“auroral”) sheet bounding the polar flux tube (e.g. [25, 40]), consistent with the open circuited model [25] - current closure occurs far away, in the nebula/interstellar medium beyond the wind termination shock or perhaps in the outer wind, plus qualitatively new features: a) part of the return current surrounding the polar flux tube is spatially distributed, even in the aligned rotator; b) in the oblique rotator, this part of the current system is not a return current at all, but couple the two polar regions together [9] - in the orthogonal rotator (i = 90◦ ), the auroral component of the current is entirely in the polar coupling flow, with the volume current out of each half of the polar cap having equal amount and opposite sign, also consistent with early expectations (e.g. Scharlemann et. al. [48]) - the orthogonal rotator automatically balances it’s charge loss. The radiative consequences of these features are as yet unexplored - for example, the spatially distributed part of he return current might be a good candidate for the site of “conal” component of pulsar radio emission,

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an idea which requires non-force modeling of the current flow and identification of a workable emission process within that current flow model2 before one can relate the theoretical force free current distributions to the observations in a testable manner (although easier kinematic comparisons are certainly possible). • The location of the return current layer having been determined, the hypothesis that the return current layer is the site of the beamed particle accelerator that gives rise to the pulsed gamma rays observed by the FERMI and earlier orbiting gamma ray telescopes (see [45] in these proceedings for a recent review) can now be investigated in the context of a self consistent magnetopspheric structure that allows a quantitative evaluation of the beaming characteristics implied by the radiating current sheet concept - see [9] for a kinematical study of the radiating current sheet idea. Making progress on a physical model for radiation from the current layers can most expeditiously take advantage of the facts that a) pulsed gamma ray emission, when observed, is the largest photon output from rotation powered pulsars, but b) generally has less luminosity than the spin-down luminosity of these stars. Figure 4 illustrates this fact, which summarizes the results from the LAT instrument as of Spring 2010: Thus the energy invested in particle acceleration is a small fraction of the enegy stored in Poynting fluxes, for radiation reaction limited acceleration, so that the force free model can be considered as a good zeroth order magnetospheric description. √ ˙ The voltage limitation prediction Lgamma ∝ Φmag ∝ E is the same as Lgamma ∝ “particle current” = particle flux = Goldreich-Julian flux in unidirectional beam models of the polar electric current flow [28] only if the accelerator carries a fixed fraction of the total electric current that enters into the spin-down torque, indepen˙ In the traditional slot or outer gap models, pair creation establishes the dent of P, P. limitation of the accelerator to a thin sheet either in the outer magnetosphere [17] or back in the polar cap [4] - in such models, the gap width w∗ of a model which successfully reproduces the sharply peaked light curves, projected onto the neutron star following the field the poloidal field lines, is necessarily small compared to the polar cap size, and varies with the pulsars’ magnetic moment and spin parameters. This is not an issue for a model based on the currents flowing in the return current layer, which necessarily carries the whole magnetospheric return current and include a substantial fraction in a thin current sheet, for most obliquities of the magnetic moment with respect to the rotation axis. That magnetospheric current sheets, with particle densities within the sheets high compared to the Goldreich-Julian value, can sustain large parallel electric fields is well known in planetary magnetopsheres - such sheets are the accelerator sites of the particle beams that stimulate the aurora observed in the upper atmospheres of the Earth, Jupiter and Saturn, for example3 An elementary illustration of this possibility 2

Some earlier ideas on this subject relating to field aligned acceleration and gamma ray emission can be found in [5, 27], for example. 3 For a review of such phenomena, see [42]. Of particular significance to pulsars is the fact that the field aligned currents that power narrow auroral arcs consist of precipitating electron

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Laccel/Lspindown << 1!

Fig. 4 Ratio of observed gamma ray luminosity Lgamma to observed spindown power E˙ = Lspindown for LAT pulsars [1]. If the acceleration of the gamma ray emitting particles is radiation reaction limited (generally true in models that assume curvature radiation as the emission mechanism, as is the case in most of the “gap” √ models). The trend at higher luminosities roughly follows the efficiency Lgamma /Lspindown ∝ ( E˙ −1 expected if some mechanism limits the accelerating voltage ∆Φ p ˙ [e.g., [6, 29]], a limitation plausito a fixed fraction of the magnetospheric voltage Φmag = E/c, bly attributed to pair creation. The large dispersion in Figure 4 comes primarily from the uncertain distances, and also to the uncertain beaming correction required to go from the fraction of the sky illuminated by the beam to the total emission that would be detected by an observer covering 4π ster - the LAT team assumed uniform phase-averaged beaming across the sky (1 sterradian).

comes from considering the inertial term in the generalized Ohm’s for the electric field parallel to B, which can be written as, in the relativistic case, as ( )   4π ∂Jk B mγ I Ek = 2 + · ∇ · γ (Jv + vJ) ∝ , (5) n ∆current ρB ω p ∂t B

with mγ the particles’ relativistic mass, n their density, I the total current set by the force free magnetosphere, ∆current is the thickness of the current carrying channel, and ρB is the radius of curvature of the magnetic field. Thus inertia of the current carriers can act as a effective resistance in these high inductance systems, which establish the currents electromagnetically, forcing a parallel electric field to appear in the presence of any parallel (to B) load - pressure and radiation reaction itself are beams launched from the reconnection region in the distant magnetotail and counterstreaming ions launched from the planetary atmosphere.

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other effects which can serve as loads, with pressure especially important in the diffusion region around the singular line shown in figure 5. the fluid velocity. Equation (5) is most useful in the corotating frame, and when the current is due to relative motion between the species (electrons and positrons, and in some circumstances heavy ions) which is slow compared to the bulk fluid velocity v. In the current circumstance, it turns out that the current is better described as counter-streaming beams - in that case, describing the beams as separate fluids is more appropriate, and they can form the total plasma density in the current flow channel, rather than being a low density component in a much denser plasma. Expression (5) does make clear that acceleration is prone to maximize when the the relativistic mass is high and the current density is high (large I/∆current ). ∆current is generally microscopic, expected to be on the order of c/ω p , and is established by the dynamics of the the singular region where the closed zone ends, illustrated (in the cartoon approximation) in Figure 5. The capture rate of pair plasma into the diffusion region is cΦmag 2lD∆L βrec in N˙ diffusion± ≈ κ± , (6) 2 β e R L wind with κ± the multiplicity (multiplier of a fiducial Goldreich-Julian outflow rate cΦmag /e) that gives the number of pairs in the total outflow, βrec the reconnection speed in units of c and βwind the polar wind outflow velocity (set equal to unity). ∆L is the thickness of the current channel at the light cylinder, assumed equal to the half height of the diffusion region, and lD is the length of the diffusion region. Pressure in the diffusion region expels the captured pairs from the diffusion region, outwards along the current sheet in the wind and inwards along the auroral current channels. Expression (6) assumes the plasma flux in the wind has a gradient across B, as is likely since the accelerating electric field in the polar cap that leads to the pair creation that feeds the wind is small near the cap edge. The pressure supported electric field provides the accelerator which sorts the particles in the diffusion region into a precipitating beam (electrons in the geometry shown in Figure 5) and an oppositely charge beam traveling outwards in the wind current sheet - the charge signs of the beams are as required by the global electrodynamics. The channel thickness is almost certainly comparable to the skin depth in the pairs. Taking the plasma gradient into account leads to the lower limit to the channel thickness !1/3 c m± c2 γ± ∆Lmin = ≈ RL , (7) ω p± (δ = c/ω p± (δ) 2κ± eΦmag where δ is the distance across B from the formal current sheet location, and a precipitating beam flux in the return current channel F∨ =

lD cΦmag /e  R L 3 κ± ; RL r 2πR2L

(8)

in the gradient case, ∆L drops out of the precipitating flux evaluation. γ± is a measure of the four velocity and of he comparable four-velocity dispersion of the po-

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lar plasma flow emerging from the inner magnetosphere, predicted by pair cascade models to be on the order of 102 . Numerically, (7) yields a very small value, on the order of meters to hundreds of meters, the specific value depending on Φmag and κ± . The kinetics of relativistic reconnection being a largely untrodden subject, lD is more or less unknown - it could be as small as ∆L itself (Petscheck style reconnection), or as large as appears in the numerical dissipation driven reconnection observed in the force free simulations, lD ∼ 0.1R L (A. Spitkovsky, personal communication). In the terrestrial magnetosphere, satellite observations suggest the diffusion region length is intermediate between the ion skin depth and the macroscopic scales. For the discussion here (and in the more detailed report in preparation), treating lD as a parameter to be constrained by model comparisons to observations appears to be the wisest strategy. In analogy to observed non-elativistic reconnection, one expects βrec ∼ 0.1vAlfven /c = 0.1, a value supported by the few PIC simulations of relativistic reconnection [e.g., [54]]. The precipitating particles form the “hanging charge clouds” invoked by [25] to cause the electrostatic extraction of return current from the star’s atmosphere, which happens if n∨ (R∗ ) = F ∨ (R∗ )/c ≫ nGJ (R∗ ), or , from (8), if lD βrec κ± ≫ 1. R L βwind

(9)

The condition in (9) is satisfied if lD is large compared to the skin depth, but still small compared to the numerical dissipation determined length observed in the force free simulations. It can be shown that the consequent minimum total potential drop in the twin beam channel is !1/3 1 R∗ m± c2 γ± βwind lD ∆Φmin ≈ − Φmag cos i 8 R L 2eΦmag κ± βrec ∆L !1/3 1 R∗ βwind lD = − Φmag cos i. (10) 8 R L βrec RL If lD /R L really is as large as 0.1, rather than comparable to the minimum scale ∆L , the accelerating potential in the return current channel is more than large enough (around 1013 Volts, in the Crab and Vela pulsars) to drive curvature gamma ray emission from the beams, which limits the particle energies by radiation reaction. Such energies are high enough to lead to pair creation, which may limit the acceleration, although as is clear from expression (5), parallel potential drops in the current carrying region can be sustained even if the plasma is dense. If one models the gamma ray emission as being directly from the beams, one needs to take account of the electron beam going inwards, in acute geometry, where the upward beam is ions (generically, protons) - for obtuse geometry, the outbound beam is electrons, with an inbound positron beam. Pair creation (through γ − γ interactions with softer photons from the star), when it is important, makes the obtuse and acute geometries equivalent. The radiation might be synchrotron emission, especially the nonthermal X-ray output. The counterstreaming beams are electromagnetically two stream and shear

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Polar Cap!

J!r ! Return current! channel!

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Fig. 5 Upper Panel: Electric current structure of the oblique force-free magnetosphere, inclination = 60◦ , from [50]. The current sheet, indicated by the darker color, bounds the closed zone. The closed zone ends at a singular Y-line (in the ideal force-free electrodynamics approximation) at the light cylinder distance from the neutron star. Lower Panel, left: Current structure at the polar cap, illustrated for acute angle between the magnetic moment and the angular velocity (electron polar current, Ω · µ > 0). The return current in the current sheet consists of a precipitating electron beam, launched from the diffusion region around the Y-line and possibly augmented by high altitude pair creation within the current sheet, with the charges in the precipitating beam extracted by reconnection flow from the pair plasma flowing from the polar cap into the wind, plus a counterstreaming ion beam extracted electrostatically from the stellar atmosphere. In obtuse geometry (ion polar current, Ω · µ < 0), positrons precipitate from the Y-line and counterstreaming electrons are extracted from the atmosphere. For clarity, the part of the return current not contained in the current sheet is omitted, even though this part of the current system is of increasing significance as i → 90◦ . Lower Panel, right: Possible structure of the Y-line region, with the termination of the closed zone to the left and the merger of the winds from the opposite polar caps to the right. The “guide field” Bφ also reverses across the mid-plane of the flow, along with the poloidal open field. As reconnection occurs, some of the ouflowing plasma (speed cβ, β ≈ 1) deflects toward the singular, unmagnetized “diffusion” region around the Y-line with speed vrec ∼ 0.1vAlfven = 0.1c. The figure represents a steady (in the co-rotating frame) flow model - in reality, the reconnection is likely to be bursty, as in Figure 3, with formation of sporadic X-lines.

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unstable. Since ω p,beam can be comparable to the relativistic cyclotron frequency in the outer magnetosphere, the growing waves can excite finite Larmor gyration of the particles in the current channel, thus producing incoherent emission through hard X-rays - gamma rays are possible, under some circumstances. These X-rays are an alternative to soft photons from the star, as targets for γ − γ pair production. If the lower frequency waves can escape the plasma, they are a direct source of coherent emission, perhaps of interest to modeling giant radio pulses, which appear to come from the outer magnetosphere. A more detailed description of the model will appear elsewhere.

2 Follow the Mass Pulsar Wind Nebulae (PWNe) demonstrate that pulsars loss rest mass at a rate large compared to the fiducial electrodynamic particle loss rate cΦmag /e [for a review, see [24]]. The only known explanation is pair creation in the pulsars’ magnetospheres. In many nebulae, the X-ray emitting particles rapidly lose energy to synchrotron radiation. Then the nebulae are particle and energy calorimeters, allowing direct inference of the pair multiplicity in the wind, of TeV to PeV pairs. The measured injection rates, up to ∼ 1038.5 pairs/s, compare well to the predictions of existing pair creation models [e.g. [31]], yielding multiplicities up to ∼ 104 . However, PWNe are also radio synchrotron emitters, radiation that samples much lower energy populations (100 MeV to 10 GeV), whose radiative efficiency is much less than their X-ray emitting cousins. The result is a much larger population of pairs, whose radiative lifetime exceeds that of the nebulae. The most efficient hypothesis is that these particles come from the embedded pulsars also, an idea supported by spectral continuity and by exotica, such as the observation of radio “wisps” near the Crab pulsars [11]. Applying simple evolutionary models allows one to infer time averaged injection rates. Recent evaluations by [16] and [49] yield lower limits for multiplicities κ± all in excess of 105 and upper limits for wind 4-velocities ˙ 2 = eΦmag /2κ± m± c2 all less than 105 in a number of nebulae. The Γwind = E˙ R / Mc data are the best for the younger systems, although even for these, the lack of far infrared data inhibits the analysis.

PWN Name Φmag (PV) Age (yr) κ¯ ± Crab 100 955 106 3C58 15 2100 104.7 B1509 120 1570 105.3 Kes 75 22 650 105 W44 1 20.3 × 103 105 K2/3 Kookaburra 5.5 13 × 103 105 HESS J1640-465 3.5 104 106

Γwind 5 × 104 3 × 104 1 × 104 7 × 104 104 104 103.6

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The inferred multiplicity excesses are a puzzle for pair creation theory, perhaps resolvable by appealing to magnetic anomalies near the neutron stars’ surfaces, the simplest being an offset of the dipole center from the stellar center, which strengthens the magnetic field at one pole [e.g., [7]]. The increase this gives to the magnetic opacity can be greatly enhanced if the magnetic axis is also tipped with respect to the radial direction, since then gravitational bending of photon orbits with respect to the B field direction much increases the magnetic opacity for pair creation. Such phenomenological modifications of the low altitude magnetic field must respect the observation that radio beaming morphology is consistent with the magnetic field being that of a star centered dipole quite close to the star [44, 36]. This problem warrants quantitative investigation. The large inferred multiplicities imply the wind 4-velocities (Γwind to be small compared to the much quoted value of 106 inferred by [34] in their model of the Crab Nebula’s optical and harder emission. The large mass loading and the inferred low wind four velocity has a large impact on the much storied “σ problem” of pulsar winds. In ideal MHD, the ratio σ of magnetic energy to kinetic energy in the wind is conserved outside the fast magnetosonic radius (since for a cold flow the wind does not substantially accelerate outside this surface) and is large - even with the increased mass loading found from recent nebular studies, σ is always well in excess of several hundred. Nevertheless the wind behaves at its termination shock as if σ is small - MHD models of the nebulae suggest σ at th termination shock is on the order of 0.02 in the Crab Nebula [e.g [23]] and similar values are plausible in other systems. [21] suggested that because the wind of an oblique rotator has the magnetically striped structure shown in Figure 6, magnetic dissipation of the corrugated B field, generically of a resistive nature propelled by instabilities of the current flow in the current sheet separating the stripes4 might destroy the magnetic field of the wind interior to the termination shock, thus converting a high σ flow into an effectively unmagnetized plasma. If the current sheets separating the magnetic stripes are to merge with a speed v s < c as measured in the proper frame of the flow, before they reach the termination shock located at distance RT S from the neutron star, the merger 2 time in the PWN frame T merge = πΓwind (R L /v s ) must be less than the flow time to √ √ the termination shock RT S /c, therefore Γwind < (RT S /πR L)(v s /c) = (Crab) v s /c must be satisfied if Coroniti’s model is to be viable. This inequality is satisfied for multiplicities above 105 , which does appear to be the case for the young PWNe recently analyzed. Possible mechanisms that can lead to the necessary dissipation are drift-kink instability of the current sheet, considered as if it were a flat sheet [54] and an interesting Weibel-like instability due to interaction between the sheets [8]. Most interesting, the dissipation of the curent sheets in the inner wind, while responsible for only a small fraction of the magnetic destruction, may have sufficient luminosity to allow detection of VHE and UHE emission. A much more elaborate paper de4

This wrinkled current sheet, frozen into the wind, is the second current sheet of this paper’s title, but really it is the continuation of the sheet separating the closed and open zones interior to the light cylinder, as is apparent in Figure 5.

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scribing these results is in preparation.

a)

d)

c)

b)

e)

f)

Fig. 6 a) Magnetic Geometry of a Force-Free Rotator for r < 2RL , for i = 60◦ , from Spitkovsky (2006). The rapid transition to inclined split monopole field geometry for r > RL is apparent. b) Geometry of the current sheet from the split monopole model for i = 60◦ , r > RL . For clarity, only one of the two spirally wound current sheets is shown. As i → 90◦ , the sheets almost completely enclose the star; for r ≫ RL , the spirals are tightly wrapped (Br ≪ Bφ ) and the current sheet surfaces closely approximate nested spheres. c) One sheet for i = 30◦ , shown for clarity. d) Meridional cross section of the current sheet for i = 60◦ . e) Equatorial cross section snapshot of the current sheet, showing the two arm spiral form. The arrows show the local directions of the magnetic field; the dots and crosses show the direction of the current flow. Panels b)-e) were constructed using Bogovalov’s [14] analytic model of the asymptotic wind. f) Current sheet from a 2D PIC simulation of the inner wind, from unpublished work by Spitkovsky (used by permission),

Acknowledgements The work described here has been supported by NSF grant AST-0507813, NASA grants NNG06GJI08G and NNX09AU05G and DOE grant DE-FC02-06ER41453.

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The high-energy emission from the pulsar striped wind J´erˆome P´etri

Abstract Since the launch of the Fermi satellite, the number of gamma-ray pulsars increased by almost one order of magnitude. These objects show pulsed emission up to tens of GeV and the associated light-curves have frequently a double-pulse structure. We study this pulsed emission by considering the striped wind model. By numerical integration of the time-dependent inverse Compton emissivity in the current sheets, we compute the phase-dependent spectral variability of this radiation. Several light curves and spectra are presented. Our model is able to explain some of the high-energy (10 MeV-10 GeV) spectral features of several gamma-ray pulsars, like Geminga and Vela.

1 Introduction The high-energy, pulsed emission from rotating magnetized neutron stars is usually explained in the framework of either the polar cap or the outer gap models. In both of these models, the radiation is produced within the light cylinder. An alternative site for the production of pulsed radiation has been investigated [6] based on the idea of a striped pulsar wind, originally introduced by [3] and [7]. In this picture emission originates outside the light cylinder and relativistic beaming effects are responsible for the phase coherence of the radiation. It has already been shown that this model can satisfactorily fit the optical polarization data from the Crab pulsar [8].

Observatoire Astronomique de Strasbourg, 11 rue de l’Universit´e, 67000 Strasbourg, France, email: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_14, © Springer-Verlag Berlin Heidelberg 2011

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2 The striped wind model We use an explicit asymptotic solution for the large-scale field structure related to the oblique split monopole [2]. The model used to compute the high-energy pulse shape and the phase-resolved spectrum arising from this solution is presented in [9]. The current sheets sustaining the magnetic polarity reversal arising in this solution are responsible for the pulsed emission. Because of the ideal MHD assumption, this surface is frozen into the plasma and therefore moves radially outwards at a constant speed V. Strictly speaking, the current sheets are infinitely thin. However, as was already done in the study of the synchrotron polarization of the pulsed emission [8] we release this prescription. Our model involves some geometrical properties related to the magnetic field structure and some dynamical properties related to the emitting particles. Furthermore, in order to compute the light curves and the corresponding spectra, we need to know the emissivity of the wind due to inverse Compton scattering. The geometry is described by the angle of inclination of the magnetic moment with respect to the rotation axis, χ, and the inclination of the line of sight, ζ. Moreover, the wind is expanding radially outwards at a constant velocity V close to the speed of light denoted by c. The innermost regions of the pulsar magnetosphere is believed to be a site of high-energy pair production feeding the wind with ultra-relativistic pairs. For these emitting particles, we adopt an isotropic distribution function in momentum space in the comoving frame of the wind. It is given by a power law in energy, with a sharp low and high-energy cut-off, γmin and γmax respectively, such that the particle number density at time t and position r with energy between γ and γ + dγ is ne (γ, r, t) dγ = Ke (r, t) γ−p dγ

(1)

with γmin ≤ γ ≤ γmax and Ke (r, t) is related to the number density of emitting particles in the current sheet. Moreover, the radial motion of the wind at a fixed speed imposes an overall 1/r2 dependence on this quantity, due to conservation of particle number. However, adiabatic losses in the current sheets due to pressure work will cool down this distribution function in such a way that Ke decreases with an additional factor 1/r2/3(p+2), see [5]. Furthermore, we assume the emission commences when the wind crosses the surface defined by r = r0 ≫ rL . We assume an isotropic distribution of mono-energetic target photons ε with density nγ (ε) in the observer frame. The total emissivity is denoted by jobs . Knowing ic the inverse Compton emissivity, the light curves are obtained by integration over the whole wind region. This wind is assumed to extend from a radius r0 to an outer radius rs which can be interpreted as the location of the termination shock. Therefore, the inverse Compton radiation at a fixed observer time t is given by Z rsZ πZ Iicobs (t) = r0

0

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2 jobs ic (r, tret ) r sin θ dr dθ dϕ

(2)

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The retarded time is expressed as tret = t − ||R0 − r||/c ≈ t − R0 /c + n· r/c. The approximation is valid if the observer, located at R0 , is very far away from the radiating system, R0 ≫ rs . Eq.(2) is integrated numerically for several frequencies from far below the low-energy cut-off to far above the high-energy cut-off. We are therefore able to predict the phase resolved spectral variability and the pulse shape simultaneously.

3 Application to γ-ray pulsars We apply the aforementioned model to inverse Compton scattering of either lowenergy photons from the cosmic microwave background or from the thermal stellar black body radiation. The former photon field is employed for Geminga whereas the latter for Vela. For the Geminga pulsar, in our best fit, we choose an inclination of the magnetic moment with respect to the rotation axis of χ = 60o . In order to obtain a phase separation of 0.5 between the two pulses, we have to adopt an inclination of the line of sight ζ = 90o . The Lorentz factor of the wind is Γ = 10. Results for the lightcurve above 100 MeV and the definition of the different phase intervals is shown in Fig. 2. The rising and falling shape of both pulses are well fitted by our model. The corresponding spectral variability is reproduced with satisfactory accuracy except for the OP phase for which the intensity is overestimated, see Fig. 2 [9]. For the Vela pulsar, in our best fit, we choose an inclination χ = 60o and ζ = 76o . The Lorentz factor of the wind is Γ = 16. Results for the light-curve above 100 MeV and the definition of the different phase intervals is shown in Fig. 2. The spectra within the two pulses, P1/2, IP1, LW2 and TW1 are well reproduced as well as the cut off energy around a few GeV, Fig. 2. The other phases still need some intensity level readjustment [10]. In the striped wind model, the pulsed high-energy emission from pulsars arises from regions well outside the light-cylinder. By computing the inverse Compton emission on the CMB or stellar thermal black body photons, we were able to fit the EGRET data of the light-curves and spectra for several gamma-ray pulsars such as

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Vela and Geminga. The new gamma-ray pulsar catalog from Fermi-LAT will help to constrain the physics of this wind [1].

References 1. Abdo, A. A, 2009, arXiv/astro-ph:0910.1608A 2. Bogovalov, S. V. 1999, A&A, 349, 1017 3. Coroniti, F. V. 1990, ApJ, 349, 538 4. Fierro, J. M., Michelson, P. F., Nolan, P. L., & Thompson, D. J. 1998, ApJ, 494, 734 5. Kirk, J. G. 1994, in Saas-Fee Advanced Course 24: Plasma Astrophysics, 225 6. Kirk, J. G., Skjæraasen, O., & Gallant, Y. A. 2002, A&A, 388, L29 7. Michel, F. C. 1994, ApJ, 431, 397 8. P´etri, J. & Kirk, J. G. 2005, ApJL, 627, L37 9. P´etri, J. 2009, A&A, 503, 13 10. P´etri, J. 2010, A&A, submitted

Gamma-rays from millisecond pulsars in Globular Clusters Włodek Bednarek

Abstract Globular clusters (GCs) with their ages of the order of several billion years contain many final products of evolution of stars such as: neutron stars, white dwarfs and probably also black holes. These compact objects can be at present responsible for the acceleration of particles to relativistic energies. Therefore, γ-ray emission is expected from GCs as a result of radiation processes occurring either in the inner magnetosperes of millisecond pulsars or in the vicinity of accreting neutron stars and white dwarfs or as a result of interaction of particles leaving the compact objects with the strong radiation field within the GC. Recently, GeV γ-ray emission has been detected from several GCs by the new satellite observatory Fermi. Also Cherenkov telescopes reported interesting upper limits at the TeV energies which start to constrain the content of GCs. We review the results of these γ-ray observations in the context of recent scenarios for their origin.

1 Introduction Globular Clusters are huge concentrations of old stars with masses of the order of the Solar mass or lower. These 105 − 106 stars are contained within a spherical volume of a few parsec. About ∼ 150 of the known clusters have been observed creating a spherical halo around the Galaxy. They are at typical distances of ∼ 10 kpc from the Sun (e.g. Harris 1996). GCs also contain remnants of evolution of stars with masses M∗ > 1M⊙ , which can be responsible for acceleration of particles to high energies. In fact, more than a hundred of millisecond pulsars (MSPs) have been discovered within globular clusters (e.g. Camilo & Rasio 2005) and large fraction of objects belonging to GCs are X-ray emitters. These sources are identified with the Cataclysmic Variables (accreting White Dwarfs) or Low Mass X-ray Binaries (LMXBs), i.e. accreting neutron stars in the binary systems. Due to the presence of these compact Department of Astrophysics, University of Ł´od´z, ul. Pomorska 149/153, 90-236 Ł´od´z, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_15, © Springer-Verlag Berlin Heidelberg 2011

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objects, GCs have been suspected to be sources of non-thermal processes which can turn to the production of high energy radiation. However, only recently GCs have been detected in high energy γ-rays (HE: E>100 MeV) by the Fermi-LAT telescope (Abdo et al. 2010a). In this paper we review the state of the knowledge on the observations and modelling of these oldest structures in the Galaxy.

2 The stellar content of Globular Clusters A large number of solar type stars in a small volume create a very well defined background radiation field (the mass to luminosity ratio in GCs is close to ∼ 2, e.g. van den Bosch et al. 2006). The observed luminosity of the globular clusters, LGC , and the density profile for the distribution of the stars inside it (Michie 1963a,b,c,d),   1, R < Rc    2 (R /R) , Rc < R < Rh D(R) =  c    (R R )2 /R4 , R < R < R , c h

h

(1)

t

allows us to calculate the energy density of stellar photons inside the cluster (Bednarek & Sitarek 2007), q 2 − 3 6R3 R − 2R2 18R c t t c LGC U rad = , (2) q 2 cRt 6( 6Rt R3c − 2R2c

where Rc is the core radius, √ Rt is the tidal radius, and the half mass radius is related to those both by Rh = 2Rc Rt /3. For typical parameters, Rc = 0.5 pc, Rt = 50 pc, and LGC = 105 L⊙ = 3 × 1038 erg s−1 , we obtain Urad ≈ 300 eV cm−3 . The energy density of this stellar radiation field clearly dominates over the energy density of the Cosmic Microwave background Radiation (CMBR), UCMBR = 0.25 eV cm−3 . However, the photon number densities of the stellar and CMBR are comparable. The radiation field inside GC can be defined as a function of distance to its center by normalizing the density profile of the distribution of stars inside GC to the total number of stars contained in the GC such as N⋆tot = 105 M⊙ . The number of stars as a function of the distance is then N⋆ (R) = AD(R)dR (where A = N⋆tot /[2Rc − 2R2c /(3Rh ) − R2c R2h /(3R3t )] ≈ N⋆tot /(2Rc )). As a first approximation can be assumed that in average stars inside GC has parameters similar to the Sun, i.e. the surface temperature 6000 K and the radius 7 × 1010 cm. The density of stellar photons at a specific distance from the center of GC is calculated by integration over the whole distribution of stars inside the GC. These density profiles for stars and stellar radiation inside the GC are shown in Fig. 1. Thus, GCs belongs to the rare class of sources in which the soft radiation field within the cluster is very well defined. This is very important since it limits the number of free parameters when modelling high energy radiation in these objects.

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Fig. 1 The density of stars (a) and density of stellar photons (b) as a function of distance R from the center of a typical globular cluster with the mass 105 M⊙ , the core radius Rc = 0.5 pc, the half mass radius Rh = 4 pc, and the tidal radius Rt = 50 pc (from Bednarek & Sitarek 2007).

3 Compact objects within Globular Clusters Due to their ages, GCs contain large population of compact objects which are the final products of the evolution of stars with masses > 1M⊙ . The white dwarfs (Cataclysmic variables) and neutron stars (LMXBs and MSPs) has been detected in many globular clusters. In contrary to isolated compact objects in the Galaxy, the evolution of compact objects within the GCs is strongly influenced by their frequent encounters with normal stars. They turn to the formation of compact binary systems. Therefore, a number of the X-ray sources related to such binary systems has been observed (see below). Here we briefly discuss these compact binaries (or their remnants) within the GCs.

3.1 Millisecond pulsars About 140 millisecond pulsars (MSPs) have been discovered in radio observations in 26 GCs (for summary see Freire 2009). They are believed to be the result of spun-up to millisecond periods of old neutron stars which accumulate the angular momentum with the matter accreting from the companion star (Alpar et al. 1982). Some of these MSPs are isolated at present due to complete evaporation-destruction of the companion star. The largest population of MSPs has been detected in 47 Tuc (23 MSPs) and Ter 5 (33 MSPs). However, many more are expected based on simulations of their formation in stellar encounters which should occur very frequently in GCs. For instance Ter 5 may contain of the order of ∼ 200 MSPs (Fruchter & Goss 2000, Kong et al. 2010). In fact, there should exist a link between stellar encounter rate in GC and the number of MSPs and LMXBs (Pooley 2003, Abdo et al. 2010). The stellar encounter rate is estimated based in the known core stellar

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density and core radius for each particular GC (Verbunt & Hut 1987). In this way it is possible to predict the MSP population. It has been recently argued (Hui et al. 2010) that the population of MSPs in GCs have different X-ray emission properties from the MSPs in the Galactic field (note however Becker et al. 2010 for counter opinions). It is not clear whether proprieties of MSPs observed at other photon energies (e.g. in γ-rays) do not differ significantly as well.

3.2 Cataclysmic Variables and LMXBs First X-ray observations of GCs (Uhuru and OSO − 7 satellites) reported a relatively large number of luminous low mass X-ray binaries (LMXBs) per unit mass within GCs with respect to those observed in the Galactic field (Clark 1975, Katz 1975). The observed emission was variable with power as high as L x > 1035 erg s−1 . More sensitive instruments a population of low-luminosity X-ray sources with luminosities L x ∼ 1031 − 1033 erg s−1 within GCs has been reported by the more sensitive instruments such as Einstein and ROSAT (Hertz & Grindlay 1983, Verbunt 2001). However, only recently a firm identification has been possible thanks to deep observations with the Chandra telescope, which was able to resolve ∼1400 X-rays sources. Many of these sources have been identified with the LMXBs and Cataclysmic Variables. The number of LMXBs within specific GC shows clear correlation with the encounter rate (Pooley et al. 2003). Similar correlation has been also discovered between the number of Cataclysmic Variables within specific GC and the encounter rate (Pooley & Hut 2006). Recently, Pooley (2010) proposed that the correlation between the number of X-ray sources within specific GC and the encounter rate has different slope for the normal and core collapsed GCs. Such effect is consistent with predictions of simulations of different types of GCs (see Fregeau 2008). In conclusion, not only the amount of MSPs within the GCs are correlated with the encounter rates but also the amount of LMXBs and Cataclysmic Variables show such correlations.

3.3 Intermediate mass black holes ? It has been suspected on theoretical grounds that in the central regions of the core collapsed GCs intermediate mass black holes (IMBHs, WBH ∼ 103 M⊙ ) should exist. Observational arguments for the existence of a black hole with mass ∼ 3 × 103 M⊙ in M 15 has been reported by Gerssen et al. (2002). On the other hand, observations of radio emission from a supposed accreting IMBHs in Tuc 47 and NGC 6397 put upper limits on the black hole mass equal to a few hundred M⊙ (De Rijcke et al. 2006). Similar upper limits of same order of magnitude have been reported on the masses of IMBHs in Galactic GCs. Note that only recently, the evidence of the existence of the intermediate black hole (∼ 500M⊙) inside another galaxy has been reported by

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Farrell et al. (2009). IMBHs in GCs can not certainly be strong persistent emitters since such sources are not observed in the Galactic GCs. However, transient activity, e.g. as a result of capturing-disruption of a star from the globular cluster, may happen rarely and can not be excluded at present.

4 Non-thermal emission from Globular Clusters Here we review the results of observations of GCs which indicate the existence of relativistic particles. The presence of such particles is explicitly proved by detection of GeV γ-ray emission from GCs. The existence of relativistic electrons of diffusive nature within the globular cluster (or near the compact objects inside GCs) can be also envisaged through the detection of non-thermal lower energy radiation, e.g. in the form of diffusive radio or X-ray emission.

4.1 Low energy radiation First reports on the extended non-thermal X-ray emission appeared in the results from the Einstein and ROSAT observatories (e.g. Hartwick et al. 1982, Krockenberger & Grindlay 1995). This emission has been identified in many cases as a result of the acceleration of particles of heating of gas in the interaction of GCs with the gas in Galactic halo. More recently, extended X-ray emission has also been reported from the direction of 6 GCs using Chandra data (Okada et al. 2007). However, most of these X-ray sources appeared not to be related with the GCs but rather with the background clusters of galaxies. Other analyses of Chandra data such the one reported by Hui et al. (2009) show X-ray emission from 10 GCs and identifies most of this emission with compact sources. Recently, Eger et al. (2010) observes diffuse X-ray emission from Ter 5 well described by a hard power spectrum. We conclude that up to now there are not clear reports on the discovery of nonthermal diffusive X-ray emission from GCs. It looks that most of the reports can be interpreted as the X-ray emission from the compact sources within the GCs or the X-ray emission from the background clusters of galaxies.

4.2 Gamma-rays High energy γ-ray emission (HE: E>100 MeV, VHE: E>100 GeV) from a population of GCs has been discovered only recently. The prediction of very high energy γ-ray emission from GCs is on the level which gives a realistic chance for detection by the next generation of Cherenkov telescopes (HESS II, MAGIC II). The production of VHE γ-rays by leptons accelerated in the vicinity of MSPs seems to be

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quite certain. However, the level of this emission is difficult to estimate based on the present stage of knowledge since it depends on the number of MSPs and the diffusion of relativistic particles within the cluster. Its discovery may have to wait for the construction the next generation of instruments such as CTA. 4.2.1 GeV emission The first upper limits on the GeV γ-ray emission were derived based on the EGRET and COMPTEL observations on the board of Compton GRO (Michelson et al. 1994, Manandhar et al. 1996, O’Flaherty et al. 1995). First clear detections of two globular clusters, Tuc 47 and Ter 5, were claimed based on the data collected by the Fermi-LAT detector (Abdo et al. 2009a, Kong et al. 2010). The analysis of 13 GCs allowed to associate 8 γ-ray sources in the directions of known GCs (see Table I in Abdo et al. 2010a). The γ-ray spectra of these GCs are incredibly similar (see Fig. 2 in Abdo et al. 2010a). They are characterised by differential spectral index in the range 0.7 ÷ 1.4, showing the maximum of the emission at a few GeV and energy of the exponential cut-offs have been estimated in the range 1.0 ÷ 2.6 GeV. The γ-ray power of specific GCs can differ by an order of magnitude. It seems not to be directly related to the mass of the cluster. Moreover, γ-ray spectra from GCs have very similar features to the average spectrum of MSPs in the Galactic field (see Tables in Abdo et at 2009b). 4.2.2 TeV emission GCs became interesting targets also for the Cherenkov telescopes at TeV energies. First upper limits have been reported based on the observations of two GCs, M 13 and M 15, by the Whipple Collaboration (Hall et al. 2003, Le Bohec et al. 2003). Recently, new much more sensitive instruments have also reported upper limits from directions of some GCs. For example, the MAGIC Collaboration (Anderhub et al. 2009) observed M 13 for more than 20 hours and reported an upper limit at energies Eγ > 140 GeV, shown in Fig. 2. This limit already starts to constrain the population of the MSPs within this GC based on the model developed by Bednarek & Sitarek (2007). The HESS Collaboration (Aharonian et al. 2009) reported the upper limit for Tuc 47 at energies > 800 GeV which is on the level of predictions of the models by Bednarek & Sitarek (2007) and Venter et al. (2009), see Fig. (2). Also the VERITAS Collaboration (McCutcheon et al. 2009), observed 3 GCs, M 5, M 13 and M 15, reporting the upper limits above 600 GeV on the level of 0.6%, 2.2%, and 1.6% of the Crab Units, respectively. These last limits allow to constrain the population of MSPs within GCs on the level of 30-50, assuming that the energy conversion efficiency from the MSPs to relativistic electrons is equal to 1%. Such observations should be continued with the enlarged MAGIC and HESS telescope systems. They will be able to search for the γ-ray signal clearly in the sub-TeV energies.

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Fig. 2 Upper limits on the TeV γ-ray emission from two globular clusters: Tuc 47 (left figure, thick solid curve, from Aharonian et al. 2009, reproduced by permission of the A&A) and M 13 (right figure, arrows, from Anderhub et al. 2009, reproduced by permission of the AAS). The additional curves show the predictions of the models by Bednarek & Sitarek (2007) and Venter, de Jager & Clapson (2009).

5 Models for gamma-ray emission Due to general similarities between radiation processes occurring in the inner magnetospheres of the millisecond and classical pulsars, these first have been also suspected to be sources of pulsed γ-rays. However, the rotational energy loss rate of the MSPs is typically orders of magnitudes lower than classical pulsars. Therefore, only the closest MSPs might be potentially detected. In fact, already the EGRET detector was able to see a hint of a signal from one of such objects, PSR J0218+4232 (Kuiper et al. 2004). Recently, the Fermi-LAT team reported detection of γ-ray emission from several MSPs in the Galactic field (Abdo et al. 2009b). Thus, confirming general theoretical predictions concerning γ-ray emission from these sources (e.g. Bulik et al. (2000), Luo et al. 2000, Harding et al. 2005, Venter & de Jager 2005). Since globular clusters contain many MSPs, their cumulative γ-ray emission might be also above the sensitivity of γ-ray telescopes. A few estimates of the γ-ray fluxes from MSPs in globular clusters have appeared before launching the Fermi Observatory. Harding et al. (2005), based on the pair starved polar cap model, predicted the γ-ray fluxes from Tuc 47 near the upper limits from the EGRET. Venter & de Jager (2008), applying the modern version of the polar cap model (general relativistic effects included), also predicted γ-ray spectra clearly above the sensitivity of the Fermi-LAT telescope. A significant part of MSPs, detected in globular clusters, are within binary systems. MSP winds can interact with the winds of companion stars creating shocks which can accelerate electrons (e.g. Klu´zniak et al. 1988, Phinney et al. 1988, Arons & Tavani 1993). The X-rays from MSPs magnetospheres can illuminate the companion star heating it to significantly larger temperatures than expected from pure nuclear burning (e.g. Bednarek & Pabich 2010). Relativistic electrons interact with

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Table 1 The γ-ray luminosities from several globular clusters detected by the Fermi-LAT telescope. Also the expected number of millisecond pulsars estimated based on the observed γ-ray luminosity, efficiency of energy conversion from the pulsars to γ-rays and the average spin-down power of pulsars (from Abdo et al. 2010a, reproduced by permission of the AAS).

this enhanced stellar radiation producing γ-rays. Some of these MSPs can be completely surrounded by the stellar winds creating the so called ”hidden” MSPs (Tavani 1991). Such MSPs in compact binary systems can in principle also contribute to the γ-ray emission observed from the globular clusters. Another scenario for GeV γ-ray emission can be envisaged in the case of accreting, fast rotating neutron stars and possibly also white dwarfs (see recent model by Bednarek 2009). In the case of slowly rotating neutron stars, the matter from the companion star can penetrate deep into the inner NS magnetosphere. It is stopped at some distance from the NS surface as a result of the interaction with rotating magnetic field. A turbulent transition region is created. Electrons can be accelerated in such a turbulent region to E e > GeV energies. They interact with the thermal radiation from the NS surface (and/or the accretion disk) producing GeV γ-rays.

5.1 Interpretation of the observed GeV γ-ray emission General features of the γ-ray spectra observed by Fermi-LAT from GCs (spectral indices, cut-offs) are incredibly similar to the spectra detected by this same telescope from the population of MSPs observed in the galactic field and from the classical pulsars (Abdo et al. 2009b). Therefore, it seems obvious that the main contribution to the GC γ-ray emission is a cumulative emission from the inner magnetospheres of the whole population of MSPs. In fact, such general γ-ray emission from MSPs fits quite well to the earlier predictions made based on the polar cap model (Harding et al. 2005, Venter & de Jager 2008). However, there are at present some doubts concerning the validity of the polar cap model as a likely scenario for the γ-ray emission from the pulsar inner magnetospheres. Recent observations of the pulsed

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Fig. 3 From top to bottom: a) γ-ray (0.1-300 GeV, 40 bins), b) X-ray (0.55-4.5 keV, 22 bins) and c) radio (1336 MHz) pulse profiles of PSR J0613−0200. The error bars represent a 1 σ deviation. The background level is indicated by the dashed line. The analysis revealed that X1 and the radio structure are aligned and of similar widths, which suggests that part of the X-ray radiation (thermal component) and the radio emission are produced in the same region.

γ-ray spectrum from the Crab pulsar at energies above ∼ 10 GeV (Aliu et al. 2008, Abdo et al. 2010b) are clearly inconsistent with the γ-ray production region close to the stellar surface. Similar features of the γ-ray emission from the classical and the millisecond pulsars suggest that they are working under similar mechanism probably located farther from neutron star surface but closer to the light cylinder radius.

5.2 TeV γ-ray emission from MSP winds and shocks The possibility of the TeV γ-ray emission from GCs has been at first discussed by Bednarek & Sitarek (2007). Here we follow the general scenario for γ-ray production within GCs proposed in this paper. It is assumed that leptons are accelerated in the millisecond pulsar winds, shocks created by such winds (as a result of collisions with the stellar winds or between themselves), or they are injected from the inner pulsar magnetospheres. These energetic leptons diffuse through the volume of the GC interact at the same time with its soft radiation content, i.e with the optical photons from stellar population and the CMBR. We assume that the diffusion process of electrons is determined only by the magnetic field strength within GC. The simplest diffusion model is applied assuming Bohm diffusion coefficient, Ddif = RL c/3, where RL is the Larmor radius of leptons, and c is the velocity of light. Due to the lack of detailed knowledge on the spectral features of leptons injected by the MSPs, a few different models for electrons are considered with the limitations expected from the comparison with classical pulsar population.

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5.2.1 Relativistic leptons from MSPs The spectra of leptons injected from the MSPs into the surrounding is simply an enigma. Recent detections of GeV γ-ray emission from MSPs in the Galactic field allow to estimate the energy conversion efficiency from the rotating pulsar to the γ-rays. It is on the average of the order of ηγ ∼ 0.1 (see Abdo et al. 2009b). The observed γ-ray luminosities of GCs and ηγ (assuming that MSPs in GCs and Galactic field are similar) allows us to estimate the total energy loss rate of MSPs in obs specific GC on LMSP rot ≈ Lγ /ηγ . The relativistic leptons leaving the light cylinder radius take a part, ηe , of LMSP rot . This power can be also related to the magnetization parameter of the pulsar wind at the light cylinder radius of the pulsar, σLC . These coefficients have been estimated in the case of classical pulsars based on the various models, e.g. σLC ∼ 104 (Cheng et al. 1986), ηe ∼ ηγ ∼ 0.1 (Harding et al. 2002), or ηe ∼ 0.01 (Venter & de Jager 2008). Based on these values we can only say that the power in relativistic electrons leaving the light cylinder radius can be of the obs −4 obs order, Le ∼ LMSP rot /σMSP ≈ Lγ /(ηγ σMSP ) ∼ (10 ÷ 1) × Lγ . These leptons can be additionally re-accelerated in the pulsar wind zone and/or the pulsar wind shock. Therefore, the above estimate on the power of injected leptons should be considered as the lower limit. The power in relativistic leptons accelerated above the light cylinder radius could be in principle estimated based on the value of the magnetization parameter of the pulsar wind, which is the ratio of the energy density of the magnetic field to the energy density of leptons in the wind. Unfortunately, we can not estimate this value for the MSP population due to the lack of observational constraints. Therefore, we base on the analysis done for the classical pulsars keeping in mind that the processes in their magnetospheres seem to be identical to those in MSPs. From modelling of two well known pulsars and their nebulae, the magnetization parameter at the pulsar wind shock has been estimated to be σ << 1 for the Crab Nebula (Kennel & Coroniti 1984), and σ ∼ 0.1 in the case of Vela pulsar (Sefako & de Jager 2003). In the case of the pulsar wind which terminates closer, e.g. due to the interaction with a companion star, σ could be of the order of ∼ 1 as expected in the model by Contopoulos & Kazanas (2002). Such small values for the magnetization parameter at the pulsar wind or shock means that the energy conversion efficiency from the pulsar wind into the relativistic leptons is ηe ∼ 1. In such a case, the power in relaobs tivistic leptons injected into the GC can be estimated on Lwind ∼ 10Lobs e γ , where Lγ is the pulsed γ-ray power produced in the inner pulsar magnetospheres which has been detected by the Fermi-LAT telescope from specific GCs. The spectrum of leptons injected through the light cylinder radius could be in principle calculated in a specific model for γ-ray production (provided that this model is known!). The spectrum of leptons injected from the pulsar wind shock is expected to be of the power law type with the low energy cut-off (corresponding to energies of leptons injected from the light cylinder radius) and the high energy cut-off which could be estimated based on the known magnetic field strength at the wind shock. We stress that up to now we have no any observational signatures from direct observations of the MSPs at very higher energies since none has been detected

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above 10 GeV. Also detailed models for γ-ray production (and lepton injection) in the inner magnetospheres are not at present available. Therefore, the cut-offs in the injected spectrum of leptons have to be assumed rather arbitrarily. It will be simply tested with the future observations in the GeV-TeV energy range. Some re-scaling from observations of the pulsar wind nebulae around classical pulsars in the TeV γ-rays (e.g. the Crab nebula) gives the values for the maximum energies of leptons from MSP winds of the order of,

Eemax ∼ 3 × 1015 ⋆ (

3 × 108G 4ms −2 )⋆( ) eV ∼ 15T eV. 12 33ms 4 × 10 G

(3)

Specific models for TeV γ-ray production in GCs apply the values of similar order. For example, based on the comparison of the advection time of leptons along the shock with the acceleration time, Bednarek & Sitarek (2007) apply E emax in the range 4-40 TeV. On the other hand, Venter et al. (2009) has got similar values by calculating the injection spectrum of leptons through the light cylinder radius by integrating over the whole population of MSPs in specific GC applying the polar cap model. 5.2.2 Gamma-ray spectra from leptons diffusing inside GC Leptons with spectra discussed above are injected into the radiation field of the GC and diffuse in the outward direction comptonizing the soft radiation field within the cluster (stellar, CMBR, infrared). The basic proprieties of the γ-ray spectra in the case of mono-energetic injection of leptons with different energies into the soft radiation field dominated by soft photons from the stellar population within the cluster and the MBR are shown in Fig. 3 (Bednarek & Sitarek 2007). GCs with two different stellar luminosities are considered. Diffusion process of leptons is followed up to 100 pc from the center of GC and an average magnetic field strength to be of the order of BGC − 10−6 G. Note the interesting features of these γ-ray spectra. For leptons with TeV energies two features in the γ-ray spectrum appear to be caused by the scattering of the MBR in the Thomson regime and the scattering of optical photons in the Klein-Nishina (KN) regime. Interestingly, the lower energy feature resambles very much a bump of GeV γ-ray emission reported by the Fermi-LAT from the globular clusters. The second feature, a sharp KN peak, has not been observed up to now. This is not so surprising since it is predicted in the sub-TeV energy range marginally accessible by the present Cherenkov telescopes. The example γ-ray spectra produced by leptons which are injected with the power law spectrum at specific energy range are shown in Fig. 4. These spectra show a maximum at ∼0.1-1 TeV which is produced by the scattering of soft radiation in the Thomson regime. At higher energies the spectral index of γ-ray emission changes due to the scattering in the KN regime. The γ-ray spectra produced within specific volume around the center of GC are also shown on this figure. For stronger

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Fig. 4 Differential γ-ray spectra (multiplied by energy squared) produced in the IC scattering of the stellar and CMBR radiation by mono-energetic leptons with energies: 10 GeV (triple dot-dashed curves, 102 GeV (dotted), 103 GeV (dot-dashed), and 104 GeV (solid). Leptons are injected from MSPs and diffuse in the GC magnetic field with the strength 10−6 G. The total stellar luminosity of the cluster is 105 L⊙ (a) and 106 L⊙ (b). The spectra are normalized to single lepton injected in 1 second(from Bednarek & Sitarek 2007).

magnetic fields within GC (BGC = 10−5 G), most of the emission is confined within the volume of GC, i.e. it creates a point like source for Cherenkov telescopes. In terms of such a model, the γ-ray spectra have been calculated for selected globular clusters assuming different spectra of injected leptons (see Fig. 5, Bednarek & Sitarek 2007). This emission depends on the total power in leptons injected from MSPs, which is determined by the number of MSPs in specific GC and the efficiency of lepton acceleration by the average pulsar. Therefore, the comparison of the predicted spectra with the observations of specific GCs allows us to put the upper limits on the product of these two free parameters. Such procedure has been performed by

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Fig. 5 As in Fig. 3 but for the power law spectrum of leptons with the spectral index 2.1 between 100 GeV and 30 TeV. Specific curves show the spectra within the central region of GC equal to 1 pc (triple-dot curve), 3.3 pc (dotted), 10 pc (dot-dashed), 33 pc (dashed), and 100 pc (solid). The magnetic field within the cluster has been fixed on 10−5 G (a) and 10−6 G (b). The spectrum of leptons is normalized to the 30 MSPs with surface magnetic field 109 G and period 4 ms within the cluster at the distance of 5 kpc. (from Bednarek & Sitarek 2007).

Bednarek & Sitarek (2007), applying the sensitivities of present Cherenkov telescopes. Similar model has been considered more recently by Venter, de Jager & Clapson (2009). In this calculations it is assumed that leptons are injected from the inner millisecond pulsar magnetospheres through the light cylinder radii in terms of an isolated pulsar polar cap model (Venter & de Jager 2008). In such a case, the injection rate of leptons is directly linked to the pulsed γ-ray emission from the MSPs observed in the GeV energies. The results of calculations are shown in Fig. 6 for two GCs, Tuc 47 and Ter 5. The TeV γ-ray emission expected in this work is quite similar to those predicted by Bednarek & Sitarek (2007). Some differences are predicted at the sub-TeV γ-rays due to different shapes of assumed spectra for leptons. However, note that the GeV γ-ray emission predicted by Venter et al. (2009) for applied example parameters of the MSP population overestimates the EGRET upper limit for Tuc 47 (and also Fermi-LAT detection) by a factor of a few. Due to the lower γ-ray flux reported by the Fermi-LAT telescope from Tuc 47, the TeV γ-ray emission predicted by Venter et al. (2009) should be reduced by this same factor being on the level below sensitivity of the present HESS telescope system.

5.3 Constraints on the MSP population The GCs identified with the LAT γ-ray sources differ in GeV γ-ray power by an order of magnitude (Abdo et al. 2010a). This power seems to be correlated with the

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Fig. 6 Comparison of the γ-ray spectra expected from Tuc 47 (left) figures) and Ter 5 (right) with the sensitivities of different instruments (E - EGRET, G - Fermi-LAT, V -Veritas, H - HESS, and M - MAGIC). The sensitivities of Cherenkov telescopes are for the 5σ detection within 50 hrs. The γ-ray spectra has been calculated for different injection spectra of leptons from MSPs (from Bednarek & Sitarek 2007).

stellar encounter rate, derived for a specific GC. It is expected that the encounter rate determines the formation rate of compact binaries which are also responsible for the origin of the MSPs inside GCs. The encounter rate, Γe , can be estimated from the observed density of stars in the core of GC and the core radius (Gendre et al. 2003). Based on the observed γ-ray luminosity of specific GC, the average energy loss rate of MSP (adopted for MSPs observed in Tuc 47, Abdo et al. 2009a), and the average spin-down to γ-ray luminosity conversion efficiency (Abdo et al. 2009a), Abdo et al. (2010a) estimate the number of MSPs, NMSP , in specific GC. This number is confronted with the encounter rate (see Fig. 3 in Abdo et al. 2010a). The correlation between these values is well fitted by NMSP = (0.5 ± 0.2) × Γe + (18 ± 9). Note that, the populations of MSPs in specific GCs derived by Abdo et al. (2010a) are in good agreement with the estimates of the number of MSPs obtained with other methods (see e.g. estimates for Ter 5 by Fruchter & Goss (2000) and Kong et al. (2010)). The theoretical estimates of the TeV γ-ray fluxes triggered recent observations of some GCs by Cherenkov telescopes (Aharonian et al. 2009, Anderhub et al. 2009, McCutcheon et al. 2009). Unfortunately, only upper limits have been reported up to

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Fig. 7 Differential γ-ray spectra produced in the MSPs inner magnetospheres (curvature) and in the MSPs surrounding (inverse Compton) expected in the polar cup model for two globular clusters Tuc 47 and Ter 5. The magnetic field in Tuc 47 is assumed 10µG and in Ter 5 1µG. The γ-ray flux predicted by Harding et al. (2005) is marked by HUM05 and by Bednarek & Sitarek (2007) by BS07. The Fermi-LAT and HESS sensitivities and the EGRET upper limits are also marked (from Venter, de Jager & Clapson 2009, reproduced by permission of the AAS).

now. Based on the comparison of the models with these upper limits, it is possible to put constraints on the total energy in relativistic leptons which depend on the number of the MSPs within specific GC and the efficiency of energy conversion from rotating MSP to relativistic leptons. The results for a few northern hemisphere GCs (M13, M15, M5) are reported by the MAGIC and VERITAS Collaborations (Anderhub et al. 2009, McCuteon et al. 2009). The limits obtained for these GCs are still consistent with the expected population of MSPs in specific objects. The HESS Collaboration (Aharonian et al. 2009) reported upper limits for Tuc 47. Based on these limits the parameter space defined by the average strength of the magnetic field within GC and the number of millisecond pulsars has been constrained (see Fig. 7). In the most limiting case, the HESS upper limits constrain the number of MSPs in Tuc 47 on ∼ 80. All these above mentioned upper limits are not able to exclude the possibility of injection of leptons with the TeV energies into the GC radiation field. Future, more sensitive observations with the stage II Cherenkov arrays (HESS II, MAGIC II, new VERITAS arrangement), are very welcomed in order to start to constrain the models for acceleration of leptons by MSPs.

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Fig. 8 Upper limit on the number of MSPs in Tuc 47 as a function of the magnetic field strength within the pulsar nebula based on the model of Venter et al. (2009) and the HESS flux upper limit (from Aharonian et al. 2009, reproduced by permission of the A&A).

6 Gamma-rays from electrons injected from other sources ? We wonder whether particles injected from other sources or within other scenarios for the present radiative processes in the MSP surroundings might also contribute to the γ-ray flux observed by the Fermi-LAT telescope on the position of detected GCs. Let us consider the injection of electrons by other sources than MSPs within GCs. Note that, the spectra of leptons injected by the MSPs can be also characterised by different components as seems to be clear from modern observations and modelling of classical pulsars (e.g. polar and equatorial components, dependence of the spectrum of injected leptons on the angle above/below the rotational plane of the pulsar). We assume that electrons are injected with some specific energies from explicitly undefined source. These electrons might contribute to GeV γ-ray emission producing also some characteristic features in the multiwavelength spectrum which might be tested by the observations at other parts of the electromagnetic spectrum. We investigate the hypothesis that characteristic bumps observed in the GeV γ-rays are produced as a result of the Inverse Compton Scattering (ICS) of the CMBR by electrons with typical energies of the order of E e ∼ 600 GeV. Such electrons should mainly contribute to the GeV energy range (showing also characteristic cut-off at a few GeV )as a result of scattering of CMBR (estimated from Eγ ≈ εMBR (E e /me )2 ). Note that electrons with such energies should also produce synchrotron radiation. For the magnetic field of the order of expected within GCs, BGC ∼ 10−6 − 10−5 G, typical energies of synchrotron photons fall at energies,

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Fig. 9 The example γ-ray spectra produced by electrons in the ICS of the MBR and stellar radiation. Electrons with energies Ee ∼ 600 GeV diffuse in the magnetic field 10−6 G through the globular cluster Tuc 47. Diffusion process of electrons occurs on a time scale τdif = 0.01τBohm (dot-dashed curve) and 0.001τBohm (dotted). The lower energy bump is produced by scattering of the MBR and the sharp higher energy bump by scattering stellar photons.

E syn ∼ me (B/Bcr)γe2 ∼ 0.05 − 0.5 eV, i.e. in the optical range. The power emitted in these optical photons should be within an order of magnitude of the power observed in GeV γ-rays. Such emission can not be observable due to much stronger radiation field coming from the stellar population in the globular cluster. On the other hand, such relativistic electrons should comptonize stellar radiation in the KN regime producing γ-rays with the spectrum extending up to ∼ 600 GeV. The power in this radiation depends on the density of stellar photons (which can be even comparable to the density of the microwave background photons) and the diffusion time scale of electrons through the volume of the globular cluster. In order not to over-produce sub-TeV γ-ray emission in such a scenario, the diffusion time scale of electrons has to be much shorter than the Bohm diffusion. We have performed example calculations of the γ-ray spectra in terms of such scenario for the globular cluster Tuc 47, assuming that diffusion of electrons occurs on the time scale equal to: τdif = 0.01τBohm and 0.001τBohm (see Fig. 8). With these parameters, the GeV γ-ray emission measured from Tuc 47 can be reasonably described by the ICS of the MBR. The hard γ-ray spectrum, which extends above ∼ 10 GeV and cuts-off abruptly at a few hundred GeV, can not be constrained by the present upper limits derived by the HESS Cherenkov array. Note that the γ-ray emission envisaged in such a scenario should have angular extend larger than the typical size of the globular cluster. This extend might be studied with the present and future γ-ray telescopes and serve as a test of the possible contribution of a few hundred GeV electrons to the GeV γ-ray bump. In principle, the characteristic γ-ray spectrum measured by Fermi-LAT can be also explained as a result of ICS of stellar photons by electrons with typical energies

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Fermi E

2 dN dE

~

UMBR Uopt

−5 G B=10

b=10

−6

G

syn ~GHz

IC−MBR ~MeV

IC−Opt ~GeV

E

Fig. 10 As in Fig. 8 but for electrons with energies Ee ∼ 20 GeV which diffuse in the magnetic field of the order of 10−6 − 10−5 G through the globular cluster Tuc 47. Diffusion process of electrons occurs on the Bohm diffusion time scale. The Fermi-LAT γ-ray spectrum is produced by ICS of stellar radiation, the soft γ-rays are produced by scattering MBR and the synchrotron radio emission is due to synchrotron process.

of the order of ∼ 20 GeV. In fact, the IC cooling time scale for electrons with such energies is comparable to the Bohm diffusion time scale of such electrons within the opt ∼ 1.5 × 104 yrs. Therefore, it is expected that energy globular cluster, τIC ∼ τBohm dif is transferred efficiently from electrons to GeV γ-rays. Moreover, these electrons will also produce soft γ-rays as a result of comptonization of the MBR with typical energies, EγMBR ∼ εopt γe2 ∼ MeV. Since the IC scattering of optical photons and the MBR occurs in the Thomson regime, the relative power in the MeV γ-rays should be on the level of ∼ UMBR /Uopt ∼ 10−3 − 10−2 . The MeV γ-ray emission on such a level is at present undetectable by any instruments. Since the magnetic field energy density within the globular cluster is expected to be of the order of the energy density of the MBR then, we expect that synchrotron emission with similar power to that one produced in ICS process of the MBR should be also expected. Typical energies of these synchrotron photons are εsyn ≈ me c2 (B/Bcr)γe2 , i.e. they fall into ∼GHz frequencies. Radio emission with such power should be detectable by the present telescopes. Therefore, discovery of such diffuse radio emission from the globular clusters can provide a test for the mechanism discussed above. The general features of the broad band emission expected in this last possibility are shown in Fig. 10. In summary, other mechanisms or sources, than magnetospheric emission from the population of the millisecond pulsars, may also contribute to the characteristic bump in the γ-ray spectrum detected by Fermi-LAT from several globular clusters.

7 Conclusions Globular Clusters are abundant with different types of compact objects such as, millisecond pulsars, accreting neutron stars (LMXBs) and white dwarfs (Cataclysmic

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Variables) and possibly also black holes. These compact objects are expected to accelerate particles. They find well defined radiation field from whole population of stars. Therefore, Globular Clusters are likely sites for non-thermal high energy emission. In fact, it has been predicted that the population of MSPs within GCs can produce observable fluxes of GeV γ-rays which results from radiation processes in the inner pulsar magnetospheres (Harding et al. 2005, Venter & de Jager 2008). The steady GeV γ-ray emission has been recently detected from several GCs by the Fermi-LAT telescope (Abdo et al. 2009a, Abdo et al. 2010a). This emission can be naturally explained as a cumulative contribution from the whole population of MSPs within specific GC due to clear similarities of their spectral features to the population of MSPs in the Galactic field detected in γ-rays (Abdo et al. 2009b). A single MSP has not enough power to provide observed γ-ray fluxes from GCs. The application of the energy conversion efficiency from MSPs to γ-rays, derived for MSPs in the Galactic field, to the γ-ray emission from GCs allows to estimate the number of MSPs in specific GC. These numbers are consistent with the estimates of the MSP population in these GCs based on other methods. Note however, that such method assumes that MSPs in GCs and Galactic field have similar proprieties which is questioned in some works (e.g. Hui et al. 2010). Moreover, such comparison assumes that MSPs are the only sources contributing to the GeV γ-ray emission observed from GCs. Other objects within GCs, might also contribute to the γ-rays at GeV energies (e.g. accreting neutron stars or white dwarfs), either in their immediate surrounding or by injecting electrons with specific energies into the volume of GCs. In fact, the characteristic features of the GeV emission (flat spectrum and the cut-off above a few GeV) can be also well described in the scenario in which electrons with specific energies scatter predominantly stellar radiation or the MBR. In both cases, characteristic emission features are predicted at other parts of electromagnetic spectrum which might serve as a diagnostic of such possible processes. Also sources at the background field (e.g. galaxy clusters) or shocks created by GCs interacting with Galactic gas might contribute to γ-ray emission as often considered in the case of the non-thermal X-ray emission observed from GCs. MSPs within GCs should likely accelerate leptons up to very high energies at the inner pulsar magnetospheres, pulsar wind zones and/or wind shocks. These leptons gradually diffuse in the GC magnetic field interacting with its soft radiation field (Bednarek & Sitarek 2007, Venter et al. 2009). As a result, TeV γ-ray emission is expected from the inverse Compton scattering of soft radiation field (stellar, MBR, and from Galactic disk). Up to now, observations of GCs with the Cherenkov telescopes (Anderhub et al. 2009, Aharonian et al. 2009, McCutcheon et al. 2009) have provided only the upper limits which already start to constrain the population of the MSPs within GCs and the conditions for the diffusing process within GCs. Note that detection of TeV γ-ray emission from the whole population of MSPs in specific GCs should provide very useful additional constraints on the acceleration and injection process of leptons from the inner pulsar magnetosphere’s and pulsar winds. Therefore, they are very welcomed by the theoreticians working on pulsar electrodynamics. It is hoping that with the future sensitive observations with the advanced

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HESS, MAGIC and VERITAS telescope systems (or planned CTA) such positive detections will be possible. Acknowledgements This work is supported by the Polish MNiSzW grant N N203 390834.

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Modelling the Growing Population of γ-ray Millisecond Pulsars C. Venter, A. K. Harding, and T. J. Johnson

Abstract The Fermi Large Area Telescope, in collaboration with several groups from the radio community, have had marvellous success at uncovering new γ-ray millisecond pulsars (MSPs). In fact, MSPs now make up a sizable fraction of the total number of known γ-ray pulsars. The MSP population is characterized by a variety of pulse profile shapes, peak separations, and radio-to-γ phase lags, with some members exhibiting nearly phase-aligned radio and γ-ray light curves (LCs). The MSPs’ short spin periods underline the importance of including special relativistic effects in LC calculations, even for emission originating from near the stellar surface. We present results on modelling and classification of MSP LCs using standard pulsar model geometries.

1 Introduction To date, Fermi Large Area Telescope (LAT) has uncovered more than a dozen new γ-ray millisecond pulsars (MSPs) [17]. These MSPs were discovered by folding the γ-ray data with the known radio period, using timing solutions provided by various radio telescopes. Discovery of the first eight Fermi-LAT MSPs [1] indicated that these MSP pulse profiles and spectral properties mimic those of the younger pulsars, and that there are non-zero lags between the radio and γ-ray peaks. However, the discovery of PSR J0034−0534 [3] exhibiting phase-aligned γ-ray and radio peaks provided evidence for co-location of the radio and γ-ray emission regions. This phenomena has previously only been observed for the Crab pulsar. Recent detection of γ-ray pulsations aligned with the radio peaks [23, 4] from the famous ‘first’ MSP C. Venter Unit for Space Physics, North-West University, Potchefstroom Campus, Private Bag X6001, Potchefstroom 2520, South Africa A.K. Harding and T.J. Johnson Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_16, © Springer-Verlag Berlin Heidelberg 2011

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PSR J1939+2134 [6], as well as the first ‘black-widow’ MSP PSR J1959+2048 [15], now provide two more examples of this exceptional behaviour. Publication of a number of new γ-ray MSP detections are awaited [22] (some resulting from followup radio observations of unpulsed Fermi-LAT sources which appear in the First Fermi-LAT source catalogue), and the growing MSP population now constitute a significant fraction of all Fermi-LAT pulsar detections to date [2]. The γ-ray MSPs exhibit a variety of light curve (LC) shapes, and have been modelled using standard two-pole caustic (TPC), outer gap (OG), and pair-starved polar cap (PSPC) models [26], an annular gap model [11], lately also altitude-limited TPC / OG models [25], and lastly using a force-free magnetic field [7]. We elaborate on some of these models in Section 2. (See [17] for a review of γ-ray pulsar population modelling.)

2 Pulsar Models Below is a brief description of some modelling aspects (see [26] for details). B-field As before, we assume the retarded vacuum dipole field [10, 13] to be the basic geometric structure of the MSP magnetosphere. The magnetic moment is inclined by an angle α with respect to the spin axis, while ζ is the observer angle. Caustics Due to the rapid increase of the co-rotation velocity with altitude, approaching c as one reaches the light cylinder, it is important to include relativistic effects when calculating LCs. The effects of (i) B-field line curvature, (ii) time-offlight delays, and (iii) aberration combine to form intense caustic emission on the trailing field lines, while the emission is spread out on the leading field lines [20, 14]. Polar Cap (PC) Model The PC model [9] assumes extraction of primary charges from the stellar surface, acceleration of these charges to relativistic velocities along B-field lines, and subsequent γ-ray curvature radiation and pair creation at a very low altitude. A pair-formation front (PFF) is formed which screens the accelerating E-field (E|| ) parallel to the B-field. Faded PC Model This is a geometric approximation [25], where we use a rising and falling exponential function to modulate the assumed emissivity close to the stellar surface, as motivated by pair cascade modelling. PSPC Model When E || is not large enough to accelerate primary electrons to sufficiently high energies so pair cascades will occur, it will be unscreened, and one expects acceleration and radiation from the full open field line region above the PC [18, 19]. SG / TPC Model When enforcing the boundary condition that E || vanishes on the last open B-field lines (LOFLs), the PFF altitude becomes dependent on magnetic co-latitude, and narrow gaps form just inside of the LOFLs [5]. The SG model [21] may provide the framework for the geometric TPC model [12].

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Fig. 1 Altitude-limited TPC / OG LC fits for PSR J1939+2134 (panel [a]: γ-rays; panel [b]: γ,TPC γ,TPC radio) with (αTPC , ζ TPC ) = (65◦ , 80◦ ), (αOG , ζ OG ) = (70◦ , 90◦ ), (Rmin , Rmax ) = (0.12, 1.05)RLC , γ,OG γ,OG radio,TPC radio,TPC (Rmin , Rmax ) = (0.12, 1.00)RLC , (Rmin , Rmax ) = (0.93, 1.20)RLC , (Rradio,OG , Rradio,OG )= max min (0.75, 1.10)RLC . Fits for PSR J1959+2048 (panel [c]: γ-rays; panel [d]: radio) with (αTPC , ζ TPC ) = γ,TPC γ,TPC γ,OG γ,OG (60◦ , 80◦ ), (αOG , ζ OG ) = (55◦ , 85◦ ), (Rmin , Rmax ) = (Rmin , Rmax ) = (0.12, 1.20)RLC , radio,TPC radio,TPC radio,OG radio,OG (Rmin , Rmax ) = (0.95, 1.05)RLC , (Rmin , Rmax ) = (0.90, 1.10)RLC .

OG Model The Goldreich-Julian charge density [16] changes sign at the null charge surface (NCS), and OGs are assumed to form close to the LOFLs, above the NCS [8, 60]. Altitude-limited TPC / OG Models We lastly investigated geometric TPC / OG models with arbitrary lower, Rmin , and upper, Rmax , radial gap extensions [3].

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3 Results First 8 MSPs We found [26] that 6 of the 8 Fermi-LAT MSPs may be modelled using standard TPC / OG models, while 2 are exclusively fit by PSPC models. PSR J0034−0534 We found altitude-limited TPC / OG LC fits [3], with (α, ζ) = γ γ (30◦, 70◦ ), (Rmin , Rmax ) = (0.12, 0.9)RLC, and (Rradio , Rradio max ) = (0.6, 0.8)RLC, with min RLC = cP/2π, and P the pulsar period. There also exist solutions [25] for the faded PC model for (α, ζ) = (10◦ , ∼ 34◦ ), although the first ones seem more credible. PSR J1939+2134 and PSR J1959+2048 Figure 2 indicates altitude-limited TPC / OG LC fits with aligned radio and γ-ray pulses [4].

4 Discussion and Conclusions Our results indicate that the high-energy (HE) radiation comes from narrow gaps in the outer magnetosphere, requiring the presence of robust pair formation to screen much of the open field line region. However, MSPs do not produce enough pairs in the standard vacuum dipole models to screen E|| . Standard geometrical models still provide suitable LC fits though, and the resulting α and ζ are in reasonable agreement with fits from radio polarization measurements. In the case of phase-aligned γ-ray and radio pulses, we infer the existence of co-located emission regions, as well as high-altitude radio emission. Future work includes investigations of HE spectra using full radiation codes, collective emission from MSPs in globular clusters, and pulsar population studies. Acknowledgements CV is supported by the South African National Research Foundation. AKH acknowledges support from the NASA Astrophysics Theory Program.

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A Joint Radio Gamma-ray Variability Study of the Crab Pulsar Glenn Jones and Ryan Shannon

1 Introduction In order to understand pulsar emission, and coherent emission processes in general, it is important to assess the relationship between high energy and radio emission. Gamma-ray radio correlations can be used to test whether observed radio variability is solely the result of modifications to the radio emission processes (e.g., non-linear wave propagation [1]) or associated with bulk changes in the pulsar magnetosphere and charged particle flow (e.g., [2] and [3]). In the former case, gamma-ray emission would not be correlated with radio variability, but in the latter case, a pronounced correlation between gamma-rays would be expected. Giant radio pulses from the Crab pulsar [4] provide the best opportunity to study this relationship because they occur relatively frequently and provide a non-stationary signal which can be correlated against the high energy emission. Previous studies of radio-gamma-ray correlation (e.g., [5]) have been limited by sensitivity and observing time, yielding lenient upper limits. Here we describe an ongoing observing campaign to study the Crab pulsar simultaneously in radio and gamma-rays. This study will employ more than 500 hours of radio observations using the 34-m Goldstone Apple Valley Radio Telescope (GAVRT) synchronized with the periods when the Fermi/GLAST LAT instrument is sensitive to the Crab pulsar.

Glenn Jones National Radio Astronomy Observatory Jansky Fellow, resident at the California Institute of Technology, e-mail: jones\[email protected] Ryan Shannon Cornell University, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_17, © Springer-Verlag Berlin Heidelberg 2011

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2 Radio Observations The radio observations for this study are being carried out at the 34-meter DSS-28 antenna at the NASA Goldstone Deep Space Communications Complex in California, USA. This antenna is now operated as part of the Goldstone Apple Valley Radio Telescope, an educational outreach program run by the Lewis Center for Educational Research and the Jet Propulsion Laboratory. DSS-28 has recently been equipped with a novel wide bandwidth feed which covers 2.7–14 GHz instantaneously [6, 7]. Four independently tunable dual-polarization receivers can each down-convert a 2 GHz wide band within this frequency range to provide a total instantaneous bandwidth of 8 GHz. A flexible digital signal processing system is available to take full advantage of the capabilities of this receiver.

2.1 Signal Processing The flexibility of the DSS-28 receiver and signal processor enables a wide variety of possible observing modes. For studying the relationship between gamma-ray emission and giant radio pulses, the most important goal of the radio observations is simply to identify as many giant pulses as possible. As a baseline, the receiver is configured to produce a 512 MHz band, centered around 3.0 GHz, which is then digitized by the signal processing system. After digitization, a polyphase filterbank divides the band into 32 subbands of 16 MHz each. Up to eight bands, a total of 128 MHz, are then transmitted via 10 gigabit Ethernet to a powerful computer with a modern graphics processing unit (GPU). The enormous computational power of the GPU is leveraged to perform coherent dedispersion. We have modified the dedispersion code developed for the NRAO GUPPI pulsar processor [8] developed for the Green Bank Telescope by adding real time searching for pulses. The GPU is programmed to produce two data products. The first is simply a standard “search-mode” PSRFITS file with coherently dedispersed, detected data from each subband downsampled to approximately 1 µs time resolution. The second is bursts of raw undetected voltage data which contain events that were detected in real time as follows. For each subband, a segment of the coherently dedispersed data is detected. An additional time series is created by applying the appropriate dispersive delays to each subband and adding them together, to form a dedispersed and detected time series for the full bandwidth. Each of the time series, both the subbands and the full bandwidth, are searched for events exceeding a preset threshold, which is set for each subband based on the statistics of that time series. Different criteria can be used to accept an event as legitimate, but currently we require events in either the full bandwidth time series, or in at least two of the subbands. If an event is detected, the raw, undetected data from this segment is written to disk for further offline analysis. Each time series is then averaged and downsampled by a factor of two and compared to another appropriately adjusted set of thresholds. The same

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criteria is used to judge if an event has occurred and should be recorded, and the process repeats until the coarsest time resolution (typically 64 µs) is reached. An example of a giant pulse detected in this way is shown in figure 1. The raw voltage data from each candidate pulses are then analyzed to obtain various parameters including the arrival time, the observation frequency, the rotational phase of the pulse, the calibrated fluence (in Jy·s), the effective pulse width, and the significance of the detection in each subband. All of these parameters are stored in a database that will eventually be globally accessible and available to all scientists interested in studying giant pulses.

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In addition to the continuously recorded, 128 MHz bandwidth data products just described, the digital signal processor can also be configured to record bursts over several gigahertz for up to one second when triggered. An early demonstration of this system is shown in figure 2. Detailed study of the phase and frequency variability of giant pulses may eventually lead to more insight into the connection with high energy emission, for example through refined correlation analysis. In this example, a 256 MHz band indicated by the dotted white lines was incoherently dedispersed in real time to provide the trigger. In the future, the coherently dedispersed 128 MHz system may be used to provide a more sensitive trigger.

3 Gamma-Ray Radio Correlation The time series of detected giant pulses will be compared to gamma-ray events associated with the Crab pulsar. The gamma-ray time series will be formed by isolating events detected by the LAT instrument on the Fermi Space Telescope originating in the direction of the Crab pulsar. We will assess if there is a correlation between the time series, using a variety of energy and flux thresholds for both the GP and gamma-ray events [5, 9].

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Fig. 2 A single giant pulse recorded from 2.8–4.8 GHz. Each polarization and sideband was processed independently. The panel to the left of the dynamic spectra shows the spectrum averaged over the on pulse region indicated by the dotted vertical red lines in the top time domain plots. On the right, time series for each of eight equal subbands are plotted.

Acknowledgements The authors thank Paul Demorest for sharing the GUPPI coherent dedispersion code and the Lewis Center for Educational Research for supporting the radio observations at DSS-28. This work was partially supported by NASA through a grant from the Fermi Space Telescope guest observer program. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

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References 1. 2. 3. 4. 5. 6. 7. 8. 9.

S. A. Petrova, A&A 424, 227 (2004). M. Kramer, A. G.Lyne, J. T. OBrien, C. A.Jordan, D. R. Lorimer, Science 312, 549 (2006) M. Lyutikov, MNRAS 381, 1190 (2007). D. H.Staelin, E. C. Reifenstein III, Science 162, 1481(1968) S. C. Lundgren, J. M. Cordes, M. Ulmer, S. M. Matz, S. Lomatch, R. S. Foster, T. Hankins, ApJ 453, 433 (1995). G. Jones, Instrumentation for wide bandwidth radio astronomy. Ph.D. thesis, California Institute of Technology (2010). URL http://resolver.caltech.edu/CaltechTHESIS:10122009094525715 W. A. Imbriale, in Proc. IEEE Aerospace Conference (2007), pp. 112. S. M. Ransom, P. Demorest, J. Ford, R. McCullough, J. Ray, R. DuPlain, P. Brandt, inAmerican Astronomical Society Meeting Abstracts, vol. 214 (2009), vol. 214, pp. 605.08 A. V. Bilous, V.I. Kondratiev, M.A. McLaughlin, M. Mickaliger, D.R. Lorimer, S.M. Ransom, M. Lyutikov, B. Stappers, G.I. Langston, ArXiv e-prints (2009)

AGILE observations of PSR B1509-58 Is QED photon splitting at work in pulsars? M. Pilia and A. Pellizzoni for the AGILE Team and Pulsar Working Group

Abstract We present the results of new AGILE observations of PSR 1622−4950 performed over a period of ∼2.5 years following the detection obtained with preliminary data. The modulation significance of the lightcurve above 30 MeV is at a 5σ confidence level and the lightcurve is similar to those found earlier up to 30 MeV by COMPTEL: a broad asymmetric first peak reaching its maximum 0.39 ± 0.02 cycles after the radio peak plus a second peak at 0.94 ± 0.03. The γ-ray spectral energy distribution of pulsed flux is well described by a power-law (photon index α = 1.87 ± 0.09) with a remarkable cutoff at E c = 81 ± 20 MeV, representing the softest spectrum observed among γ-ray pulsars so far. The unusual soft break in the spectrum of PSR B1509-58 has been interpreted in the framework of polar cap models as a signature of the exotic photon splitting process in the strong magnetic field of this pulsar. In the case of an outer-gap scenario, or the two pole caustic model, better constraints on the geometry of the emission would be needed from the radio band in order to establish whether the conditions required by the models to reproduce AGILE lightcurves and spectra match the polarization measurements.

1 Introduction PSR 1622−4950 was discovered as an X-ray pulsar with the Einstein satellite and soon detected also at radio frequencies (Manchester et al. 1982), with a derived distance supporting the association with the SNR MSH 15-52 (d ∼ 5.8 kpc). With a period P ≃ 150 ms and a period derivative P˙ ≃ 1.53 × 10−12 s s−1 , assuming the M. Pilia Dipartimento di Fisica, Universit`a dell’Insubria, Via Valleggio 11, I-22100 Como, Italy, e-mail: [email protected] A. Pellizzoni INAF–Osservatorio Astronomico di Cagliari, localit`a Poggio dei Pini, strada 54, I-09012 Capoterra, Italy e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_18, © Springer-Verlag Berlin Heidelberg 2011

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standard dipole vacuum model, the estimated spin-down age for this pulsar is 1570 years and its inferred surface magnetic field is one of the highest observed for an ordinary radio pulsar: B ≈ 3.1×1013 G, as calculated at the pole. Its rotational energy loss rate is E˙ ≈ 1.8 × 1037 erg/s. The young age and the high rotational energy loss rate made this pulsar a promising target for the γ-ray satellites. In fact, the instruments on board of the Compton Gamma-Ray Observatory (CGRO) observed its pulsation at low γ-ray energies, but it was not detected with high significance by the Energetic Gamma-Ray Experiment Telescope (EGRET), the instrument operating at the energies from 30 MeV to 30 GeV. The Italian satellite AGILE (Tavani et al. 2009) obtained the first detection of PSR 1622−4950 in the EGRET band (Pellizzoni et al. 2009b) confirming the occurrence of a spectral break. Here we present the results of a ∼ 2.5 yr monitoring campaign of PSR 1622−4950 with AGILE, improving counts statistics, and therefore lightcurve characterization, with respect to earlier AGILE observations. With these observations the spectral energy distribution (SED) at E < 300 MeV is assessed, where the remarkable spectral turnover is observed.

2 AGILE Observations, Data Analysis and Results AGILE devoted a large amount of observing time to the region of PSR 1622−4950. For details on AGILE observing strategy, timing calibration and γ-ray pulsars analysis the reader can refer to Pellizzoni et al. (2009a,b). A total exposure of 3.8 × 109 cm2 s (E > 100 MeV) was obtained during the 2.5 yr period of observations (July 2007 - October 2009) which, combined with AGILE effective area, gives our observations a good photon harvest from this pulsar. Simultaneous radio observations of PSR 1622−4950 with the Parkes radiotelescope in Australia are ongoing since the epoch of AGILE’s launch. Strong timing noise was present and it was accounted for using the f itwaves technique developed in the framework of the TEMPO2 radio timing software (Hobbs et al. 2004, 2006). Using the radio ephemeris provided by the Parkes telescope, we performed the folding of the γ-ray lightcurve including the wave terms (Pellizzoni et al. 2009a). An optimized analysis followed, aimed at cross-checking and maximization of the significance of the detection, including an energy-dependent events extraction angle around source position based on the instrument point-spread-function (PSF). The chi-squared (χ2 )-test applied to the 10 bin lightcurve at E > 30 MeV gave a detection significance of σ = 4.8. The unbinned Zn2 -test gave a significance of σ = 5.0 with n = 2 harmonics. The difference between the radio and γ-ray ephemerides was ∆Pradio,γ = 10−9 s, at a level lower than the error in the parameter, showing perfect agreement among radio and γ-ray ephemerides as expected, further supporting our detection and AGILE timing calibration. We observed PSR 1622−4950 in three energy bands: 30–100 MeV, 100–500 MeV and above 500 MeV. We did not detect pulsed emission at a significance σ ≥ 2 for

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E > 500 MeV. The γ-ray lightcurves of PSR 1622−4950 for different energy bands are shown in Fig. 1. The AGILE E > 30 MeV lightcurve shows two peaks at phases φ1 = 0.39 ± 0.02 and φ2 = 0.94 ± 0.03 with respect to the single radio peak, here put at phase 0. The phases are calculated using a Gaussian fit to the peaks, yielding a FWHM of 0.29(6) for the first peak and of 0.13(7) for the second peak, where we quote in parentheses (here and throughout the paper) the 1σ error on the last digit. The first peak is coincident in phase with COMPTEL’s peak (Kuiper et al. 1999). In its highest energy band (10–30 MeV) COMPTEL showed the indication of a second peak (even though the modulation had low significance, 2.1σ). This second peak is coincident in phase with AGILE’s second peak (Fig. 1). AGILE thus confirms the previously marginal detection of a second peak. Based on our exposure we derived the γ-ray flux from the number of pulsed counts. The pulsed fluxes in the three AGILE energy bands were Fγ = 10(4) × 10−7 ph cm−2 s−1 in the 30–100 MeV band, Fγ = 2.1(5) × 10−7 ph cm−2 s−1 in the 100–500 MeV band and a 1σ upper limit Fγ < 8 × 10−8 ph cm−2 s−1 for E > 500 MeV. Fig. 2 shows the SED of PSR 1622−4950 based on AGILE’s and COMPTEL’s observed fluxes. COMPTEL observations suggested a spectral break between 10 and 30 MeV. AGILE pulsed flux at energies E > 30 MeV confirms the presence of a soft spectral break, but the detection of significant emission at E > 100 MeV hints to a cutoff at slightly higher energies. As shown in Fig. 2, we modeled the observed fluxes with a power-law plus cutoff fit using the Minuit minimization package (James et al. 1975): F(E) = k × E −α exp[−(E/Ec )β ], with three free parameters: the normalization k, the spectral index α, the cutoff energy Ec and allowing β to assume values of 1 and 2. No acceptable χ2 values were obtained for β = 2, while for an β = 1 we found χ2ν = 3.2 for ν = 2 degrees of freedom, corresponding to a null hypothesis probability of 0.05. The best values thus obtained for the parameters of the fit were: k = 1.0(2) × 10−4, α = 1.87(9), Ec = 81(20) MeV.

3 Discussion The bulk of the spin-powered pulsar flux is usually emitted in the MeV-GeV energy band with spectral breaks at ≤ 10 GeV (e.g. Abdo et al. 2010). PSR 1622−4950 has the softest spectrum observed among γ-ray pulsars, with a sub-GeV cutoff at E ≈ 80 MeV. When PSR 1622−4950 was detected in soft γ-rays but not significantly at E > 30 MeV, it was proposed that the mechanism responsible for this low-energy spectral break might be photon splitting (Harding et al. 1997). The photon splitting (Adler et al. 1970) is an exotic third-order quantum electro-dynamics process expected when the magnetic field approaches or exceeds the critical value defined as Bcr = m2e c3 /(e¯h) = 4.413 × 1013 G. In very high magnetic fields the formation of pair cascades can be altered by the process of photon splitting: γ → γγ.

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In the case of PSR 1622−4950 a polar cap model with photon splitting would be able to explain the soft γ-ray emission and the low energy spectral cutoff, now quantified by AGILE observations. Based on the observed cutoff, which is related to the photons’ saturation escape energy, we can derive constraints on the magnetic field strength at emission, in the framework of photon splitting: sat ǫesc ≃ 0.077(B′ sin θkB,0 )−6/5

B′

(1)

where ǫesc is the photon saturation escape energy, = B/Bcr and θkB,0 is the angle between the photon momentum and the magnetic field vectors at the surface and is here assumed to be very small: θkB,0 ≤ 0.57◦ (Harding et al. 1997). Using the observed cutoff (E = 80 MeV) we find that B′ ≥ 0.3, which implies an emission altitude ≤ 1.3R NS , which is the height where also pair production could ensue. This altitude of emission is in perfect agreement with the polar cap models (see Daugherty & Harding 1996). The scenario proposed by Harding et al. (1997) is strengthened by its prediction that PSR B0656+14 should have a cutoff with an intermediate value between PSR 1622−4950 and the other γ-ray pulsars. Additionally, PSR 1622−4950 (Kuiper et al. 1999, Crawford et al. 2001) and PSR B0656+14 (De Luca et al. 2005, Weltevrede et al. 2010) show evidence of an aligned geometry, which could imply polar cap emission. The polar cap model as an emission mechanism is debated. From the theoretical point of view, the angular momentum is not conserved in polar cap emission (Cohen & Treves 1972, Holloway 1977, Treves et al. 2010). And a preferential explanation of the observed γ-ray lightcurves with high altitude cascades comes from the recent results by Fermi (Abdo et al. 2010). In the case of PSR 1622−4950, the derived γ-ray luminosity from the flux at E > 1 MeV, considering a 1 sr beam sweep, is Lγ = 5.7+0.1 × 1035 erg/s. The convertion efficiency of the rotational energy loss −0.5 (E˙ ≈ 1.8 × 1037 erg s−1 , see §1) into γ-ray luminosity is 0.03. If the γ-ray luminosity cannot account for most of the rotational energy loss, then the angular momentum conservation objection becomes less cogent for this pulsar. Alternatively, an interpretation of PSR 1622−4950 emission can be sought in the frame of the three dimensional outer gap model (Zhang & Cheng 2000). According to their model, hard X-rays and low energy γ-rays are both produced by synchrotron self-Compton radiation of secondary e+ e− pairs of the outer gap. Therefore, as observed, the phase offset of hard X-rays and low energy γ-rays with respect to the radio pulse is the same, with the possibility of a small lag due to the thickness of the emission region. According to their estimates a magnetic inclination angle α ≈ 60o and a viewing angle ζ ≈ 75o are required to reproduce the observed lightcurve. Finally, using the simulations of Watters et al. 2009), the observed lightcurve from AGILE is best reproduced if α ≈ 35◦ and ζ ≈ 90◦ , in the framework of the two pole caustic model (Zyks & Rudak 2003). The values of α and ζ required by the Zhang & Cheng model are not in good agreement with the corresponding values obtained with radio measurements. In fact, Crawford et al. (2001) observe that α must be < 60◦ at the 3σ level. The prediction obtained by the simulations of Watters et al. better agrees with the radio polarization

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observations. In fact, Crawford et al. also propose that, if the restriction is imposed that ζ > 70◦ (Melatos 1997), then α > 30◦ at the 3σ level. For these values, however, the Melatos model for the spin down of an oblique rotator predicts a braking index n > 2.86, slightly inconsistent with the observed value (n = 2.839(3)). Therefore, at present the geometry privileged by the state of the art measurements is best compatible with polar cap models. Acknowledgements M.P. thanks A. Treves for useful discussion and comments. AGILE is funded by the Italian Space Agency (ASI), with programmatic participation by the Italian Institutes of Astrophysics (INAF) and Nuclear Physics (INFN). The Parkes radiotelescope is funded by the Commonwealth Government as part of the ATNF, managed by CSIRO.

Fig. 1 Phase-aligned γ-ray light-curves of PSR 1622−4950 with radio peak at phase 0. From the top: AGILE > 100 MeV, 20 bins, 7.5 ms resolution; AGILE < 100 MeV, 10 bins, 15 ms resolution; COMPTEL 10–30 MeV and COMPTEL 0.75–30 MeV (from Kuiper et al. (1999).

References 22. Abdo, A. A. et al. 2010, ApJS, 187, 460 22. Adler, S. L., et al. 1970, PhRevL, 25, 1061 22. Cohen, R. H. & Treves, A. 1972, A&A, 20, 305

Fig. 2 SED of PSR 1622−4950 (solid line) obtained from a fit of pulsed fluxes from soft to hard γ-rays. The circular points represent COMPTEL observations. The square points represent AGILE pulsed flux at 30 < E < 100 MeV and 100 < E < 500 MeV. The horizontal bar represents AGILE upper limit above 500 MeV.

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22. Crawford, F., Manchester, R. N., & Kaspi, V. M. 2001, AJ, 122, 2001 22. Daugherty, J. K. & Harding, A. K. 1996, ApJ, 458, 278 22. De Luca, A., Caraveo, P. A., Mereghetti, S., Negroni, M., & Bignami, G. F. 2005, ApJ, 623, 1051 22. Dyks, J. & Rudak, B. 2003, ApJ, 598, 1201 22. Harding, A. K., Baring, M. G., & Gonthier, P. L. 1997, ApJ, 476, 246 22. Hobbs, G., Lyne, A. G., Kramer, M., Martin, C. E., & Jordan, C. 2004, MNRAS, 353, 1311 22. Hobbs, G. B., Edwards, R. T., & Manchester, R. N. 2006, MNRAS, 369, 655 22. Holloway, N. J. 1977, MNRAS, 181, 9P 22. James, F. & Roos, M. 1975, Computer Physics Communications, 10, 343 22. Kuiper, et al. 1999, A&A, 351, 119 22. Manchester, R. N., Tuohy, I. R., & Damico, N. 1982, ApJL, 262, L31 22. Melatos, A. 1997, MNRAS, 288, 1049 22. Pellizzoni et al. 2009a, ApJ, 691, 1618 22. Pellizzoni, A. et al. 2009b, ApJL, 695, L115 22. Tavani, M. et al. 2009, A&A, 502, 995 22. Treves, A., Pilia, M. & Lopez, M. 2010, A&A, submitted 22. Watters, K. P., Romani, R. W., Weltevrede, P., & Johnston, S. 2009, ApJ, 695, 1289 22. Weltevrede, P. et al. 2010, ApJ, 708, 1426 22. Zhang, L. & Cheng, K. S. 2000, A&A, 363, 575

Understanding the fundamental parameters of millisecond pulsars Benoit Pancrazi

Abstract How the high energy emission from millisecond pulsars (MSPs) is generated is currently unclear. It has been proposed that the acceleration of charged particles and the radiation of high energy photons can occur in the neutron star vicinity (polar cap model), along the last open field line (slot gap model) and/or further into the magnetosphere, in a region close to the light cylinder (outer gap model). Different signatures are expected for these models that can be identified through spectral and timing analysis. For this purpose, we have explored the XMM-Newton datasets of five millisecond pulsars that have not previously been observed in X-rays. Thanks to the accurate timing analysis of this sample, we compare for the first time radio, X-ray and γ-ray absolute pulse profiles of these faint X-ray sources. This study combined with spectral analysis allows us to make constraints on the size and location of the emission regions in each energy domain. Furthermore, the orientation as well as the mass and radius of the neutron star can be estimated through modelling of the brightest MSP X-ray pulse profiles. We present the latest models that account for the thermal emission produced by a heated polar cap on the surface of a rapidly rotating neutron star, and show how we can use them to constrain the equation of state of the neutron star dense matter.

1 Introduction Millisecond pulsars (MSPs) are rapidly rotating neutron stars that are known to emit mainly in radio. However, observations in other energy domains carried out in recent decades show substantial evidence for an emission in X-rays and/or in γ-rays [11, 1]. How this high energy radiation is generated is still unclear. It is thought that the acceleration of charged particles (e± ) to extreme relativistic energies Benoit Pancrazi Centre d’Etude Spatiale des Rayonnements, CNRS/UPS, 9 avenue du Colonel Roche, 31028 Toulouse Cedex 04, France, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_19, © Springer-Verlag Berlin Heidelberg 2011

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could occur in regions of magnetospheric charge depletion (gaps), where a very high electric potential exists. Three main models based on different acceleration region geometries and locations have been proposed : the polar cap (PC), the slot gap (SG) and the outer gap (OG) models [7, 2, 5]. Whether one or a combination of these models can account for the high energy emission from MSPs is still an open question. Using absolute timing in the radio, X-rays and γ-rays, we can evaluate the width, shape and phase shift of the pulsed emission in each energy domain, and draw conclusions on the size and location of the emitting regions. Furthermore, the nature of the emission can be constrained using phase resolved spectroscopy. It has been shown that the X-ray emission coming from rotation powered pulsars consists of thermal and non-thermal components [6]. Thermal radiation is expected to arise from heating of the PC by backflowing e± , as non-thermal emission could be due to synchrotron emission at high altitude. Furthermore, the low surface magnetic fields of MSPs imply that the accelerating field (Ek ) is unscreened over most if not all of the PC, and e± will consequently continue to accelerate and radiate to high altitudes. In this context, high-energy emission could also be produced by Inverse Compton Scattering (ICS) of thermal X-rays by primary e± , or by resonant cyclotron absorption of radio photons at high altitude followed by spontaneous synchrotron radiation [8]. ICS pair fronts have also been shown to be very important for heating the PC and producing detectable thermal X-rays [7]. Moreover, pulsar-driven synchrotron nebulae or the interaction of pulsar winds with a close companion star can play a significant role in the X-ray emission coming from MSPs. So far, ten detections of MSPs in X-rays associated with spectra and timing solutions have been reported [11]. The enlargement of this sample is of crucial importance if we want to discriminate between the competing high energy models. Thus the present study is a significant step forward. Taking advantage of the large collecting area and high timing accuracy of XMM-Newton, it is becoming possible to perform reliable spectral and timing analysis of faint MSPs in X-rays. Recently, Fermi Large Area Telescope (LAT) observations revealed a pulsed emission in γ-rays coming from MSPs [1]. It has been shown that γ-ray MSPs are divided into two sub-classes, either described by pair-starved PC (PSPC) or by SG/OG models [10]. In this study, an empirical model which assumes that the radio emission consists of a core beam centred on the magnetic axis, and one or more surrounding hollow cone beams was also developed. These hypotheses combined with absolute timing analysis will allow us to improve our knowledge of MSPs. Finally, important information can be obtained through modelling of the X-ray pulse profile, when the emission is dominated by thermal radiation [3]. The model considers a relativistic rotating neutron star with two identical hot spots located at the magnetic poles, and accounts for gravitational light bending, aberration, Doppler boosting and propagation time delays in a nonrotating Schwarzschild metric. Radiative transfer processes are also included in the context of an unmagnetized (B < 109 G), optically thick H atmosphere. By fitting parameters such as viewing angle or magnetic inclination, it is possible to constrain the mass to radius ratio of the brightest MSPs, and therefore the equation of state of neutron star matter.

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2 Observations and data analysis PSR J0613−0200, PSR J1911−1114, PSR J2129−5721, PSR J1600−3053 and PSR J1853+1303 were observed in X-rays with XMM-Newton. We processed the data and extracted the events using standard techniques (see [9]). We used the task barycen and the coordinates given by radio observations to convert times of arrival (TOAs) measured in the local satellite frame to Barycentric Dynamical Time (TDB). The γ-ray data were taken during the first year survey of the Fermi LAT. To derive γ-ray pulse profiles, we selected events above 100 MeV within a region of interest (ROI) of 1◦ or 0.5◦ , depending on the Galactic latitude of the MSP, using the task gtselect of the Fermi Science Tools1 . TOAs were converted to TDB with gtbary. For both X-ray and γ-ray timing analysis, the TEMPO22 package was used to convert barycentred TOAs into phase values with the ephemerides provided by the the Nanc¸ay or Parkes radio telescopes. We compare the phase alignment of the absolute pulse profiles by fitting the main fluctuations using the software QDP/PLT3 . The extraction of γ-ray spectra was done by considering ROI of angular width 10◦ , and modelling the nearby strong pointlike sources as well as the diffuse Galactic plus extra-Galactic γ-ray emission using gtlike. We fitted the spectrum of the MSP with an exponential cutoff power law of the form N0 (E/100 MeV)−Γ e−E/Ec where N0 is the normalisation factor and E c , the cutoff energy.

3 Discussion and conclusion The X-ray timing analysis of PSR J0613−0200 (Figure 1) reveals a main peak (X1 ) aligned and of similar width to the radio peak which is expected to be produced in a region close to the PC, as stated above. X1 is therefore consistent with thermal emission coming from the PC of the pulsar. Interestingly, the similar widths of X1 and the radio peak suggest that the extensions of the emitting regions are of comparable size. This conclusion is strengthened by the spectral analysis which revealed that it was possible to fit the soft X-ray spectrum with a thermal component, when using the γ-ray fitting parameters to constrain the non-thermal X-ray radiation. Furthermore, it has been shown that the best model fits to the γ-ray lightcurve are likely to be given by magnetospheric models (SG/OG) [10], which is consistent with a phase shift between the main γ-ray and the radio peaks. For both PSR J1911−1114 and PSR J2129−5721, the X-ray pulse profiles show two main fluctuations, one that is aligned and of similar width to the radio peak, and a second one that could result from the emission coming from the antipodal heated PC of the pulsar. As for PSR J0613−0200, the X-ray spectral analysis revealed possible further support for thermal emission coming from the PC. 1 2 3

http://fermi.gsfc.nasa.gov/ssc/data/analysis/ http://www.atnf.csiro.au/research/pulsar/tempo2 http://heasarc.gsfc.nasa.gov/docs/software/ftools/others/qdp/qdp.html

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Fig. 1 From top to bottom: a) γ-ray (0.1-300 GeV, 40 bins), b) X-ray (0.55-4.5 keV, 22 bins) and c) radio (1336 MHz) pulse profiles of PSR J0613−0200. The error bars represent a 1 σ deviation. The background level is indicated by the dashed line. The analysis revealed that X1 and the radio structure are aligned and of similar widths, which suggests that part of the X-ray radiation (thermal component) and the radio emission are produced in the same region.

Evidence for pulsations in the X-ray emission coming from PSR J1600−3053 and PSR J1853+1303 were found, although these MSPs appear to be very faint Xray sources. Amongst our sample, PSR J1600−3053 is the only one for which radio and X-ray pulse profiles show a shift in phase. The current models accounting for thermal emission in X-rays [3] are limited by the spin period P of the considered neutron star, as the effect of rotation-induced oblateness becomes important when P . 3 ms [4]. We have included this in a model based on [3], and used the constraints that can be made on the viewing geometry from the modelling of the γ-ray lightcurves. Thus, we will be able to make much tighter constraints on the neutron star equation of state for MSPs showing predominantly thermal X-ray spectra, and for which X-ray pulsations have been detected such as PSR J0437−4715 or PSR J2124−3358.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Abdo, A. A., et al. (Fermi LAT Collaboration) 2009, Science, 325, 848 Arons, J., Scharlemann, E. T. 1979, ApJ, 231, 854 Bogdanov, S., Rybicki, G. B., Grindlay, J. E. 2007, ApJ, 670, 668 Cadeau, C., et al. 2007, ApJ, 654, 458 Cheng, K. S., Ho, C., Ruderman, M. 1986, ApJ, 300, 500 Cheng, K. S., Zhang, L. 1998, ApJ, 515, 337 Harding, A. K., Muslimov, A. G. 2002, ApJ, 568, 862 Harding, A. K., Usov, V. V., Muslimov, A. G. 2005, ApJ, 622, 531 Pancrazi, B., et al. in prep. Venter, C., Harding, A. K., Guillemot, L. 2009, arXiv, 0911.0872 Webb, N. A., et al. 2004, A&A, 419, 269

Pulsars as gravitational wave detectors George Hobbs

Abstract Pulsar timing array projects are carrying out high precision observations of millisecond pulsars with the aim of detecting ultra-low frequency (∼ 10−9 to 10−8 Hz) gravitational waves. We show how unambiguous detections of such waves can be obtained by identifying a signal that is correlated between the timing of different pulsars. Here we describe the ongoing observing projects, the expected sources of gravitational waves, the processing of the data and the implications of current results.

1 Introduction The first strong evidence for the existence of gravitational waves (GWs) was obtained by measuring the orbital period decay in the PSR B1913+16 binary pulsar system [25, 59, 62]. Various ground- and space-based detectors have been developed with the aim of making a direct detection of GW signals. Unfortunately, to date, no such detection has been made. Millisecond pulsars are amazingly stable rotators. In many cases a simple model for the pulsar spin-down can be used to predict pulse times-of-arrival (TOAs) with an accuracy and precision of < 1µs over many years of observation. The pulsar timing technique relies on this stability to obtain precise measurements of a pulsar’s spin, astrometric and orbital parameters. However, in some cases the pulse TOAs are not exactly as predicted, suggesting that the model and analysis procedure do not parameterise all of the physical effects that are affecting the pulse emission, propagation and detection. As the effects of GWs are not included in the analysis, the existence of any such waves will induce deviations between the actual and predicted TOAs (commonly known as the ‘timing residuals’). Here we describe how these George Hobbs CSIRO Australia Telescope National Facility, PO Box 76 Epping NSW 1710, Australia, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_20, © Springer-Verlag Berlin Heidelberg 2011

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signals may be unambiguously confirmed as being caused by GWs and provide upper bounds on their amplitude. In §2 we provide a basic explanation of how pulsar data sets may be used in the search for GWs, §3 describes current data sets and highlights some aspects of the data that need careful consideration when the data are processed, §4 lists potential sources of GWs, §5 describes how data sets may be accessed and §6 highlights future possibilities.

2 Using pulsars to search for GWs Pulsar observations lead to measurements of TOAs at an observatory. The tempo2 software package [10, 23] can be used to convert these TOAs to a time of emission by 1) transforming the TOAs to the Solar System barycentre, 2) determining excess propagation delays caused by the interstellar medium and, for binary systems, 3) transforming to the pulsar frame. The derived time of emission can then be compared with a pulsar model to form the timing residuals. The induced pulsar timing residuals caused by a GW signal were first calculated at the end of the 1970s [9, 52]. This early work showed that a GW signal causes a fluctuation in the observed pulse frequency, δν/ν, which induces pulsar timing residuals at time t from the initial observation as Z t δν(t) R(t) = − dt. (1) ν 0 The Dopper shift can be shown to have the form (e.g. [17]) δν p = H i j (heij − hi j ) ν

(2) p

where heij is the GW strain at the Earth at the time of observation, hi j the strain at the pulsar when the electromagnetic pulse was emitted and H i j is a geometrical term that depends upon the angle between the Earth, pulsar and GW source. The GW strains evaluated at the positions of multiple pulsars will be uncorrelated, whereas the component at the Earth will lead to a correlated signal in the timing residuals of all pulsars. Hobbs et al. (2009 [21]) demonstrated how pulsar TOAs affected by GWs can be simulated using the tempo2 software package. Since the intrinsic pulsar pulse period, spin-down, orbital motion and various astrometric parameters are a priori unknown, they need to be determined from the pulsar timing data. Initial estimates of the pulsar parameters are used to form pre-fit timing residuals. A least-squares fitting procedure is subsequently used to fit an analytical model to obtain improved pulsar parameters and “post-fit” timing residuals (see [23]). In Figure 1 we plot preand post-fit timing residuals for a simulated pulsar in the presence of GWs from 1)

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Fig. 1 Simulations of pre-fit (left column) and post-fit (right column) timing residuals. The first row simulates a non-evolving, black-hole binary system defined by A+ = AX = 5 × 10−14 and ω = 1 × 10−7 . The second row contains a simulation of the predicted timing residuals from the evolving source 3C66B (see Section 4). The third row contains a GW burst with memory source leading to a change in rotational frequency ∆ν = 1 × 10−12 Hz and the bottom row is a realisation of a GW background defined by α = −2/3 and A = 10−14 .

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Fig. 2 The expected correlation in the timing residuals of pairs of pulsars as a function of angular separation for an isotropic GW background (solid line). The points correspond to simulated pulsar data sets in the presence of a GW background with power-law index α = +3/2 and amplitude A = 0.01; Figure from Hobbs et al. (2009, [21]).

a single, non evolving binary black-hole system, 2) an evolving binary black-hole system, 3) a burst GW source and 4) an isotropic stochastic background of GWs. It is not possible to determine the exact origin of the timing residuals for a single pulsar data set. Any observed residuals may have been caused by, for example, irregularities in terrestrial time standards [48], errors in the planetary ephemeris, irregular spin-down of the pulsar [19], calibration effects (e.g. [66]) or GWs. These effects can only be distinguished by searching for correlations in the timing residuals of multiple pulsars. For instance, residuals caused by the irregular spin-down of one pulsar will be uncorrelated with the residuals observed for a different pulsar. Irregularities in terrestrial time standards will lead to correlated residuals for all pulsars (this is only true for data sets which have the same data span; see Section 3). For an isotropic, stochastic GW background, the GW strain at each pulsar will be uncorrelated, but the GW strain at the Earth provides a common signal. The common signal for such a background was determined by Hellings & Downs (1983) and is reproduced in Figure 2. More recently it has been shown that approximately 20 pulsars are necessary, timed with an rms timing residual of ∼100 ns or better over five years with observations every week, in order to make a significant detection of a possible GW background signal [28]. Pulsar timing experiments are sensitive to GW signals in the ultra-low frequency band (f ∼ 10−9 to 10−8 Hz) as individual pulsars are typically only observed once every few weeks, have maximum data spans of years to decades and require the

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Fig. 3 Characteristic strain sensitivity for existing and proposed GW detectors as a function of GW frequency. Predicted signal levels from various astrophysical GW backgrounds are shown. The current limit is that published by Jenet et al. (2006). The ‘PPTA limit’ is a predicted limit if the PPTA project achieves its design sensitivity. The SKA limit is a prediction of the sensitivity of the planned Square Kilometre Array telescope.

fitting of a pulsar timing model. The pulsar timing method is therefore complementary to other GW detection methods such as the Laser Interferometer Space Antenna (LISA)1 and ground based interferometer systems (such as the Laser Interferometer Gravitational Wave Observatory, LIGO2 ), which are sensitive to high frequency GWs. In Figure 3 we plot the sensitivity of the pulsar timing experiments, LISA and LIGO as well as some expected GW sources.3 Pulsar timing projects that aim to obtain data sets on the most stable millisecond pulsars with the aim of searching for correlated timing residuals are known as pulsar ‘timing arrays’. The first attempts to undertake such projects are described by Romani (1989) and Foster & Backer (1990).

1

http://lisa.nasa.gov http://www.ligo.caltech.edu/advLIGO/ 3 Various authors e.g. [35, 44] have indicated that it may be possible to limit the existence of GWs with even lower frequencies (10−12 to 10−8 Hz) where the minimum sensitive GW frequency is determined by the distance to the pulsar. However, the methods required to achieve this sensitivity are different to those described in this paper. We also note that a few other methods exist that can limit the ultra-low frequency GW background. One example is reported by Gwinn et al. (1997) who obtained an upper bound on the background amplitude by analysing limits on proper motions of quasars. 2

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3 Current data sets The International Pulsar Timing Array (IPTA) project has the main aim of detecting GW signals using pulsar observations and is a collaboration between three separate projects. The European project (EPTA [13]) currently obtains data using the Effelsberg, Jodrell Bank, Nanc¸ay and Westerbork telescopes (a new telescope in Sardinia is currently under construction and, when commissioned, will be used as part of the EPTA). The North American project (NANOGrav [27]) uses the Arecibo and Green Bank telescopes and the Parkes project (PPTA; e.g. [22, 39, 68]) uses the Parkes radio telescope in Australia. In total approximately 37 different pulsars are being observed by these projects4 (see [18]). Some of the most precise timing residuals have been obtained for the brightest millisecond pulsar, PSR J0437−4715. The rms timing residuals over ∼ 1 yr obtained with the Parkes telescope at an observing frequency close to 3 GHz is ∼60 ns and some individual TOA uncertainties are ∼30 ns. Achieving such low rms timing residuals relies on removing the effects of dispersion measure variations [74], precisely calibrating the data [67] and determining many post-Keplerian binary parameters [70]. However, over longer data spans clear irregularities are observed in the timing residuals (see Figure 4; R. Manchester, private communication). These residuals differ from those published by Verbiest et al. (2008) as 1) new data have been added between the years 2006 and 2010 and 2) the time offsets between different backend systems at the observatory have been measured and subsequently not included in the fitting procedures. The cause of the observed variations is not currently known. Pulsars exhibit two main types of timing irregularity: ‘glitches’ in which the pulsar’s rotation rate suddenly increases before undergoing a period of relaxation and ‘timing noise’ which consists of low-frequency features in the timing residuals. Hobbs et al. (2010) analysed a sample 366 pulsars and showed that the timing noise, in general, consisted of quasi-periodic oscillations with periodicities of years to decades. However, the “amount” of timing noise decreases with characteristic age and millisecond pulsars, which are used in timing array experiments, are typically extremely stable. In a few cases, timing noise and glitches are clearly seen in the residuals for millisecond pulsars. For instance, the timing residuals for PSR J1939+2134 have long been known (e.g. [33]) to be dominated by timing noise. The first glitch in a millisecond pulsar was found in PSR B1821−24 which is located in the globular cluster M28 [6]. The glitch was shown to follow the main characteristics of glitches seen in the slower pulsars. Verbiest et al. (2009) studied the timing stability for 20 millisecond pulsars included in the PPTA project, over time scales up to 10 yr. Apart from PSR J1939+2134 it was concluded that the timing of most of the other pulsars is stable enough for GW detection on decadal time scales. 4

The exact number of pulsars varies as new pulsars are discovered and added to the IPTA sample. Radio pulsar surveys are being carried out (Keith et al., submitted to MNRAS,[7]) and the Fermi gamma-ray spacecraft, has recently discovered numerous previously unidentified gammaray sources. Many of these have now been shown to be millisecond pulsars (P. Ray, these proceedings) some of which are likely soon to be included in the IPTA.

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Fig. 4 The timing residuals for PSR J0437−4715 over 14 years.

The basic method to detect a GW background signal in pulsar data is to search for correlated timing residuals between different pairs of pulsars. However, we note that these correlations only hold in the case where all pulsar data sets are processed using the same fitting procedure and have the same data span. In Figure 5 post-fit timing residuals are shown that include simulated clock irregularities. Even though the same signal has been added to each data set, the residuals are not highly correlated because of the differing data spans and the model fits that have been carried out. The following need to be taken into account when attempting to detect or limit GW signals in pulsar timing data: • Pulsar timing residuals are irregularly sampled, have large gaps and different pulsars have different sampling and data spans. • The uncertainty on each TOA for a given pulsar can vary by an order-ofmagnitude because of interstellar scintillation, different observing durations for different observations and when combining data sets obtained from different observatories. For an unknown reason it is often found that the TOA uncertainties are under- or over-estimated (by factors of ∼2). • Timing residuals are always related to a pulsar timing model for which various fits have been carried out to determine the pulsar’s spin, astrometric and orbital parameters. • Arbitrary offsets can exist between TOAs measured with different instruments or at different observatories. • The timing residuals may be affected by timing noise or glitch events.

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Fig. 5 Post-fit timing residuals for three simulated pulsars. Each pulsar data set consists of white noise plus a clock irregularity that is the same for each pulsar. The post-fit residuals are not correlated because of model fitting and because each data set has a different data span.

4 Potential sources of gravitational waves Theoretical models predict that pulsar timing experiments are sensitive to individual, periodic sources of GWs, burst sources and a background of GWs. This section describes the various possible sources that have been discussed in the literature.

4.1 Single sources GWs are generated by the acceleration of massive objects. For a two-body orbital system the GW frequency is twice the orbital frequency implying that supermassive binary black-hole systems can produce GW signals that are strong enough, and are in the correct frequency regime, to be detectable by pulsar timing experiments. An estimate of the timing residual for a massive black-hole binary system can be obtained from [27]:

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t ∼ 10ns

1Gpc d

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!

M 109 M⊙

!5/3

10−7 Hz f

!1/3

(3)

where d is the distance to the black-hole binary which has a total mass of M/(1 + z) and emits GWs at frequency f . Sesana, Vecchio & Volonteri (2009) showed that it is likely that the maximum timing residuals induced by such a system will be in the ∼ 5 − 50 ns range. Any such source is likely to be from a massive system (with a chirp mass Mc > 5×108 M⊙ ) and at a redshift between 0.2 < z < 1.5. More recently Sesana & Vecchio (2010) showed for a “fiducial” timing array project containing 100 pulsars uniformly distributed in the sky that, if a source is detected with a signal to noise ratio of 10, the source position could be determined to within ∼ 40 deg2 with a fractional error on the signal amplitude around 30% and the source inclination and polarisation angles could be recovered to within ∼ 0.3 rad. Unfortunately there has not yet been any clear detection of a supermassive binary black hole system where the black holes are close enough, and massive enough, for the system to be emitting detectable GW emission. Rodriguez et al. (2006) discovered a system in the radio galaxy 0402+379, which has a projected separation between the two black holes of just 7.3 pc. However, this is still too wide to be emitting detectable GWs. Sudou et al. (2003) reported the possible detection of a supermassive black hole binary in the radio galaxy 3C 66B and provided the orbital parameters for the postulated system. Jenet et al. (2004) showed that such a system should have produced detectable GW emission and managed to rule out its existence with high confidence. Lommen & Backer (2001) unsuccessfully searched for GW emission from Sagittarius A∗ which had also been suggested to be part of a binary system. Sillanpaa et al. (1996) have identified a candidate supermassive black hole binary system in the blazar OJ287 with member masses of 1.3 × 108 M⊙ and 1.8 × 1010 M⊙ . However, Yardley et al. (2010) showed that this system will require the sensitivity of future telescopes (such as the Square Kilometre Array, SKA) for detection. Searches for more supermassive binary black hole candidates are ongoing. Wen, Liu & Han (2009) selected 1209 pairs of galaxies from the Sloan Digital Sky Survey and searched for features indicative of merging events. More recently Burke-Spolaor (submitted to MNRAS) used archival VLBI data to search 3114 radio-luminous active galactic nuclear for binary supermassive black holes. Only one such source (the same as that previously discovered by Rodriguez et al. 2006) was detected. Wen et al. (submitted to ApJ) described the basic methods in which existing pulsar timing observations can be used to place constraints on the coalescence rate of binary supermassive black holes in the Universe. Yardley et al. (2010) determined the sensitivity of the Verbiest et al. (2008, 2009) data sets to individual GW sources and obtained a sky-averaged constraint on the merger rate of nearby (z < 0.6) blackhole binaries in the early phases of coalescence with a chirp mass of 1010 M⊙ of less than one merger every seven years. This work is summarised in Figure 6 which plots the current sensitivity to single sources and predicted future sensitivity (with the Square Kilometre Array, SKA, telescope).

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Fig. 6 Figure from Yardley et al. (2010) showing the sensitivity of current and future GW observatories to individual, periodic GW sources as a function of the GW frequency.

4.2 Burst sources Sources of detectable burst GW emission include 1) the formation of supermassive black holes which leads to a day-long burst of radiation [63], 2) highly eccentric supermassive black hole binaries [12], 3) close encounters of massive objects [34] and 4) cosmic string cusps [8]. Pshirkov & Tuntsov (2010) constrained the cosmological density of cosmic string loops using photometry and from pulsar timing showing that the pulsar timing data provides the most stringent constraints on the abundance of light strings. Seto (2009), Pollney & Reisswig (2010), van Haasteren & Levin (2010) and Pshirkov, Baskaran & Postnov (2010) all considered GW bursts “with memory”. In general such events consist of a rise in the GW field, followed by an oscillatory behaviour for a few cycles and finally convergence to a non-zero value. The permanent change is known as the burst’s “memory”. Such events can occur during close encounters of massive bodies on hyperbolic trajectories or in an asymmetric supernova. Pshirkov, Baskaran & Postnov (2010) showed that one such event could be detected from distances of up to 1 Gpc (for the case of equal mass supermassive binary black hole systems of M = 108 M⊙ ). A similar event can occur if the line of sight to a pulsar passes a cosmic string (Pshirkov & Tuntsov 2010). Such an event would instantaneously change the apparent frequency, ν, of the pulsar by a small amount ∆ν in the same way as that of a GW burst with memory although the

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Fig. 7 Upper bounds from Jenet et al. (2006) for stochastic backgrounds with various values of the GW spectral exponent α (solid line). The dotted lines indicate regions predicted by various GW background models. The dashed line indicates potential future limits from the PPTA project. The star symbol provides the upper bound given by Kaspi, Taylor & Ryba (1994). Figure from Jenet et al. (2006).

memory phenomenon would apply to all observed pulsars whereas this line-of-sight effect is specific to an individual pulsar. Amaro-Seoane et al. (2010) discussed the possibility that supermassive black holes do not coalesce before the merger with a third galaxy. This leads to orbits with high eccentricity leading to an intense burst of GWs. They showed that, for reasonable supermassive black-hole evolution models, a few bursts will induce timing residuals > 1 ns, however, if pulsar timing were sensitive at the nanosecond level, most of these bursts would be undetectable because of confusion with the GW background. A detection of a burst source using pulsar timing would provide the ability to localise the position of the source with the hope of identifying an electromagnetic counterpart. The angular resolution of a given timing array experiment depends upon the number of pulsars in the array, the timing precision and the distribution of the pulsars on the sky.

4.3 Stochastic background A stochastic background of GWs is expected from the early phases of coalescence for supermassive black holes [47, 26, 72, 11, 53], cosmic strings or relic GWs from the big bang [38]. In most models, the GW strain spectrum, hc ( f ), is represented by a power-law in the GW frequency, f ,

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hc ( f ) = A

f yr−1

!α

(4)

where the spectral exponent, α = −2/3, −1 and −7/6 for likely GW backgrounds caused by coalescing black hole binaries, cosmic strings and relic GWs respectively. The energy density of the background per unit logarithmic frequency interval can be written as 2 π2 2 ΩGW ( f ) = f hc ( f )2 (5) 3 H02 where H0 is the Hubble constant. Various predictions suggest that A ∼ 5 × 10−16 − −10−14 [72, 55]. Post-fit timing residuals over a time span ∼ 5 yr may reach ∼ 100 ns for such values of A implying that this such a background may be detectable with only small improvements in the data sets. It is therefore likely that such a background will be the first gravitational wave signal detected. Sesana, Vecchio & Colacino (2008) showed that the expected form of the stochastic background is not simply hc ∝ f −2/3 , but the frequency dependence becomes steeper above ∼ 10−8 Hz. They showed that the major contributors to the background come from massive > 108 M⊙ binary black hole systems that are relatively nearby (z < 2). In contrast to backgrounds formed from supermassive black-hole binary systems, Saito & Yokoyama (2009) showed that the formation of intermediate-mass (∼600 M⊙ ) black holes at the end of the inflationary era will lead to a potentially detectable background of GWs. Current pulsar upper bounds already limit the process for the formation of such black holes. Both “kinks” and “cusps” on cosmic string loops can also contribute to a background of GWs. Olmez, Mandic & Siemens (2010) showed that both phenomena contribute at the same order to the background. The most recent constraints, and their implications, on the cosmic string tension using pulsar timing experiments have been provided by Battye & Moss (2010). A background of GW radiation from the early universe is also expected, if detected, to provide a unique view of the physics of the very early universe (e.g. [15]). Boyle & Buonanno (2007) showed that combinations of cosmic microwave background experiments and GW detection experiments lead to strong constraints on the existence and properties of various energy components that may have dominated the universe at the end of the inflationary era. One of the first limits on a GW background was placed by Stinebring et al. (1990). Kaspi, Taylor & Ryba (1994) used observations of PSRs J1857+0943 and J1939+2134 from the Arecibo observatory to provide an upper bound on the GW background. Their data sets were made publically available allowing other algorithms to be applied to their data sets [40, 29]. Jenet et al. (2006) developed a method that took into account all the effects of fitting a pulsar timing model to data sets of different data spans and applied the technique to carefully selected PPTA data sets as the technique can only be applied to data sets that are statistically “white”. Van Haasteren et al. (2008) developed a Bayesian algorithm which has been applied to EPTA data sets [13]. Anholm et al. (2009) developed an independent method which currently does not address some issues relating to real pulsar data. Work is ongoing

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to develop a method that correctly detects the GW background or limits its amplitude and can easily be applied to the IPTA data sets. The most stringent limits published to date on the amplitude of a background caused by these various phenomena were obtained using observations from the PPTA project combined with archival data from the Arecibo telescope [29]. These upper bounds on A are shown in Figure 7. These results were shown to 1) constrain the merger rate of supermassive black hole binary systems at high redshift, 2) rule out some relationships between the black hole mass and the galactic halo mass, 3) constrain the rate of expansion in the inflationary era and 4) provide an upper bound on the dimensionless tension of a cosmic string background.

5 Accessing pulsar data sets The IPTA pulsar data sets contain some of the most precisely measured observations yet made of radio pulsars. These data sets can be used to search for GW sources and for numerous other purposes. Details of the only currently publically available data sets are provided in Kaspi, Taylor & Ryba (1994). Hobbs et al. (2009) provided a sample of simulated data sets for comparison of GW detection algorithms that are available for download. In the near future it is expected that all observations from Parkes Observatory (after an embargo period of 18 months) will be available for download providing access to most PPTA data. A few data sets relating to the PPTA project are also available as part of the PULSE@Parkes outreach project[20, 24]. The tempo2 package provides a few “plugin” packages and routines suitable for GW analysis: • GWsim.h: a library that implements the mathematics described by Hobbs et al. (2009). The routines in this library can be used to create new tempo2 plugins easily. • fake: plugin that simulates pulsar TOAs given a timing model. • GWsingle: plugin that simulates a single non-evolving GW source and produces a file of site-arrival-times that can be used for subsequent processing. • GWevolve: plugin that simulates a single evolving GW source. • GWbkgrd: plugin that simulates a background of GW sources. A new plugin is currently under development that will either provide limits on the amplitude of the GW background or give the significance of any detection by searching for correlations in the timing residuals of multiple pulsars.

6 The future It is likely that the signature of a GW background will be discovered in IPTA data sets shortly. However, any such initial “detection” will only have a low significance

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(e.g. σ ∼ 2 to 3). How this significance will increase with time will depend upon the intrinsic pulsar timing noise, the amplitude and spectral exponent of the background, whether new pulsars are discovered and whether observing systems are improved. A very high significance detection, enabling detailed studies of the astrophysical objects that form the background and the physics of the GWs themselves (e.g. [36]), will require large numbers of pulsars to be observed with high precision. Various new telescopes are being developed that should detect a large number of new pulsars or be able to observe pulsars with high precision (e.g. the Australian Square Kilometre Array Pathfinder [31, 32], MeerKAT [4] and FAST [41]). These telescopes are pathfinders to the Square Kilometre Array which should be fully operational by 2024. This telescope should revolutionise pulsar and GW astronomy by allowing almost all pulsars in our Galaxy to be detected and GW detection using pulsar observations should become commonplace.

7 Conclusion Pulsar timing experiments can detect gravitational wave signals. The most likely detectable source is an isotropic, stochastic background from a large number of coalescing supermassive binary black hole systems. It is possible that a detection of such a background could be made with existing data, but it will require a further 5-10 yr to have a definitive, highly significant detection. It is expected that GW astronomy using pulsars will become a standard astronomical tool during the Square Kilometre Array era when the background will be analysed in detail and individual binary black-hole systems and burst GW sources will be detectable. Acknowledgements This work is undertaken as part of the Parkes Pulsar Timing Array project, which is a collaboration between CSIRO Astronomy and Space Science, Swinburne University, the University of Texas, Brownsville and the University of California, San Diego. The Parkes radio telescope is part of the Australia Telescope, which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. GH thanks D. Yardley, J. Verbiest, R. Manchester and A. Sesana for comments on early drafts of this text.

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Magnetar outbursts: an observational review Nanda Rea & Paolo Esposito

Abstract Transient outbursts from magnetars have shown to be a key property of their emission, and one of the main way to discover new sources of this class. From the discovery of the first transient event around 2003, we now count about a dozen of outbursts, which increased the number of these strongly magnetic neutron stars by a third in six years. Magnetars’ outbursts might involve their multi-band emission resulting in an increased activity from radio to hard X-ray, usually with a soft Xray flux increasing by a factor of 10–1000 with respect to the quiescent level. A connected X-ray spectral evolution is also often observed, with a spectral softening during the outburst decay. The flux decay times vary a lot from source to source, ranging from a few weeks to several years, as also the decay law which can be exponential-like, a power-law or even multiple power-laws can be required to model the flux decrease. We review here on the latest observational results on the multiband emission of magnetars, and summarize one by one all the transient events which could be studied to date from these sources.

1 Author’s preface The magnetar field have been recently boosted by the discovery of transients magnetars, and more in general by their possible role in GRB and gravitational wave researches. However, probably ”because” of the rapid development of the field , there is still a large confusion in the literature on when a source can be labelled as a magnetar candidate, and what exactly this word means: is the super-critical dipolar magNanda Rea Institut de Ciences de l’Espai (CSIC-IEEC), Campus UAB, Facultat de Ciencies, Torre C5-parell 2a planta, Bellaterra (Barcelona), Spain; e-mail: [email protected] Paolo Esposito Osservatorio Astronomico di Cagliari, Localit´a Poggio dei Pini, strada 54, 09012, Capoterra, Italy; e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_21, © Springer-Verlag Berlin Heidelberg 2011

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netic field which defines a magnetar? Is the bursting behavior? Is the low rotational power with respect to their X-ray luminosity? Is the blackbody plus power-law Xray spectrum? Is the erratic radio pulsed behavior? When do we define a source an Anomalous X-ray Pulsar (AXP) or a Soft Gamma Repeater (SGR)? Apparently in the recent literature, even groups working in the magnetar field since decades are not fully in agreement with their exact definition (see the archetypical example of the AXP 1E 1547−5408= SGR 1550-5418= PSR J1550-5418 which has been discovered only 2 years ago and it already has three names, or PSR J1846−0258 which showed all the typical magnetar-like activity but it is still labelled as a rotational powered pulsar since as such it was first discovered). On the other hand, most of the questions above can be answered with a counter-example, it is then indeed becoming very difficult to give a definite and unique answer on when we can call a source an AXP, an SGR, or a magnetar in general. With this preface we aim at warning non-expert readers on the assumption and conceptual choices we will make in this review. In particular, this is a pure observational review, mainly foscussed on transients. We will then enter very little in the theoretical interpretations. We will not discuss about X-ray bursts or flares, but only the magnetar outbursts. Furthermore, a part from the historical section, we will consider hereafter AXPs and SGRs as the same class of sources, calling them ”magnetar candidates”. We apologize in advance if from time to time we drop the ”candidate” label in the text, but this is only due to the page limitation, while we do consider the magnetar as one of the most viable explanation to date, but possibly not the final solution, at least in its current form. We will include PSR 1622−4950 and PSR J1846−0258 in the magnetar list, given the discovery of their magnetarslike behavior, which clearly shows that (at least occasionally) they cannot be only rotational powered. This review is structured as follow: a brief historical overview followed by the description of the multi-band emission of magnetars (with detailed numbers reported in the two tables rather than in the text). Then, we report one by one on all magnetars’ outburst observed to date.

2 A bit of history Neutron stars (NSs) are the debris of the supernova explosion of massive stars, the existence of which was first theoretically predicted around 1930 [12, 1] and then observed for the first time more than 30 years later [55]. We now know many different flavours of these compact objects, and many open questions are still waiting for an answer after decades of studies. The NS world is mainly populated by the radio pulsars and the binary pulsars (thousands of objects), however in the last decades also extreme and puzzling small sub-classes of NSs were discovered: Anomalous X-ray Pulsars (AXPs), Soft Gamma Repeaters (SGRs), Rotating Radio Transients (RRATs), X-ray Dim Isolated Neutron Stars (XDINs), and Central Compact Objects (CCOs). The large amount of different acronyms might already show how diverse is

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Fig. 1 Diagram of the P– P˙ of all isolated pulsars known to date. Stars represents all sources which showed magnetar activity: in red all SGRs and AXPs, and in magenta PSR J1846−0258 and PSR 1622−4950.

the neutron star class, and on the other hand, how far we are from a unified scenario. In particular, despite being presumably governed by a single equation of state, the NS zoo manifest itself as a puzzling multicoloured class, whose bewildering variety of observational properties is still largely unexplained. These objects are amongst the most intriguing populations in modern high-energy astrophysics and in physics in general. In fact, besides being interesting themselves in terms of studying the NS equation of state and the physical processes and mechanisms involved in their emission, they are precious places to test gravitational and particle physics, relativistic plasma theories, as well as strange quark states of matter and physics of atoms and molecules embedded in extremely high magnetic fields (impossible to be reproduced on Earth). The focus of this review is the outburst emission of strongly magnetized NSs, having magnetic fields close or stronger than the electron critical magnetic field of Bcrit = m2e c3 /e¯h ∼ 4.4 × 1013 Gauss, at which the cyclotron energy of an electron reaches the electron rest mass energy.

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3 General observational characteristics Before presenting these ultra-magnetic objects, it is instructive to indicate how the magnetic field of isolated pulsars is estimated. Assuming that the spin-down torque is due to magnetic dipole radiation, the surface magnetic field can be estimated from ˙ for each pulsar: the measured pulsar spin period P and its derivative P, ˙ 1/2 Gauss Bsurface = (3 I c3 P˙ P/2π2 R6 )1/2 ∼ 3 × 1019(PP) (where P is in units of seconds, and I ∼ 1045 g cm2 and R6 cm are the assumed neutron star moment of inertia and radius). Presently there are almost 1800 spindown powered radio pulsars known, with periods from about 1.5 ms to 8 s [87], and on average they have magnetic fields of ∼ 1012 Gauss. However, beside the magnetar candidates which are the topic of this review, there are also a handful of radio pulsars and other newly discovered type of pulsars having super critical magnetic fields ( > Bcrit ): namely the high–B pulsars, a few XDINSs and RRATs. We will not report on those in this review, however we want to point out that they might represent somehow quiescent or evolved magnetars . The “magnetars” are a small group of X–ray pulsars (16 objects with spin periods between 2–12 s) the emission of which is very hardly explained by any of the common scenario for the radio pulsar or the X-ray binary pulsar populations [91]. In fact, the very strong X–ray emission of these objects is too high and variable to be fed by the rotational energy alone (as in the radio pulsars), and no evidence for a companion star has been found so far in favour of any accretion process (as in the X–ray binary systems). Moreover, roughly assuming them being magnetic dipole radiator, their inferred magnetic fields appear to be as high as B ∼ 1014 − 1015 Gauss, definitely larger than the quantum electron critical magnetic field limit Bcrit . On the other hand, the indication for possible proton resonant cyclotron lines in the X–ray emission of two of these objects, whether confirmed, supports this estimate [113, 60]. Because of these high B fields, magnetars emission is thought to be powered by the decay and the instability of these strong fields [39, 129] but despite valuable recent theories [128, 3] a complete physical interpretation of all different aspects of their emission is still missing. Very interestingly, the magnetars are also characterised by catastrophic and peculiar X-ray bursting, flaring and outbursting events where luminosities of the order of 1046 erg s−1 are reached. In Tab. 1-3 we list the magnetar’s main characteristics, and in the rest of this review we discuss one by one the multiband properties of these objects, finishing with reviewing their transient activity as known to date.

4 Multiband view of magnetars Until about 10 years ago, magnetars were thought to be emitting exclusively in the X-ray energy range, while having sporadic flares reaching the soft γ-ray energies. It was only recently that the availability of new instruments, as well as a progressively

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Table 1 Accurate positions and timing characteristics of magnetars. Magnetars

RA (J2000)

Dec (J2000)

P (s)

P˙ −12 (s/s)

B14 (G)

db (kpc)

1E 2259+586 4U 0142+614 1RXS J1708−4009 1E 1048.1−5937 1E 1841−045 CXOU J0100−7211 CXOU J1647−4552 XTE J1810−197 1E 1547−5408 SGR 1806−20 SGR 1900+14 SGR 0526−66 SGR 1627−41 SGR 0501+4516 SGR 0418+5729 SGR 1833−0832 PSR 1622−4950 PSR J1846−0258 AX J1844−0258a

23 01 08.29 01 46 22.44 17 08 46.87 10 50 07.14 18 41 19.34 01 00 43.14 16 47 10.2 18 09 51.08 15 50 54.11 18 08 39.33 19 07 14.33 05 26 00.89 16 35 51.84 05 01 6.78 04 18 33.86 18 33 44.38 16 22 44.8 18 46 24.94 18 44 54.68

+58 52 44.45 +61 45 03.3 -40 08 52.44 -59 53 21.4 -04 56 11.16 -72 11 33.8 -45 52 16.9 -19 43 51.74 -54 18 23.7 -20 24 39.94 +09 19 20.1 -66 04 36.3 -47 35 23.3 +45 16 34.0 +57 32 22.91 -08 31 07.71 -49 50 54.4 -02 58 30.1 -02 56 53.1

6.98 8.69 10.99 6.45 11.77 8.02 10.61 5.54 2.07 7.55 5.17 8.05 2.59 5.76 9.08 7.56 4.32 0.32 6.97

0.5 2.0 24* 50* 41 19 0.9* 10* 23 * 10* 100* 65 19 6.8 <0.04 4.0 17 7.1 -

0.6 1.3 4.7* 4.4 7.1 3.9 1.3 1.6* 2.2* 18* 6.5* 7.3 2.2 2.0 <0.3 1.8 2.8 0.5 -

3.0 3.0 3.8 9.0 7.0 60 5.0 2.5 4.0 15 15 55 11 5.0 2.0 10 9.0 6.0 8.5

a

Candidate magnetar. We report here on the most recent values for the distances, however we caveat that for most of these objects the distance determination is very uncertain or controversial. We used these distance to infer the luminosity in Tab. 2, which can be easily scaled if in the future more precise distances will be available. b

better understanding of these objects, prompted the search and the following discovery of their emission at other wavelengths. Below we summarize the multiband properties of magnetars.

4.1 Radio emission of magnetars For a long time magnetar candidates were thought to be radio quiet. However, their radio detections started about ten years ago, when radio observations of one SGR (SGR 1806−20) performed with the Very Large array (VLA), revealed the presence of elongated structures with a variable shape and orientation over a year timescale [139, 37]. These jet-like features suggested that outflows from SGR 1806−20 have been occurring, most probably connected with its cospicuous bursting and flaring activity. In fact, after a few years transient radio emission were discovered from SGRs which showed giant flares (see [133, 91] and reference therein). Only three these events were detected in the last 30 years and after two of them a transient radio counterpart was discovered [36, 38], while in the first case no data were available. In particular, radio observations after the recent giant flare from SGR 1806−20 [109,

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Table 2 X-ray spectral properties and luminosities in different wavebands. The stars denote varying values; see http://www.physics.mcgill.ca/∼pulsar/magnetar/main.html for alternative values. Magnetar

kT 1 /kT 2 (keV)

Γ1

Γ2

L35,soft (erg s−1 )

L35,hard (erg s−1 )

S d2 (mJy kpc2 )

Ks mag

Ref.

1E 2259+586 4U 0142+614 1RXS J1708−4009 1E 1048.1−5937 1E 1841−045 CXOU J0100−7211 CXOU J1647−4552 XTE J1810−197 1E 1547−5408 SGR 1806−20 SGR 1900+14 SGR 0526−66 SGR 1627−41 SGR 0501+4516 SGR 0418+5729 SGR 1833−0832 PSR 1622−4950 PSR J1846−0258 AX J1844−0258a

0.4* 0.4* 0.5* 0.6* 0.4 0.3/0.7 0.6* 0.3/0.7* 0.6* 0.8 * 0.5* – 0.5* 0.7* 0.9* 1.2 0.3 0.9* 0.6

4.1* 3.9* 3* 3.4* 2 – 2.3* – 1.7* 1.2* 1.9* 3.3 0.6* 2.9* 2.6* – – 1.9* –

– 0.9* 1.1* – 1.5 – – – 1.5* 2 3.1 – – 0.8 – – – 2b –

0.2* 3* 1.4* 1.2* 2.6 1.5 2.5* 0.35* 1.6* 12* 2.3* 4 0.15* 1.8* 0.042* 0.9* 0.018 3.1* 1*

– 0.6* 0.7 – 2.6 – – – 2.4* 12* 4 – – 1.1* – – – 2.8c –

– – – – – – – 80* 40* – – – – – – – 390 – –

21.7* 19.7 – 19.4* – – – 20.8* 18.5* 19.3* – – – 19.1 – – – – –

[145, 125] [115, 19, 57] [50, 18] [133, 141] [101, 49] [130] [65] [45, 9, 71] [8, 72, 45] [92, 62] [94, 49] [131] [33] [131, 120] [29, 30] [30] [86] [87, 85, 89] [47]

a

Candidate magnetar. The soft and hard X-ray luminosities are given in the 1–10 keV and 20–100 keV ranges, and in units of 1035 erg s−1 . The radio flux S is calculated at 1.4 GHz. If only absorbed flux was found in literature or the flux was given for ranges other than 2–10 or 20–100 keV, XSPEC was used to estimate the unabsorbed flux. Luminosities assume the distances given in Table 1. c Including the (dominant) contribution from the pulsar wind nebula, that cannot be resolved from the pulsar emission by the current-generation gamma-ray instruments. b

58] clearly showed a radio structure moving out from the source and changing in polarization, believed to be an outflow [44, 126, 34]. Furthermore, recently pulsed radio emission were also discovered in a few magnetars. The first detection of pulsed radio emission was from the transient AXP, XTE J1810−197 , which has been first detected in the radio band as a continuum source (4.5mJy; [52], and soon after recognized as a radio pulsar [9, 7]. Another transient AXP has been observed to show radio pulsed emission, 1E 1547−5408 [8], with similar characteristics as the XTE J1810−197 . In particular, magnetars’ radio pulsars show many properties at variance with canonical radio pulsars, as a flat spectrum, large flux variability (until a factor of ∼10) on timescales as short as fraction of hours, and a transient behaviour thought to be connected with the X-ray outburst of the source. However, the discovery of the third radio magnetar, PSR 1622−4950 [86], has instead showed that the strong connection between the transient pulsed radio emission and the X-ray outbursts of magnetar candidates, does not always necessarily hold. In fact PSR 1622−4950 has shown in the past 7 years all typical radio-magnetar emission, it has in fact a field of B ∼ 3 × 1014 Gauss, but its X-ray counterpart never showed so far and X-ray outburst coincident with the radio transient activity. For many other magnetars deep upper limits were derived on their radio pulsed emission [5, 15, 30].

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1 mCrab

keV2 cm-2 s-1 keV-1

SGR 1806-20

4U 0142+61

1E 1841-054

No HXD-PIN data due to a contamination

SGR 0501+4516

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CXOU J164710.2-455216

1RXS J170849.0-400910

SGR 1900+14

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1E 2259+586 1

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Energy (keV)

Fig. 2 Hard X-ray emission of magnetars as observed by suzaku (from Enoto et al. 2010b).

4.2 Optical and infrared emission of magnetars The availability of large telescopes as the Very Large Telescope, Gemini or Keck, made feasible the detection of the weak optical and infrared counterparts to magnetar candidates. Furthermore, the new adaptive optics technology allowed the detection of such counterparts even in the very crowded regions of the Galactic plane. The first discovery of such counterparts was ten years ago, with the detection of 4U 0142+614 in the optical band [56]. An exact modeling of the entire SED of a magnetar has not yet been done. By comparing the entire spectral energy distribution, an infrared ”excess” (or ”flattening”) is seen with respect to the extrapolation of the black body used to account for the optical emission. However, instead if we connect the IR points with the nonthermal γ-ray observations (as for the typical radio pulsars), we end up with an excess in the optical band. Thus, whether this optical and infrared emission comes from a thermal process or not is still unclear and would be an important information for constraining the models: in fact, if this emission comes from a disk it is expect to be thermal [111] , while if it comes from processes on the magnetosphere of a magnetars we expect the optical spectral continuum to be non thermal [26]. srael

4.3 Soft X-ray emission of magnetars Magnetar X-ray emission may be qualitatively separated into two components, a low-energy, <10 keV, and a higher energy one, >20 keV. It is likely, although not proved yet, that different emission mechanisms are responsible for the two components. The low energy component is typically fit with either a blackbody with

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a temperature kT ∼0.3 – 0.6 keV and a power-law with a relatively steep photon index, Γ ∼ 24, or two blackbodies with kT1∼0.3 keV and kT2 ∼ 0.7 keV [91]. In a few cases the low-energy component of SGR spectra has been fit with a single power-law, but recent longer observations have shown that, also for these sources, a blackbody component is required [98]. Thomson, Lyutikov & Kulkarni [128] first pointed out that resonant scattering in magnetar magnetospheres may explain the nonthermal emission observed in magnetar candidates. Due to the presence of hot plasma in the neutron star coronae, the thermal emission from the neutron star surface/atmosphere gets distorted through efficient resonant cyclotron scattering. Recent applications of resonant scattering models to the soft X-ray emission of magnetars have shown that indeed this interpretation fits well the data [133, 148], and finds that these sources are characterized by magnetospheric plasma with a density which, at resonant radius, is about 3 orders of magnitude higher than the Goldreich-Julian electron density.

4.4 Hard X-ray emission of magnetars Thanks to INTEGRAL-ISGRI and RXTEHEXTE, hard Xray emission until ∼200 keV has been discovered for some magnetars (namely the following: 1E 2259+586, 1RXS J1708−4009, 1E 1841−045, SGR 1806−20, SGR 1900+14, 1E 1547−5408, SGR 0501+4516; [43, 44, 98, 19, 49, 131, 45]; see also Figure 2). Hard Xray variability has also been discovered in two cases: for SGR 1806−20 and recently in the SGR 0501+4516(see [48, 131]). The discovery of magnetars hard Xray emission opened a new window in the study of magnetars, making crucial to revise the current knowledge of magnetars being steady soft Xray sources. However, despite recent theoretical works [3, 2], a clear physical idea on how this hard X-ray emission is generated is still missing. Very promising are recent models invoking resonant cyclotron scattering in the relativistic regime [107, 2] although current codes does not allow any observational tests so far.

5 Magnetars’ Outbursts In this section we report one by one on the outbursts that have been detected so far from magnetars. A comprehensive picture of the decay of most these outbursts (the ones successfully followed by X-ray imaging instruments) are reported in Figure 3 .

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100

1E 1547−5408 (2009)

SGR 0418+5729 (2009)

SGR 0501+4516 (2008) Flux (10−12 erg cm−2 s−1)

1E 1547−5408 (2008) SGR1900+14 (2001)

10

CXOU J164710−455216 (2006) SGR 1833−0832 (2010)

1 0.1

SGR1627−41 (2008) 1 10 Time (days from burst activation)

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Fig. 3 Flux evolution over the first ∼ 200 days of recent magnetar outbursts (all observed with imaging instruments). Fluxes are reported in the 1–10keV energy range, and the reported times are calculated in days from the detection of the first burst in each source. In particular we show CXOU J1647−4552 in red [68], SGR 1627−41 in grey [28], SGR 1806−20 in orange [35], 1E 1547−5408 in green and blue for the 2008 and 2009 outbursts, respectively [67, 105], SGR 0501+4516 in black [131], SGR 0418+5729 in yellow [33], and SGR 1833−0832 in light blue [51, 30].

5.1 XTE J1810−197 It was only in 2003 that the first transient magnetar was discovered, namely XTEJ1810197, which displayed a factor of >100 persistent flux enhancement with respect to the unpulsed pre-outburst quiescent luminosity level (> 1033 erg s−1 ; [59, 63, 46]. Unfortunately, the initial phases of the outburst were missed and we do not know whether a bursting activity phase occurred in cohincidence with also for this source. During the latest 5 years it was extensively observed, covering a flux variability over a factor of about >60. Since the very first 2003 observations of XTEJ1810-197, carried out approximately one year after the onset of the outburst, it was evident [46] that the source spectral shape (initally of two blackbodies with kT=0.29±0.03 keV and kT=0.70±0.02 keV) was significantly different from that serendipitously recorded by ROSAT in 1992 (one BB with kT∼160 eV [46]). Moreover, the source showed a 5.54 s pulsation with a pulsed fraction of nearly 45% during outburst, while an upper limit of 24% was inferred from the ROSAT data. In 2006 the source was discovered to be one of the most intense and polarised radio pulsar in our sky with single peak flux density reaching few Jy [9] On the one

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hand, this finding provided direct evidence that the radio pulsar emission can also be at work in magnetars, corroborating the analogy between the spectral properties of AXPs and RPs. On the other hand however, this finding strongly suggested that a better way to study these objects (when in a high state) is taking into account the whole emission properties of the source from the radio to the hard X-ray bands. Simultaneous X-ray and radio observations have been performed. These suggested that the Xray and radio emitting regions are likely coincident (or superimposed), the Xrays likely coming from a larger area. Moreover, during all these campaigns large radio flux (∼50%) and pulse shape variations have been detected which do not correlate with any change (at a few percent level) of the Xray timing and/or spectral parameters (Burgay et al. in preparation). This suggests that the Xray emission likely originates deep in the crust (or more in general, the radio and Xray mechanisms are not closely related). A variable infrared counterpart have been discovered for this object [63, 116], although no clear correlattion between the X-ray and infrared variability haver been confirmed [127].

5.2 1E 1547−5408 1E 1547–5408 was first proposed as a possible magnetar in the candidate supernova remnant G327.24–0.13 through X-ray observations [43] and subsequently recognized as a transient radio magnetar thanks to the discovery at radio frequencies of its spin period of ∼2.1 s [8] (later detected also in X-rays [53]). In recent years, 1E 1547–5408 has been one of the most active magnetars. A first outburst occurred during the Summer 2007, when Swift observations caught 1E 1547–5408 at an Xray flux level of ∼5 × 10−12 erg cm−2 s−1 , more than one order of magnitude brighter than in quiescence [53]. However, the early phases of this outburst were missed and no bursts were observed (possibly due to a sparse X-ray coverage). A new outburst started on 2008 October 3 [67, 105]. This time several bursts were detected by Swift and in the data taken immediately after the Swift trigger, 1E 1547– 5408 was found at a flux level of ∼6 × 10−11 erg cm−2 s−1 . Then the luminosity declined by 70% in three weeks, following a power-law fading trend with decay index ∼−0.2 [67]. During this period, the source displayed a complex timing and spectral variability [67, 105]. No further bursts were reported until 2009 January 22, when the source entered a new stretch of much stronger activity, with thousands of bright bursts detected by many instruments [96, 74, 121, 105]. A spectacular event connected with this giant outburst was the appearance around the source of multiple expanding X-ray rings due to scattering by different layers of interstellar dust of a particularly bright burst [134]. From the analysis of these structures, a distance to the source of ∼4

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Fig. 4 Dynamic Spectral Profiles (DSPs). Each row corresponds to one XMM-Newton observation (epoch increases from top to bottom: 2008 August 23, 29, 31, September 02 and 30) of SGR 0501+4516(Rea et al. 2009). The three columns represent in the phase/energy plane the contour plots for the total (left), power-law (middle) and blackbody (right) νFν flux. The colour scale is in units of 0.01 keV(keV cm−2 s−1 keV−1 ).

kpc was proposed [134].1 Shortly after the onset of the outburst, pulsations were detected with INTEGRAL and Fermi up to ∼150 keV [80, 74] and the source topped a flux level of ∼8 × 10−11 erg cm−2 s−1 (see Fig. 3). The (ongoing) intensive X-ray monitoring of 1E 1547–5408 shows that the flux is slowly decaying with an overall power-law trend with index ∼−0.3 (Bernardini et al in preparation). 1

This value agrees with the distance suggested by the possible association of 1E 1547–5408 with the supernova remnant G327.24–0.13 [43]. A distance of 9 kpc was instead derived from the dispersion measure obtained from radio observations [8].

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As periods of activity and enhanced luminosity are the most promising to search for radio and optical/infrared emission from magnetars, the 2009 outburst of 1E 1547–5408 triggered several multiwavelength follow ups. Multiple radio observations were carried out at Parkes on 2009 January 22, 23 and 25. Pulsed emission from 1E 1547–5408 was detected at 3 GHz during a 1.2-hour-long observation on January 25, but, notably, not in the other two occasions [4]. Moreover, a relatively bright transient (near) infrared source (Ks ∼ 18.5 mag) was discovered with ESO/VLT within the radio positional uncertainty of the AXP and identified with its counterpart [72]. Deep infrared observations taken with ESO/VLT during the 2007 outburst revealed four objects consistent with the radio position of 1E 1547–5408 [100]; none of them, however, showed variability and the likely counterpart was not detectable at the time. This sets an upper limit of about 21 mag in the Ks band on the infrared emission of the AXP during the 2007 outburst.

5.3 AX J1844−0258 This source was discovered in a 1993 observation of the (not associated) supernova remnant Kes 75 during a search for pulsating sources [135, 47]. The observed flux was ∼4 × 10−12 erg cm−2 s−1 . The long period (7 s) together with the spectral properties and the lack of a companion suggested that AX J1845.0–0258 is an AXP. The source was observed again with ASCA in 1997 and 1999 and revealed only in the 1999 observation, at a ten times lower flux (which is consistent with the marginal 1997 non detection) [138]. Subsequent BeppoSAX, Chandra, and XMM-Newton observations revealed an X-ray source at a flux level similar to that observed from AX J1845.0–0258 in 1999 [63, 142]. The low flux precluded new measurements of pulsations and therefore there is no information about the rate of change of the spin period (for this reason the source is often indicate as a candidate AXP). If AX J1845.0–0258 is indeed an AXP, it is plausible that like other magnetars it has a transient behaviour and that the 1993 ASCA observation was carried out during (or shortly after) an outburst and then AX J1845.0–0258 settled into a low luminosity state. Moreover, Tam et al. [142] noticed that, given the large uncertainty on the ASCA position, it is not ruled out that the X-ray source observed by the other satellites is a field-source unrelated to the 7-s pulsar AX J1845.0–0258. If so, the upper limit on the flux that they obtained from a deep Chandra observation of the field of the candidate AXP points to a flux decrease of a factor 200 or more.

5.4 1E 2259+586 This 7s X-ray pulsar was discovered a few decades ago, and it was believed to be a very stable X-ray emitter and pulsator. However, in 2002, it emitted the first notable recorded case of flux variability from a magnetar [75]. Its active phase, with a factor

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of ∼10 persistent flux enhancement, was followed by the onset of a bursting activity phase during which the source displayed more than 80 short bursts [41, 145] . Furthermore, despite being the first case of an outburst from an otherwise persistent and quiet magnetar candidate, 1E 2259+586 was also the first connected X-ray and infrared outburst [125], and it showed a glitch during the enhanced activity, corroborating the idea of these outbursts being due to crustal stresses impareted by the unstable magnetic fields [75]. Furthermore, this magnetar lies in the Supernova Remnant G109.1-1.0 (CTB 109), being one of the few associations between magnetars and SNR which still holds [40] .

5.5 1E 1048.1−5937 The 6.4-s X-ray pulsar 1E 1048.1–5937 was serendipitously discovered by Einstein during observation of the Carina Nebula [122]. Immediately suggested to be highly variable,2 it was tentatively classified as a binary with a V ∼ 19 mag Be companion [122]. Subsequent observations however ruled out the candidate optical counterpart and 1E 1048.1–5937 was placed in the emerging (at the time) class of the anomalous X-ray pulsars [54, 137, 97]. During October/November 2001 a couple of SGR-like bursts – the firsts ever found in an AXP – were detected from 1E 1048.1–5937 with RXTE, virtually unifying the SGR and AXP classes [42]. 1E 1048.1–5937 is one of the most frequently observed magnetars and in the last decade in particular it has been extensively monitored with RXTE since, because of its unstable spin down, frequent RXTE observations are necessary in following the spin evolution [41]. The long-term light curve of 1E 1048.1–5937 shows two consecutive outbursts in the 2002–2004 and a third event in 2007 [123]. The late-2001 bursts marked the start of the first stretch of enhanced flux that persisted a few months [41]. The peak flux was ∼2 times the mean quiescent value (≈7 × 10−12 erg cm−2 s−1 ). Another larger (the peak flux reached ∼3 times the quiescent one) and longer-lived flux increase started in Spring 2002 and lasted into 2004. A third burst was observed from 1E 1048.1–5937 in June 2004, during the final phases of the outburst. Both events had a few-weeks-long rise time and much longer and gradual decays. These flux variations were accompanied by substantial timing irregularities (including glitches) which, however, do not correlate in an obvious way with the flux enhancements [41]. On the other hand, anti-correlation between pulsed fraction and flux and a correlation between spectral hardness and flux have been reported for this source [133, 123]. In March 2007 1E 1048.1–5937 entered a new outburst accompanied by a large spin-up glitch [28]. This time, the flux rose to the peak (slightly higher than that of the 2002–2004 outburst) in less than a week. Also a fourth burst was detected by

2

The flux variability of 1E 1048.1–5937 had been long debated and could be confirmed only twenty years later [99, 41].

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RXTE about a month after the outburst onset [28]. For a distance3 of 9 kpc [23], the total energy emitted has been estimated in roughly 4.8 × 1041 , 3.5 × 1042, and 4.3 × 1042 erg for the three outbursts in chronological order [28]. A candidate infrared counterpart to 1E 1048.1–5937 (Ks = 19.4 mag) was selected in 2001 with the Baade (Magellan I) telescope[141] and confirmed by subsequent observations of large variability (∼2 mag) [66, 22]. Changes in the infrared flux were initially suggested to be anti-correlated with those in the X-ray flux [22]. Recent observations however showed a behaviour inconsistent with this hypothesis, with infrared flux enhancements near those at X-rays, indicating that neither disposition holds all the time [123, 140]

5.6 CXOU J1647−4552 CXOU J0100−7211 was discovered when it underwent a large outburst in 2006 [102, 103], preceeded by a bright X-ray burst detected with the Swift observatory on 2006 September 21. This 10.6 s X-ray pulsar is located in the young cluster of massive stars, Westerlund 1 [102]. Several observations with multiple X-ray telescopes were performed following the burst detection, showing a the flux from this magnetar increased by a factor of ∼100 following the outburst. XMM-Newton observed the source just 4 days prior to the outburst, providing one of the few cases where the beginning of the outburst could be assessed with relative precision. Muno et al. [103] showed that the spectrum of CXOU J0100−7211 hardened significantly when the flux increased and that the pulse profile changed dramatically from a simple near-sinusoidal shape to a complex profile with three distinct peaks per cycle. A glitch as large as ∆ν/ν > 1.5 × 10−5 was detected in coincidence with the outburst ([68] but see also Woods et al. 2010).

5.7 4U 0142+614 4U 0142+614 is one of the brightest magnetar known to date, and it was first detected by Uhuru in 1978. However, mainly because of the presence of the accretionpowered binary pulsar RX J0146.9+6121 nearby, only in 1994 was an ∼8-s periodicity reported using EXOSAT data taken in 1984 [69]. Long-term spin-period variations were discovered thanks to a large RXTE campaign [42], leading to the measure of the period derivative P˙ ∼ 2 × 10−12s s−1 . Despite deep searches [69, 144], no evidence for orbital motion has been found, supporting the isolated NS scenario. Further observations [143, 70] revealed a soft (110 keV) X-ray spectrum typical of an AXP, best fitted by an absorbed blackbody (kT∼0.4 keV) plus a power-law (Γ ∼3.7). More recent Chandra [73, 110], XMMNewton [115] and Swift X-ray Tele3

We note that Gaensler et al. [39] propose an association between 1E 1048.1–5937 and the hydrogen shell GSH 288.3–0.5–28 at a much shorter distance of 2.7 kpc.

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scope (XRT) [118] observations have shown that 4U 0142+614 is a relatively stable X-ray emitter. In the last few years, two peculiar characteristics of 4U 0142+614, have been found in comparison with other AXPs: (i) an optical counterpart [56] dispaying 8-s pulsation with a 30 per cent pulsed fraction [76] and (ii) mid-infrared emission, tentatively interpreted as the signature of a non-accreting disc around the NS [142]. Furthermore, like in other magnetars, a hard X-ray emission up to 250 keV has been revealed [17, 44].

5.8 SGR 1806−20 SGR 1806–20 is arguably the most burst-prolific magnetar and showed several periods of bursting activity since the time of its discovery in 1979 [83, 84]. Its persistent X-ray counterpart was observed for the first time with the ASCA satellite in 1993 [104]. Subsequent observations with RXTE led to the discovery of coherent pulsations (the first time in an SGR) at P ≃ 7.5 s and a secular increase of the period at a rate of ∼8 × 10−11 s s−1 [78]. These values confirmed the debated neutron star nature of the SGRs and, since under the assumption of pure magnetic dipole braking they imply a surface magnetic field strength of 8 × 1014 G, provided strong support for the magnetar model, that was developed in the early 1990s [39, 108]. The source luminosity remained fairly constant for many years at ∼5 × 1035 erg −1 s (for a distance of 15 kpc [14, 90]), until both the burst rate and the X-ray persistent emission started increasing during 2003 and throughout 2004, when the luminosity approximately doubled with respect to the “historical” level [98, 146]. This period of intense activity culminated with a giant flare recorded on 2004 December 27 [58, 95, 109]. This giant flare was exceptionally intense (assuming isotropic luminosity ∼1047 erg were released) and produced strong disturbances in the Earth’s ionosphere [11, 61] and detectable effects on the geomagnetic field [88]. The initial flash was followed by a tail clearly modulated at the spin frequency of SGR 1806–20 that persisted for ∼380 s. Comparing this giant flare with those seen from SGR 0526–66 and SGR 1900+14, it is found that the energy in the pulsating tails of the three events was roughly of the same order (∼ 1044 erg), while the energy in the initial spike of SGR 1806–20 (a few 1046 erg) was at least two orders of magnitude higher than that of the other events. Observations with RXTE unveiled, for the first time in an isolated neutron star, rapid quasi-periodic oscillations in the pulsating tail of the flare, likely related to global seismic oscillations on the neutron star surface [64]. The flare was accompanied by the emission of relativistic particles which powered a synchrotron nebula (a “mini-plerion”) that faded in a few months [6, 38, 126, 34]. A similar “radio afterglow” was observed also following the giant flare from SGR 1900+14 [36] (in the case of the 1979 event from SGR 0526–66, no data at radio wavelengths were available). The small positional uncertainty of the radio observations permitted the identification of the infrared counterpart of the SGR [77, 62]. The fluxes observed in

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the infrared and gamma energy bands show a variability correlated with that observed in the 2–10 keV energy range [92]. After the giant flare, the persistent Xray flux of SGR 1806–20 started to decrease from its outburst level, and its X-ray spectrum to soften, but the source has remained moderately burst-active to to date [117, 92, 132, 146, 32]. During the Spring 2006 the source recovered its pre-outburst luminosity [92] and about five years after the flare (on 2009 September 7–8) the value measured with XMM-Newton was ∼ 3 × 1035 erg s−1 . A flux decrease have been observed also from its infrared counterpart [62, 112, 92].

5.9 SGR 1627−41 SGR 1627–41 was discovered in 1998, when about one hundred bursts in six weeks were observed by CGRO/BATSE and other high-energy instruments [147]. Soon after the discovery of the bursts, its soft X-ray counterpart was identified with BeppoSAX at a flux level of ∼ 7 × 10−12 erg cm−2 s−1 (unabsorbed, 2–10 keV), corresponding to a luminosity of ∼ 1035 erg s−1 for a distance to the source of 11 kpc [13]. In the following 10 years no further bursting activity was reported while various observations carried out with BeppoSAX, ASCA, Chandra, and XMM-Newton showed a spectral softening and a monotonic decrease in the luminosity, down to a level of ∼1033 erg s−1 [79, 93, 31]. The long-term fading of SGR 1627–41 was suddenly interrupted by its burst reactivation on 2008 May 28, when several bursts were detected by the Swift/BAT during a short period of activity (about one day) [31]. This episode was associated with an abrupt and temporary large enhancement of the persistent X-ray flux (a factor of about 100 above the last measurement, in February 2008 with XMM-Newton) and a marked spectral hardening [31]. In September 2008, a deep XMM-Newton observation yielded the first measure of the spin period of the source (2.6 s, making SGR 1627–41 the second fastest spinning magnetar after 1E 1547–5408) and, together with searches in Chandra archival data, of its spin-down rate (1.9 × 10−11 s s−1 ) [33, 27]. In fact, while the detection of strong SGR-like bursts from SGR 1627– 41 made it a bona fide member of the SGR class, these two strong pieces of evidence in favour of the identification were still missing. Follow-up observations at near infrared and radio wavelengths were carried out in response to the 2008 burst activation, but they failed to detect the source [16, 10]. In particular, the limit on the radio pulsed emission of SGR 1627–41 at 1.4 GHz obtained at Parkes on 2008 May 30 and June 1 was 0.5 mJy (for a sinusoidal pulse profile) [10].

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5.10 SGR 0501+4516 A new magnetar candidate, SGR 0501+4516 was discovered on 2008 August 22nd by the Swift Burst Alert Telescope (BAT), thanks to the detection of SGR-like bursts . The activation of this new SGR followed a very long quiescent interval: the all sky X-ray monitors which were operative during the last three decades never observed activity from the source. Tens of bursts were observed [96, 24, 131, 51] with fluxes exceeding the underlying continuum by a factor >105. The bursts reached a maximum luminosity of ∼ 1041 erg s−1 and had a durations of <1 s, typical of those usually emitted by SGRs. Thanks to the rapid response of many X-ray satellites (Swift, Chandra, Suzaku, XMM-Newton,Fermi-GBM, AGILE) the source was repeatedly observed during and after its “burst forest” emission, leading to the best monitoring of an SGR outburst ever performed. Archival ROSAT data dated September 1992 showed a faint unpulsed X-ray source consistent with the position of this new SGR, most probably its quiescent X-ray counterpart [131], at a flux level of ∼ 10−12 erg s−1 cm−2 , and with a thermal spectrum well modeled by a blackbody with a temperature of kT∼0.3 keV (although a power-law fit is also consistent with the data). Since the very first XMM-Newton observation of SGR 0501+4516, carried out one day after the source bursting activation, it was already clear that the source spectral and timing properties changed enormously with respect to the ROSAT quiescent level, with a flux increase of almost 2 orders of magnitude and a much harder spectrum. The source characteristics evolved rapidly during the outburst decay showing a significant spectral softening in the first month of monitoring correlated with the flux decay [131]. The source rotate at ∼5.7 s , and a period derivative of P˙ = 6.8 × 10−12s s−1 . Its pulse profile is highly varible (in time and as a function of energy), and it has a quite stable pulsed fraction of ∼40%, Given the good monitoring of this outbursts, a phase resolved decay has been observed for the first time. We show this in Figure 4 . This clearly shows how different is the outburst evolution in phase, as well as the different decays of the thermal (much slower) and non-thermal (much faster) components.

5.11 SGR 0418+5729 SGR 0418+5729 was discovered due to its bursting activity in 2009 June 5 [136] and then its post-outburst behaviour was intensively monitored for about 160 days [29]. Only three bursts were detected from this SGR (all on 2009 June 5 [136]) and archival searches could not reveal any previous period of intense activity [136]; no new bursts have been detected until the time of writing (2010 August). SGR 0418+5729 has a spin period of 9.1 s and intriguingly its period derivative has thus far eluded measurements. This makes this object special, as the corresponding upper limit on the surface (dipolar) magnetic field is B < 3 × 1013 G, well below the value of any magnetar currently known [29].

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After the outburst onset, the source spectrum gradually softened and the persistent X-ray emission faded by a factor of ∼10 in about 160 days following a brokenpower-law decay, with a steepening about 19 days after the activation, when the index changed from −0.3 to −1.2 [29]. At the same time, the complex and energyvariable pulse profile of the source showed a substantial evolution, pointing to a nearly orthogonal rotator seen at a large inclination angle and to the presence of two emitting caps, one of which became hotter during the outburst [29].

5.12 SGR 1833−0832 This recent addition to the magnetar family was discovered on 2010 March 19, when the Swift triggered on a short hard X-ray burst and localised it in a region close to the Galactic plane [51]. Swift immediately slewed to the the BAT field and unveiled the existence of a previously unknown bright X-ray source. Given the proximity to the Galactic plane and the burst properties, the X-ray source was immediately suggested to be an SGR. Its SGR/magnetar nature has been confirmed shortly after by the discovery with Swift and RXTE of pulsations at 7.57 s and the measure of a period derivative of a few 10−12 s s−1 [51, 30]. Follow-up observations could not reveal SGR 1833–0832 in the optical, infrared, and radio wavebands [51, 30]. The source was monitored in the X-rays with various instruments for about three months [51, 30], during which it displayed a low bursting activity, while the persistent flux decreased from ∼ 4 × 10−12 erg cm−2 s−1 by about 50% with an approximately linear decay at a rate of ∼3 × 10−14 erg cm−2 s−1 day−1 [30]. Somewhat atypically, the spectrum of this source is well described by an absorbed single hot blackbody (kT ∼ 1.2 keV). However, the high absorbing column towards the source makes it difficult to properly model its emission and an additional spectral component cannot be excluded [30].

6 Conclusions In this review we reported on all the magnetars’ outbursts recorder to date (see also Figure 3). Although far from having an exhaustive understanding on the mechanism and observational behavior of magnetars’ outbursts, some common lines can be drawn. Before listing the few common properties as they appear up to know, we caveat that many bias might be in place. In particular, in several cases we have no information on the exact time of the outburst on-set, hence the observations we are comparing for different sources might be relative to different times during the outburst decay. Despite the apparent differences among each source, several common properties can be reliably disantangled, while others are still debated. • A clear softening is observed in all cases. There is a larger amount of higher energy photons emitted at the beginning of the outburst than during the fading

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• •

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toward quiescence. In some cases this was even connected to the detection of a transient hard X-ray emission days after the on-set of the outburst, which faded away very rapidly (∼ a week; see the case of SGR 0501+4516). There is a connection between the enhancement of the persistent emission and the source bursting activity, although the sparse observations does not allow to figure out whether there is a connection between the fluence of those outbursts and the amount or energetic of the short bursts. A single source can emit several outbursts (see e.g. the case of 1E 1547−5408), of different intensities and timescale. There is no clear understanding on the radio, infrared and optical emission during outbursts. In the radio band, in some cases radio pulsed emission were detected in connection to the X-ray enhancements (it is not clear yet who triggers who, though), in others not. On the other hand, infrared and optical emission were sometimes found to get enhanced by the X-ray outburst activity, while in other cases they were not. Large differences in the timescales and decay-laws are observed among different outbursts, even in the same source.

Acknowledgements NR acknowledges support from a Ramon y Cajal Fellowship and from grants AYA2009-07391 and SGR2009-811. PE acknowledges financial support from the Autonomous Region of Sardinia through a research grant under the program PO Sardegna FSE 2007–2013, L.R. 7/2007 “Promoting scientific research and innovation technology in Sardinia”.

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Wide-band X-ray Studies of Magnetars with Suzaku T. Enoto, K. Makishima, N. Rea, Y. E. Nakagawa, K. Nakazawa, and T. Sakamoto

Abstract From its launch in 2005, the Suzaku satellite has been observed 10 magnetars including 7 persistent objects and 3 activated ones. The hard-tail component was successfully detected from 7 of them, including two activated sources (SGR 0501+4516 and 1E 1547.0-5408), together with the soft component from all of them. Unified spectral studies over the 0.8–70 keV range revealed a clear wide-band spectral evolution, in which the hard-tail component become weaker and harder towards sources with older characteristic age. Specifically, a tight correlation was found between the characteristic age and the hardness ratio between the two components. In addition, the photon index of the hard emission, ranging from ∼1.7 to ∼0.4, is negatively correlated to the characteristic age.

1 Suzaku Observations of Magnetars Recent observations are accumulating growing evidence that Soft Gamma-ray Repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs) are new kind of X-ray pulsars powered by their ultra-strong magnetic fields, or “magnetars” [19, 20, 15]. The INTEGRAL long-exposure imaging observations enabled a discovery of hard-tail emission above ∼10 keV with extremely hard photon indices of Γh ∼ 1 [13, 9]. It forms a spectral component distinct from the long known soft (thermal) component, Teruaki Enoto · Kazuo Makishima · Kazuhiro Nakazawa The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-0033, Japan e-mail: [email protected] Nanda Rea Institut de Ciencies de l′ Espai (ICE-CSIC, IEEC) Kazuo Makishima · Yujin. E. Nakagawa Cosmic Radiation Laboratory, RIKEN Takanori Sakamoto GoddardSpaceFlight Center, NASA N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_22, © Springer-Verlag Berlin Heidelberg 2011

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which has a temperature of kT ∼ 0.5 keV. Although the newly discovered hard-tail emission is expected to open a new observational window onto magnetars, its emission mechanism has not yet been conclusively understood [22, 10, 1]. In addition, it is still unclear whether the hard-tail component is common to all magnetars, or specific to some of them depending on their states of activity. The X-ray satellite Suzaku [16] can observe these soft and hard components of magnetars simultaneously over the 0.2–600 keV energy range, combining the Xray Imaging Spectrometer (XIS) [12] and the Hard X-ray Detector (HXD) [18]. Since the launch of Suzaku, 3 SGRs and 7 AXPs have already been observed. We analyze in a unified way all the archival magnetar data as of 2009 November; our sample covers 9 sources of all the ∼15 magnetars known to date. Figure 2 shows the persistent νFν spectra of these sources, thus obtained over the 0.8–70 keV range. The soft component was recorded from all of them, and the hard-tail component was detected from 7 magnetars. For example, the hard X-ray emission of the prototypical AXP 4U 0142+61 was successfully detected in a short exposure of ∼100 ks, even thought it has only 1 mCrab intensity at ∼30 keV. Among our sample, 3 sources were observed in their apparent activated states as target-of-opportunity (ToO) programs. Newly discovered SGR 0501+4516 [2, 17] was observed with Suzaku on 2008 August 26–27, four days after the onset of the burst activity. Together with a bright short burst (∼23 Crab at ∼ 40 keV), the 51 ks observation yielded detections of both soft and hard components [3]. The hard-tail component, detected up to ∼70 keV, was fitted by a power-law with its photon index of Γh = 0.79 (Fig 2). Another ToO observation, the transient magnetar 1E 1547.05408, was performed on 2009 January 28–29 for 33 ks, following multiple short

1 mCrab

keV2 cm-2 s-1 keV-1

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No HXD-PIN data due to a contamination

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CXOU J164710.2-455216

1RXS J170849.0-400910

SGR 1900+14

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1E 2259+586 1

10

Energy (keV)

Fig. 1 Persistent νFν spectra of magnetars observed with Suzaku [5]. Green, red and blue lines represent the soft component, hard-tail component, and the SNR contamination, respectively. Purple dashed lines indicate a 1 mCrab intensity. The HXD-PIN data of CXOU J164710.2-455216 is not shown due to contamination by GX 340+0 within the same field of view.

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burst activities on January 22 [7]. An enhanced hard-tail components was also discovered up to ∼110 keV with Γh = 1.54 [4] (Fig 2).

2 Spectral Evolution of Magnetars

Hardness Ratio ξ = Lh/Ls

In Figure 2, the magnetar νFν spectra are arranged in the increasing order of the characteristic age τc = P/2 P˙ s from left/top to right/bottom, where P and P˙ are the period and its derivative, respectively. As shown in this figure, the hard-tail component clearly becomes weaker and flatter towards objects with older τc . To quantify this trend, we employed a hardness ratio (HR) ξ between the un-absorbed 1–20 keV soft-component flux and the 1–60 keV hard-tail flux, and plotted ξ as a function of τc in Figure 2. This reveals a tight negative correlation between them as ξ ∝ τ−0.7 with c a significant correlation coefficient of r = −0.989. Similarly, Γh changes in Fig. 2 systematically with τc from ∼1.7 to ∼0.4 [6]. These results are considered to represent a common evolution path of magnetars depending on the characteristic age. The HR is also positively√correlated (r = 0.873) with the magnetic field B, which is derived as B = 3.2 × 1019 PP˙ G.

10

0501+45

1900+14 1806-20

(2009)

1547-54 1841-04

1

0501+45 (2008)

1708-40 less active states

0.1

2259+58 0142+61

activated states (ToO)

0.1

1 10 100 Characteristic age (kyr)

Fig. 2 The HR ξ versus the characteristic age τc [5]. Errors are statistical and systematic 1σ. Green solid and dashed lines represent the best fit and its boundaries multiplied by a factor of two.

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Although the correlation between P˙ and photon index was already reported in the soft X-ray emission [14] and recently extended to the hard X-ray emission [11], our strictly simultaneous measurements of the two components yielded the correlation of the flux ratio to the characteristic age. In Fig 2, the two activated magnetars (SGR 0501+4516 and 1E 1547.0-5408) lie on the same correlation with the other quiescent objects. Therefore, in the active state, the luminosities of the two components are thought to increase approximately in proportion to each other, and that the same mechanism of the hard-tail emission is retained at higher magnetic dissipation rates. The hard-tail component, extending at least up to a few tens of keV range [13, 4], clearly indicates the production of energetic particles in the magnetar environments. Although acceleration and emission mechanisms in magnetars have not yet been clear, these properties may be explained by any of theoretical models, including “twisted magnetosphere” model [21, 22]. Since it is not easy to produce such a flat hard-tail component with Γh ∼ 1 through ordinary emission processes, one interesting speculation is that the hard-tail component is produced through softening via photon splittings of sub-MeV photons originating from electron-positron annihilations, or other processes.

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Bursts and Flares from Highly Magnetic Pulsars GianLuca Israel and Simone Dall’Osso

Abstract In January 1979, for the first time, recurrent short (<100ms) and intense γ-ray bursts were detected from a source in the direction of the Galactic center, later named SGR1806-20. Two months later, in March 1979, rapid (∼8s) coherent X-ray pulsations were discovered during an extremely intense flare (F X ∼ 1044 ergs s−1 cm−2 ) from SGR0506-66, the prototype of the magnetar class. Since then, many advances have been achieved in the study of this class of high energy emitting isolated neutron stars, thought to shine in the X-rays due to the decay of the strongest magnetic fields present in the Universe (> 1015 Gauss). The results obtained through the study of the transient phenomena (mainly burst and flares) displayed by some of them and covering more than 10 orders of magnitudes in terms of time scale variability (from fraction of milli-seconds up to years) and of flux (from 10−9 up to 1 ergs s−1 cm−2 ), will be presented and discussed with particular emphasis on the most recent results obtained. Among others are: the discovery of rapid QPOs in the giant flares of SGR1806-20 and SGR1900+14, the study of intermediate flares from SGR1900+14, 1E1547.0-5408 and SGR0501+4516. The high frequency oscillations discovered in the tails of giant flares from two magnetars are thought to be the first direct detections of seismic vibrations from neutron stars. The possibility of starquakes associated with the giant flares triggering global vibrations opens up the prospect of using seismology to study the interior structure and composition of neutron stars, and to infer information on the crust thickness. This is a major breakthrough in the study of the nature of matter under conditions of extreme pressure. The time resolved spectroscopic studies of the flare emission from magnetars was instead used to infer information related to the neutron star and magnetosphere structure, the emitting processes, and the confined fireball properties. In particular, GianLuca Israel INAF - Astronomical Observatory of Rome, Monte Porzio Catone (RM), I-00040, Italy e-mail: [email protected] Simone Dall’Osso INAF - Astronomical Observatory of Rome, Monte Porzio Catone (RM), I-00040, Italy e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_23, © Springer-Verlag Berlin Heidelberg 2011

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within the magnetar model, the majority of these findings can be accounted for in terms of thermalised emission from the E-mode and O-mode photospheres.

1 MAGnetic NEutron sTARS Soft Gamma-ray Repeaters (SGRs; seven confirmed members) and Anomalous Xray Pulsars (AXPs; ten confirmed members) are two classes of X-ray pulsating sources with no evidence for companion stars and first identified due to their rather different phenomenology with respect to other classes of high energy sources. The SGRs were discovered as sporadically bursting objects, while the AXPs were regarded as peculiar pulsars with long spin periods. Besides that, more recent observations unveiled several similarities between these two classes. These include rotation periods of several seconds (P∼2-12 s), rapid spin down(P˙ ∼10−11 s s−1 ), large and variable X-ray luminosities, and the emission of flares and short bursts (see [1] for a review). Moreover, they are distributed around the galactic plane (two magnetar are in other galaxies), while some are associated with supernova remnants (SNRs), others are associated with young open clusters. Their spectra in the 0.1–10 keV band are relatively soft and can be empirically fitted with a two-component model, an absorbed blackbody (kT ∼ 0.2–0.6 keV) plus a power-law (Γ ∼ 2–4). INTEGRAL observations revealed the presence of sizeable emission up to ∼ 200 keV, which accounts for up to 50% of the total flux [2, 3, 4]. Hard X-ray spectra are well represented by a power-law, which dominates above ∼ 20 keV in AXPs. SGRs and AXPs are currently interpreted as observational manifestations of magnetars, namely neutron stars endowed with ultra-strong magnetic fields [5, 6]. In this framework, the high energy emission of these objects, including the peculiar bursting activity, is ultimately powered by the decay of the enormous magnetic field. In order to explain the observed phenomenology, magnetars magnetic fields are expected to be ∼1014-1015 Gauss > BQED ≃ 4.4 × 1013 Gauss on the surface and one (or more) order of magnitude higher in the interior [7, 8, 9, 10]. This picture is compatible with the magnetic fields of ∼1014 Gauss inferred for SGRs and AXPs from their period and period derivative according to the magnetic dipole radiation for˙ 0.5 G mula for a neutron star of 10 km radius, and 1.4 solar masses, B∼3.2×1019(PP) (e.g. [11]). In the magnetar model, the magnetic field is the dominant source of free energy (orders of magnitudes higher than the rotational energy of the star), powering the persistent emission through low-level seismic activity and heating of the stellar interior [145]. When magnetic stresses build up sufficiently to crack a patch of the neutron star crust, the resulting “crustquake” ejects hot plasma particles into the magnetosphere, which results in an SGR burst [8]. Alternatively, the short SGR bursts may arise from magnetic reconnection events in the stellar magnetosphere [12]. Giant flares likely result from a sudden reconfiguration of the star’s magnetic field that produces large fractures in the crust and propagates outwards through Alfv´en waves of enormous power. The ∼0.2 s initial spike of giant flares marks the ejection of the

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Fig. 1 The ∼92 Hz oscillation as seen by the PCA during the 2004 December event from SGR 1806-20. (a) Spectrogram with 2 s time step and resolution. The contours represent Leahy powers from 3.2 to 3.7; (b) Light curve corresponding to the same time axis as panel (a). The time resolution is 0.75 s. The grey-shaded area indicates the time interval shown in panel (c); (c) Close–up of the grey area in panel (b). The different symbols mark the first peak (black circles), the second peak (stars) and the DC level (grey circles); (d) average power spectrum (at 0.5 Hz resolution) of the grey area in panel (b); (e) average power spectrum (at 1.33 Hz resolution) of the phase interval including the first peak as seen in panel (c); (f) same as (e) for the second peak; (g) same as (e) for the DC level (adapted from [15]).

largest part of the total event energy (up to ∼1047 ergs) as well as the onset of a relatively large surface fracture [13]. The ringing tail that follows results most likely from the part of the fireball that remains trapped in the stars magnetosphere. The energy release in the ringing tail yields a limit for the external field of magnetars ( >1014 Gauss) in agreement with the values inferred from spin-down dipole losses [8, 14]. The detection of deca-, hecto-, and kilo-Hertz Quasi Periodic Oscillations (QPOs) in the decaying phases (tails) of giant flares have been interpreted in terms of global seismic oscillations following the fracture formation [15, 16]. The superEddington fluxes observed in the tails of these events are thought to be possible because of the suppression of the electron scattering cross sections in the presence of very strong magnetic fields [5]. In the following we will focus on the results, outlined in the latest two sentences, and on the information that have been obtained in recent years by means of the study of the timing and spectral properties of the flaring activity of magnetars.

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2 SGRs Giant Flares and their magnetic fields In 2005 QPOs were discovered in the X-ray flux of the ringing tail of SGRs’ giant flares [15][; see Figure 1]. Different QPO modes were detected, some of which were excited simultaneously. The ringing tail of the December 2004 event from SGR 1806-20 displayed clear QPO signals at about 18, 30, 93, 150, 625 and 1840 Hz [17]. Similarly, QPOs around frequencies of 28, 54, 84 and 155 Hz were detected during the ringing tail of the 1998 giant flare of SGR 1900+14 [16], while hints for a signal at ∼43 Hz were found in the March 1979 event from SGR 0526-66 [18]. These QPOs show large variations of the amplitude with time and, especially, of the phase of the spin modulation in the giant flare’s tail. The similarity in some of the QPO modes and frequencies across different SGRs suggests that the production mechanism is the same. Indeed, giant flares are thought to be powered by catastrophic global reconfigurations of the magnetic field. As the field is anchored to the charged particles in the neutron star crust, it had long been suspected that giant flares might be closely related to starquakes [23, 8, 14, 13] strong enough to excite global seismic vibrations of the NS crust [24]. In the model of [8] the field twists and puts the crust under strain, but crustal rigidity prevents movement and reconnection. Stresses build up until the crust reaches its breaking strain and a flare is thus triggered. In the alternative model of [25] the crust deforms plastically as the field twists, and flares occur when the field reaches an instability point [82]. The colossal and rapid reconfiguration of the field can drive strong, global magneto-elastic vibrations in this case, even without crustal yielding. Indeed, the frequencies of the detected QPOs are in good agreement with models of torsional shear modes of neutron star crusts - in accordance with early theoretical suggestions. The models used to make these identifications were based on early calculations that assumed free slip of the solid crust over the fluid neutron star core [19, 20, 21, 22]. In the nice review by Watts (2006, [27]), it was however noted that neutron stars can sustain many types of oscillation restored by various different forces. Early calculations for neutron star models with a fluid core and a solid crust indicated that the modes most likely to be excited by a magnetar crustquake were the torsional shear oscillations of the crust, with a fundamental frequency at ≈ 30 Hz [28, 20, 21, 24]. These oscillations are primarily horizontal (as opposed to radial) and the crustal shear modulus provides their restoring force. Which harmonic would exactly be excited in this case depends on fracture properties (location, geometry, speed), and subsequent coupling and damping processes. These findings hold in themselves a great potentiality in using seismology to study the interior structure and composition of neutron stars. This would be a major breakthrough in the study of the nature of matter under conditions of extreme pressure. In fact, the frequencies of the fundamental n = 0 torsional shear modes deduced from the low-frequency QPOs in SGRs 1806-20 and 1900+14 are different, the latter source having a lower fundamental. This most likely reflects differences in the mass, radius or magnetic field strength of the two stars (mass and radius having a strong effect due to gravitational redshift). [16] analysed the differences in mass

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n = 0, l = 2 n = 0, l = 4 n = 0, l = 6 n = 0, l = 10 n = 0, l = 11 n=1 n=3

Table 1 Summary of QPO frequencies (in Hz) detected in the tails of the SGR 1806-20 and SGR 1900+14 giant flares. QPOs with asterisks have been detected in the datasets of both the Rossi X-ray Timing Experiment (RXTE) and RHESSI missions. The 150 Hz and 1840 Hz QPOs in the SGR 1806-20 flare have fractional amplitudes too low to be detected in RHESSI. The third column indicates the identification as torsional shear modes on the basis of models that do not include crust-core coupling. The mode identification given for the n = 0 modes is consistent with that given in [29]. l marks the different angular harmonic number. This differs very slightly from the identification given in previous papers, and reflects the use of (more accurate) spherical geometry in the more recent paper (from [27]).

and magnetic field that would be necessary to explain the different frequencies, for various different equations of state [30]. Estimates of the magnetic field derived from timing constrain the parameter space to rule out both very hard and very soft equations of state [31]. For intermediate equations of state reasonable results were obtained that support the finding that SGR 1806-20 has a stronger field than SGR 1900+14. Additionally, the possible identification of an n = 1 radial overtone is particularly exciting, as it might allow to estimate crust thickness. This is on its own an independent constraint on the nuclear equation of state. In the Newtonian perturbation calculations of [19], one can show that in the thin crust limit the ratio of first radial overtone to fundamental frequency is proportional to the ratio of crust thickness to stellar radius. Subsequent Newtonian perturbation calculations included a correction to the frequency for gravitational redshift; a factor which cancels when one takes the ratio of two frequencies. Strohmayer & Watts [16] used this fact to compute mode frequencies for realistic (non-thin) neutron star crust models in spherical geometry. Using the SGR 1806-20 observations, assuming a fundamental at 30 Hz and a first overtone at 625 Hz, this resulted in a crust thickness estimate of 0.1 – 0.13 times the stellar radius. Recent more detailed modelling is now refining this initial value. General relativistic mode calculations by [29] and [32], which take into account not only gravitational redshift but also the effect on crust thickness associated with relativistic models, have already resulted in revised estimates. Efforts to include crust/core coupling will doubtless lead to further changes [33, 34]. This is nonetheless the first time that there has been the possibility of making a direct measurement of crust thickness in a neutron star (for constraints on strange stars see [35]).

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2.1 The Cavallo-Fabian-Rees Variability Limit The QPO properties, in particular those of SGR 1806-20 at 625 and 1840 Hz, have been used to infer a lower limit on the magnetic field strength at the neutron star surface in a way which is model-independent and based on very simple assumptions [36]. This is based on the Cavallo-Fabian-Rees Variability Limit on the rate of change of the luminosity of any given source ([37, 38, 39], see also [40, 41]). The QPO rms amplitude reached a maximum of arms ∼ 18%. Approximating the QPOs with sinusoids, their highest luminosity derivative is ∆L/∆t = 23/2πLarms νQPO , with νQPO the QPO frequency. Here L ∼ 1041 ergs s−1 is the average luminosity in the relevant section of the ringing tail (for the likely source distance of 15 kpc). This gives ∆L/∆t ∼ 1043 and 6 × 1043 ergs s−2 for the 625 and 1840 Hz QPOs, respectively (the effect of beaming is taken into account). Moreover, the presence of spin pulsations during the giant flare tail indicates that the emission in the ringing tail originates from a region that remains stably anchored to the star’s magnetosphere, and thus that (relativistic) bulk motions are not present at this stage of the flare. Finally, the blackbody temperature and luminosity in the ringing tail translate into a lower limit on the size of the emitting region of about ∼ 30 km, i.e. significantly larger than the neutron star. On the other hand the black body-like spectral shape testifies that the emitting region is optically thick (or at least effectively thick), implying a scattering optical depth ≫ 1. The Cavallo-Fabian-Rees Variability Limit is based on the fact that the total energy released within ∆t due to a large luminosity variation ∆L is related to the total mass within the source dimension R by ∆L∆t = η

4π 3 R nm p c2 , 3

(1)

where n is the average baryon density, and η is the energy extraction efficiency. At the same time the time-scale ∆t must obviously exceed the time over which the photons escape from the source ∆t > Rc (1 + τT ) where τT = σT nR is the Thomson optical depth and σT the Thomson cross-section. This yields the limit ∆t >

3 σT ∆L 2π m p c4 η

(2)

which is independent of both R and n, or any combination thereof: only the dependence on ∆L, a directly observable quantity, is left. The Cavallo-Fabian-Rees, CFR, limit thus writes ∆L/∆t < η 2 × 1042erg s−2 . (3)

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The 625 and 1840 Hz QPO signals from SGR1806-20 exceed the CFR limit by about an order of magnitude1: the largest value found in the previous section is ∆L/∆t = 6 × 1043 erg s−2 , which is a whole factor 30/η larger than the CFR’s limit. Vietri et al. 2006 ([36]) demonstrated that, in this specific case, there is only one way to circumvent the CFR limit, i.e. the scattering cross-section may differ from Thomson’s because of the presence of a strong magnetic field B, exceeding the quantum value Bq = m2 c3 /(e¯h) = 4.4×1013G. In this case, the photon scattering cross section for the ordinary (O) and extraordinary (E) modes, and for the conversion of photons into the other state, are given by [42], when the dielectric tensor is dominated by vacuum polarization effects. In fact, for photons emitted in the extraordinary mode, the cross section is reduced, with respect to the Thomson value, by a factor ≈ (ǫBq /(me c2 B))2. Thus, to bring the observed value, △L/ △ t = 6 × 1043 erg s−1 , in agreement with Eq. 2, we just need to have (ǫBq /(me c2 B))2 ≤ η/30; here we take for ǫ the value ǫ ≈ 14 keV, which is the peak of the Planck distribution for the observed temperature T = 5 keV. So our conclusion is that the QPOs’ luminosity variation agrees with the CFR limit provided B ≥ 1.5Bq

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as inferred at the surface of the observed black body with radius of 30 km. Given the rapid decrease of the dipole field (and a fortiori of the other multipoles) with distance from the star, the surface magnetic field must certainly satisfy B ≥ 1.8 × 1015 G

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The above result is strongly suggesting that two species of photons, those corresponding to ordinary (O) and extraordinary (E) polarized modes, are present in presence of a magnetic field with strength in excess of Bq . This is still debated and not easy to prove or disprove unambiguously. However, in the latest years, several indirect proofs have been collected all in favour of this scenario (see Section 3).

3 SGRs Intermediate Flares in the Swift era Burst activity in SGRs occurs sporadically and is quite diverse in behavior. Burst active phases of SGRs vary both in total energy released and duration, tending to be concentrated into relatively narrow intervals (weeks or months) separated by relatively long periods (years) of quiescence. Since its discovery in 1979, when bursts where detected three times in three days, SGR 1900+14 remained in quiescence until 1992, when a handful of bursts were again detected within a few days [43, 44]. 1

We note that also the slower ∼ 90 − 150 Hz QPOs signals in the giant flares’ tail of SGR1806-20 and SGR1900+14, exceed the CFR limit, though by a smaller factor.

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In 1998 the source entered an unprecedented level of activity during which more than 1000 burst were recorded within 9 months, and culminated with the ∼ 400 s long and rather intense 1998 August 27 giant flare event (∼ 4 × 1044 erg s−1 ). Burst activity was detected until 1999. Particularly interesting, are two events detected in May and September 1998, during which ”bunching” of short and long burst were detected [45, 46]. Finally, after almost two years of inactivity, on 2001 April 18, an intense and long (∼ 40 s) burst was detected from SGR 1900+14 [47]. The energy released by this flare (few × 1042 ergs) was less than that of the giant flare, though larger than that of the most common short SGR bursts. Consequently the flare was dubbed an “intermediate flare” [48]. Indeed, looking back at the burst history of SGR 1900+14, it was realized that a handful of similar events, characterized by a longer duration (few seconds–few tens of seconds) and a higher fluence than those characterizing short bursts, were present. These bursts were then grouped into the class of intermediate flares likely forming a continuum in terms of duration and fluences [49]. A number of broad-band spectroscopic studies of short and intermediate flares were carried out in the past by different missions. These found that, above 15– 20 keV spectra are usually well fitted by an optically-thin thermal bremsstrahlung (OTTB) with characteristic temperatures ranging from 20 to 40 keV [50]. Moreover, the study of the cumulative spectral properties of 100 bursts from SGR 1806−20 in the 5–200 keV energy range showed that the number of the photons in the spectrum of the detected bursts was remarkably stable in spite of the large intensity spread (a factor of 50) and that the low-energy (below 15 keV) data were inconsistent with the back-extrapolation of an OTTB model that provided a good fit to the high-energy portion of the spectrum [86, 52]. Qualitatively similar spectral properties were measured during a bright intermediate flare from SGR 1900+14 using HETE–2 data, which also showed that the OTTB model largely overestimated the flux at low energies (<15 keV,[49]). The broadband spectrum (7–100 keV) was best fitted by the sum of two blackbody (BB) laws. Similar conclusions were reported by using data from the Rossi X-Ray Timing Explorer confirming the OTTB limits below 15 keV [53]. Feroci et al. (2004,[54]) analyzed the 1.5–100 keV BeppoSAX spectral properties of 10 short burst from SGR 1900+14, further confirming that the widely used optically-thin thermal-bremsstrahlung model provides acceptable spectral fits for energies higher than 15 keV but severely overestimates the flux at lower energies. A better fit was obtained by means of an alternative spectral model such as two blackbodies or a cut-off power law. Most of these studies were hampered by one or more of the following limitations: relatively poor statistics, narrow energy bandpass, poor time resolution, off-axis data, and low sensitivity of wide field of view instruments. Cumulative analysis of 50 bursts detected by HETE-2 from SGR 1900+14 showed the presence of a time lag of about 2.2±0.4 ms between the 30–100 keV and 2– 10 keV radiation bands implying a rapid spectral softening and energy re-injection mechanism [55]. Alternatively, the softer spectral component could be reprocessed radiation from the harder emission which might be generated near the neutron star surface. More generally, the observed time lag favours spectral models with (at least)

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two components. In any case the temperatures of the 2BB model does not seem to depend on either the burst intensity or morphology.

3.1 The March 2006 Burst Storm of SGR 1900+14 A step forward in the understanding of the physical mechanism(s) acting in magnetar flares was obtained through the study of a unique Swift observation. In fact, in 2006 March the Soft Gamma-ray Repeater SGR 1900+14 resumed its bursting activity after about 2 years of quiescence. The Swift mission observed a the intense burst “storm” which lasted for ∼30 s, when Swift was pointing at the source with the narrow field of view instruments. More than 40 bursts were detected both by BAT and by XRT, seven of which are rare intermediate flares (IFs): several times 1042 ergs were released (see [56] for details). With respect to the former studies of the broad-band spectrum of similar events, the Swift observation of 2006 March 29 has the advantage of a number of events (>40 between short bursts and IFs), therefore largely improving the statistics over which the detailed analysis can be carried out. The impact of the increased statistics and time resolution is evident when comparing the Swift results with previous ones. On 2001 July 2, the HETE-2 instruments recorded a 3.5 s IF from SGR 1900+14 and a time resolved (∆t >30 ms) spectral analysis was carried out in the 2–100 keV range [49]. They found that the 2BB model fitted the spectra well, the higher temperature blackbody (BBhard ) evolving in a manner consistent with a shrinking emitting region, the lower temperature one (BBsoft ) showing a constant radius. They also suggested that, within the magnetar model, the 2BB model might be an approximation of a more complex multi-temperature spectrum. Figure 3 includes both the results obtained from the Swift and HETE-2 data: clearly, the Swift data fill in those regions on the kT -R2 plane, which remained unexplored with HETE-2. Several properties can be inferred: a) the Swift data populate, almost homogeneously, all temperatures between ∼2 and 12 keV, and the HETE-2 measurements (black diamonds in Figure 3) can be regarded as a subset of them; b) the distribution

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is such that a sharp edge between the populated regions and the rest of the kT -R2 plane is clearly present, with a cut-off (or sharp turn) in the distribution of RBBh at kT h ≈ 12–13 keV. This sharp edge provides an estimate of the typical size of the relevant emitting regions (by assuming a reference distance of 10 kpc; [57, 58]): 30– 200 km range for the BBs component and 3-30 km range for the BBh one. c) there is an additional turn in the BBh component size between 6 and 16 km, at approximately 10 keV (see Figure 3), and d) there is a strong correlation between kT and R2BB in the brightest phases of the IFs, corresponding to BB temperatures ≤ 10 keV. This correlation is consistent with a power-law with index of about −3 (while, were the luminosity the same for all events, the relationship expected for a BB component would be y=x−4, where x = kT and y = R2BB). The sharp edge in the distribution of the 2BB parameters suggests that a saturation effect occurs. In order to investigate this effect further, we divided the data points of the two BB components in two samples, below and above a bolometric luminosity of L = 3×1040 erg s−1 (see Figure 3). The luminosity threshold was chosen so as to roughly separate the peaks of the bursts and flares from the inter-burst/flare time intervals. We note that the HETE-2 data lie just above and below the flux threshold, but never reach the values corresponding to the peaks and tops of the Swift IFs. As we can see from right panel of Figure 3, as long as both BB component are below ∼ 3 × 1040 erg s−1 , their two luminosities are strongly correlated (L(BBhard) versus L(BBsoft) is well fitted by a power law with index 0.7±0.3 at 1σ c.l.). This correlation, which seems indicative of a physical link between the two BB components, was already noticed by Feroci and collaborators who analyzed the time-averaged spectral properties of 10 short bursts from SGR 1900+14 recorded by BeppoSAX in April 2001 (filled squares in Figure 3, right panel; [54]). It is apparent that the BeppoSAX measurements are fully consistent with those obtained with Swift and can be regarded as a subsample of the latter. On the other hand, this trend was not reported for the IF observed by HETE-2 in 2001 (empty diamonds in Figure 3, right panel; [49]). Intriguingly, the correlation no longer holds above ∼ 3 × 1040 erg s−1 for the Swift data. Above this value, the luminosity of the BBsoft component reaches a maximum in the (7–14)×1040 erg s−1 range, while that of the BBhard continues to increase up to ∼ 3 × 1041 erg s−1 . Clearly, this previously unknown behavior strengthens the idea of a saturation mechanism in the burst emission. In the following, we will concentrate on the information (mainly concerning the brightest part of IFs) which can be inferred from spectral analysis of IFs. i) the existence of two blackbody components, the harder one (kT h ∼ 7–11 keV) having a systematically smaller radius (RBBh ≤ 25 km) than the softer one (RBBs ∼ 25–100 km).

This first finding shows that different thermal components originate from different regions around the NS, ranging from its surface (at R < RNS ) to well up in the magnetosphere, at a height of several stellar radii. The maximum observed flare luminosity is ∼3×1041 erg s−1 , attained by the hard blackbody component at an effective temperature of ∼10 keV and radius of ∼15 km. Interestingly, this matches well the magnetic Eddington luminosity, LEdd,B , at that same radius, for a surface dipole field ≃8×1014 G (this value of the B-field is very close to that deduced from the spindown

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rate of SGR 1900+14), where (cfr. [5, 8]): LEdd,B (r) ≃ 2LEdd



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If radiation originated from a trapped hot fireball this would be in line with the theoretical expectation that the radiative efficiency of a magnetic confined fireball never exceeds (to within a small factor) the magnetic Eddington flux [8, 14]. In fact, ablation of matter from the NS surface would increase the scattering depth in a super-Eddington radiation field, thus providing a self-regulating mechanism. The radius and temperature that we inferred at maximum burst luminosity are also in good agreement with the prediction for the emission coming from a trapped fireball ([8], cfr. their discussion for the best fit temperature and radius in the case of SGR 1806−20). Most remarkably, the luminosity of the soft component can be larger than 1040 erg s−1 out to R∼100 km. For R>(30-40) km this value exceeds the magnetic Eddington luminosity at the corresponding radius (for a dipole field geometry). This suggests that magnetospheric confinement plays an active role at those distances, with magnetic stresses balancing radiation forces. If this were the case, the saturation of the soft component at ≃ 1041 erg s−1 would be related to the magnetic field strength at the relevant radii and its maximum ability to retain the trapped fireball

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matter which is subject to very high radiation pressure. ii) the existence of a clear correlation between the luminosities of the two components up to ∼ 3 × 1040 erg s−1 , above which value the luminosity of softer blackbody shows signs of saturation, while that of the harder blackbody still grows up to a few times 1041 erg s−1 .

This second finding implies that, in the luminosity range 1040–1041 erg s−1 , the total radiation energy is divided almost equally between the two components. Combining the information of the two panels of Figures 3 we can see that, for a given luminosity ≤ 1041 erg s−1 , there are two separate emission regions: a smaller and hotter one, whose radiating area suggests emission from (part of) the NS surface with a relatively high effective temperature (10–12 keV), plus a second, possibly magnetospheric region, with significantly larger emitting area and lower effective temperature (3–7 keV). The hotter component attains the highest luminosities, i.e. > 1041 erg s−1 , as its radius grows slightly and the effective temperature decreases. On the other hand, the colder component is characterized by a minimum blackbody radius of ∼ 25 km and maximum temperature of ∼ 7 keV. A possible interpretation involves the different way in which photons with ordinary (O) or extraordinary (E) polarization mode (a property introduced by the presence of a birefringent medium, such as the magnetic field; [59]) propagate across the magnetosphere. Since the scattering cross section of E-mode photons is much reduced in presence of strong magnetic fields, E-mode photons have a scattering photosphere which is located much closer to the NS than that of O-mode photons. On the other hand, in supercritical magnetic field (B > BQED ), E-mode photons have a non-negligible probability of splitting (and switching to the O-mode). The probability is a strong function of energy, so that E-mode photons of high energy cannot travel far from their scattering photosphere before splitting into O-mode photons. On the other hand, O-mode photons will be entrained with streaming electrons and baryons and advected out to where their scattering optical depth becomes τ(O) ∼ 1 [8, 12]. As a consequence of Compton scattering (and, with lower efficiency, photon merging), a fraction of O-mode photons can also switch back to the E-mode. Therefore, the two modes are effectively coupled and are advected at comparable rates as long as mode switching is efficient: an approximately equal distribution of energy in the two modes is thus to be expected [8, 12]. This may suggest that the two observed spectral components reflect the population of photons in the two polarization modes and, thus, the regions from which they are emitted. We note that the minimum radius of the cold blackbody almost corresponds to the maximum radius of the hot component, the distribution of points in the R2 versus kT plane being continuous across this point. This suggests the existence of a narrow zone of separation between the two emission regions. In order to further characterize this zone, we studied the R2 versus kT distribution for each of the seven longest IFs and for one short burst (see Figure 4). Remarkably, the transition between the two BB components is more evident for the brightest flares (IF1 and IF7 in Figure 4) where the upper left edge of the parameter distribution of the hard component is confined to smaller radii (R ≤ 20 km) and correspondingly higher temperatures (kT ≥ 8 keV). The soft component seems less dependent on the flux than the hard

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one, its minimum size being of the order of ≥ 25-35 km in all IFs. Qualitatively, this behavior is in agreement with the above scenario. In fact, a larger brightness can be reached when the burst energy is trapped closer to the NS surface, where the stronger magnetic field allows a larger flux (of E-mode photons) to be released. Moreover, the sharp and narrow gap between the emitting regions of the two BBs, at a radius of (∼ 20–30 km), can be interpreted as the signature of the presence of an E-mode splitting photosphere; this represents the surface (at radius R = RQED ) below

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which the magnetic field is supercritical (B ≥ BQED ), photon splitting is efficient and the two polarization modes can remain coupled. E-mode photons can stream freely to the observer from the splitting photosphere (at radius RQED ∼ 20–30 km), which then would naturally define a maximum size for the emission region of radiation in this polarization mode. On the other hand, O-mode photons could not originate from regions internal to the splitting photosphere, as their scattering optical depth is still much larger than unity within that volume. If this scenario is correct, it implies that the emission region of E-mode photons can range from the base of the trapped fireball (near the NS surface) to a slightly higher region in the magnetosphere, but well within the splitting photosphere. In this case, part of the internal energy of the coupled E and O-mode photons is lost in the E-mode photosphere due to (adiabatic) expansion from near the NS to the splitting photosphere. This degrades the original spectrum towards lower temperatures and larger radii, up to RQED . On the other hand, O-mode photons might either be released near the splitting photosphere or advected to much larger radii, depending on the value of their optical depth at that location (see [8]). iii) the existence of a correlation between temperature and blackbody radius, which holds for the most luminous parts of the flares (approximately for Ltot > 4 × 1040 erg s−1 ).

Finally, our third finding is the apparent correlation between the surface and temperature of the spectral components at different luminosities. This behavior does not have a clear interpretation. As shown in Figure 3, the top part of the data strip is −3 , where Σ is the radiating blackbody surface. Since well fit by a power-law Σ ∝ T BB 4 ΣT BB = L, this implies T BB ∝ L. Therefore, along lines of constant luminosity, the radiating surface would scale like T −4 , i.e. steeper than the data points (on the edge of the allowed region in the kT versus R2 plane). The ΣT 3 =const relation that implies a roughly constant number of emitted photons per unit time. At the highest luminosities (≥ 1041 erg s−1 ) of the flares, where the softer blackbody saturates, the observed correlation involves both components. It is tempting to attribute this to the fact that, in this luminosity range, Comptonization, and/or adiabatic losses play a dominant role in the formation of the emerging spectrum, both processes being characterized by conservation of the photon number (photon splitting should have only a minor impact). This is in agreement with the prediction by [8], that at effective temperatures less than ∼ 10 keV photon splitting would not be efficient in maintaining a pure Planck spectrum for both modes. However, if the photon chemical potential is sufficiently small compared to the photon temperature, deviations from a Planck spectrum are expected only at low energies, which we do not observe given they are masked by absorption [8, 12]. On the other hand, at luminosities ≤ 1041 erg s−1 , the two blackbodies approximately share the same luminosity, therefore the colder one emits a larger number of photons. This suggests that efficient photon number-changing processes (such as photon splitting or double Compton scattering) may play a key role in the formation of the spectrum. Indeed, we note that the photon number ratio is roughly the same as the temperature ratio in this case, since the luminosities are approximately equal. As this ratio peaks at around 2 and extends from 1.5 to 4, it appears to be

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qualitatively compatible with the combined effects of photon splitting and double Compton scattering (cfr. [12]). Finally, we briefly comment on the sharp turn in the hard component distribution at around kT∼10 keV and subsequent cut-off at ∼12÷14 keV which, together with the ΣT3 =const relation, are among the most distinctive properties of Figure 3 (left panel). Among others, these features clearly imply that no thermal component with characteristic temperature above the cut-off is detected, though the BAT energy interval extend up to at least 100keV. Within the discussed scenario it is tempting to account for the above properties in terms of photon splitting process and, in particular, its efficiency as a function of (mainly) flux and energy. In fact, the turn at kT∼10 keV marks the drift of the parameter distribution from the ΣT3 =const relation, identifying the passage between photon number-conservation (such as Comptonization) and photon number-changing (photon splitting) emitting processes. As reported by [8], the minimum temperature at which photon splitting is efficient in maintaining a nearly Planckian spectrum for E-mode photons, is ≃10 keV.

3.2 Further Observations: the case of SGR 0501+4516 and 1E 1547.0-5408 The results outlined in the previous section are certainly interesting, though they should be confirmed and tested through the study of similar events (IFs or bursts) with sufficient statistics detected both from the same source or from other magnetars. It is worth emphasizing that the data of the burst “storm” has been collected due to the specific Swift capabilities (unique among current high energy missions) of rapid slew of the satellite which ensure an on-axis source observation within 12 minutes from the initial trigger. Correspondingly, obtaining an additional dataset with similar high statistics is not an easy task. During 2008 three outbursts from three different magnetars were detected, namely SGR 1627−41 , SGR 0501+4516 and 1E 1547.0-5408. In all cases the outburst onsets were studied by Swift after the detection of one or more bursts from the sources in the BAT (for details see [35, 131, 63]). In all cases the statistics collected by BAT was not sufficient (both in terms of detected bursts and statistics within each burst) to allow a detailed time-resolved study of the spectral parameters during the bursts. However, in the case of SGR 0501+4516 more than 50 bursts were identified out of which 18 had enough counts to carry out a relatively detailed time-averaged spectral analysis ([60]; see Figure 5). Among the several different spectral models used, the cut-off powerlaw and the two-blackbody models provided the best fit in the 15–150 keV energy range. The cut-off powerlaw model fit yields a mean photon index Γ = 0.5±0.1 and a cut-off energy Ecut = 19±2 keV for the bursts [60]. The mean hard and soft blackbody temperatures are found to be kT = 12.8±0.7 keV and kT = 4.6±0.5 keV for the BBsoft and BBhard components, respectively. Moreover, they are anti-correlated with the square of the radii of the hard and soft emitting regions (RBBh and RBBs ) as R2BBh ∝ kT −5.8 and R2BBs ∝ kT −2.7 , respectively ([60];

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similarly to the case of SGR 1900+14). The soft and hard component temperatures with different indices support the idea of two distinct emitting regions with the hard component corresponding to a smaller radius and the soft component corresponding to a larger radius, which further corroborate the idea of the propagation of extraordinary (E) and ordinary (O) mode photons across the photosphere, as predicted in the magnetar model. However, by comparing datapoints in Figure 4 and 5, it is evident that the “saturation” effect was not reached during SGR 0501+4516 bursts, or at least not observable within the time-averaged spectra. The properties of a peculiar burst (bouble-peaked) observed from SGR 0501+4516 with the Fermi GBM have been studied by [64]. They show that a phenomenology similar to that of the Photospheric Radius Expansion (PRE) seen in some bright thermonuclear bursts on accreting neutron stars, is also possible during magnetar bursts. After having identified the factors necessary to generate double-peaked PRE events, [64] showed that the direct measurement of the magnetic Eddington limit (see Eq. 6) in a magnetar would constrain the magnetic field strength and the distance and might, in principle, enable a measurement of gravitational redshift. Though the confirmation of the presence of PRE events in magnetar requires more detailed radiative models for bursts, the properties of the peculiar burst observed from SGR 0501+4516 are in agreement with the predicted critical flux (by using the magnetic field strength inferred from timing and the distance suggested by its probable location in the Perseus arm of our Galaxy). It was only in January 2009 that a large outburst was detected from 1E 1547.05408 after only three months from the previous one (see [65, 66] for more details).

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Fig. 6 Similar to Figure 3 but for SGR 1900+14 and 1E 1547.0-5408 together. Radii and luminosities (the latter without uncertainties in order to better appreciate the comparison with the corresponding quantities inferred for SGR 1900+14) are normalized to the distances of 15 kpc for SGR 1900+14 and 4.5 kpc for 1E 1547.0-5408 (adapted from [65, 66]). Left panel: grey points refer to SGR 1900+14, while those in blue and violet mark the hard and soft blackbody components of 1E 1547.0-5408, respectively. Right panel: grey points refer to SGR 1900+14.

1E 1547.0-5408 is very peculiar magnetar, first discovered in 1980 with the Einstein X−ray satellite [67], but studied in detail for the first time only in 2007 [68]. The source is associated with the young supernova remnant G327.24-0.13. Using data collected in June 2007 with both the Parkes radio telescope and the Australia Telescope Compact Array, the source was unambiguously classified as a transient magnetar by measuring P ∼ 2.069 s and P˙ ∼ 2.3 × 10−11 s/s [69]. During January 22, 2009, the source entered in a rather strong state of burst activity (first detected by Swift BAT), accompanied by a strong enhancement of the continuum X−ray flux, which culminated when more than 200 bursts (some of which were classified as IFs) were recorded by the INT EGRAL SPI instrument in a few hours [106]. Moreover, the distance to 1E 1547.0-5408 was independently found to be in the 4−5 kpc range on the basis of the possible association with the supernova remnant G327.24−0.13 [68], and, more convincingly, from the analysis of multiple expanding rings around the source (due to scattering by different layers of interstellar dust of a bright burst emitted by the source on January 22, 2010; [71]). Several tens of bursts were also detected by Swift BAT for several weeks since the outburst onset, ensuring a reliable dataset to carry out time-resolved spectroscopy of the brightest events and to prove (or disprove) the findings inferred for SGR 1900+14. About 1300 spectra were analysed, similarly to the case of SGR 1900+14, in an automatic and systematic fashion (see [65] for the details). The radius and luminosity values were corrected for the distance of the source (we assumed 4.5 kpc) and were compared with those of SGR 1900+14 already presented in Figure 3 (rescaled to 15 kpc with respect to Figure 3). Figure 6 summarizes the comparison between the two sources. A number of properties can be immediately noticed: i) the datapoint distributions for the two sources in the kT versus R2BB plane are very similar, ii) the two distributions have a significant relative shift both

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in kT and R2BB, which could partially be caused by the different distances of the two sources iii) the “saturation” effect (the sharp edge in the distribution of datapoints described by the R2 = kT −3 relation) and the cut-off at around (10-15) keV is present in both sources, iv) the “saturation” is also clearly present in the Lhard versus Lsoft plane, where the Lsoft inferred for 1E 1547.0-5408 saturates at a flux of about 2 × 1040erg/s, a factor of 10 smaller then that of SGR 1900+14 [65]. While the greatest part of the above listed properties are not that unexpected, it is worth commenting on the overall shift of the Lsoft distributions. In fact, according to Eq. 6 the saturation occurs when the magnetic field ability to confine the fireball is itself saturated. It is therefore strictly dependent on the value of the magnetic field at the given radius. If this hypothesis is correct, then it would be possible to infer a number of properties comparing the distributions and checking that the so obtained results quantities (such as B or d) are in agreement with the same quantities obtained with different approaches (e.g. from timing analysis or other techniques). In particular, Eq. 6 can be rewritten in the following form ! !−1/2 !5/4 " # B sur f 1/4  RNS 5/8 d F max kT ≃ 0.4 × kpc keV 10km 1014G 10−5 erg/cm2 /s

(7)

where the flux and the distance have been explicitly reported (decoupling them from L and R). The importance of this relationship is that, if the magnetic field strength has been inferred by means of different techniques (timing analysis as an example) it is then possible to derive an approximate value for the distance by using the saturation flux value recorded for the sources. Viceversa, if the distance is known from other considerations (the presence of a supernova remnant as an example, or a dust-scattering X-ray rings) it is then possible to infer the magnetic field strength. In fact, due to the different power-law indices of the BB luminosity (kT −4 ) and of the saturation (kT −3 ) in the left panel of Figure 6, the cut-off value (around 1015 keV) of the the BBhard component represents the highest luminosity value observed from the given source. By inserting the (unabsorbed) bolometric fluxes (3 and 6 times 10−5 ergs cm−2 s−1 for SGR 1900+14 and 1E 1547.0-5408, respectively) and the kT values corresponding to the cut-off regions (∼13 keV and ∼11 keV for SGR 1900+14 and 1E 1547.0-5408, respectively) in relation (7) above, the following distance estimates are obtained: dS GR1900 ∼ 8.5 kpc and d1E1547 ∼ 4.0 kpc. Note that bona fide values of the magnetic field strength of ∼ 5 ×1014 G and ∼ 2.2 ×1014 G were assumed for SGR 1900+14 and 1E 1547.0-5408, respectively [72, 63]2 . It is worth noticing that the distance to SGR 1900+14 is highly uncertain, with only a lower limit of 5 kpc and a maximum possible distance in the 12-15 kpc range [57, 58]. On the other hand, 1E 1547.0-5408 has a reliable distance measurement obtained in two independent ways, SNR-association and dust (expanding) rings, both pointing to a distance in the 4-5 kpc range. These numbers corroborate the idea of using the saturation observed in magnetars as a powerful and alternative Note that both sources have displayed, during years, a relatively large range of P˙ values corresponding to an similarly large range of B values. This is particularly true for SGR 1900+14 for which values in between 2 and 8 times 1014 G were inferred for the magnetic field [72]. 2

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way of assessing either the distance or the magnetic field strength if one of the two quantities is already inferred independently. Since the distance is in many cases the quantity inferred with the largest uncertainty, the above relation is likely more suited for inferring the distance once B is known from the timing analysis, especially when the weak dependence of d on B in eq. 7 is considered. Acknowledgements This research is based on observations with the NASA/UK/ASI Swift mission. Authors acknowledge the support from ASI (ASI/INAF contracts AAE DA-044, DA-006 and DA-017 ). GLI thanks Dr. H. Kumar for providing Figure 5 with high resolution.

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Activated Magnetospheres of Magnetars Andrei M. Beloborodov

Abstract Like the solar corona, the external magnetic field of magnetars is twisted by surface motions of the star. The twist energy is dissipated over time. We discuss the theory of this activity and its observational status. (1) Theory predicts that the magnetosphere tends to untwist in a peculiar way: a bundle of electric currents (the “j-bundle”) is formed with a sharp boundary, which shrinks toward the magnetic dipole axis. Recent observations of shrinking hot spots on magnetars are consistent with this behavior. (2) Continual discharge fills the j-bundle with e± plasma, maintaining a nonthermal corona around the neutron star. The corona outside a few stellar radii strongly interacts with the stellar radiation and forms a “radiatively locked” outflow with a high e± multiplicity. The locked plasma annihilates near the apexes of the closed magnetic field lines. (3) New radiative-transfer simulations suggest a simple mechanism that shapes the observed X-ray spectrum from 0.1 keV to 1 MeV: part of the thermal X-rays emitted by the neutron star are reflected from the outer corona and then upscattered by the inner relativistic outflow in the j-bundle, producing a beam of hard X-rays.

1 Introduction Term “magnetars” was coined for neutron stars with ultrastrong magnetic fields B ∼ 1014 −1015 G (Duncan & Thompson 1992; Paczy´nski 1992). There is substantial evidence for ultrastrong fields in soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs) (see e.g. reviews by Woods & Thompson 2006; Mereghetti 2008). Alternative models for SGRs and AXPs are not discussed here. The current magnetar catalogue contains 18 objects (13 confirmed and 5 candidates).1 Host supernova remnants were identified for some of them, confirming their young ages t ∼ 103 − 105 yr. The young age, combined with the currently observed number of objects, implies that > ∼ 20% of all neutron stars are born as magnetars. Andrei M. Beloborodov Physics Department and Columbia Astrophysics Laboratory, Columbia University, 538 West 120th Street New York, NY 10027, e-mail: [email protected] 1

http://www.physics.mcgill.ca/ pulsar/magnetar/main.html

N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_24, © Springer-Verlag Berlin Heidelberg 2011

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The rotation rates of all observed magnetars are moderate by neutron-star standards. Their spin periods P are in a rather narrow range from 2 to 12 s. On the other hand, their spindown rates P˙ show large temporal variations, usually related to the X-ray outbursts. This activity contrasts with the traditional view of neutron stars as passive stellar remnants. Unlike ordinary pulsars, whose activity is associated with the open field lines that extend to the light cylinder, the magnetar activity must be generated in the closed magnetosphere. Its energy output greatly exceeds the rotational energy of the star and must be fed by magnetic energy. A distinct feature of these objects is their huge nonthermal luminosity, exceeding the spindown power by 1-3 orders of magnitude. Between the outbursts, magnetars display persistent or slowly decaying X-ray emission with luminosities L ∼ 1034 − 1035 erg s−1 . Two peaks are observed in the X-ray spectrum: one near keV and the other above 100 keV (see e.g. Kuiper et al. 2008). The energy fluxes in the two peaks are comparable. The keV peak is dominated by emission from the hot surface of the neutron star. The 100-keV component is clearly nonthermal and demonstrates the existence of a hot corona around magnetars, which provides a large fraction of the total observed luminosity. For comparison, the corona of the sun radiates only ∼ 10−6 of the solar luminosity. The observed magnetospheric activity must be generated by motions of the star surface. The crust of a magnetar is stressed by the ultrastrong magnetic field and can yield to the stresses through episodic starquakes or a slow plastic flow (Thompson & Duncan 1996). The magnetosphere is anchored in the crust and inevitably twisted by the crustal motions, resembling the behavior of the solar corona. It becomes non-potential, ∇ × B , 0, and threaded by electric currents (Thompson et al. 2002, hereafter TLK02; Beloborodov & Thompson 2007, hereafter BT07). The currents can flow only along B, and the twisted magnetosphere remains nearly force-free, j × B = 0. No quantitative theory has been developed for the crust motion in magnetars. The theory does not predict the geometry of the magnetosphere and its deformations, however, it is possible to predict what happens after a twist has been implanted. Part of the magnetosphere becomes filled with plasma and gradually dissipates the magnetic energy, creating a long-lived luminous corona. The theory of this activity can be tested with observations of the post-burst behavior of magnetars. Besides the nonthermal emission, bright hot spots are observed on magnetars after their bursting activity. The spots slowly shrink, on a timescale of months to years. Understanding this behavior may help reconstruct the geometry of the implanted twists and perhaps the crust motion that created them. The theory is developed in two steps. First, an electrodynamic model is formulated to describe the deformed magnetosphere and its evolution (§ 2). Second, basic properties of plasma filling the magnetosphere are evaluated (§§ 4 and 5). Observational tests of the theory are discussed in §§ 3 and 6. In this contribution, we focus on the X-ray emission mechanism in magnetars. The related topics of their spindown behavior and optical/IR/radio emission are discussed elsewhere in this volume.

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2 Electrodynamics of untwisting Twisted force-free magnetospheres were extensively studied in the context of the solar corona. In axial symmetry, they are described by the Grad-Shafranov equation, and various force-free equilibria can be constructed numerically by solving this equation. A simple example is a self-similarly twisted dipole (Wolfson 1995). Pavan et al. (2009) studied multipolar self-similar solutions. Realistic non-self-similar equilibria do not admit a simple description and are less explored, except for the case of weak twists (Wolfson & Low 1992; Beloborodov 2009, hereafter B09). The twisted magnetosphere stores additional energy – the magnetic energy of the electric currents maintaining ∇ × B. The magnetosphere tends to dissipate the stored energy and untwists with time. Apart from the rare flares, the evolution proceeds slowly through a sequence of force-free equilibria. A key agent in this evolution is the moderate electric field Ek parallel to B. It has three important functions (BT07): (1) maintains the current flow, (2) regulates the dissipation rate E k j and the observed luminosity, and (3) determines the evolution of B in the untwisting magnetosphere. This section describes the untwisting theory for axisymmetric magnetospheres. A simple electrodynamic equation governs the evolution of B.

2.1 Evolution equation for axisymmetric twist Any axisymmetric magnetic field B may be expressed in the following form, B=

∇ f × eφ + Bφ eφ . 2πr sin θ

(1)

Here r, θ, φ are spherical coordinates, φ is the angle of rotation about the axis of symmetry, and eφ is the unit vector in the φ direction. For example, a dipole magnetosphere with dipole moment µ has f (r, θ) = 2πµ sin2 θ/r and Bφ = 0. Function f (r, θ) has the meaning of the magnetic flux through the circle 0 < φ < 2π of constant r and θ. Note that f is constant along any field line ( B · ∇ f = 0) and by symmetry f is also constant on any 2D “flux surface” formed by rotating a field line about the symmetry axis. Any axisymmetric magnetosphere can be thought of as a set of nested flux surfaces labeled by f . Note that f = 0 on the axis. If Bφ = 0 then the axisymmetric magnetosphere is potential, ∇× B = 0, and carries no electric currents. Any axisymmetric starquake is, in essence, a latitude-dependent rotation of the crust. It inevitably imparts a twist into the magnetosphere. Its amplitude is measured by the azimuthal extension of field lines outside the star, ψ( f ) = φ Q − φP =

Z

Q P

Bφ dl , B r sin θ

(2)

where the intergal is taken along the field line between its footprints P and Q on the star surface. The appearance of Bφ , 0 implies a non-zero circulation of B along cir-

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z P1 P2 Fig. 1 Field line C1 with footprints P1 , Q1 on a flux surface f1 and its neighbor field line C2 with footprints P2 , Q2 on a flux surface f2 . Closed contour C is formed by connecting P1 with P2 and Q1 with Q2 along the star surface.

Q2 Q1

C2

C1

cles of constant r, θ. The circulation must be sustained by an electric current through the circle, according to Stokes’ theorem. Current can flow only along B and must be maintained by a longitudinal voltage, Φe =

Z

Q P

E k dl,

(3)

where Ek is the electric field component parallel to B. Note that both footprints P, Q of the field line are “grounded” in a good conductor — the neutron star — and the electrostatic voltage between P and Q is negligible. Voltage Φe is inductive, not Relectrostatic. RIt is directly related to the rate of untwisting of the magnetic field, E k dl = c−1 (∂Ak /∂t) dl where A is the magnetic vector potential (BT07). The gradual dissipation of the magnetospheric twist is, in essence, Ohmic dissipation in the electric circuit. The dissipation rate is proportional to Φe . How does the twist ψ( f ) evolve as a result of Ohmic dissipation? The electrodynamic equation ∂ B/∂t = −c∇ × E states that electric field determines the evolution of magnetic field. Its integral version (Faraday’s law) can be used to derive the evolution equation for ψ. Consider two infinitesimally close field lines C1 and C2 on different flux surfaces f1 and f2 = f1 + δ f . A closed contour C can be formed by connecting the footprints along the stellar surface: P1 with P2 and Q1 with Q2 (Fig. 1). Let δΦ be the magnetic flux through contour C. The Faraday’s law states I Z Z 1 dδΦ =− E · dl, = Ek dl − E k dl, (4) c dt C C2 C1 where we neglected the infinitesimal contribution from curves P1 P2 and Q1 Q2 to the H line integral C . Only Bφ contributes to flux δΦ. This can be seen if we continuously deform C1 and C2 so that their points slide at constant r, θ in the φ-direction until both C1 and C2 end up in one meridional plane φ = 0. In this deformation, C1 and C2 slide along their flux surfaces f1 and f2 , and hence δΦ remains unchanged by the deformation (magnetic flux through any part of a flux surface is zero). Only Bφ

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contributes to the magnetic flux through the deformed contour in the meriodinal plane. One can show that δΦ is related to the twist angle ψ( f ) by δΦ =

ψ( f ) δ f . 2π

(5)

This geometrical identity gives a quick way to derive the evolution equation for ψ( f , t). Combining equations (3), (4), and (5) we immediately obtain2 ∂ψ ∂Φ = 2πc e . (6) ∂t f ∂f

Here we used d/dt = (∂/∂t) f taking into account that contour C remains on the same flux surfaces f , f + δ f as the magnetosphere untwists (the flux surfaces can change their shapes in the evolving magnetosphere). Equation (6) describes the twist evolution assuming that the footprints of field lines are frozen in the static crust of the star. The untwisting of field lines is due to their “slipping” in the magnetosphere, which changes the connectivity between the footprints so that ψ is reduced. It is straightforward to generalize the evolution equation for magnetospheres with moving footprints, ∂ψ ∂Φe = 2πc + ω( f, t), ∂t ∂f

(7)

where ω = dφ Q/dt − dφ P/dt is the differential angular velocity of the moving crust.

2.2 j-bundle Equation (6) has an interesting feature: the evolution of ψ on a given flux surface f is governed by the transverse gradient of the voltage ∂Φe /∂ f rather than its value Φe ( f ). This leads to a paradoxical result: if Φe ( f ) = const i.e. the voltage is the same for all field lines, then the twist must “freeze” — the magnetic configuration does not change with time. How can this be reconciled with the continuing Ohmic dissipation in the electric circuit Φe j , 0? The circuit is ought to dissipate the magnetic (twist) energy, and the unchanged B appears to violate energy conservation. The paradox is resolved if one notices that Φe cannot be the same for all field lines. In particular, field lines f > fR are confined inside the star where Ek ≈ 0. To fix ideas, suppose the star is a perfect conductor, which implies Φe ( f ) = 0 for f > fR . Only field lines extending beyond the stellar surface, i.e. forming the magnetosphere, have Φe , 0, which implies a gradient ∂Φe /∂ f , 0 near the flux surface f = fR . Then the twist evolution equation (6) implies that ∂ψ/∂t < 0 is maintained 2

This evolution equation was derived in B09 for weak twists ψ ≪ 1. As the derivation here shows, the same equation is also valid for strong twists. Equation (17) in B09 is not accurate for strong twists, it neglects the motion of flux surfaces in the process of untwisting.

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near f = fR . Effectively, the magnetospheric electric currents are “sucked” into the star through the flux surface fR . This behavior is demonstrated by the explicit solutions to the evolution equation (6) in B09. There is another nontrivial feature of the untwisting process. Under normal conditions, plasma density in the closed magnetosphere3 is not sufficient to conduct interesting electric currents. Plasma in the twisted magnetosphere is supplied by a continual discharge, which has a threshold voltage Φe = V( f ) ∼ 109 V (BT07). The voltage is well described by a step function (see § 3 for details),   V j>0    0 j=0 Φe =  (8)    −V j < 0

The threshold nature of the discharge has a rather peculiar implication. Two distinct regions immediately form in an untwisting magnetosphere: “cavity” near the flux surface fR and “j-bundle” where j , 0 (see B09 and Fig. 2). The two regions are separated by a sharp boundary along a flux surface f⋆ . The untwisting process is the slow motion of the boundary f⋆ that gradually erases the remaining electric currents. The erased magnetospheric currents end up closed below the stellar surface. If the discharge voltage V( f ) = const, the twist freezes in the j-bundle f < f⋆ and passively waits for the front f⋆ to come. Realistically, V( f ) , const and dV/d f > 0 is possible. Then equation (6) gives ∂ψ/∂t > 0, i.e. the twist grows inside the jbundle while waiting for the front to come. In all cases, the magnetic energy of the shrinking j-bundle decreases with rate equal to the rate of Ohmic dissipation. The behavior of untwisting magnetospheres is illustrated in B09 by solving the electrodynamic equation (6) for a concrete configuration: a centered dipole with a weak twist ψ < 1. The “cavity + j-bundle” structure forms immediately, and then the cavity gradually expands, while the twist angle ψ inside the j-bundle grows linearly with time. This growth leads to ψ > 1 where the model breaks. General considerations (e.g. Uzdensky 2002) show that the magnetosphere with ψ > ψcr = O(1) must lose equilibrium and restructure itself. Two possible types of restructuring are known: (1) Partial opening of field lines, which can lead to a configuration with lower energy (Wolfson & Low 1992). In an axisymmetric magnetosphere, this change may occur without breaking the symmetry. (2) Kink instability, which breaks the axial symmetry. Then an asymmetric plasmoid must be ejected by the magnetosphere and the twist amplitude must be reduced. The exact threshold for the kink, the energy of the ejected plasmoid, and the new equilibrium configuration following the kink are unknown. One can expect that the amplitude of the growing twist is regulated by the instability so that it remains close to the critical value ψ ∼ 1. The j-bundle and its footprints can be a bright source of radiation, with luminosity equal to the rate of Ohmic dissipation in the bundle. If the footprint of the j-bundle experiences heating by the bombarding magnetospheric particles (BT07) then f⋆ defines the boundary of a hot spot on the star θ < θ⋆ . The area of this spot is given 3

The usual estimate for plasma density is ρGJ /e where ρGJ = −Ω · B/2πc is the charge density induced by rotation of the star with an angular velocity Ω (Goldreich & Julian 1969).

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Fig. 2 Snapshot of the magnetospheric evolution. A global twist with a moderate ψ = 0.2 was implanted into the magnetosphere at t = 0, and the snapshot shows the magnetosphere at t ∼ 1 yr. Details of the calculations are described in B09. The plane of the figure is the poloidal cross section of the magnetosphere. The black curves are the poloidal magnetic field lines; they are symmetric about the vertical axis and the equatorial plane. Left panel: current density. The cavity is shown in white ( j = 0); its boundary f⋆ is marked by the magenta curve. The cavity expands with time, and the j-bundle shrinks toward the vertical axis. Right panel: twist amplitude ψ at the same time. The neutron star is shown by the black circle.

by

A ≈ π(R sin θ⋆ )2 = πR2 u⋆ .

(9)

Here we used the dimensionless variable u = f / fR and approximated the poloidal structure of the magnetosphere by the dipole field.4 As the cavity expands in an untwisting magnetosphere (Fig. 2), the spot θ < θ⋆ shrinks. The simplest model with V(u) = const gives the following estimate for the jbundle luminosity (B09), L = VI⋆ ≈

 u 2 cµ ⋆ 2 34 ψ V u ≈ 1.3 × 10 V B R ψ erg s−1 , 9 14 6 ⋆ 0.1 4R2

(10)

where V9 ≡ V/109 V and B14 = Bpole /1014 G. The evolution timescale of the luminosity is given by u  L µu⋆ ⋆ tev = − ≈ ≈ 1.5 V9−1 B14 R26 ψ yr. (11) dL/dt cRV 0.1 Similar calculations have been done for the more detailed model where voltage V is different on different field lines (B09). The theoretical expectations are compared with observations in the next section. Dipole field has f /2π = µ sin2 θ/r = µ/Rmax , where µ is the magnetic dipole moment. Then u = R/Rmax = sin2 θ1 where θ1 is the polar angle of the field-line footprint on the stellar surface. 4

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3 Transient magnetars Recent observations revealed that many magnetars spend a significant fraction of time in a quiescent state with a low luminosity L ∼ 1033 − 1034 erg s−1 and remain unknown until they produce an X-ray outburst. The post-outburst decay of the luminosity back to the quiescent level is monitored in these “transient magnetars.” The data can be compared with the theoretical model of untwisting magnetosphere.

3.1 Magnetospheric activity or deep crustal heating? The mechanism of the magnetar bursts (e.g. Thompson & Duncan 1995; Woods & Thompson 2006) is not settled yet. It may be associated with starquakes. It may also be associated with sudden reconnection events in the magnetosphere that is slowly deformed by the plastic crustal flow (Lyutikov 2003). In either case, a strong and brief magnetospheric dissipation is invoked to explain the burst emission. Following the burst, a bright afterglow is observed, which continues to decay for months to years. The blackbody area of this emission is much smaller than the surface area of the neutron star, and it can be associated with the hot footprint of the j-bundle in the untwisting magnetosphere. This model relies on the external heating of the stellar surface by the energetic particles accelerated in the j-bundle. An alternative to external heating was considered by Lyubarsky et al. (2002). Their model assumed that during the burst a significant heat is deposited inside a deep region of the stellar crust. The subsequent passive cooling of this region due to heat diffusion through the crust can produce a bright thermal afterglow. Its expected spectrum is quasi-blackbody. Observations of several transient magnetars in the past few years give enough information to judge which of the two heating mechanisms — external or internal — is responsible for the long-lived afterglow. Two features point to external heating. • Nonthermal X-ray spectrum. The X-ray emission shows significant deviations from blackbody (BB) and is usually fitted by BB + power-law model. A highenergy X-ray component was discovered in the transient magnetar 1E 1547.05408 (Enoto et al. 2010a). Its luminosity is comparable to the luminosity of the blackbody component, and the overall spectrum of 1E 1547.0-5408 was similar to the spectra of magnetars with persistent coronal activity. The energy dependence of pulse profiles resembled that of persistent emission in 4U 0142+61 and 1RXS J170849-400910 (den Hartog et al. 2008a,b), suggesting a similar magnetospheric emission mechanism. In another transient magnetar SGR 0501+4516, bright 100-keV emission was reported at t = 4 d after the outburst (Enoto et al. 2010b), with a similar spectrum. • Shrinking area of the hot spot. The emission area of the blackbody component A decreases following the outburst together with its luminosity L. The transient blackbody emission evolves along tracks in the A-L plane as seen in Figure 3.

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Fig. 3 Area A and luminosity L of the hot spots observed on five transient magnetars at different times following their outbursts; see text for references and discussion of the individual objects. One can see from the figure that the spot area decreases together with its luminosity. The j-bundle model is shown by the strip between the two lines. It predicts the relation L = 1.3 × 1033 B14 R−3 V9 ψ A211 erg s−1 . 6 B14 R−3 V ψ = 1 on the lower 9 6 line and 20 on the upper line.

The tracks are inconsistent with the model of impulsively heated deep crust, as cooling due to heat diffusion would give a hot spot that tends to spread with time, not shrink. The shrinking spot is consistent with the untwisting magnetosphere model (§ 2.2). The theoretical relation between A and L (obtained from eqs. 9 and 10, see caption to Fig. 3) appears to agree with the data. Caution should be taken though when interpreting the details in Figure 3, as there may be significant systematic errors in observed A — it depends on the details of spectral fits. Besides, the distance d is poorly known for many magnetars. Note, however, that the shape of the observed track in the A-L plane does not depend on d, because both A and L scale as d2 . These observations do not rule out deep crustal heating during the burst. The internal heating may dominate the thermal afterglow during first few days following the burst. After a few days, the observed light curve significantly flattens (Woods & Thompson 2006), suggesting a possible transition from internal to external heating.

3.2 Individual objects XTE J1810-197 is a canonical transient magnetar. It has spin period P = 5.54 s and magnetic dipole moment µ ≈ 1.5 × 1032 G cm3 , which corresponds to the surface field B ≈ 3 × 1014 G. An X-ray outburst was detected from this object in January 2004 (Ibrahim et al. 2004) and then its luminosity approximately followed an ex-

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Andrei M. Beloborodov Fig. 4 Comparison of the model with the observed evolution of the area A and luminosity L of the hot spot after the outburst in XTE J1810-197. The data (open squares) are from Gotthelf & Halpern (2007). Dashed line shows the object luminosity in quiescence. Solid curves show the proposed theoretical model. The starquake occurred in the region u < u0 = 0.15 with amplitude ψ0 = 0.5. The discharge voltage is assumed to drop linearly from 5.5 GeV at u = 0.15 to 1 GeV at u = 0. (From B09.)

ponential decay on a timescale of 233 days for 3 years (Gotthelf & Halpern 2007). All data points for this object in Figure 3 were taken during the afterglow of this outburst. Remarkably, the source switched on as a bright radio pulsar (Camilo et al. 2007). The radio observations provided an estimate for the distance d = 3.3 kpc (which is used in Fig. 3) and accurate measurements of the spindown rate. In a few years, the object returned to its quiescent (pre-outburst) state: the radio pulsations and the spindown enhancement gradually disappeared, and the X-ray luminosity decreased to its quiescent level. These observations show that the magnetosphere of XTE J1810-197 changed in the outburst. Its footpoints must have moved, imparting a twist in the magnetosphere. The data give significant hints about the twist geometry and evolution: (1) The change in spindown rate suggests that the open field-line bundle was strongly affected, and hence the twist reached large amplitudes ψ > ∼ 1 near the magnetic dipole axis. Recall also that ψ is limited to ψcr = O(1) by the MHD instability. (2) The luminosity was observed to decrease from ∼ 1035 erg/s to ∼ 1033 erg/s. The theoretically expected luminosity from a global twist with ψ ∼ 1 would be much higher: L ∼ 1037 V9 erg/s (eq. 10). We conclude that the twisted region was small: the current-carrying field lines formed a narrow bundle emerging from a small spot on the star surface.

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(3) The spot was discovered: a hot blackbody component with a small emission area was found in the X-ray spectrum following the outburst (Gotthelf & Halpern 2007; Perna & Gotthelf 2008; Bernardini et al. 2009). Its emission area shrank with time until the spot became undetectable (Fig. 4). (4) The X-ray and radio pulse profiles had almost simultaneous peaks, consistent with the X-ray emitting spot being on the magnetic dipole axis (Camilo et al. 2007). This behavior is consistent with the untwisting magnetosphere model described in § 2. The theoretical estimates for A, L, and tev (eqs. 9, 10, 11) are in remarkable agreement with the data. Figure 4 compares the detailed model with observations of XTE J1810-197. The data constrain the magnetospheric voltage V to be between 1 and 6 GeV, which is close to its expected theoretical value (§ 4). 1E 1547.0-5408 is known as the magnetar with the shortest spin period P = 2 s. Its estimated magnetic field is B ∼ 2 × 1014 G. The object shares many features of XTE J1810-197. A similar dynamic hot spot was detected (Halpern et al. 2008). The data points for 1E 1547.0-5408 in Figure 3 assume d = 4 kpc following Tiengo et al. (2010). One data point shows a pre-outburst state and two points show the decay after the outburst in 2007. The spot size was decreasing, however later the luminosity and the spot grew again. In October 2008 new burst activity was detected, the emission area quickly increased to A ≈ 1012 cm2 and remained approximately constant for 20 days (Israel et al. 2010). A similar luminosity and area were observed after the outburst in January 2009 (Enoto et al. 2010a); this gave another data point in Figure 3. The activity level of 1E 1547.0-5408 is clearly higher than that of XTE J1810-197. Apparently, many deformation events occurred in its magnetosphere in the past few years, and it may be hard to see the long-timescale untwisting behavior because it is interrupted by new bursting activity. CXOU J164710.2-455216 is a transient magnetar with spin period P = 10.6 s and magnetic field B ∼ 9 × 1013 G. Its outburst in September 2006 was accompanied by the increase of persistent luminosity from ∼ 1033 erg s−1 to ∼ 1035 erg s−1 (Muno et al. 2007). The subsequent slow decay of emission was observed for about 150 days (Woods et al. 2010). All eight data points for this object in Figure 3 are based on these observations; distance d = 5 kpc was assumed following Muno et al. (2007). The decay timescale is comparable to that in XTE J1810-197. SGR 0501+4516 was discovered due to its bursting activity in August 2008 and then its post-burst behavior was observed (Rea et al. 2009). The results of these observations are shown by the five data points in Figure 3, assuming d = 5 kpc. The object has spin period P = 5.7 s and magnetic field B ∼ 2 × 1014 G. Its postoutburst track in Figure 3 is consistent with a shrinking hot spot on the star. The track is close to that of XTE J1810-197. The luminosity decayed on a timescale of ∼ 24 days, about 10 times faster than in XTE J1810-197. This behavior is consistent with the j-bundle model if the voltage V in SGR 0501+4516 is ∼ 3 times higher and the twist amplitude ψ is ∼ 3 times smaller than the corresponding parameters in XTE J1810-197. This difference in parameters may not affect much the track in the

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A-L plane since L ∝ ψ V (eq. 10). At the same time, it explains the short evolution timescale since tev ∝ ψ−1 V (eq. 11).

SGR 0418+5729 was discovered due to its outburst in 2009 and its post-outburst behavior was followed for 160 days (Esposito et al. 2010). Its track in the A-L plane is shown in Figure 3 assuming a distance d = 5 kpc. The object has spin period 13 P = 9.1 s and magnetic field B < ∼ 3 × 10 G. The low magnetic field (by magnetar standards) makes this object special, which could explain the offset of its track from the tracks of other transient magnetars. Note also that the track location would be different for different d. A large distance d ∼ 15 kpc would imply ∼ 10 times larger L and A, and would place the track of SGR 0418+5729 into the strip between the two lines in Figure 3. The timescale of the post-burst decay is a few months (the luminosity decreased by a factor of 6 in four months). SGR 1627-41 is another transient magnetar whose spin period and magnetic field are close to those of 1E 1547.0-5408. The object displayed bursting activity in 1998 and then its luminosity gradually decayed toward the quiescent state with no new bursts detected until 2008 (Kouveliotou et al. 2003; Mereghetti et al. 2006; Esposito et al. 2008). The luminosity decayed in ∼ 3−5-years, with a light curve similar to the post-outburst behavior of XTE J1810-197. The published spectral analysis provides almost no information on the blackbody emission area in this object except for one XMM observation when the source luminosity was only 4 × 1033 erg −1 (Mereghetti et al. 2006). A large fraction of observed magnetars are persistent bright sources with luminosities L ∼ 1035 erg s−1 . The 100-keV emission component was observed in several of these “persistent magnetars,” indicating quasi-steady magnetospheric activity 12 2 (Kuiper et al. 2008). Their blackbody components have emission areas A > ∼ 10 cm (e.g. Perna et al. 2001), significantly larger than in transient magnetars with similar luminosities L ∼ 1035 erg−1. The reason for this difference is presently unclear. Quasi-steady magnetospheric emission is expected if the twist decay timescale tev is longer than the timescale of the crust motion imparting the twist. Note that tev may be long if the voltage along the twisted field lines is somewhat below 109 V and/or the magnetic flux in the j-bundle is large (i.e. u⋆ is large, cf. eq. 11). Moreover, it is possible that the j-bundle is persistently deformed by the plastic flow of the crust, and a quasi-steady twist is maintained near the threshold of MHD stability, ψ ∼ 1. The luminosity of persistent magnetars L ∼ 1035 erg s (e.g. Durant & van Kerkwijk 2006) is consistent with a twist created by rotation of a small cap on the star, 12 with area A < ∼ 10 cm (see eq. 10 and B09). Apparently, the footprints of the jbundle in persistent magnetars are not strongly heated, as no hot spots with small A were detected in these objects. Persistent magnetars also display sudden increases and gradual decays of luminosity. For example, the outburst of SGR 1900+14 in 1998 led to a rise in its persistent luminosity, and in a few months it decayed back to the pre-outburst level (Woods et al. 2001). Similar behavior was observed in AXPs, for instance in 1E 2259+586 (Woods et al. 2004) and 4U 0142+61 (Gavriil et al. 2009; Gonzalez et al. 2010). The rise in luminosity and its subsequent decay was reported for 1E 1048.15937 (Dib et

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al. 2009). The transient behavior in these objects is not necessarily associated with the same j-bundle that creates their persistent activity. The additional energy may be released on different field lines and after their untwisting the object returns to the pre-outburst persistent state. The timescale for this additional activity depends on the voltage, twist amplitude, and magnetic flux of the transiently deformed field lines. The variations in tev may be similar to those in transient magnetars – at least a factor of 10. Observations of PSR J1846-0258 suggest that the transient activity of the closed magnetosphere may also occur in rotation-powered pulsars (Gavriil et al. 2008).

4 Pair creation Magnetospheric activity manifests itself through relativistic particles that can bombard the stellar surface and also generate nonthermal emission. We now discuss the origin of these particles, their energies, number, and circulation in the magnetosphere. Particles are accelerated along the magnetic field lines by the longitudinal voltage R Φe = Ek dl. The particles can resonantly scatter the stellar photons of energy h¯ ω once they reach the Lorentz factor 3

γ ≈ 10 B15

h¯ ω 10 keV

!−1

,

(12)

which requires Φe ∼ 109 B15 (¯hω/10 keV)−1 V. The scattered photons are boosted in energy by the factor of ∼ γ2 . These high-energy photons convert to e± pairs off the magnetic field, creating more particles. A similar process of e± creation operates in the polar-cap discharge of ordinary pulsars, but in a different mode. In ordinary pulsars, the high-energy photons convert to e± with a delay. The scattered photon initially moves nearly parallel to B and converts to e± only when it propagates a sufficient distance where its angle θγ with respect to B increases so that the threshold condition for conversion is satisfied. This delay leads to the large unscreened voltage in the polar-cap models for pulsars. In contrast, the magnetic field of magnetars is so strong that pair creation can occur immediately following resonant scattering (BT07). The energy of the scattered photon is related to its angle θγ by   1/2  m2e c4 2   E B   2 E(θγ ) = 1 − cos θγ + 2 sin θγ   , EB sin2 θγ

(13)

where E B = (2B/B Q + 1)1/2 me c2 is the energy of the first Landau level and BQ = m2e c3 /¯he ≈ 4.4 × 1013 G. The scattered photon may immediately be above the threshold for conversion, E > Ethr = 2me c2 / sin θγ , if B > 4BQ. This suggests that e± discharge in magnetars screens E k more efficiently and buffers the voltage growth.

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Pair creation on field lines with apexes Rmax < ∼ 2R

The discharge on closed field lines can be explored using a direct numerical experiment where plasma is represented by a large number of individual particles. The existing numerical simulations (BT07) describe the discharge on field lines that extend to a moderate radius Rmax < ∼ 2R, where R is the radius of the neutron star. The magnetic field is ultrastrong everywhere along such field lines, B ≫ B Q, and resonant scattering events may be effectively treated as events of pair creation – a significant fraction of scattered photons immediately convert to e± . The simulations demonstrate that voltage and pair creation self-organize so that a particle scatters on average ∼ 1 photon as it travels through the electric circuit, maintaining the near-critical multiplicity of pair creation M ∼ 1. This criticality condition requires voltage V ∼ 109 V, which accelerates e± particles to Lorentz factors γ ∼ 103 . The electric circuit operates as a global discharge, in the sense that the accelerating voltage is distributed along the entire field line between its footprints on the star. It is quite different from the localized “gap” that is often pictured above polar caps in pulsars. The discharge fluctuates on the light-crossing timescale ∼ R/c and persists in the state of self-organized criticality. The behavior of the circuit resembles a continually repeating lightning: voltage between the footprints of the field line quasiperiodically builds up and discharges through enhanced production of charges. The average plasma density in the circuit n is close to the minimum density nmin = j/ec, as required by the criticality condition M = n/nmin ∼ 1. As discussed in § 2.2, the currents tend to be quickly erased on field lines with small Rmax . It may be that this part of the magnetospheres of observed magnetars is potential, ∇ × B = 0, with no discharge. Then the observed activity is associated with currents on field lines with large Rmax , i.e. extending far from the star. Pair creation on field lines with apexes Rmax ≫ R

The discharge on extended field lines is likely to have a similar threshold voltage V ∼ 109 V, because the conversion of upscattered photons to e± is efficient near the footprints where B ≫ B Q. In this zone, particles are able to resonantly scatter soft X-rays once they are accelerated to γ ∼ 103 (cf. eq. 12), which requires voltage ∼ 109 V. Further growth of voltage should be stopped as it would cause the excessive creation of e± moving in both directions, toward and away from the star, leading to efficient screening of E k . The discharge is expected to occur near the star, and some of the created particles outflow to r ≫ R along the extended field lines. The rate of resonant scattering by a relativistic particle increases as it moves from B ≫ BQ to B < ∼ B Q. The particle scatters many more photons, because the resonance condition shifts toward photons of lower energy h¯ ωres ∝ B whose number density is larger. Note also that the effective cross section for resonant scattering, σres = 2π2 re c/ωres increases as B−1 . Photons 12 ± scattered in the region B > ∼ 10 G convert to e , which scatter more photons. In essense, the particles outflowing from the discharge zone lose energy to scattering as they enter weaker fields, and this energy is transformed to new generations

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of e± . A similar cascade above polar caps of pulsars was studied recently by Medin & Lai (2010). As a result, the e± multiplicity of the outflow increases from M ∼ 1 to M ≫ 1.5 It means no charge starvation in the outer corona — there are plenty of charges to conduct the current demanded by the twisted magnetic field.

5 Plasma circulation in the magnetosphere Dynamics of the e± flow in the outer corona (r ≫ R) is strongly influenced by resonant scattering, which exerts a strong force F on the particles along the magnetic field lines. F vanishes only if the particle has the “saturation momentum” p⋆ such that the radiation flux measured in the rest frame of the particle is perpendicular to B. In a weakly twisted magnetosphere with approximately dipole magnetic field exposed to central radiation p⋆ is given by6 p⋆ (r, θ) =

2 cos θ sin θ

(14)

(momentum in units of me c). The radiative force always pushes the particle toward p = p⋆ . This effect may be measured by the dimensionless “drag coefficient,” D≡

rF . p me c2

(15)

Momentum p⋆ is a strong attractor in the sense that deviations p − p⋆ generate D ≫ 1 in the outer corona. Consider a steady e± outflow in the outer region where no new pairs are produced. The outflow satisfies two conditions: (a) it is nearly neutral, n+ ≈ n− , and (b) it carries the electric current j demanded by ∇× B. Electric field E k immediately reacts to violations of these conditions and enforces them. From (a) and (b) one can derive the relation between the velocities β± of e± (details are given in Beloborodov 2010), 1−

β− 2 = . β+ M + 1

(16)

Here “+” corresponds to positrons, which carry current j+ > 0 and “−” corresponds to electrons, which carry j− < 0; we assume a positive net current j = j+ + j− for definiteness. The multiplicity is defined by M = ( j+ + | j− |)/ j. An electric field Ek must be generated in the outflow to sustain the condition (16) against the radiative drag that tends to equalize β− and β+ at β⋆ . This electric field is generated by a small deviation from neutrality, δn = n+ − n− ≪ n+ . 5

A steady relativistic outflow without pair creation would have M = const along the field lines. This follows from conservation of magnetic flux, charge, and particle number, which give n/B = const, j/B = const, and n/ j = const along a field line. 6 This expression is valid in the region where 1 − B /B > (R/r)2 . In this region, stellar radiation r may be approximated as a central flow of photons, neglecting the angular size of the star ∼ R/r.

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Fig. 5 Lorentz factors γ+ (left panel) and γ− (right panel) in the two-fluid model of outer corona. In this example, the electric current is carried by the e± outflow of a fixed multiplicity M = 50. The plasma is injected at radius r = 2R and outflows along the magnetic field lines (white curves). The flow is illuminated by the star with temperature kT = 0.5 keV (magenta circle at the origin), which exerts radiative forces F (γ± ) on the e± plasma. The Lorentz factors γ+ and γ− change as the flow enters the drag-dominated region |D| ≫ 1. The region |D| > 3 is shown by the thick black curve and shadowed in black. D < 0 for positrons (γ+ > γ⋆ ) and D > 0 for electrons (γ− < γ⋆ ). The radiative drag stops the plasma in the equatorial plane outside ∼ 8R. A nearly dipole magnetic field (weakly twisted) with Bpole = 1015 G is assumed in this example. R is the neutron-star radius.

The two-fluid dynamics of the outflow is governed by equations, me c2

dγ+ = F (γ+ ) + eE k, dl

me c 2

dγ− = F (γ− ) − eEk , dl

(17)

where l is the length measured along the magnetic field line. Since γ− and γ+ are not independent — they are related by condition (16) — it is sufficient to solve one dynamic equation, e.g. for γ+ (and use the dynamic equation for γ− to exclude E k ). Straightforward algebra gives, me c 2

dγ+ F (γ+ ) + F (γ− ) = , dl 1 + dγ− /dγ+

dγ− M−1 = dγ+ M+1

!2

γ− γ+

!3

.

(18)

In the region of strong drag, |D| ≫ 1, one finds F (γ+ ) ≈ −F (γ− ) ≈ −eE k . Here both e+ and e− components of the outflow have velocities that are “locked” by the balance of two strong forces — radiative and electric. To illustrate the drag effect on the e± flow around magnetars, consider the following simplified model. Suppose that the e± plasma is injected near the star with

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a given multiplicity, e.g. M = 50, and a given high Lorentz factor, e.g. γ+ = 100. The corresponding γ− is determined by equation (16). Suppose that the plasma is illuminated by the blackbody radiation of the star of temperature kT = 0.5 keV and neglect the radiation from the magnetosphere itself (see below). The steady-state solution for γ± established in the outer corona is shown in Figure 5. The solution is not sensitive to the precise radius of e± injection as long as it is small enough, before the plasma enters the drag-dominated region. The most significant electric field develops in the region where |D| ≫ 1. It is given by eEk ≈ −F (γ+ ), and the corresponding longitudinal voltage establishedR in the outer corona is found by integrating F (γ+ ) along the field line, eΦe ≈ − F (γ+ ) dl. Its typical value for the model in Figure 5 is ∼ 107 V. Flows with lower M develop stronger electric fields, however in all cases of interest (M ≫ 1) the drag-induced voltage is below 109 V. The calculations shown in Figure 5 assume that the plasma is optically thin to resonant scattering. This is not so for real magnetars. TLK02 showed that the optical depth of a strongly twisted magnetosphere is comparable to unity. When the large pair multiplicity M is taken into account, the estimate for the optical depth becomes τ∼

Mψ ≫ 1. β±

(19)

The large optical depth has two implications. First, there is a lot of scattered radiation in the magnetosphere, which is quasi-isotropic. This increases the drag and reduces p⋆ . Second, there is a self-shielding effect: the drag force F experienced by an electron (or positron) is reduced by the factor of τ−1 . These two effects will change γ± (r, θ) shown in Figure 5. However, the main feature will persist: the outflow remains to be drag-dominated in the equatorial region at r ∼ (10 − 20)R. The initial momentum of the e± flow ejected from the discharge zone to the outer corona is taken away by the radiative drag and the e± pairs accumulate near the apexes of the closed magnetic field lines. The pairs annihilate there. The annihilation rate is given by N˙ ann ≈ 2M(I/e). Here I is the electric current through the annihilation region, I ∼ (ψcµ/4R21 ), ψ is the twist amplitude, R1 is the inner boundary of the annihilation region, and µ is the magnetic moment of the star. The corresponding annihilation luminosity is given by Lann = 2me c2 M

 R −2 I 1 ∼ 4 × 1031M ψ µ32 erg s−1 . e 8R

(20)

The proposed picture of the magnetar corona is schematically shown in Figure 6. The exact position R1 of the boundary between the two regions in Figure 6 has not been calculated and may be inside 8R. Consider, for instance, the plasma flow along the field lines with Rmax = 5R. It experiences scattering with rate that is high enough to generate a large e± multiplicity, however, not enough to bring the plasma to a stop at the equatorial plane. The opposite flows in the northern and southern hemispheres meet in the equatorial plane and try to penetrate each other. The two-stream instability then develops and a strong Langmuir turbulence is generated, which will inhibit the penetration. Effectively, the opposite flows collide in the equatorial plane and

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+

−

+−

+

−

− Fig. 6 Schematic picture of plasma circulation in the magnetosphere with surface B ∼ 1015 G. Two regions are indicated. (1) “Inner corona.” Here e± have a moderate multiplicity M ∼ 1. The particles do not stop in the equatorial plane. The electric field Ek ensures that electrons and positrons circulate in the opposite directions along the magnetic field lines, maintaining the electric current demanded by ∇ × B. The particles are lost as they reach the footprints of the field line and continually replenished by pair creation. (2) “Outer corona” — extended field lines with Rmax ≫ R. Electrons and positrons are created by the discharge near the star and some of them flow outward to the region of weaker B. Here resonant scattering enhances the pair multiplicity, M ≫ 1, and decelerates the outflow. The e± particles stop at the apexes of magnetic field lines (blue region in the equatorial plane), accumulate, and annihilate there. The number fluxes of electrons and positrons toward the annihilation region differ by a small fraction ∼ M−1 , so that the outflow carries the required electric current j = (c/4π)∇ × B.

should stop there. This behavior contrasts with the inner corona where the counterstreaming e− and e+ never stop; their circulation is maintained by the induced electric field. The outer corona is different because of its high pair multiplicity M; then the electric current is organized while both e− and e+ outflow from the star. The above analysis assumed a steady e± outflow. Then the current is organized by locking the electrons and positrons at two different velocities β− and β+ . In reality, the two-fluid flow is prone to two-stream instability that generates strong Langmuir waves and broadens the momentum distribution of e± . The robust generation of plasma waves gives a mechanism for low-frequency emission from magnetars (different from drag-induced waves in normal pulsars, cf. Lyubarsky & Petrova 2000). The instability has been simulated numerically, and the results are described in detail elsewhere (Beloborodov 2010). The fluctuating electric field E k is so strong that it could stop a particle with Lorentz factor γ+ on a short scale, much shorter than the free path to resonant scattering. A strong anomalous resistivity could be expected in this situation. Surprisingly, the simulations indicate that the effective resistivity (and the corresponding voltage) remain low. A complicated time-dependent pattern is organized in the phase-space, which allows the charges to find small-resistance paths through the waves of Ek and conduct the current at a low net voltage and a low dissipation rate.

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6 Magnetospheric emission Various ideas have been proposed for the mechanism of hard X-ray emission from magnetars (Thompson & Beloborodov 2005; Heyl & Hernquist 2005; BT07; Baring & Harding 2007; Lyubarsky & Eichler 2008). One possible source is the transition layer between the corona and the star. The layer can reach temperatures kT > ∼ 100 keV and produce bremsstrahlung emission. The other possible source is the extended corona itself. It generates nonthermal X-rays via resonant scattering of the thermal X-rays emitted by the neutron star. A simplest model assumes that the high-energy spectrum forms via single scattering by an optically thin flow that interacts with the stellar radiation. This model was developed for ordinary pulsars (e.g. Kardashev, Mitrofanov, & Novikov 1984; Daugherty & Harding 1989; Sturner 1995; Lyubarsky & Petrova 2000) and also applied to magnetars (Baring & Harding 2007). It does not, however, explain the magnetar spectrum. Several works emphasized that radiative transfer with multiple resonant scattering in the closed magnetosphere has a strong impact on the observed X-ray spectrum (TLK02; Lyutikov & Gavriil 2006; Fernandez & Thompson 2007; Nobili, Turolla & Zane 2008; Rea et al. 2008; Pavan et al. 2009; Zane et al. 2009). The key unsettled problem is what parameters of the scattering plasma should be assumed in the transfer calculations. Resonant scattering depends on the Lorentz factors of the coronal particles and the direction of their motion. One popular assumption is that the corona is filled with counter-streaming positive and negative charges with mildly relativistic velocities. The scattering in this picture can reproduce the 1-10 keV part of the magnetar spectrum (e.g. Rea et al. 2008). However its theoretical basis is problematic. The keV photons are resonantly scattered at radii r ∼ 10R where B ∼ 1011 − 1012 G. The plasma strongly interacts with the stellar radiation in this region, and the counter-streaming model needs Ek to push charges of one sign toward the star against the radiative drag. This electric field accelerates the charges of the opposite sign away from the star. In the presence of e± plasma (which is inevitable), no self-consistent solution exists for the mildly relativistic counter-streaming model. A different picture of plasma circulation is shown in Figure 6. We argued that in the outer corona both + and − charges must outflow from the star and annihilate in the equatorial plane of the magnetic dipole. A moderate electric field Ek is generated to maintain a small difference ∆β/β ∼ M−1 ≪ 1 between the average velocities of the positive and negative charges, so that the outflow carries the required electric current. This picture offers a self-consistent solution for the drag-dominated electric circuit, which needs to be tested against observations. The theoretical X-ray spectrum can be found by solving for the transfer of the stellar radiation through the e± outflow. Then one can compare the theoretical prediction with the data. The technical difficulty is that the outflow dynamics is coupled to the radiation field, and hence the radiative transfer must be solved together with the plasma motion. This nonlinear problem is well defined and can be solved exactly (numerically), however this is a rather formidable task. As a first step, let us consider a simplified model which provides the Lorentz factor γ(r, θ) of the scattering medium, motivated

318

Andrei M. Beloborodov Fig. 7 Magnetar spectrum formed by resonant scattering in the e± outflow. Solid histograms show models A and B (see text). The line of sight is chosen at angle θ = 60o with respect to the magnetic axis. The star is assumed to emit the blackbody radiation with temperature kT = 0.5 keV. The result of single (first) scattering in Model B is shown by the dotted histogram.

by the results of § 5. Given γ(r, θ) it is straightforward to calculate the transfer of the stellar radiation through the corona. The result will not depend on the optical depth τ as long as τ ≫ 1 (this is a special feature of resonant scattering). We use the MonteCarlo method for the transfer calculations; it is described elsewhere (Beloborodov 2010). First, consider the outflow model in Figure 5 and suppose γ(r, θ) = γ+ (r, θ) (model A). The emerging spectrum after multiple scattering in this outflow is shown in Figure 7 for an inclination angle θ = π/3. The model is inconsistent, as Figure 5 assumed that the drag force F is created by the central thermal radiation field, neglecting the scattered radiation, which would be appropriate only if τ ≪ 1. The central radiative drag leads to the artificially high γ+ near the axis where the central radiation is beamed along the outflow direction. In reality, τ ≫ 1 (even for moderate twists, see eq. 19), the scattered radiation fills the magnetosphere and contributes to the drag force, decelerating the outflow near the axis. This will lead to small γ(r, θ) at all θ in the outer corona and change the scattered radiation spectrum. To see the trend of this change, let us modify the drag force F in Figure 5. Let α be the angle between the photons and the outflow velocity. In the region where cos α > 0.5 for all photons emitted by the star, let us set cos α = 0.5 when calculating F . This intrusion makes the radiation field less anisotropic so that it is never strongly beamed along the outflow. Re-calculating γ± (r, θ), we find that they are reduced compared with those in Figure 5. Now consider the scattering medium with the new Lorentz factor γ = γ+ and calculate the radiative transfer through this medium (model B). The result is shown in Figure 7. Toy models A and B allow one to make some preliminary conclusions. In both models, the spectrum has two distinct peaks, at a few keV and near 1 MeV, and a

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minimum near 10 keV. This shape appears to be a robust result of radiative transfer through the e± outflow. The result is consistent with the observed spectra of magnetars (e.g. Kuiper et al. 2008). The photon index Γ above 10 keV is close to the typical observed Γ ∼ 1. Multiple scattering is essential for the formation of the high-energy peak. For illustration, the dotted histogram in Figure 7 shows the spectrum obtained in model B after single scattering; its high-energy component is weak. The first scattering of the thermal keV photons occurs mainly at radii r ∼ 10R where the outflow is slow. It generates quasi-isotropic radiation with a spectrum that is slightly modified from blackbody. A fraction of the scattered photons propagate back to the star and approach head-on the relativistic outflow in the inner region. The second scattering for such photons dramatically boosts their energy, contributing to the high-energy component in the observed spectrum. This mechanism will also operate in the exact model where the accurate distribution of the Lorentz factor in the outflow is found consistently with the radiative transfer. In this model, the high-energy luminosity will be explicitly fed by the initial power of the outflow injected near the star (which is determined by the electric current and the discharge voltage). The radiative drag transforms this power to radiation. Similar spectra are generated when the outflow is confined to the j-bundle of moderate magnetic flux u⋆ > ∼ 0.1. The spectrum evolves as the j-bundle shrinks to u⋆ ≪ 0.1. Note also that the high-energy component is anisotropic — it is preferentially beamed along the magnetic dipole axis. This may help explain the energy dependence of the pulse profiles in observed magnetars (den Hartog et al. 2008a,b). The pulse profiles of magnetars are expected to change as the magnetosphere untwists and the j-bundle shrinks. Previous discussion of pulse profiles assumed that the entire magnetosphere is twisted in a self-similar way and has a moderate optical depth τ proportional to the amplitude of the global twist ψ (e.g. Fern´andez & Thompson 2007). The calculations presented here suggest a different picture. The twists of magnetars quickly evolve to narrow j-bundles (and twists may always be confined to a small part of the magnetosphere). The plasma in the j-bundle is opaque to resonant scattering even for weak twists ψ ∼ 0.1. The result of radiative transfer (and the corresponding pulse profile) does not directly depend on τ as long as τ ≫ 1. It may depend on τ indirectly, because the deceleration of the e± outflow depends on its optical depth. Further analysis is needed to explore the implications for the pulse profile and to test the model against observations. A robust result of the radiative transfer (especially in the more reasonable model B) is the sharp break in the spectrum at Ebr ≈ 2me c2 ≈ 1 MeV. It is caused by photon absorption in the strong magnetic field. The emission of multi-MeV photons occurs in the region where B ∼ 1013 G, and they see a large optical depth to absorption. Absorption is reduced for photons emitted along the magnetic axis, and the emerging high-energy spectrum depends on the line of sight. Note that somewhat smaller Ebr ∼ 0.5 MeV could be possible for the emission produced by the transition layer between the corona and star (Thompson & Beloborodov 2005; BT07). In that model, Ebr may be controlled by the temperature of

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the layer rather than absorption in the magnetosphere. Observations of Ebr may help distinguish between the two mechanisms of high-energy emission.

7 Conclusions Nonthermal X-ray emission and shrinking hot spots on magnetars are associated with magnetospheric activity — the release of the energy stored in the twisted closed magnetosphere. The rate of energy release is proportional to the voltage established along the magnetic field lines, which is regulated by the continual discharge to Φe ∼ 109 V. This voltage has a pure inductive origin, directly related to the rate of untwisting of the magnetic field. For axisymmetric configurations, the untwisting evolution is described by the electrodynamic equation (7). The untwisting theory predicts the formation of shrinking hot spots on “transient magnetars” whose magnetospheres are temporarily activated and gradually relax back to the quiescent state. Shrinking hot spots were indeed reported in these objects (Fig. 5), and their evolution appears to agree with the theoretical expectations. Self-similar twists (Wolfson 1995; TLK02) do not form in magnetars, because the electric currents tend to be quickly removed from field lines with moderate apex radius Rmax . Currents have longest lifetime on field lines with Rmax ≫ R, forming the extended j-bundle. An e± outflow of a high multiplicity streams in the j-bundle and creates the outer corona around the neutron star. The outflow stops at the apexes of the closed magnetic field lines and the e± pairs annihilate there. The e± outflow is opaque to resonant scattering and impacts the observed X-ray spectrum. The simulations of radiative transfer through the outflow suggest a natural explanation for the hard X-ray component in magnetar spectra. The strong radiative drag and the imposed electric current lock the j-bundle plasma in a peculiar two-fluid state. The two-stream instability is then inevitable; it creates strong Langmuir oscillations, which can convert to escaping low-frequency radiation. This mechanism is discussed in more detail elsewhere (Beloborodov 2010). Acknowledgements This work was supported by NASA grant NNX-10-AI72G.

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Suzaku Detection of Hard X-ray Emission in SGR 0501+4516 Short Burst Spectrum Yujin E. Nakagawa, Teruaki Enoto, Kazuo Makishima, Atsumasa Yoshida, Kazutaka Yamaoka, Takanori Sakamoto, Nanda Rea, Kevin Hurley, Suzaku SGR 0501+4516 Team and HETE-2 Team

Abstract Spectral studies of bursts from SGR 0501+4516 are presented using Suzaku data. We discovered hard X-ray emission in a summed spectrum of short bursts with low fluences, which has been found only in quiescent emission spectra so far. This result supports our idea that there are common emission mechanisms between the quiescent emission and the bursts of soft gamma repeaters and anomalous X-ray pulsars. The quiescent emission could consist of numerous micro-bursts. If this is the case, total released energy of small fluence (< 10−8 erg cm−2 , 2-100 keV) bursts of a cumulative number-intensity distribution can be comparable to the energy released in the quiescent emission. We found that the total released energy can easily maintain the quiescent emission energy.

Yujin E. Nakagawa, Kazuo Makishima Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan, e-mail: [email protected],[email protected], Teruaki Enoto University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan, e-mail: enoto@juno. phys.s.u-tokyo.ac.jp, Atsumasa Yoshida, Kazutaka Yamaoka Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan, e-mail: [email protected],[email protected], Takanori Sakamoto NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA, e-mail: takanori@milkyway. gsfc.nasa.gov, Nanda Rea Institut de Ciencies de l’Espai (ICE-CSIC, IEEC), Torre C5-parell, 2a planta, 08193, Bellaterra (Barcelona), Spain, e-mail: [email protected], Kevin Hurley Space Sciences Laboratory, 7 Gauss Way, University of California, Berkeley, CA 94720-7450, USA, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_25, © Springer-Verlag Berlin Heidelberg 2011

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1 Introduction Astrophysical interest in magnetars, strongly magnetized neutron stars with surface fields up to ∼ 1015 G [1], has been growing for the last decade. They emit X-, and gamma-ray photons through magnetic field dissipation. The magnetars are unique objects to study interactions between magnetic fields and photons. Soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are phenomenologically defined to be magnetars. They exhibit X-, and gamma-ray quiescent emission (∼ 10−11 erg cm−2 s−1 , 2-10 keV) and super-Eddington burst activity (∼ 10−6 erg cm−2 s−1 , 2-100 keV). Since there are several common characteristics between the SGRs and the AXPs such as rotation periods of 2-12 s, they are thought to be same class of objects. However the emission mechanisms of the quiescent and burst phases remain unknown. The X-ray quiescent emission spectra below 10 keV are well modeled by a photoelectrically absorbed two blackbody function (2BB) or blackbody plus a power law (BB+PL). Hard X-ray emission above 10 keV discovered by INTEGRAL (e.g., [5]) is well described by a power law (PL) with very hard indices of ∼ −1. The most acceptable spectral model of SGR short bursts detected by the High Energy Transient Explorer 2 (HETE-2) is 2BB [6]. Given that the quiescent emission and the bursts are both energized by the magnetic fields which is thought to be a promising energy source, there could be very similar physical processes between them. Consequently, their spectra could emerge alike. Interestingly, the spectra of both the bursts and the quiescent emission show a strong linear correlation between the lower and higher temperatures of the 2BB spectrum [7]. This correlation suggests common radiation mechanisms between the bursts and the quiescent emission [7]. If this is the case, the burst spectra may also display hard X-ray emission which has only been found in the quiescent emission spectra so far. In this paper, we present spectral studies of bursts from SGR 0501+4516 detected by Suzaku. All quoted errors are 90% confidence levels.

2 Hard X-ray Emission in Burst Spectra SGR 0501+4516 was discovered by Swift on 22 August 2008. Since it was undergoing intense burst activity, a Suzaku ToO observation was performed on 26 August 2008 with the Suzaku narrow field instruments; the X-ray imaging spectrometer (0.2-12 keV) [4], and the hard X-ray detector (10-700 keV) [9]. Suzaku detected the X-, and gamma-ray quiescent emission, and 32 bursts during a ∼20 ks observation [2] (Paper I). Analyses of a strong burst were reported in Paper I. Then we analyzed 31 short bursts with low fluences which were not affected by pile-up. Since there was not enough statistics in each short burst, we summed their light curves and spectra. The summed light curve is shown in figure 2. In spectral analyses, the photoelectric absorption was fixed to 8.9 × 1021 cm−2 (Paper I).

Suzaku Detection of Hard X-ray Emission in SGR 0501+4516 Short Burst Spectrum 10

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Fig. 2 Panel (a): a summed spectrum of 31 short bursts fitted with 2BB+PL. Panel (b) and (c): residuals using 2BB and 2BB+PL.

The summed spectrum of the 31 short bursts cannot be reproduced by 2BB, despite the fact that this model is known as the most acceptable model for the SGR short bursts [6]. As shown in figure 2 (b), there is an excess above ∼20 keV. The which is comparable to excess is well reproduced by a PL with an index of −1.0+0.4 −0.3 the indices of the hard X-ray emission in the quiescent emission spectra. Therefore we have discovered hard X-ray emission in a burst spectrum which was found only in the quiescent emission spectra so far.

3 Discussion From what has been shown in section 2, we suggest that the quiescent emission and the bursts are similar, comprising not only a soft X-ray 2BB spectrum, but also a hard X-ray PL spectrum. If there are common emission mechanisms between the quiescent emission and the bursts, the quiescent emission could be formed as a result of numerous micro-bursts. The hard X-ray emission was not reported for bright short bursts (∼10−6 erg cm−2s−1, 2-100 keV) from SGR 1806−20 and SGR 1900+14 detected by HETE-2. To estimate contributions of the hard X-ray emission to short burst spectra, we analyzed 50 and 5 short bursts from SGR 1806−20 and SGR 1900+14 respectively using 2BB+PL. All short bursts were not affected by pile-up. The indices were fixed to −1.3 for SGR 1806−20 derived from Suzaku data and −3.1 for SGR 1900+14 [3]. Hard X-ray emission fluxes for 8 short bursts from SGR 1806−20 were constrained. Figure 4 presents a relation between bolometric luminosities of 2BB and 2-100 keV luminosities of PL which were derived from the Suzaku and HETE-2 data. There seems to be a correlation over a few orders of magnitude.

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SGR 0501+4516

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We also estimated a contribution of the hard X-ray emission for the strong burst. Since the strong burst was subject to pile-up, we used a pile-up corrected spectrum examined by Paper I. The spectrum was fitted by 2BB+PL with a fixed photon index of −1 which was estimated from the summed spectrum of the 31 short bursts. The photoelectric absorption was fixed to 8.9 × 1021 cm−2 (Paper I). The 2-100 keV flux of hard X-ray emission was < 2 × 10−8 erg cm−2 s−1 . The energy released in low fluence (<10−8 erg cm−2 , 2-100 keV) bursts estimated from a cumulative number-intensity distribution [6] can be comparable to the released energy of the quiescent emission. The total released energy can easily maintain the quiescent emission energy. Acknowledgements This work is supported in part by a special postdoctoral researchers program in RIKEN.

References 1. 2. 3. 4. 5. 6. 7. 8.

R. C. Duncan & C. Thompson 1992, ApJ, 392, L9 T. Enoto, et al. 2009, ApJ, 693, L122 D. G´’otz, S. Mereghetti, A. Tiengo, & P. Esposito, 2006, A&A, 449, L31 K. Koyama, et al. 2007, PASJ, 59, S23 L. Kuiper, W. Hermsen, & M. Mendez, 2004, ApJ, 613, 1173 Y. E. Nakagawa, et al. 2007, PASJ, 59, 653 Y. E. Nakagawa, et al. 2009, PASJ, 61, 109 N. Rea, S. Zane, R. Turolla, M. Lyutikov, D. G´’otz, 2008, ApJ, 686, 1245

Suzaku Detection of Hard X-ray Emission in SGR 0501+4516 Short Burst Spectrum 9. T. Takahashi, et al. 2007, PASJ, 59, S35

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The magnetar emission in the IR band: the role of magnetospheric currents Silvia Zane, Luciano Nobili and Roberto Turolla

Abstract There is a general consensus about the fact that the magnetar scenario provides a convincing explanation for several of the observed properties of the Anomalous X-ray Pulsars and the Soft Gamma Repeaters. However, the origin of the emission observed at low energies is still an open issue. We present a quantitative model for the emission in the optical/infrared band produced by curvature radiation from magnetospheric charges, and compare results with current magnetars observations.

1 Introduction The Anomalous X-ray Pulsars and the Soft Gamma Repeaters (AXPs and SGRs) are peculiar X-ray pulsators which exhibit erratic phases of bursting/outbursting activity (e.g. Mereghetti 2008). There is now a wide consensus that these sources indeed host an ultra-magnetized NS, or magnetar (Duncan & Thompson 1992), with a magnetic field B ≈ 1014 –1015 G, well in excess of the quantum critical field B Q ≃ 4.4 ×1013 G. The magnetar scenario provides a quite coherent interpretation of the observational properties of SGRs/AXPs, in particular of both their bursting and persistent emission at X/γ-ray energies (Wood & Thompson 2006). In particular, it has been suggested that the magnetosphere of a magnetar is twisted (∇ × B , 0), in which case the density of magnetospheric currents is substantial and the observed soft Xray spectrum (< 10 keV) can be explained in terms of resonant cyclotron scattering (RCS) of thermal surface photons onto mildly relativistic particles flowing along

Silvia Zane Mullard Space Science Laboratory, University College of London, Holmbury St Mary, Dorking, Surrey, RH5 6NT, UK, e-mail: [email protected] Luciano Nobili, Roberto Turolla Dept. of Physics, University of Padova, Via Marzolo 8, 35131 Padova, Italy, e-mail: luciano. [email protected],[email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_26, © Springer-Verlag Berlin Heidelberg 2011

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the closed field lines (see Zane et al. 2009 for a recent application, and references therein). Observations at IR/optical wavelengths led to the discovery of faint (K ∼ 19– 21), and in some cases variable IR counterparts to several AXPs/SGRs (see again Mereghetti 2008). In two sources optical pulsations at the X-ray period were found (Kern & Martin 2002, Dhillon et al. 2009). However, the origin of the IR/optical emission is not clear as yet. The proposed scenarios involve emission/reprocessing by a fossil disk (see e.g. Perna et al. 2000), or non-thermal emission from the inner magnetosphere (Eichler et al. 2002, Beloborodov & Thompson 2007, hereafter BT07). Although this latter option appears promising, no detailed computations have been presented as yet. In this paper we reassess this issue, and provide a quantitative estimate of the IR emission expected from curvature radiation.

2 Pair production in the inner magnetosphere In the inner magnetosphere, the magnetic field is so strong that the conversion of high-energy photons produced by RCS into pairs may give rise to a quasiequilibrium configuration in which the e± Lorentz factor is locked at about the threshold value required to ignite the pair cascade (50 < γ < 1000, BT07). In order to estimate the spatial extension of this region, we proceed as follows. We assume that primary photons have a typical energy ǫ ∼ 1 keV, and the magnetic field scales as B ∼ B p (R/R NS )−3 , where B p ∼ 10Bq is the polar field and R NS is the star radius. We assume that the magnetosphere is force free. Charges, flowing along B, are accelerated by the parallel electric field which is provided by the decay of the twist, ∂(B2 /8π)/∂t = −E k j. A thermal photon scatters where its energy in the particle frame, γ(1 − β cos θ)ǫ, equals the local cyclotron energy, ǫB = me c2 (B/BQ) (here β = v/c ∼ 1 and θ is the angle between the incident photon and the magnetic field), i.e. when the particle Lorentz factor is γ = γres ∼ (me c2 /ǫ)(B/BQ). Because the potential drop at the endpoints of a flux tube (of length L) is enormous, eΦ0 > 106 me c2 (see below), the electron Lorentz factor, which is ∼ 1 at the star surface, monotonically increases up to a value which is much higher than Fig. 1 Geometry of the curvature emission. See text for details.

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γres,max ∼ 500(1 keV/ǫ)(B p/B Q) ≈ 5000. This ensures that the resonant condition (γres = γ) is met after the electron travelled a typical distance λacc,res = γ|dx/d(γβ)| ≈ γres L/(eΦ0 /me c2 ) ≪ L. On the other hand, this is not a sufficient condition for RCS to occur: even if they can be accelerated up to γres , electrons are able to scatter only if λ < λacc,res , where λ ∼ (ǫ/me c2 )/(n phσe f f ) ≈ 10−3 (T/1 keV)−2 (R/R NS )2 cm is the particle mean free path for resonant scattering (here n ph is the density of thermal photons and σe f f = 3πσT /4αF ; e.g. Dermer 1990). This translates into: eΦ0 B < 5 × 1011 BQ me c 2

!

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We approximate the left hand quantity with the potential drop which produces the conduction current in a 1D, relativistic double layer (where j ∝ Φ20 ; Carlqvist 1982): eΦ0 ≈ 2 × 109 me c 2

r

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where m+ is the mass of the positive charge. If the magnetosphere is populated by e− /e+ pairs then m+ = me , and for a polar magnetic field ∼ 10B Q the inequality given by Eq. (1) is satisfied up to B/BQ > 0.05, or R/R NS < 6. The upscattered photon produced in the region B/B Q > 0.05 has an energy 2 ǫ ′ ∼ γres ǫ/(1 + γres ǫ/me c2 ) and may convert into a e± pair in the strong magnetic field provided that the threshold condition ǫ ′ > 2me c2 / sin θ′ is met, where θ′ is the angle of the scattered photon with the magnetic field. For ǫ ∼ 1 keV, pair creation requires γres > 30 (i.e. B > 0.05BQ). Since electrons are relativistic, the scattered photon initially moves parallel to B and a pair can be produced only after a large enough pitch angle has built up. Moreover, pair production is efficient only if its characteristic length-scale is less than the dimension of the circuit, i.e. α± > 1/RNS where α± is the absorption coefficient for ordinary and extraordinary photons (see Baring 2007). Accordingly, the limiting value of magnetic field above which the process is effective decreases with increasing photon energy, and it is B ∼ 0.05B Q for pairs created near threshold. In summary, in the region B > 0.05BQ a quasi-equilibrium configuration is reached with a pair multiplicity ∼ L/λacc,res of a few. Screening of the electric field limits the potential drop to eΦ0 /me c2 ≈ γres ∼ 500(B/BQ) and the maximum e± Lorentz factor is γres . Charges undergo only few scatterings with thermal photons, but they loose most of their kinetic energy in each collision. A steady situation is maintained against such Compton losses because e− /e+ are re-accelerated by the electric field before they can scatter again. RCS may occur also at larger radii provided that the charges Lorentz factor is limited to ∼ γres , which decreases as B ∼ 1/R3 . The pairs energy depends on the electrostatic potential (in turn fixed by conduction current), and also on the efficiency of the radiative (Compton) drag. If pairs with γ ∼ γres are injected in the external region (B/BQ < 0.05), the circuit is likely to behave much differently from a double layer, allowing the current to be conducted with only a small potential drop (see also Beloborodov, this volume).

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Fig. 2 Model spectra for different values of θobs and B p = 4.3 × 1014 G. The XMM-Newton X-ray spectrum of 1RXS J1708−4009 is from Rea et al. (2008; red solid line). The AXPs IR/optical data are from Duncan & van Kerkwijk 2005 (4U 0142+614 and 1E 1048.1−5937) and Mignani et al. 2007 (XTE J1810−197 and 1E 2259+586). The adopted distances for de-reddening are 5 kpc (4U 0142+614, 1RXS J1708−4009), 3 kpc (1E 1048.1−5937, 1E 2259+586), 4 kpc (XTE J1810−197 ), 8.5 kpc (1E 1841−045). Left: Spectra computed for incoherent curvature emission. Right: Same as in the left panel, but accounting for particle bunching.

3 IR/Optical emission In order to estimate the amount of curvature emission from the inner magnetosphere, as seen by a distant observer, we use a simple geometrical model. We approximate the twisted field with a dipole, B = B p(R/RNS )−3 (cos θ, sin θ/2, 0), while the current is still taken to be j = (c/4π)|∇ × B|twist ≈ B(R/RNS )−1 . The particle density is then n± = B(R, θ) (R/RNS )−1 / (4πe), for a pair velocity ≃ c. With reference to a generic flux tube labelled by θ0 (0 ≤ θ0 ≤ π/2), curvature photons will reach the observer if they are emitted in the volume ∆V = XRc sin θobs | dZ/dθ0 | ∆θ0 /γ2 , around the point P of cartesian co-ordinates (X, Z) where B is parallel to the LOS (Fig.1). Here θobs is the viewing angle,i.e. the angle between the line-of-sight (LOS) and the magnetic axis. In general there are two emitting regions along each flux tube one above the other below the magnetic equator, because of electrons and positrons, and for any θ0 there are two azimuthally symmetric flux tubes. The(polarization CR ispectral hR ∞ power i can be expressed as h R ∞ per particle Raveraged) ∞ ′ ′ ˙ p(ǫ) = E/ǫc (ǫ/ǫc ) ǫ/ǫ K5/3 (x)dx / 0 xdx x K5/3 (x )dx , where K5/3 (x) is the c modified Bessel function, ǫc = (3/2)¯hcγ3 /Rc , E˙ = (2/3)e2cγ4 /R2c , and Rc is the curvature radius of the field line. The monochromatic luminosity emitted by the volume ∆V is ∆L = p(ǫ)n± ∆V, and, since radiation is collimated in the solid angle ∆Ω = π/γ2 , the observer at infinity measures a luminosity 4π∆L/∆Ω. The total received power is then obtained summing the individual contributions over all the flux tubes, assuming the pair Lorentz factor is locked at γres . Fig. 2 (left panel) shows the computed CR spectrum for B p = 4.3 × 1014 and different viewing angles θobs , together with the optical/IR luminosities observed for a sample of AXPs. It should be noted that all these sources typically show variability in all energy bands. The data shown in Fig. 2 were not selected according to any

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particular criterion and are just meant to be representative of the IR emission of magnetar candidates. As it appears from Fig. 2, model spectra severely underpredicts optical/IR data. Basically, this is due to the fact that the particle density is too low for incoherent CR emission to produce the required power. The point has been already noted, on the basis of a qualitative analysis, by BT07 who concluded that particle bunching would be likely present, providing the required amplification of CR emission. Many models have been suggested to explain the origin of the interactions which push particles together and can lead to the formation of bunches of charged particles localized in phase-space, but the most promising explanation seems to be connected with plasma instabilities, like the two-stream (electron-positron/electron-ion) instability. If N particles are contained in a bunch of spatial scale lB , they radiate like a single particle of charge Q = Ne. This collective emission produces an amplification of the radiated power by a factor N with respect to the standard, non-coherent emissivity by N individual charges. The details of the emission depend on the shape of the bunch. In the simplest, one-dimensional case the power per unit frequency emitted by a bunch is pB (ν) ∼ N 2 p(ν) sin2 (πν/νl )/(πν/νl )2 = N 2 P(ν) (Saggion 1975). The main source of uncertainties lies in the size of the bunch, and here we assume that lB is associated to the local plasma frequency, lB ∼ c/ν pe = πme c2 /(γe2 ne ) (e.g. Lesch 1998). Since a single bunch emits a spectral power (ne l3B )2 P(ν) and there are NB ∼ ∆V/l3B bunches in each emitting volume, the total spectral power radiated within ∆V is ∆LB = NB (ne l3B )2 P(ν) = (ne l3B )∆L. We stress that it has to be N = ne l3B > 1 for the process to be effective, meaning that only emission at frequencies ν < νl < νco = n1/3 e c is efficiently amplified. Where N < 1 emission is from individual particles. Finally, because of the strong absorption below the plasma frequency, a low-energy cut-off is present around ν pe . We have recalculated the emergent spectrum including particle bunching (Fig. 2, right panel), finding that coherent curvature radiation can indeed produce sufficient IR/optical emission to account for the observed one. Given the limitations of our model, we are not in a position to attempt any fit of the data. What we aim to, instead, is verifying that magnetospheric CR emission is able of reproduce the gross characteristics of the observed low-energy emission, its energetics in particular. The predicted spectrum vary with the viewing angle, and the luminosity is higher when the star is viewed nearly pole-on. The curvature spectrum is far below the observed one in the soft X-rays, indicating that a different mechanism is necessary to account for the X-ray emission below ∼ 10 keV. In the twisted magnetosphere scenario this is RCS onto mildly relativistic pairs populating the external magnetosphere.

4 Discussion and Conclusion Despite the magnetar scenario is now regarded as the most likely interpretation for the observed properties of SGRs and AXPs, and the many investigations aimed at

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producing detailed models for the spectral and timing properties of magnetars, a number of key issues are still unresolved. In particular, the origin of the low-energy emission (in the IR/optical band) of a magnetar is still under debate. In this paper we gave a quantitative estimate of the IR/optical emission, under the assumption that it arises from curvature radiation from pairs in the inner magnetosphere. A comparison with observations of AXPs shows that the predictions of the model are in general agreement with observations, provided that curvature radiation is not coherent and a bunching mechanism is at work at long wavelengths. Our model is based on a number of simplifying assumptions. For instance, the computation is based on a globally twisted dipolar magnetosphere while in some magnetars, the transient AXPs in particular, the twist might affect only a limited bundle of field lines close to a magnetic pole (Beloborodov 2009) . If the inner part of the magnetosphere is (or becomes) untwisted, no currents are present that can produce the IR/optical curvature radiation. Also, we used a simple double layer model (eq. 1) for the linear accelerator, which may not be valid in presence of intense pair creation (BT07). Furthermore, and more important, the details of the charges motion in the external region of a twisted magnetosphere, which are essential ingredients in providing a model for the high energy emission in the soft and hard X-ray band (∼ 0.5–200 keV), are still unclear. In order to reach firmer conclusions about the entire multi-wavelength spectrum a more detailed study of the magnetosphere is required, and will be matter of future work (see also Beloborodov, this volume). Acknowledgements LN and RT are partially supported by the INAF/ASI grant AAE-I/088/06/0. The authors thank the organizers of the Sant Cugat forum for the hospitality and support.

References 1. Baring, M.G.. In: Astrophysics of Compact Objects, AIP Conference Proceedings, 968, 93 (2008) 2. Beloborodov, A.M., & Thompson, C.: ApJ, 657, 967 (2007) 3. Beloborodov, A.M.: ApJ, 703, 1044 (2009) 4. Carlqvist, P.: Ap&SS, 87, 21 (1982) 5. Dermer, C.D.: ApJ, 360, 197 (1990) 6. Dhillon, V.S., et al.: MNRAS, 394, L112 (2009) 7. Duncan, R.C., & Thompson, C.: ApJ, 392, L9 (1992) 8. Durant, M., & van Kerkwijk, M.H.: ApJ, 627, 376 (2005) 9. Eichler, D., Gedalin, M., & Lyubarsky, Yu.: ApJ, 578, L121 (2002) 10. Kern, B., & Martin, C.: Nature, 417, 527 (2002) 11. Lesch, H., Jessner, A., Kramer, M., & Kunzl, T.: A&A, 332, L21 (1998) 12. Mereghetti, S.: A&A Review, 15, 225 (2008) 13. Mignani, R., et al.: A&A, 471, 265 (2007) 14. Perna, R., Hernquist, H., & Narayan, R.: ApJ, 541, 344 (2000) 15. Rea, N., Zane, S., Turolla, R., et al.: ApJ, 686, 1245 (2008) 16. Saggion, A.: A&A, 44, 285 (1975) 17. Zane, S., Rea, N., Turolla, R., & Nobili, L.: MNRAS, 398, 1403 (2009)

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18. Woods P. M., Thompson C.. In: Lewin W.H.G., van der Klis M. (eds.) Compact Stellar X-ray Sources, p. 547 Cambridge University Press (2006)

Double features in mean pulsar profiles and the nature of their radio emission George I. Melikidze and Janusz Gil

Abstract In the talk presented at this Workshop by J.Dyks, the author claimed that the long-sought Rosetta Stone needed to decipher the nature of pulsar radio emission has been finally identified as the double features in averaged pulsar profiles. The author argued that highly symmetric bifurcated features are produced by a split-fan beams of extraordinary-mode curvature radiation emitted by thin microscopic streams of magnetospheric plasma conducted by a very narrow bundle of magnetic field lines. We examined arguments leading to these intriguing conclusions and found a number of flaws. At least one of them is fatal, namely there is not enough available energy within such thin microscopic plasma streams.

1 Frequency dependence of the bifurcation angle Generally, the pulsar radio emission can be generated by means of either a maser– like or the coherent curvature mechanism. Without any doubt this radiation is emitted in a strongly magnetized electron–positron plasma well inside the light cylinder. Once the waves are generated in the emission region, in the propagation region they naturally split into the ordinary and extraordinary waves corresponding to the normal modes of this plasma. The ordinary waves interact strongly with plasma particles (causing charge-separation along field lines), and thus encounter difficulty in escaping from the magnetosphere. On the other hand, the extraordinary waves can propagate freely through the plasma and escape to the interstellar medium. G. Melikidze J.Kepler Institute of Astronomy, University of Zielona Gora, Lubuska 2, Zielona Gora, Poland Abastumani Astrophysical Observatory,Ilia State University, 2a Kazbegi ave, Tbilisi 0160, Georgia e-mail: [email protected] J.Gil J.Kepler Institute of Astronomy, University of Zielona Gora, Lubuska 2, 65-265, Zielona Gora, Poland e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_27, © Springer-Verlag Berlin Heidelberg 2011

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Therefore, from a theoretical point of view the bulk of the observed pulsar radiation originates when the extraordinary waves escape from the magnetosphere. There exists also strong observational indication that the extraordinary mode is dominant in pulsar radiation [1], as the radiation observed at a given longitude is polarized perpendicularly to the plane of dipolar magnetic field lines, along which the sources are moving [2]. The analysis of highly polarized (nearly 100%) single pulses in a number of strong pulsars show that they can be produced only by the extraordinary mode excited in the plasma by means of the curvature radiation [3]. Recently, the double symmetrical features (called the bifurcated components; BFC hereafter) observed in mean profiles of some pulsars were used to decipher the nature of the observed radio emission [4, DRD hereafter]. The idea was to fit these features with the elementary emission pattern of selected radiation mechanisms: the parallel acceleration beam and the curvature radiation beam. Although we do not believe that the actual pulsar radiation mechanism can be identified from the analysis of the properties of average waveforms alone, we do not intent to argue with the approach itself. Rather, we intend to verify the arguments and claims of DRD using different and independent methods. The most important feature considered by DRD is a bifurcated component (BFC) in the mean profile of PSR J1012+5307. This feature has a high degree of a mirror symmetry and as DRD argues it reflects a pure morphology of an extraordinary mode of curvature radiation. Indeed, waves polarized perpendicularly to the plane of the charge motion are not emitted along the instant velocity vector (see lower panel of Figure 3 in [2]). DRD argued that the important property of BFC supporting the model of curvature radiation is the frequency dependence of the bifurcation angle (angular separation between component peaks) ∆bfc ∝ ν−0.35 . Interestingly, the value obs of this exponent is close to 1/3 = 0.33, which indeed follows from the properties of

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the particle curvature radiation in vacuum (provided that ∆bfc = 1/γ and νobs ∝ γ3 ). However, in the realistic theory, i.e. in the strongly magnetized electron-positron plasma, this exponent can differ from 1/3 and/or 0.35. As an example we explored the formalism developed in [2], which corresponds to the general case of curvature radiation emitted by the point–like (smaller than the emitted wave–length) charged bunch/soliton moving relativistically along curved magnetic field lines. The results are presented in Fig.1, where on the horizontal axis is the normalized observational frequency ν/νcr (where νcr = 7.2 × 109γ3 /ρ [Hz], and γ is the Lorentz factor of the charge moving along the trajectory with the radius of curvature ρ), while on the vertical axis is the normalized angle ϕ/ϕcr between the direction of maximum power emission and the local magnetic field vector (where ϕcr = 1/γ). Unlike the vacuum case, the bifurcation frequency dependence is not exactly a power–law like for the curvature radiation in a plasma (thick solid line in Fig. 1). However, when the formal power–law fit was applied we obtained ϕ/ϕcr ∝ (ν/νcr )−a , where a = 0.45 ± 0.01. This value of bifurcation exponent is far from 1/3 that can be derived for the vacuum case. Moreover, it does not depend on the actual bunching mechanism (e.g. soliton model), just any point–like emitter of curvature radiation will give the BFC exponent equal to 0.45 in the pulsar plasma [2].

2 Energy considerations We can make simple estimates of the upper limits of a possible emission power, and compare them to the observed radio luminosities. The mean flux density from PSR J1012+5307 at 1.4 GHz is about 3 mJy (ATNF database), which for the distance d = 0.52 kpc translates into the radio luminosity Lr ∼ 6 × 1027 erg s−1 . Judging from the mean profiles shown in Fig. 2 of DRD it is reasonable to assume that the BFC feature contains not less than about 10% of the total energy associated with the whole pulse profile. The same must hold for the emitted power, so we can assume that LBFC ∼ 0.1Lr = 6 × 1026 erg s−1 . The highest available energy source is determined by the spin down power LSD ∼ 4.7×1033 erg s−1 . We can now calculate the socalled pulsar kinematic luminosity Lkin , which is the power carried by charged particles accelerated within the pulsar inner gap [2]. This luminosity can be expressed as Lkin = γpr me c3 nGJ S PC erg s−1 , where γpr < 5 × 106 is the “primary” Lorentz factor of electrons (or positrons) leaving the acceleration region (“polar gap”), nGJ is the Goldreich-Julian number density and S PC is the canonical polar cap surface area. For the parameters of this pulsar nGJ = 8 × 109 cm−3 and S PC = 1.3 × 1011 cm2 and thus Lkin < 1032 erg s−1 , which is few percent of L SD (as should be expected in general). The radiation efficiency η of the observed radio emission referred to the kinematic pulsar luminosity is η = Lr /Lkin = 6 × 10−5 , which is quite typical for radio pulsars. Below we argue that such low efficiency should also be expected in conversion of the particle’s kinematic luminosity into the power of coherent curvature radiation. Indeed, the charge density inside the coherently emitting bunches moving with the Lorentz factor γ cannot exceed the Goldreich-Julian value, and

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thus we can estimate the kinetic energy flux of the bunches as L˜ kin = γme c3 nGJ S . If we assume that the entire L˜ kin is converted into the radio emission (i.e. Lr = L˜ kin ), the efficiency would be ηCR = L˜ kin /Lkin = γ/γpr . For the typical values of γ = 400 and γ pr = 106 (see [2] for details), we get ηCR = 4 × 10−4 as a maximum possible efficiency estimate. According to DRD the BFC feature is emitted via curvature radiation of sources flowing within a very narrow flux tube of magnetic field lines, although its actual cross–section is not specified. On one hand, this flux tube should be broad enough to carry much more than LBFC = 6 × 1026 erg/s in the particle flux. On the other hand, to reveal signatures of elementary emitters it should be narrow enough so that its divergence ∆χ = ε/γ is much smaller than the opening angle of curvature radiation 1/γ. Thus, the auxiliary dimensionless parameter ε << 1. Now we can roughly estimate the required cross-section of the flux tube satisfying the above condition as S = S PC ε2 /γ2 = 1.3 × 1011ε2 /γ2 and the associated kinematic luminosity carried along the BFC flux tube is L = L0 S = 1032ε2 γ−2 erg/s. We can estimate γ ≈ 200 for the frequency about 1 GHz. Therefore the kinematic luminosity of BFC flux tube L < 2.7 × 1027ε2 erg/s. We still need to estimate the value of ε which should be much less than unity. Let us note that even if we adopt as the most upper limit ε ≃ 0.3, we get the kinematic luminosity L < LBFC = 2.1 × 1026 erg s−1 . This kinematic power still does not include the efficiency of curvature emission. Once this efficiency is taken into account then one obtains LBFC < Lγ/γpr = 2.5 × 1025 ε2 /γ. r The left–hand side of this equation represents the radio luminosity of the BFC feature, which should account for about LBFC = 6 × 1026 erg s−1 . In summary, the model of the BFC emission presented by DRD has an energy deficit amounting to several orders of magnitude and it cannot be balanced by any means. This conclusion is independent of the actual pulsar radiation mechanism, i.e. it holds for any bunching mechanism in the pulsar plasma, the parallel acceleration beam, maser-like emission, etc. The BFC feature can be emitted from the bundle of field lines base of which covers at least 10% of the polar cap area irrespective of the actual radiation mechanism. We believe that BFC feature in PSR J1012+5307 is just a normal part of the multi-component average profile of this pulsar. Acknowledgements This paper was partially supported by research Grants N N 203 2738 33 and N N 203 3919 34 of the Polish Ministry of Science and Education. GM was partially supported by the GNSF grant ST08/4-442.

References 1. 2. 3. 4.

Lai D., Chernoff D. F. & Cordes J. M. (2001) ApJ, 549, 1111 Gil J., Lyubarsky Y. & Melikidze G. I. (2004) ApJ, 600,872 Mitra, D., Gil J. & Melikidze G. (2009) ApJL, 696, L141 Dyks J., Rudak B. & Demorest P. (2010) MNRAS, 401, 1781, (DRD)

Can the magnetic field of long-period X-ray pulsars be supercritical ? N.R. Ikhsanov and N.G. Beskrovnaya

Abstract Several neutron stars associated with the accretion-powered long-period X-ray pulsars are observed to experience rapid spin-down years-long trends. Modeling of these trends in terms of the canonical spin-down scenario for accretionpowered compact stars in close binaries suggests that the surface field of these neutron stars is supercritical. This conclusion contradicts, however, observations of the cyclotron resonance scattering feature which suggest the surface field of the neutron stars to be subcritical. This contradiction may indicate that the canonical value of the spin-down torque is underestimated. A possibility for the spin-down torque applied to an accreting neutron star to be larger than the canonical value is briefly discussed.

1 Magnetar hypothesis About a dozen of galactic Long-Period X-ray Pulsars (LPXPs) are identified with accreting neutron stars rotating with the periods of 500–10000 s. Most of them are members of the wind-fed massive close binaries and about half of them are persistent X-ray emitters (see, e.g. [9], and references therein). Why are the neutron stars rotating so slowly? The equation governing the spin evolution of an accreting star reads I(dωs /dt) = Ksu − Ksd , where I and ωs = 2π/Ps are the moment of inertia and angular velocity of the star, and Ksu and Ksd are the spin-up and spin-down torques applied to the star. The spin period of the star, therefore, evolves to the equilibrium period, Peq , which is defined by equating |Ksu | = |Ksd |. Hence, the large periods of LPXPs may reflect the large value of the equilibrium period of neutron stars in these systems. N.R. Ikhsanov NASA/MSFC, Huntsville, AL, 35805, USA, e-mail: [email protected] N.G. Beskrovanya Pulkovo Observatory, 196140 St. Petersburg, Russia, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_28, © Springer-Verlag Berlin Heidelberg 2011

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The spin-up torque applied to a neutron star of the mass Mns accreting mate1/2 [19]. The inner ˙ from a Keplerian disk is K (d) ≃ M(GM ˙ rial at a rate M ns Rd ) su,0 radius of the disk, Rd , is usually normalized to the canonical magnetospheric ra  √ ˙ 2GMns 2/7 , where µ is the dipole magnetic moment of the dius, RM = κ µ2 /M neutron star, and 0.5 ≤ κ ≤ 1, [8]. The spin-down torque applied to the neutron (d) star accreting from a disk has first been given in [17] as Ksd,0 ≃ µ2 /R3cor , where Rcor = (GMns /ω2s )1/3 is the corotation radius of the neutron star [16]. Putting the above torques to equation Ps = Peq (µ) and solving it for µ, one finds µ ≥ µd,0 , where  P 7/6 s 7/24 5/6 ˙ 1/2 µd,0 ≃ 1032 κ0.5 m M15 G cm3 . Here κ0.5 = κ/0.5, m = Mns /1.5 M⊙ , 1000 s 15 ˙ 15 = M/10 ˙ and M g s−1 . This corresponds to the surface field of about 1014 − 1015 G [21], which is significantly larger than the quantum critical field, BQ ≡ m2e c3 /(e¯h) ≃ 4.4 × 1013 G. In the case of Bondi (quasi-spherical) accretion the spin-up torque applied to the (s) ˙ orb R2 , where Ωorb = 2π/Porb is the orbital angular star is limited to [4] Ksu ≤ ξMΩ G 2 velocity, RG = 2GMns /V∞ is the Bondi radius, V∞ is the relative velocity between the neutron star and ambient material, and ξ is the factor by which the angular momentum accretion rate is reduced due to inhomogeneities in the accretion flow. Numerical studies (see e.g., [20], and references therein) show the average value of this parameter to be in the range 0.05–0.2. The spin-down torque in this case has been explained in terms of viscous interaction between the magnetosphere and (s) the accretion flow. Its value, Ksd,0 ≃ kt [µ2 /R3cor ] has been discussed in [4], [5], [2], [16], where kt = 1/3(ℓt/Rm )(Vt /ωs Rm ) (here ℓt and Vt are the scale and velocity of the turbulent motions at the magnetospheric boundary). The surface field estimated from the condition Ps ∼ Peq (µ) in this case is smaller than that in the case of the disk accretion. However, it still appears to be in excess of BQ at least for several LPXPs (see [15], [7], [6]). An independent estimate of the surface field of LPXPs can be found considering their spin-down trends. The spin-down torque applied to the neutron star during these events can be limited to Ksd ≥ 2πI ν˙ sd , where ν˙ sd = −P˙ s /P2s is an average spindown rate. The spin-down rate of 4U 2206+54 reported in [7] in terms of this crite(0) ria indicates that the surface field of the neutron star under the condition Ksd = Ksd exceeds 1014 G. A conclusion about the supercritical surface field of the slowly spinning neutron stars can be made analyzing the spin-down rate of GX 301–2 recently reported in [6] and the spin behavior of Vela X-1 [1]. Analysis of the spin-down trends provides us with the following additional information. The trends usually last from a few weeks up to a few years (see e.g. recent report on the spin-down of X Per, [13]), which significantly exceeds the characteristic time of the flip-flop instability of the accretion flow (under the conditions of interest is about a few days). Furthermore, observations show no correlation between the spin behavior and variations of the X-ray flux of LPXPs. This challenges models in which the spin evolution is solely associated with variations of the masstransfer rate. Finally, the existence of the spin-down trends argues against scenarios in which the origin of the long periods of LPXPs is explained in terms of the spin-

Can the magnetic field of long-period X-ray pulsars be supercritical ?

343

down of the neutron star in the previous propeller epoch. It rather suggests that the periods of LPXPs are indeed close to the equilibrium period of the neutron stars in these systems. Thus, an application of the canonical prescriptions for the spinup/spin-down torques to the interpretation of the spin behavior of LPXPs leads us to a hypothesis about the magnetar nature of neutron stars in these systems.

2 Feedback hypothesis While an application of the canonical spin-down scenarios to the LPXP GX 301–2 suggests the surface field of the neutron star to be > 1014 G [15], the measurement of the field strength through observations of the cyclotron resonance scattering feature (CRSF) in the X-ray spectrum of this source gives B0 ≃ 4 × 1012 G [12]. Furthermore, the spin-down time of a neutron star in the spin-powered pulsar and propeller stages is under the conditions of interest comparable to or even longer than the typical time of the magnetic field decay of magnetars [3], [9]. Therefore, LPXPs could be considered as magnetar descendants rather than magnetars [14]. These inconsistencies raise a question about the correctness of the magnetar hypothesis on LPXPs. If the surface field of the neutron star is indeed close to B0 derived from observations of CRSF, then the spin-down torque applied to the star is significantly larger (s) than Ksd,0 . The magnetospheric radius of the neutron star in this case turns out to be significantly smaller than its corotation radius. This makes ineffective the models of spin evolution based on the assumption Rm ∼ Rcor (see, e.g., [10], [18]). Furthermore, the month-long rapid spin-up events observed in this source can be explained in terms of the transient disk formation scenario with the surface field being consistent with B0 measured through observations of CRSF [11]. This indicates that the accretion flow during the spin-down trends has quasi-spherical rather than disk geometry. The maximum possible value of the spin-down torque applied to a neutron star ˙ from a non-rotating hot spherical envelope surroundaccreting material at a rate M (sph) ˙ s R2m , where αdis is the efficiency paraming its magnetosphere is Ksd = αdis Mω (sph)

eter. One finds this value from the equation Ksd = αdis (1/ωs )(dEkin,φ /dt), where ˙ s Rm )2 is the rate of transformation of the rotational energy of the dEkin,φ /dt = M(ω star to the kinetic energy of material penetrating into the magnetopause. Solving the (sph) inequality Ksd ≥ 2πI ν˙ sd for the parameters of GX 301–2 (see, e.g., [6]) yields, ˙ −1/2 ν˙ 1/2 Rm ≥ 1.5 × 109 α−1/2 I 1/2 M 17 −13 0.5 45



Ps 680 s

1/2

cm.

(1)

Here α0.5 = αdis /0.5 and ν˙ −13 = ν˙ /10−13 Hz s−1 . This indicates that the required rate of the spin-down can be achieved if the magnetospheric radius of the star is a factor of 3 larger than the canonical Alfv´en radius. As shown in [5], such a situation can be realized if the magnetosphere of the neutron star is surrounded by a turbulencedominated hot envelope. The upper limit to the Alfv´en radius of the star in this

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−4/9 ˙ −2/9 case is RA,max ≃ 2 × 109 µ4/9 m2/9 V7.6 M17 cm. Hence, the observed spin-down 30.3 may reflect that the neutron star is accreting material from a turbulence-dominated accretion flow or a hot envelope surrounding its magnetosphere. The rate of energy transfer into the envelope material required for keeping it hot and turbulent significantly exceeds the rotational energy loss rate by the neutron star. It, however, constitutes only about 0.1% of the energy release rate at the stellar surface. Therefore, a reconstruction of the accretion process from the turbulence-dominated medium requires a feedback from the neutron star on the accretion flow to be taken into account. An evaluation of the efficiency of the feedback needs further investigations of the dissipative processes in the magnetosphere of an accreting neutron star (e.g., anomalous dissipation of electric currents in the magnetopause, emission of MHD-waves, and non-thermal processes of energy release).

Acknowledgements N.R.I acknowledges support from NASA Postdoctoral Program at NASA Marshall Space Flight Center, administered by Oak Ridge Associated Universities through a contract with NASA. The research has been partly supported by the program of Prezidium of RAS “Origin and Evolution of Stars and Galaxies”, the program of the Department of Physical Sciences of RAS “Extended Objects in the Universe”, and the Grant from President of the Russian Federation ”The Basic Scientific Schools” NSh-3645.2010.2.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

Anzer, U., B¨orner, G. 1995, A&A, 299, 62 Bisnovatyi-Kogan, G.S. 1991, A&A, 245, 528 Colpi, M., Geppert, U., Page, D. 2000, ApJ, 529, L29 Davidson, K., Ostriker, J.P. 1973, ApJ, 179, 585 Davies, R.E., Pringle, J.E. 1981, MNRAS, 196, 209 Doroshenko, V., et al. 2010, A&A, in press (arXiv 0907.3844) Finger, M.H., et al. 2010, ApJ, 709, 1249 Ghosh, P., Lamb, F.K. 1978, ApJ, 223, L83 Ikhsanov, N.R. 2007, MNRAS, 375, 698 Kli´zniak, W., Rappaport, S. 2007, ApJ, 671, 1990 Koh, D.T., et al. 1997, ApJ, 479, 933 La Barbera, A., et al. 2005, A&A, 438, 617 La Palombara, N., Mereghetti, S. 2007, A&A, 474, 137 Li, X.-D., van den Heuvel, E.P.J. 1999, ApJ, 513, L45 Lipunov, V.M. 1982, Soviet Astronomy, 26, 537 Lipunov, V.M. 1992, Astrophysics of neutron stars, Springer-Verlag, Heidelberg Lynden-Bell, D., Pringle, J.E. 1974, MNRAS, 168, 603 Perna, R., Bozzo, E., Stella, L. 2006, ApJ, 639, 363 Pringle, J.E., Rees, M.J. 1972, A&A, 21, 1 Ruffert, M. 1999, A&A, 346, 861 Shakura, N.I. 1975, Sov. Astron. Letters, 1, 223

X-ray emission from isolated neutron stars Sandro Mereghetti

Abstract X-ray emission is a common feature of all varieties of isolated neutron stars (INS) and, thanks to the advent of sensitive instruments with good spectroscopic, timing, and imaging capabilities, X-ray observations have become an essential tool in the study of these objects. Non-thermal X-rays from young, energetic radio pulsars have been detected since the beginning of X-ray astronomy, and the long-sought thermal emission from cooling neutron star’s surfaces can now be studied in detail in many pulsars spanning different ages, magnetic fields, and, possibly, surface compositions. In addition, other different manifestations of INS have been discovered with X-ray observations. These new classes of high-energy sources, comprising the nearby X-ray Dim Isolated Neutron Stars, the Central Compact Objects in supernova remnants, the Anomalous X-ray Pulsars, and the Soft Gamma-ray Repeaters, now add up to several tens of confirmed members, plus many candidates, and allow us to study a variety of phenomena unobservable in ”standard” radio pulsars.

1 Introduction With more than 1800 detections, rotation powered pulsars (RPP) constitute by far the largest class of isolated neutron stars (INS), despite only one out of ∼10 radio pulsars is visible because of beaming. Accounting for the selection effects of radio observations, a total population of ∼ 106 RPP is estimated for the whole Galaxy [40]. Observations at gamma-ray energy, where pulsar beaming angles are larger, are now contributing to increase the number of known RPP [1]. About one hundred RPP have been detected also at X-ray energies [7]: they include the youngest and more energetic pulsars (like the Crab), a few older neutron stars at small distances Sandro Mereghetti INAF, IASF-Milano, v. E.Bassini 15, I-20133 Milano, Italy e-mail: sandro@iasf-milano. inaf.it N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_29, © Springer-Verlag Berlin Heidelberg 2011

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Sandro Mereghetti

(e.g. Vela and Geminga) and several tens of recycled millisecond pulsars (most of which are found in globular clusters [56]). All kinds of INS, not only the RPP, are X-ray emitters. X-ray observations have been crucial to discover other manifestations of INS, that for various reasons were missed in the standard searches for radio pulsars. The nearby X-ray Dim Isolated Neutron Stars (XDINS), the Central Compact Objects (CCOs) in supernova remnants, the Anomalous X-ray Pulsars (AXPs), and the Soft Gamma-ray Repeaters (SGRs) are examples of these new classes, which, despite totalling only a few tens of sources, are particularly interesting because they offer a different view on a variety of phenomena unobservable in ”standard” radio pulsars. This review is focussed on the main properties of the X-ray emission from these new classes of INS. For an excellent review of the X-ray emission from RPP see [7]. The location on a P–P˙ plot diagram of some of the objects discussed here is shown in Fig. 1. The figure also gives lines of constant magnetic field (computed ˙ 1/2 G), characteristic age (τc = 1 P/P), ˙ assuming dipole braking, B = 3.2 1019 (P P) 2 46 3 −1 ˙ ˙ and spin-down luminosity (LS D = I ΩΩ = 4 10 P / P erg s ).

Fig. 1 P–P˙ diagram for different classes of INS: XDINS (×), CCO (⋄), AXP (squares), SGR (△), RRAT (+). The vertical bars indicate the range of P˙ variations observed in SGR and AXP. Lines of constant magnetic field (dashed), characteristic age (dotted), and spin-down luminosity (dashdotted) are also indicated.

X-ray emission from isolated neutron stars

347

2 Origin of the X-ray emission in isolated neutron stars The X-ray emission observed from INS can be powered by internal heat, rotational energy, accretion, and magnetic field decay. The relative importance of these energy sources, that can also operate at the same time, depends on the age and physical properties of the neutron star. Neutron stars have internal temperatures of ∼ 1011 K at birth, that rapidly drop to ∼ 109 K. For the following ∼ 105 − 106 years the dominant cooling mechanism is neutrino emission from the star’s isothermal core. This leads to surface temperatures of several 105 to 106 K, with thermal emission peaking in the soft X-ray band. Temperature gradients on the star’s surface generally produce observable modulations at the rotation period. Thermal X-ray emission can be observed in INS with ages of ∼ 104 − 106 years, provided they are sufficiently close and not too absorbed by the interstellar medium. Older neutron stars are too cool to significantly emit X-rays, while in the youngest pulsars the thermal radiation is difficult to detect because it is outshined by the brighter non-thermal emission. A recent review on the thermal emission from neutron star is given by [171]. Non-thermal emission, that extends over a broad energy range, originates from charged particles accelerated in the NS magnetospheres at the expense of rotational energy (see, e.g., [17]). Non-thermal X-rays are characterized by power-law spectra and strongly anisotropic emission patterns, giving rise to large pulsed fractions. The pulse profiles often show narrow (double) peaks, but in many cases nearly sinusoidal profiles are observed. The most luminous RPP are the Crab and two young pulsars in the Large Magellanic Cloud (the only three pulsars with LS D > 1038 erg s−1 ). The efficiency with which the rotational energy is converted to non-thermal luminosity is about 10−3 [8, 90], but there is a large dispersion around the average value [130], as expected because of different viewing orientations and, possibly, also other effects. Studies of the LX –LS D relation with a large sample are complicated by the fact that a significant fraction of the rotational energy loss powers pulsar wind nebulae, which are difficult to disentangle in the more distant and/or fainter objects without adequate spatial resolution. Accretion is a well established process in X-ray binaries (e.g., [43]). In the lack of a companion star, accreting matter could originate directly from the interstellar medium. However, the relatively large space velocity of neutron stars, and the low density of the interstellar medium, make this process unable to provide sufficiently high luminosities. Alternatively, the matter could be supplied by a debris disk formed by fall-back in the supernova explosion that produced the neutron star. Although this possibility seems more promising, no unambiguous evidence for an INS powered by accretion has been found yet. The relevance of magnetic energy in powering the emission from neutron stars has been recognized only recently, with the observation of SGRs and AXPs (see [166, 101] for reviews). High magnetic fields (B∼1014 –1015 G) were first invoked to explain the SGRs and, in particular, the unique properties of the exceptional event of March 5, 1979 from SGR 0526−66 [119, 29]. Objects in which magnetic field decay is the dominant energy source have been named Magnetars. They are particularly

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Sandro Mereghetti

interesting because they offer the unique possibility to study physical processes in magnetic fields of unequalled strength.

3 The X-ray Dim Isolated Neutron Stars A handful of X-ray sources with large X-ray-to-optical flux ratios, F x /Fopt ∼104 – 105 , typical of INS, were discovered in the ROSAT satellite All Sky Survey. Their INS nature was confirmed by the measurement of a large proper motion in the brightest source, RX J1856.5−3754 [161], and by the discovery of pulsations at few seconds in other sources [58, 65]. The original members of this class1 and two new candidates are listed in Table 1. Recent reviews on the XDINS are given in [57, 154]. XDINS have very soft thermal spectra (blackbody temperatures TBB ∼40–110 eV), X–ray luminosities L X ∼ 1030 − 1032 erg s−1 , spin periods in the 3–12 s range, faint optical counterparts (V>25), and no radio emission. Period derivatives of the order of 10−14 –10−13 s s−1 have been measured for several XDINS through phase connected timing, but in some cases these values are still poorly constrained (see Table 1). The temperatures of XDINS are consistent with neutron stars cooling curves if they have ages of 105 –106 years and the effect of their strong magnetic field is taken into account [2]. It is thus generally believed that the XDINS are powered by residual thermal energy. X-ray sources with such soft spectra can only observed if the interstellar absorption is small: all the M7 are closer than ∼0.5 kpc and have NH <4 1020 cm−2 . Their proximity allowed in several cases the measurement of parallax and and proper motion showing a distribution of transverse velocities consistent with that of radio pulsars [113]. For these velocities, and typical ISM densities, accretion from the ISM, originally invoked to explain the XDINS emission, cannot provide the observed luminosity. Although the timing parameters give spin-down ages τc ∼ 1–2 million years, the measured spatial velocities and likely birth places in nearby OB associations strongly suggest that their true ages are smaller (see Table 2). Despite various attempts, none of the XDINS has been detected in the radio band. The most recent upper limits of 0.14–5 µJy kpc2, obtained at 1400 MHz [81], correspond to pulsed luminosities well below those of the faintest observed radio PSRs. However, given the small sample and considering the anticorrelation between beaming aperture angle and pulse period, it cannot be excluded that the lack of radio emission be simply due to unfavorable orientations. The X-ray light curves of XDINS are nearly sinusoidal, with pulsed fractions, ranging from 1.5% to ∼20%, and moderate energy dependence. Only in the case of RX J1308.6+2127 two peaks are clearly seen. These properties indicate that we are likely seeing emission from a large fraction of the star’s surface.

1

they have been nicknamed ”The Magnificent Seven” (M7, hereinafter)

X-ray emission from isolated neutron stars

349

Table 1 Isolated Neutron Stars P (s)

P˙ (s s−1 )

RX J0420.0−5022

3.45

-

RX J0720.4−3125

8.39

7.01 10−14

RX J0806.4−4123

11.37 (5.5±3.0) 10−14

0.25

-

[59, 77]

RX J1308.6+2127

10.31

1.120 10−13

0.5

-

RBS1223 [65, 74]

-

-

Name

RX J1605.3+3249

D(a) Association Notes(b) and (kpc) References XDINS 0.345 0.36

-

[59]

-

G? [58, 78, 157, 68]

0.39

-

RBS1556 [112, 169]

RX J1856.5−3754

7.06 (2.97±0.07) 10−14 0.16

-

[161, 151, 156, 158]

RX J2143.0+0654

9.43

(4.1±1.8) 10−14

0.43

-

RBS1774 [168, 76]

2XMM J104608.7–594306

-

-

2

-

candidate [127]

RX J1412.9+7922

-

-

3.6

-

candidate, Calvera [137, 140]

RX J0822.0–4300

0.122

<8 10−15

2.2

-

-

1

0.424

<2.5 10−16

2

G296.5+10.0 [102, 21, 53]

CXOU J160103.1–513353

-

-

5

G330.2+0.1 [121]

RX J1713.4–3949

-

-

1.3

G347.3–0.5 [87]

8.7 10−18

7.1

Kes 79

CCO CXOU J085201.4–461753 1E 1207.4–5209

CXOU J185238.6+004020 0.105

Puppis A

[126, 52]

G266.1–1.2 [123]

[63, 62]

1E 161348–5055.1

-

-

3.3

RCW 103

CXOU J232327.8+584842

-

-

3.4

Cas A

XMMU J172054.5–372652

-

-

4.5

G350.1–0.3 candidate [44]

XMMU J173203.3–344518

-

-

3.2

G353.6–0.7 candidate [147]

CXOU J181852.0–150213

-

-

8.5

G15.9+0.2 candidate [136]

CXOU J010043.1−721134 8.02

AXP and SGR 1.9 10−11 60

SMC

T [39] [15, 110, 122]

AXP [85, 96, 148]

4U 0142+614

8.69

2 10−12

3.6

-

B, G? [73, 26]

1E 1048.1−5937

6.45

(1–10) 10−11

8

-

B, G [139, 152, 46, 28]

1E 1547.0−5408

2.07

2.3 10−11

5

PSR J1622–4950

4.33

1.7 10−11

9

CXOU J0100−7211

10.6

9.2 10−13

1RXS J1708−4009

11.0

2.4 10−11

5

-

XTE J1810−197

5.54

(0.8–2.2) 10−11

3.1

-

1E 1841−045

11.77

4.1 10−11

8.5

Kes 73

1E 2259+586

6.98

4.8 10−13

4

AX J1844.8–0256

6.97

-

8.5

SGR 0418+5729

9.1

<1.1 10−13

2

-

R [88]

3.9 Westerlund 1 T, B, G [114, 71]

10−12

1.5 55

SGR 0501+4516

5.76

7.1

SGR 0526−66

8.05

6.5 10−11

SGR 1627−41

2.59

1.9 10−11

11

SGR 1806−20

7.6

(8–80) 10−11

8.7

SGR 1833–0832

7.6

7.4 10−12

10

SGR 1900+14

5.2

(5–14) 10−11

15

(a)

G327.2–0.1 T, B, R [12, 64, 33, 106]

CTB 109

G [141, 72, 18, 27] T, B, R [70, 13, 163, 9] G [159, 49, 111, 27] B, G [39, 80]

G29.6+0.1 candidate, T [160, 142] -

T, B [155, 34]

-

T, B [131, 4, 30]

LMC, N49 B, GF [95, 93, 149] -

T, B [165, 103, 37, 32]

star cluster B, GF [82, 120, 109, 162] -

T, B [55, 38]

star cluster B, GF, G? [94, 164, 104]

in several cases the distances have large uncertainties; the values adopted in the figures of this work are indicated here. (b) B = bursts, G = glitches, GF = giant flares, R = radio emission, T = transient

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Table 2 Comparison of estimated and spin-down ages of INS Source

Spin-down age (τc )

Estimated age

Method

RX J0720.4−3125

1.9 Myr

RX J1308.6+2127

1.5 Myr

RX J1856.5−3754

3.8 Myr

0.4 Myr

proper motion

1E 1841−045

4.5 kyr

0.5–1 kyr

SNR age

1E 2259+586

230 kyr

(11.7±1.2) kyr

SNR age

SGR 0526−66

2 kyr

5 kyr

SNR age

3.7 kyr

SNR age

>27 Myr

7 kyr

SNR age

CXOU J185238.6+004020 190 Myr

7 kyr

SNR age

CXOU J085201.4–461753 >240 kyr 1E 1207.4−5209

(0.7+0.3 −0.2 ) Myr proper motion

(0.5–1.4) Myr proper motion

The first spectra of XDINS, obtained with ROSAT, could be well described with blackbody curves. With the better data of XMM and Chandra, significant deviations from this simple model have been detected in most XDINS (the only exception is RX J1856.5−3754 [11]). The features consist of broad absorption lines in the energy range ∼0.2–0.8 keV (see [156, 57] and references therein). Multiple lines, with energy spacings consistent with harmonic ratios, are present in nearly half of the sources. They have been interpreted as proton cyclotron lines or as H and/or He atomic transitions, falling in the soft X-ray range due to the effect of a high magnetic field on the binding energies. Both interpretations require B∼ 1013 − 1014 G, broadly consistent with the values of 2.5 and 3.4 1013 G derived from the timing parameters of RX J0720.4−3125 and RX J1308.6+2127 assuming dipole braking2. Variability on a time scale of few years was discovered in RX J0720.4−3125 [23], a target regularly observed for XMM calibrations because it was believed to be a constant source. If we exclude AXPs and SGRs, this has been the first INS to show significant changes in its X-ray flux, spectrum and pulse profile. Based on the first observations, it was suggested that the variations had a periodicity of 7.1±0.5 years and could be caused by precession of the neutron star [60]. However, the most recent analysis, which include new observations and take into account the variable phase shifts between hard and soft energy bands, do not support the periodicity [67]. Most of the spectral variation occurred in a relatively short timescale of half a year [157], in coincidence with a possible glitch. A change in the temperature and/or composition of part of the NS surface might have been caused by the energy released in the glitch, or alternatively by a sudden accretion episode. The other XDINS seem to be constant in flux, but small variations might have been unnoticed since, with the exception of RX J1856.5−3754 , they have not been observed very often with sensitive instruments. On the other hand, RX J1856.5−3754 2

Note that the lines measure the surface field, which can be higher than the dipole component dominating at large radii and responsible for the spin-down.

X-ray emission from isolated neutron stars

351

is twice as bright as RX J0720.4−3125 and has been observed repeatedly, but no variability has been reported. Interestingly this is the only XDINS without spectral lines [11] and with the smallest pulsed fraction (∼1.5% [151]). Until recently, attempts to enlarge the XDINS sample had little success. Ongoing searches in the ROSAT Bright Sources Catalogue are reported in [153]. Looking for new INS among the tens of thousands serendipitous XMM and Chandra sources requires a long and difficult multi-wavelength effort, also considering that they are fainter and more distant than the bright M7. One promising source has been selected among XDINS candidates discovered with XMM [127], but its temperature (kTBB=117 eV) and estimated luminosity (∼ 1033 erg s−1 ) are larger than those of the M7. The same is true for another candidate, RX J1412.9+7922 [137], for which other interpretations (e.g. a nearby millisecond pulsar) cannot be excluded yet. Its blackbody temperature is kTBB ∼200 eV. A hydrogen atmosphere model (kT∼122 eV), with a possible emission line at 0.53 keV, gives a better fit to the Chandra data [140]. If the emission comes from the whole star’s surface, its distance would be 3.6 kpc, while a smaller emission region and distance should give rise to pulsations. Only the detection of a periodicity could clarify the real nature of these new XDINS candidates.

4 Central Compact Objects in Supernova Remnants The group of Central Compact Objects (CCOs) consists of several radio quiet X– ray sources located at the center of shell-like SNRs and with high F x /Fopt [124, 19]. The association with SNRs (see Table 1) imply ages at most of a few tens kyrs, and gives the possibility to know their distances. Three CCOs show X-ray pulsations with periods in the 0.1–0.4 s range, consistent with young neutron stars, but with unexpectedly small spin-down rates [51, 62]. The extremely small P˙ measured for the CCO in Kes 79 implies a dipole magnetic field of only 3.1 1010 G, while the upper limits for the sources in G296.5+10.0 and Puppis A give B<3.3 1011 G and B<1012 G, respectively. The spin-down ages of these three CCOs exceed by orders of magnitude the ages of their associated SNRs (see Table 2), indicating that these INS were probably born with spin periods very close to the current values. It is likely that their relatively long initial spin period and low magnetic field be causally connected. This has led to the ”anti-magnetar” nickname for these objects. The three ”anti-magnetars” show a variety of different pulse profiles: the CCOs in Kes 79 has a > pulsed fraction of ∼ 60%, one of the highest among thermally emitting INS [63]. A < more standard value of ∼ 10% is shown in 1E 1207–5209, but with the peculiarity that most of the pulsation can be attributed to phase variations in the shape of its prominent absorption lines at 0.7, 1.4, 2.1 and possibly 2.8 keV [21]. The pulsations in the Puppis A CCOs eluded an earlier detection because of a phase shift of 180◦ between nearly sinusoidal profiles in the soft (<1.2 keV) and hard bands [52]. Most CCOs have thermal-like X-ray emission, with blackbody temperatures in the range ∼0.2–0.5 keV, and no evidence for additional non-thermal components.

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The rotational energy loss of the three pulsed COOs is certainly too small to give a detectable contribution to their observed X-rays, assuming a typical efficiency of 10−3 . The emission could be due to residual cooling and/or weak accretion from a residual disk. When data of good statistical quality are available, single-temperature blackbody spectra do not provide acceptable fits. Better fits are obtained with the sum of two blackbodies with kT1 in the range 0.16–0.4 keV and kT2 ∼2 kT1 . This simple model can be thought as a first approximation of a non-uniform temperature distribution. The hotter blackbody is energetically significant: the bolometric luminosities of the two components are in the ratio L2 /L1 ∼0.2–0.7. The two-blackbody model implies small X-ray emitting areas (R1 ∼0.4–4 km, R2 ∼0.06–0.8 km), which are difficult to explain in weakly magnetized neutron stars. The situation does not significantly change if atmosphere models, which give lower temperatures and larger radii, are used instead of the blackbody fits. It is unclear whether also the CCOs with unknown spin period can be interpreted as ”anti-magnetars”. The lack of pulsar wind nebulae and of radio/gamma emission suggests that also these COOs have a small LS D , but this can result equally well from a small P˙ or from a long spin period. Thus it cannot be excluded that CCOs constitute a heterogenous class comprising objects of different kinds. The source at the center of the ∼330 years old Cas A SNR is one of the most studied CCOs. It has a very soft spectrum and most spectral fits, with a variety of thermal models, indicate an emitting area smaller than the whole surface of a neutron star. No pulsations have been detected, down to quite stringent limits [110, 122, 62], but an anti-magnetar interpretation remains plausible, considering the possibility of an unfavorable orientation and the variety of pulsed fractions seen in other INS. On the other hand, the CCO in RCW 103, with a clear periodicity at 6.67 hours and long term variations spanning more than two orders of magnitude [39], has unique properties requiring an ad-hoc explanation. The periodicity, if interpreted as an orbital motion, suggests a low mass binary [39, 10], but the deep optical limits pose severe constraints on the companion star [22]. Models involving magnetars, isolated or in a synchronous binary, and fall-back disks have also been proposed [129, 89].

5 The Magnetar candidates: Anomalous X-ray Pulsars and Soft Gamma-ray Repeaters Anomalous X-ray Pulsars (AXPs) and Soft Gamma-Ray Repeaters (SGRs) are spinning-down pulsars characterized by a luminosity in the soft and hard X-rays larger than their available rotational energy loss and by the emission of bursts and flares. The first AXPs, discovered as bright pulsars in the soft X-ray range (<10 keV), were initially classified as X-ray binaries powered by accretion. Further X–ray data, coupled to deep searches for optical/IR counterparts, revealed their different nature

X-ray emission from isolated neutron stars

353

[108]. In particular, these observations showed that the narrow period distribution, long-term spin-down, and soft spectrum of the AXPs were at variance with the properties of the larger population of pulsars in massive binaries. Furthermore, no signs of binary companions could be found in the AXPs [107]. The SGRs were instead discovered through the detection of bright and short bursts in the hard X-ray/soft gamma-ray range, and initially considered a particular subclass of gamma-ray bursts [86, 5], with the notable property of “repeating” from the same sky direction. When accurate localizations became available, it was possible to identify the X-ray counterparts of SGRs, finding that they are pulsating sources very similar to the AXPs. Although historically divided in two classes, many similarities indicate that AXPs and SGRs are probably the same kind of astrophysical objects (see [166, 79, 101] for reviews). The most successful model to explain AXPs and SGRs involves highly magnetized neutron stars, or “magnetars” [29, 144, 145], but other possibilities have been proposed, e.g., models based on INS accreting from residual disks [16, 125, 3, 31], or different kinds of quark stars [167, 69, 118, 14]. Magnetars differ from the normal pulsars, not only for their higher field intensity, but also because their magnetosphere is not dipolar. It is believed to consist of a twisted dipole, i.e. a field with a significant azimuthal component. This causes the presence of large-scale currents with high charge density flowing in the magnetosphere and affecting the emerging spectra by resonant scattering. At energy below 10 keV, the X-ray spectra of AXP and SGRs have been traditionally described with a two-components model consisting of a power-law plus a blackbody with kT BB ∼0.5 keV. The steepness of the power-law component (especially in the AXPs, photon index ∼3–4) requires NH values higher than those independently estimated in other ways and leads to overestimate the flux of the near infrared and optical counterparts (unless a drastic, and possibly un-physical, spectral cut-off is invoked). This problem is solved by adopting a two-blackbody model, that gives equally good fits [61]. XMM observations of CXOU J010043.1−721134 in the Small Magellanic Cloud, less affected by the interstellar absorption than the Galactic AXPs/SGRs, have clearly demonstrated that the power-law plus blackbody model can be rejected with high confidence, while a good fit to the soft X-ray spectrum is obtained with the sum of two blackbodies [148]. > Magnetars have been detected also in the hard X-ray range ( ∼ 20 keV), with INTEGRAL and RXTE. Hard power-law tails, extending to ∼150 keV, have been seen both in AXPs [84, 25, 24] and SGRs [105, 54, 36, 131]. The hard X-ray emission is pulsed, and gives a luminosity comparable to, and in some cases higher than, that in the soft X-ray band. Considerable effort is ongoing in the analysis and interpretation of the AXPs and SGRs spectra, in order to progress from purely phenomenological fits to more physical models. The presence of a relatively dense plasma in magnetospheres with a twisted configuration [146] is expected to affect the emergent spectrum through resonant cyclotron scattering (RCS) of the thermal photons emitted by the underlying neutron star’s surface. A simplified model, based on a semi-analytical treatment of these effects [92], has been systematically applied to several magnetar candidates

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[133]. This showed that at E<10 keV the RCS model can replace the blackbody plus power-law model (in most sources an additional power-law is still required to fit the hard X-ray tails). More realistic 3-D simulations have also been performed to compute the magnetar’s spectral models [41, 117, 116] and quite successfully applied to the spectra of several magnetar candidates [170]. Two possibilities have been proposed to explain the high-energy tails in the context of the twisted magnetosphere model [143]: bremsstrahlung from a thin turbulent layer of the star’s surface heated to kT∼100 keV by magnetospheric currents and synchrotron emission from mildly relativistic pairs produced at a height of ∼ 100 km above the neutron star. Compton up-scattering of soft thermal photons, emitted from the star surface, by relativistic electrons threaded in the magnetosphere has also been considered [66, 47, 6]. Compared to all the other INS, AXPs and SGRs stand apart for their striking variability properties. I refer not only to the short bursts and (giant) flares, but also to the so called ”persistent” emission, which for historically bright sources varies around 1036 erg s−1 , while for newly-discovered transients has been seen to span up to five orders of magnitude. About half of the AXPs/SGRs have been always seen at relatively high flux levels since the time of their discovery. They were thought to be steady sources, but, as more sensitive imaging observations became available, it appeared that variations of ∼50% on timescales from days to months are quite common. Long term variations are sometimes correlated with changes in the spin-down properties. This is not unexpected in the magnetar model involving variations in the magnetospheric twist angle. For example, the luminosity variations, the correlation between spectral hardness and spin-down rate, and the increase in the bursting activity observed before the 2004 giant flare of SGR 1806−20 [109] are consistent with

SGR 0501+4516 (2008)

10

SGR1900+14 (2006)

CXOU J164710−455216 (2006) SGR1627−41 (2008)

1

Flux (10−12 erg cm−2 s−1)

1E 1547−5408 (2008)

0.1

1 10 Time (days from burst activation)

100

Fig. 2 X-ray light curves of outburst decays observed in several AXPs and SGRs (from [131]).

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355

a gradually increasing magnetospheric twist angle. This gives rise to a larger optical depth for resonant scattering (causing a hardening of the X-ray spectrum), a higher rate of crustal fractures (responsible for the bursts), and a faster spin-down (because of the larger fraction of field lines that open out across the speed of light cylinder). The spectral softening and the decrease in the flux and spin-down rate observed after the giant flare [132, 150] are also consistent with this picture, suggesting a twist angle reduction as consequence of the global magnetic rearrangement following the giant flare. The first transient AXP, XTE J1810−197 , was serendipitously discovered during the decay phase of an outburst in 2003 [70]. Comparison of the highest observed luminosity with archival data, showing a faint soft source with L x ∼ 1033 erg s−1 , indicated a dynamic range of two orders of magnitude. Several other transient AXP/SGR have been discovered after XTE J1810−197 (see Table 1). When bright, their spectral and timing properties are similar to those of the persistent sources. During their low (or ”quiescent”) states they have luminosity of ∼ 1032 erg s−1 and soft thermal spectra, that make them similar to the CCOs. Transient AXPs/SGRs now outnumber the persistent members of the class, and their number will certainly increase in the future. It is difficult to estimate how many AXP/SGRs are present in the Galaxy, because the duty cycle of transient magnetars is poorly known. At least two sources have shown more than one outburst (SGR 1627−41 in 1998 and in 2008 [35]; 1E 1547.0−5408 in Summer 2007 [64] and 2008–2009 [106]), but other events might have been missed. In fact the rate of discoveries of new transients has increased in the latest years, thanks to the presence of satellites with large field of view and continuous sky monitoring, like Fermi and Swift. These new data revealed a variety of behaviors for what concerns the outburst evolution of the different sources, as shown by the examples plotted in Fig. 2. Poorly sampled light curves can be roughly described by power-law decays with a variety of slopes, while the well sampled light curves show that the time decay is initially steeper and flattens after about one day. This could indicate the presence of two different mechanisms operating on different timescales, e.g. dissipation of magnetospheric currents followed by cooling of the star’s crust. Re-brightenings, or ”bumps”, superimposed on the decaying trends have also been observed, for example in SGR 1900+14 [42]. The observation of outburst decays, and, more in general, of the spectral and flux variability of transient AXPs/SGRs, has the potential to greatly advance our understanding of neutron stars. For example, detailed studies of the long term spectral evolution have been reported for XTE J1810−197 [50, 9]. However some caveats should be remembered when interpreting the observational data. Often the observations have a poor and irregular time sampling, especially in the initial and possibly more variable phases, and/or are obtained with different instruments. This reduces the possibility of determining correlations between the different energy ranges in a robust way. At late times, when the fluxes are small, spectral uncertainties can be significant, also in view of the bolometric corrections required by the high interstellar absorption. Furthermore, the observed fluxes most likely result from the superposition of various physical components with different variability behaviors and

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difficult to disentangle. Part of these problems will be reduced when broad-band, sensitive instruments able to react in a short time to the discovery of new transient events will become available.

6 Rotating Radio Transients New techniques of analysis for transient radio signals, applied to data of the Parkes Multibeam Survey, have led to the discovery of Rotating Radio Transients (RRATs) [99]: neutron stars which emit short (2-30 ms) radio pulses at intervals of minutes to hours. Their rotation periods, ranging from 0.4 to 7 s, have been inferred from the largest common divisors of the time intervals between bursts. RRATs are probably a large galactic population, that remained undiscovered for a long time due to lack of adequate radio searches, but their relation to other classes of INS is unclear (see [97] for a review). The radio properties of RRATs show analogies with those observed in some peculiar radio RPP, and they might represent extreme cases of some of these phenomena. On the other hand, their long rotation periods, and the fact that transient radio emission has been observed in a couple of AXPs [13, 12], suggest a possible relation with magnetars. The period derivatives, determined to date for only ∼6–7 of the nearly twenty known RRATs [98], indicate magnetic fields above 1013 G only in about half of the cases (see Fig. 1). PSR J1819−1458 is the only RRAT that has been detected at X-ray energies [135]. It has a luminosity of ∼(2–5) 1033 erg s−1 (for d=3.6 kpc) and its X-ray emission is pulsed at the rotation period of 4.26 s. The light curve is nearly sinusoidal, with a pulsed fraction of about 35%. The spectrum, well fit by a blackbody (TBB ∼0.14 keV) plus a possible feature around 1 keV [100], indicates that the emission is of thermal origin (the luminosity is subject to the distance uncertainty, but most likely larger than LS D =3 1032 erg s−1 ). A Chandra observation has shown evidence for diffuse X-ray emission surrounding PSR J1819−1458 [134]. If this nebula is powered by the rotational energy of the RRAT, an efficiency of ∼20%, much higher than that of all the other pulsar wind nebulae, is required. This discrepancy could be reduced by a smaller distance, or by invoking a shock caused by a large spatial velocity of PSR J1819−1458, but the possibility that magnetic energy contributes to power the observed diffuse emission has also been proposed [134]. X-ray upper limits at a level much smaller than the flux of PSR J1819−1458 have been reported for other two RRATs [75]. If the X-ray emission from RRATs is simply due to cooling, this could be caused by a larger age of these two objects (their spin-down ages are 0.4 and 0.8 Myr, compared to τS D =0.1 Myr for PSR J1819−1458 ). However, the significant uncertainties on distance and absorption prevent a firm conclusion.

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Table 3 Rotation Powered Pulsars with B>4 1013 G. Name

Period P˙ (s) (s s−1 )

B (G)

Lx (erg s−1 )

J1847–0130

6.7

1.3 10−12 9.4 1013

<5 1033

J1718–3718

3.4

1.6 10−12 7.4 1013

6 1033

J1814–1744

4.0

7.5

10−13 10−12

5.5

1013

5.2

1013

<2 1033

J1734–3333

1.2

2.3

J1846–0258

0.3

7.1 10−12 4.9 1013

4 1034 in SNR Kes 75

–

J1119–6127

0.4

4.0 10−12 4.1 1013

3 1033 in SNR G292.2–0.5

7 Rotation-powered pulsars with high magnetic field Table 3 lists all the RPP for which the timing parameters indicate a dipolar field 2 3 greater than, or close to, the quantum critical value Bc = mh¯ ec =4.4 1013 G. Most of them have spin periods of a few seconds and in the P-P˙ diagram lie in the same region of the AXPs/SGRs. However, these four pulsars do not show magnetar characteristics, such as the production of bursts/flares or particularly strong and variable emission. In fact their X-ray luminosity is smaller than LS D [128], as expected for standard RPP. The situation is quite different for the young PSR J1846–0258, located in the supernova remnant Kes 75. In this 0.3 s pulsar, the high inferred B derives from ˙ the highest of all RPPs. Its spin-down luminosity of 8 1036 erg s−1 its large P, is certainly sufficient to power the X-ray emission observed from the pulsar, LX = 2.6 1034 (d/6 kpc)2 erg s−1 , and from the associated pulsar wind nebula, LPWN = 1.4 1035 (d/6 kpc)2 erg s−1 [115]. Thus the discovery of magnetar-like activity from PSR J1846–0258 was quite surprising, because this pulsars was considered a bona-fide RPP, despite the lack of a radio detection (easily explained as due to an unfavorable orientation). Four short bursts from PSR J1846–0258 were seen with RXTE on May 31, 2006 [45]. The onset of the bursting activity was coincident with a large spin-up glitch and with the beginning of an enhancement in the pulsed X-ray flux which lasted about one month [91]. Spectral and flux variations associated with this event were seen also in the hard X-ray range [83]. PSR J1119–6127 [48, 138], has timing parameters very similar to those of PSR J1846–0258, and, like the latter, it is located in a young SNR (G 292.2–0.5) and is surrounded by a pulsar wind nebula. Its X-ray emission shows a large pulsed fraction and a spectrum consisting of a thermal-like component with temperature kTBB ∼0.2 keV and a hard power-law. The strong thermal emission, quite remarkable for a young pulsar, might be the result of some recent magnetar-like activity, similar to that observed in PSR J1846–0258. It would be important to monitor this pulsar, and other RPP with similar parameters, to look for bursts.

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8 Conclusions X-ray observations have revealed an unexpected variety of manifestations of INS. The thermal components in these objects span more than four orders of magnitude in luminosity (see Fig. 3), with a dependence on temperature broadly consistent with the blackbody relation L∝T4 for objects of similar size. The observed spectral and timing properties indicate that different energy sources, besides the obvious cooling of the primeval internal heat, are at play in powering such thermal-like components. The effects of a strong and dynamic magnetic field are especially evident in the paroxysmic behavior of SGRs and AXPs, but it is also possible that the variability observed in the XDIN RX J0720.4−3125 be due to changes in the magnetic field configuration, and certainly the magnetic field plays an important role in the thermal evolution of INS. This is well demonstrated by the relatively high surface temperatures of XDINS. It is now clear that at least a fraction of the enigmatic CCOs are young pulsars with very weak magnetic fields. However, also in these sources, localized regions of stronger field might be present and be responsible for the small emitting areas inferred from the spectral fits.

Fig. 3 Temperature-Luminosity diagram for different classes of INS (XDINS (×), CCO (⋄), persistent AXP (squares)). For the sake of uniformity, all the temperatures are from blackbody fits (model atmospheres generally yield values smaller by a factor ∼2–3). For the CCO the luminosities and temperatures of the two-blackbody fits are indicated. For RCW 103 the figure shows two intensity states. In AXPs the contribution to the luminosity from the power-law spectral components are neglected. The lines indicate the blackbody relations for emitting radii of 1 km and 10 km.

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The magnetar-like behavior of PSR J1846–0258, together with the recent discovery of PSR J1622–4950 [88], the first ”radio-selected” magnetar, point to a closer connection between radio pulsars and magnetars than previously thought. It is also noteworthy that SGR 0418+5729, one of the most recently discovered SGRs, has an inferred (dipolar) field smaller than ∼3 1013 G. The data collected in the latest years, besides enlarging the sample of INS, are leading to recognize objects with ”intermediate” properties. While this makes the boundaries between the different INS classes less well defined, it gives the prospects of unifying in a global coherent picture all the varieties of INS manifestations.

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X-ray thermal radiation from hot polar cap in pulsars Janusz Gil and George I. Melikidze

Abstract We discuss the partially screened gap (PSG) model of the pulsar inner accelerator, which implies that the temperature of the polar cap surface is almost equal to the so called critical temperature defined by the strength of the magnetic field at the polar cap surface. Observations of thermal X-ray emission reveal an important correlation between the hot spot area and its surface temperature, both derived from the blackbody fit. The hot spot surface area is generally much smaller than that of the conventional polar cap, implying that geometry and strength of the actual surface magnetic field differ essentially from the pure dipolar field. We believe that major characteristics of the pulsar radiation, including correlation between observed features of X-ray and radio emissions can be naturally explained within the framework of the PSG model.

1 Introduction It is widely believed that drifting subpulses commonly observed in radio pulsars correspond to circulation of the radiation sub-beams around the pulsar beam axis. In most cases one can clearly identify a low frequency feature (in the fluctuation spectrum of intensity modulation) corresponding to the time interval P4 , after which these sub-beams (non-corotating with a star) complete one full circulation around the beam axis. This P4 period is called the pulsar carousel rotation time. If the subpulse associated sub-beams are emitted by the electron-positron plasma produced J.Gil J.Kepler Institute of Astronomy, University of Zielona Gora, Lubuska 2, 65-265, Zielona Gora, Poland e-mail: [email protected] G.Melikidze J.Kepler Institute of Astronomy, University of Zielona Gora, Lubuska 2, 65-265, Zielona Gora, Poland and Abastumani Astrophysical Observatory,Ilia State University, 2a Kazbegi ave, Tbilisi 0160, Georgia e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_30, © Springer-Verlag Berlin Heidelberg 2011

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Fig. 1 The conditions for the formation of the acceleration region above condensed iron polar cap surface in pulsars following from the cohesive energy calculations presented in [2]. Notice the precise localization of the PSG model on this diagram (due to thermostatic regulation mechanism).

via sparking discharges of the inner accelerator potential drop, then one should expect an intense thermal radiation from the hot polar cap. Indeed, the positrons leave the acceleration region and contribute to the observed radio emission, while the electrons bombard the polar cap surface, heating it to MK temperatures. At the same time thermal ejection of iron ions should occur, which partially screens the polar cap electric field. Such model is called the Partially Screened Gap [1] (PSG). It is clear that functioning of the PSG model requires that the cohesive energy of iron ions is high enough to bound them at least partially at the polar cap surface. We refer to the most recent calculations of cohesive energies performed by Medin & Lai [2], reproduced here in Fig. 1 and also represented by the curved line in Fig.2. As shown by Medin & Lai in [2] the critical surface temperature T i below which the PSG can form depends strongly on the actual surface magnetic field B s , which must be higher than 1014 G in all pulsars for which the polar cap temperature T s is few MK (as strongly suggested by X-ray spectral observations of a number of pulsars). Both the critical T i and the actual T s temperatures must be close to each other by means of the thermostatic regulation mechanism (for more details see [1]).

2 Surface magnetic field The parameters of the black body fit to the X-ray spectrum of some pulsars provide very important information for the understanding of the physical conditions at the stellar surface. The black body fit allows us (provided that the distance to the pulsar is known) to obtain directly both the hot spot area ABB and its temperature T BB . In most cases ABB is much smaller than the conventional polar cap area A0 (P) ≃ 6.6 × 108 P−1 [cm2 ], where P is the pulsar period. This can be easily explained by assuming that the surface magnetic field of pulsars differs significantly from the pure dipole one. We assume that the entire stellar surface is populated by the strong small-scale magnetic anomalies generated in the crust [3,4]. These anomalies strongly modify the pulsar magnetic field near the surface, but their influence decays with the distance and is negligible at altitudes of the order of few stellar radii. If such anomaly occurs close to the convectional polar cap then the

X-ray thermal radiation from hot polar cap in pulsars

5

B0943+10

4

-6

K

J0108-1431

3

B1133+16

s

T x10

Fig. 2 Surface temperature T s versus surface magnetic field B s in a number of pulsars for which these parameters were measured by means of XMM-Newton and/or Chandra observations, compared with the theoretical calculations presented in [2]. Within the error bars, all cases show good agreement between the PSG model (see Fig.1) and observations.

367

2

B0834+06

0633+17 (Geminga)

1

Medin & Lai (2007)

101

102

103

B x10

-12

s

G

bunch of the open field lines (crossing the light cylinder) will get modified near the surface. Using continuity of magnetic field lines we can calculate the actual shape of the polar cap [3]. The magnetic flux through the modified polar cap surface must be equal to the flux through the surface of the light cylinder defined by the open dipolar field lines and thus the same as through the canonical dipolar polar cap. Then, one can estimate an actual surface magnetic field using the magnetic flux conservation law as b = A0 /ABB = B s /Bd , where Bd ≃ 2 × 1012(PP˙ −15 )0.5 [G] is a dipolar magnetic field and P˙ −15 = P˙ × 10−15 is a period derivative. Then the value of the actual surface magnetic field at the hot polar cap is −0.5 ˙ 0.5 B s ≃ 1.3 × 1021A−1 P−15 BB P

[G],

(1)

In most cases b >> 1 implying B s ≃ 1014 G >> Bd , while T BB ≃ (2 − 4) × 106 K. This is shown in Fig. 2, which also confirms observationally the cohesive energy calculations performed by Medin & Lai in [2].

3 Drifting subpulses Within the PSG model one can obtain a simple relationship between the carousel circulation time P4 and the X-ray bolometric luminosity Lb from spark-heated polar cap. The latter can be compared with the spin-down power E˙ = IΩΩ˙ = 3, 95 × 1031P˙ −15 P−3 [erg/s], which leads to the so-called radiation efficiency Lb /E˙ = (0.63/I45)(P/P4 )2 ,

(2)

which is very useful for another comparison of the PSG model with observations. The above equation expresses the fact that both the drifting rate (P4 ) and the heating rate (Lb ) are related to the two components of gap electric field [5], which we assumed to be of the same order. Both these components in the PSG model are about

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B0628-28

L /E)

10

3

10

B0656+14

b

.

(

Fig. 3 The efficiency of thermal X-ray emission from hot polar cap L x versus carousel circulation period P4 of drifting subpulses in the radio band. The solid curve represents the equation (2) with I45 = 1, while the dotted curves correspond to uncertainties in determining of the moment of inertia (0.78 < I45 < 1.25).

B1133+16

1 B1055-52

B1929+10 B0834+06 B0943+10

10

20

30

40

50

P /P 4

an order of magnitude lower than in the pure vacuum gap model. This warrants both the drifting and the heating rates to be at the observed level. Moreover, the above correlation between the heating and the drifting rates is uniquely satisfied within the PSG model. In Fig. 3 we present a number of cases of radio and X-ray pulsars, for which an appropriate data exists (carousel period P4 and thermal X-ray luminosity Lb ) to allow testing the PSG pulsar model represented by equation (2). As one can see they all seem to satisfy the model predictions quite well. Indeed, the data points seem to follow the model curve. Notice wide ranges of variables on both axes. For detailed discussion of both the radio and X-ray measurements used to produce this figure see [6](in this paper we present our own XMM-Newton measurement of the black-body thermal radiation from small hot spot in PSR B0834+06). Acknowledgements This paper was partially supported by research Grants N N 203 2738 33 and N N 203 3919 34 of the Polish Ministry of Science and Education. GM was partially supported by the Georgian NSF grant ST08/4-442.

References 1. 2. 3. 4. 5. 6.

Gil J., Melikidze G. and Geppert U. (2003)A&A 407, 315 Medin Z. and Lai L. (2007) MNRAS, 382,1833 Gil J., Melikidze G. I. and Mitra D. (2002) A&A, 388, 235 Geppert U., Rheinhardt M. and Gil J. (2003) A&A, 412, L33 Gil J., Melikidze G. and Zhang B. (2007) MNRAS, 376, 67 Gil J., Haberl F., Melikidze G., Geppert U. Zhang B. and Melikidze G.(Jr.) (2008) ApJ 686,497

Radio polarization of RRAT J1819-1458 A. Karastergiou

Abstract Rotating radio transients, although clearly part of the radio emitting neutron star family, have atypical properties. They emit pulses for only a very small fraction of the time and they seem to occupy a defined region in the P-P˙ diagram, with their long periods and relatively high magnetic fields. We use polarization observations of the most prolific RRAT, J1819−1458 to identify similarities and differences with other characteristic populations in the P-P˙ diagram, namely young ˙ pulsars, magnetars and the bulk of normal pulsars. We find that this RRAT (high E) mostly resembles normal, slow and low E˙ pulsars. From the polarization average pulse profile we draw conclusions on the geometry of this source and measure its Faraday rotation measure.

1 Introduction A number of observational discoveries in the last few years has extended the family of radio emitting neutron stars to include magnetars (Camilo et al. 2006), intermittent pulsars (Kramer et al. 2006), and Rotating Radio Transients like RRAT J1819−1458 (McLaughlin et al. 2006) that emit extremely sporadic but periodic pulses. McLaughlin et al. (2006) report a rate of roughly 1 pulse detection every 3 minutes, while Esamdin et al. (2008) report a detection of 162 bright (> 5σ) pulses in a total of 94 hours of observation, albeit with a less sensitive instrument. The period P and period derivative P˙ (Fig. 1) place this RRAT in a region between the main pulsar population, including the population of young, high E˙ pulsars, and magnetars. The estimated surface magnetic field is B s ≈ 4.9 × 1013 Gauss, the characteristic age is a relatively young τc ≈ 119.8 kyr and the rate of rotational energy loss is a relatively A. Karastergiou Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_31, © Springer-Verlag Berlin Heidelberg 2011

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Fig. 1 RRAT J1819−1458 (center of the star symbol) in the P-P˙ diagram. Lines of constant characteristic age, surface magnetic field and E˙ (in erg/s) are drawn and labelled.

average E˙ ≈ 2.88 × 1032erg s−1 . It can therefore be used to further test whether high E˙ or young age is associated with high degrees of polarization as shown by various studies (e.g. von Hoensbroech et al. 1998; Johnston et al. 2006; Weltevrede & Johnston 2008). The degree of linear polarization is regulated by the relative intensity of competing orthogonal polarization modes of propagation in the pulsar magnetosphere (e.g. Stinebring et al. 1984, Karastergiou et al. 2002). In many young and highly energetic pulsars, as well as the two known radio emitting magnetars (Camilo et al. 2007; Kramer et al. 2007; Camilo et al. 2008), the degree of linear polarization is often close to 100%, indicating that one polarization mode dominates. Weltevrede et al. (2006) discuss the similarities of RRAT J1819−1458 with B0656+14, a typical middle aged pulsar and source of pulsed, high-energy emission. As with other highly energetic pulsars (for PSR B0656+14, E˙ = 3.8 ×1034 erg s−1 ) the polarization of this pulsar is very high (Gould & Lyne 1998) at 1.4 GHz. The polarization position angle (hereafter PA) also shows smooth variation (Lyne & Manchester 1988) in accordance with the rotating vector model of Radhakrishnan & Cook (1969).

2 Polarization characteristics The data presented here were obtained at the Parkes radio telescope using the central beam of the Parkes 21cm multi-beam receiver and the Caltech Parkes Swinburne Recorder Mk II (CPSR2), (Bailes 2003), and analysed as presented in Karastergiou et al. (2009). The 72 bright pulses observed over 13 epochs were initially used to estimate the Faraday rotation measure (≈330±30 rad/m2 ) in order to recover the total linear polarization.

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Fig. 2 does not distinguish RRAT J1819−1458 from normal pulsars and the three component profile supports the S-shaped PA swing. The timing solution used was not constructed with any prior knowledge of the polarization, however it yields an integrated PA swing that follows the RVM.

3 Discussion and conclusions ˙ RRAT J1819−1458 clearly With low linear polarization and an average value of E, follows the observational paradigm of normal pulsars, also providing further evidence of the link between E˙ and the degree of polarization. The orthogonal PA jumps seen are typical of pulsars with average E˙ and distinguish this source from the two radio emitting magnetars, and PSR B0656+14. Acknowledgements AK is indebted to the Leverhulme Trust for financial support.

References 1. F. Camilo, S.M. Ransom, J.P. Halpern, J. Reynolds, D.J. Helfand, N. Zimmerman, J. Sarkissian, Nature 442, 892 (2006). 2. M. Kramer, A.G. Lyne, J.T. O’Brien, C.A. Jordan, D.R. Lorimer, Science 312, 549 (2006) 3. M.A. McLaughlin, A.G. Lyne, D.R. Lorimer, M. Kramer, A.J. Faulkner, R.N. Manchester, J.M. Cordes, F. Camilo, A. Possenti, I.H. Stairs, G. Hobbs, N. D’Amico, M. Burgay, J.T. O’Brien, Nature 439, 817 (2006). 4. A. Esamdin, C.S. Zhao, Y. Yan, N. Wang, H. Nizamidin, Z.Y. Liu, Monthly Notices of the Royal Astronomical Society 389, 1399 (2008) 5. A. von Hoensbroech, J. Kijak, A. Krawczyk, A&A 334, 571 (1998) 6. S. Johnston, A. Karastergiou, K. Willett, MNRAS 369, 1916 (2006). 7. P. Weltevrede, S. Johnston, MNRAS 391, 1210 (2008). 8. D.R. Stinebring, J.M. Cordes, J.M. Rankin, J.M. Weisberg, V. Boriakoff, ApJS 55, 247 (1984) 9. F. Camilo, J. Reynolds, S. Johnston, J.P. Halpern, S.M. Ransom, W. van Straten, ApJ 659, L37 (2007). 10. M. Kramer, B.W. Stappers, A. Jessner, A.G. Lyne, C.A. Jordan, MNRAS 377, 107 (2007) 11. F. Camilo, J. Reynolds, S. Johnston, J.P. Halpern, S.M. Ransom, The Astrophysical Journal 679, 681 (2008). 12. P. Weltevrede, B.W. Stappers, J.M. Rankin, G.A.E. Wright, ApJ 645, L149 (2006). 13. D.M. Gould, A.G. Lyne, MNRAS 301, 235 (1998) 14. A.G. Lyne, R.N. Manchester, MNRAS 234, 477 (1988) 15. V. Radhakrishnan, D.J. Cooke, Astrophys. Lett. 3, 225 (1969) 16. M. Bailes, in Radio Pulsars, ed. by M. Bailes, D.J. Nice, S. Thorsett (Astronomical Society of the Pacific, San Francisco, 2003), pp. 57–64 17. A. Karastergiou, A.W. Hotan, W. van Straten, M.A. McLaughlin, S.M. Ord, MNRAS 396, L95 (2009)

Multiwavelength Observations of Pulsar Wind Nebulae Patrick Slane

Abstract The extended nebulae formed as pulsar winds expand into their surroundings provide information about the composition of the winds, the injection history from the host pulsar, and the material into which the nebulae are expanding. Observations from across the electromagnetic spectrum provide constraints on the evolution of the nebulae, the density and composition of the surrounding ejecta, the geometry of the central engines, and the long-term fate of the energetic particles produced in these systems. Such observations reveal the presence of jets and wind termination shocks, time-varying compact emission structures, shocked supernova ejecta, and newly formed dust. Here I provide a broad overview of the structure of pulsar wind nebulae, with specific examples from observations extending from the radio band to very-high-energy γ-rays that demonstrate our ability to constrain the history and ultimate fate of the energy released in the spin-down of young pulsars.

1 Introduction The basic structure of a pulsar wind nebula is determined by the spin-down energy injected by the central pulsar and the interaction of the nebula with the interior regions of the supernova remnant (SNR) in which it evolves. Losses from synchrotron radiation in the nebular magnetic field, whose strength depends both on the nature of the injected wind and on the evolving size of the PWN, inverse-Compton (IC) scattering of ambient photons by the energetic electron population within the nebula, and adiabatic expansion as the nebula sweeps up the surrounding supernova ejecta, all combine to determine the emission structure and long-term evolution of the nebula. (See [18] for a review.) Multiwavelength observations of PWNe provide crucial information on the underlying particle spectrum and strongly constrain both Patrick Slane Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138 (USA) e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_32, © Springer-Verlag Berlin Heidelberg 2011

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the magnetic field strength and the stage of evolution. Of particular interest is the spectrum of low-energy particles contained in the PWN. These retain the history of early energy losses as well as possible signatures of features in the pulsar injection spectrum. Complex structure in PWN spectra can originate in a number of ways that are associated with the long-term evolution as well [32, 19]. In particular, when the reverse shock compresses the PWN, the resulting increase in the magnetic field initiates a new epoch of fast synchrotron cooling that adds to the population of low energy particles. Models which do not account for the reverse shock interaction will thus underestimate this population and its associated radiation. In addition, recent studies of the spectrum immediately downstream of the wind termination shock show that the injection spectrum itself can deviate significantly from a simple power law [38], and particle-in-cell simulations of the acceleration process produce a Maxwellian population with a power law tail [40]. Any such structure in the injected particle spectrum imprints itself on the broadband emission of the entire nebula. The resulting breaks or regions of curvature in the PWN spectrum, and the frequencies at which they are observed, depend upon the energy at which features appear in the electron spectrum as well as the means by which the photons are produced (e.g. synchrotron radiation or IC emission). To fully understand the nature of the particle injection, as well as the long-term evolution of PWNe, it is thus crucial to study the emission structure over the entire electromagnetic spectrum.

2 Dynamical Evolution of PWNe The evolution of a PWN within the confines of its host SNR is determined by both the rate at which energy is injected by the pulsar and by the density structure of the ejecta material into which the nebula expands. The location of the pulsar itself, relative to the SNR center, depends upon any motion given to the pulsar in the form of a kick velocity during the explosion, as well as on the density distribution of the ambient medium into which the SNR expands. At the earliest times, the SNR blast wave expands freely at a speed of ∼ (5 − 10) × 103 km s−1 , much higher than typical pulsar velocities of ∼ 400 − 500 km s−1 . As a result, for young systems the pulsar will always be located near the SNR center. The energetic pulsar wind is injected into the SNR interior, forming a highpressure bubble that expands supersonically into the surrounding ejecta, forming a shock. The input luminosity is generally assumed to have the form (e.g. [30]) t E˙ = E˙ 0 1 + τ0 where τ0 ≡

!− (n+1) (n−1)

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Fig. 1 Composite image of Crab Nebula. X-ray emission from Chandra is concentrated in a central jet/torus structure (shown in blue), while optical emission from HST (shown in yellow and red), and the infrared emission from Spitzer (shown in purple) dominates the exterior regions where the nebula sweeps up ejecta material.

is the initial spin-down time scale of the pulsar. Here E˙0 is the initial spin-down power, P0 and P˙ 0 are the initial spin period and its time derivative, and n is the so-called “braking index” of the pulsar (n = 3 for magnetic dipole spin-down). The pulsar has roughly constant energy output until a time τ0 , beyond which the output declines fairly rapidly with time. In the spherically symmetric case, the radius of the PWN evolves as −1/2 6/5 R PWN ≈ 1.5 E˙ 01/5 E S3/10 (3) N Me j t

where ES N is the energy released in the explosion and Me j is the mass of the ejecta [10]. Thus, at least at early times when the pulsar input is high, the PWN expansion velocity increases with time. The√ sound speed in the relativistic fluid within the PWN is sufficiently high (c s = c/ 3) that any pressure variations experienced during the expansion are quickly balanced within the bubble; at early stages, we thus expect the pulsar to be located at the center of the PWN. The pressure balance within the PWN results in a termination shock where the energetic pulsar wind meets the more slowly-expanding PWN. Studies of this region of the PWN provide

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the most direct information available on particles that are being freshly injected into the nebula. The geometry of the pulsar system results in an axisymmetric wind [77], forming a torus-like structure in the equatorial plane, along with collimated jets along the rotation axis. The higher magnetization at low latitudes confines the expansion here to a higher degree, resulting in an elongated shape along the pulsar spin axis for the large-scale nebula [11, 44]. This structure is evident in Figure 1, where Xray and optical observations of the Crab Nebula clearly reveal the jet/torus structure surrounded by the elongated wind nebula bounded by filaments of swept-up ejecta. A thorough review of the MHD-driven jet/torus structure is presented by N. Bucciantini in these Proceedings. Beyond the PWN, the outer blast wave of the SNR drives a shock into the surrounding interstellar/circumstellar medium (ISM/CSM), forming a shell of hot gas and compressed magnetic field. As the shell sweeps up additional mass, and decelerates, a reverse shock (RS) propagates back into the expanding ejecta. When the SNR has swept up an amount of mass that is roughly equal to the mass of the ejecta, the evolution approaches the Sedov phase in which the radius is described by RS NR ≈ 6.2 × 10

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where n0 is the density of the ambient medium. This is illustrated in Figure 2 where dashed lines show R PWN and RS NR as a function of time using Equations 3 and 4. Here we have assumed Me j = 5M⊙ and E S N = 1051 erg, and have used a range of values for E˙ 0 and n0 . As indicated, eventually the PWN would overtake the SNR boundary under such conditions. However, because the initial expansion of the SNR occurs more rapidly than in the Sedov phase, and the injection rate from the pulsar is highest at the earliest times, the actual behavior differs from that shown. In addition, as the reverse shock of the SNR propagates inward, it eventually reaches the PWN boundary and begins crushing the nebula. This is indicated in the solid curves in Figure 2, where the early-phase behavior as well as the reverse shock propagation is taken into account (see [19]). Ideally the PWN radius decreases until the nebula pressure is sufficiently high for the system to rebound. The crushing of the PWN results in an increase in the magnetic field. This causes a rapid burn-off of the most energetic particles in the nebula. The PWN/RS interface is Rayleigh-Taylor (R-T) unstable, and is subject to the formation of filamentary structure where the dense ejecta material is mixed into the relativistic fluid [16]. The nebula subsequently re-forms as the pulsar injects fresh particles into its surroundings, but a significant relic nebula of mixed ejecta and relativistic gas will persist. In cases where the pulsar and its PWN have moved considerably from the center of the PWN, or in which the SNR has evolved in a medium of nonuniform density, the reverse shock will interact with the PWN asymmetrically, encountering one portion of the nebula well before another. This results in a complex interaction that leaves a highly distorted relic nebula that may be highly displaced from the pulsar position [16].

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Fig. 2 Time evolution of the SNR and PWN radii for a range of values for the ambient density and initial spin-down power of the pulsar. The solid curves correspond to models from Gelfand et al. (2009) [19] using E˙0 = 1040 erg s−1 , Me j = 8M⊙ , n0 = 0.1 cm−3 , and E51 = 1. See text description for details. (From [39]. Reproduced by permission of the AAS.)

In the later stages of evolution, the PWN can expand to a very large size, with a correspondingly lower magnetic field strength. As described below, such PWNe may be best identified through their high-energy γ-ray emission, with only weak X-ray emission observed close to the pulsars.

3 Spectral Evolution of PWNe As particles are injected from a pulsar into its PWN, the resulting emission is determined by the evolved particle spectrum and magnetic field, as well as the energy density of the ambient photon field.1 The injected spectrum is often characterized as a power law: Q(Ee , t) = Q0 (t)(E e /E0 )−a (5) The integrated energy in the electron spectrum is then Z 1 ˙ Q(E, t)EdE = E(t) (1 + σ)

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In addition, emission from ejecta gas and dust swept up by the expanding nebula can be significant – and even dominant in some wavebands.

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Fig. 3 Synchrotron (left) and IC (right) emission (for scattering off of the CMB) from a PWN at ages of 1000 (solid), 2000 (dotted), and 5000 (dashed) years. Here we have assumed E51 = 1, Me j = 8M⊙ , and n0 = 0.1 cm−3 for the SNR evolution, and n = 3, E˙ 0 = 1040 erg s−1 , and τ0 = 500 yr for the pulsar. For the wind, we assume that 99.9% of the energy is in the form of electrons/positrons with a power law spectrum with γ = 1.6.

where σ is the ratio of the spin-down power injected in the form of Poynting flux to that in the form of particles. It is important to note one expects the postshock flow of particles to be characterized by a Maxwellian distribution accompanied by a nonthermal tail – a result confirmed by recent particle-in-cell simulations of relativistic shocks [40]. The development of the nonthermal tail depends on the shock conditions, and the total residence time of the particles in the acceleration region, which may vary at different locations in the inner nebula. Thus, it is reasonable to expect that the injected spectrum may actually deviate considerably from a pure power law form, a point that recent observations may be beginning to illustrate, as we discuss below. The resulting emission spectrum is found by integrating the electron spectrum over the emissivity function for synchrotron and IC radiation using, respectively, the nebular magnetic field and spectral density of the ambient photon field. As illustrated in Figure 3, the build-up of particles in the nebula results in an IC spectrum that increases with time. The synchrotron flux decreases with time due to the steadily decreasing magnetic field strength associated with the adiabatic expansion of the PWN. This behavior is reversed upon arrival of the SNR reverse shock (not shown in Figure), following which the nebula is compressed and the magnetic field strength increases dramatically, inducing an episode of rapid synchrotron losses. Upon re-expanding, however, IC emission again begins to increase relative to the synchrotron emission. At the latest phases of evolution, when the nebula is very

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large and the magnetic field is low, the IC emission can provide the most easilydetected signature. As described below, such behavior is seen for a number of PWNe that have been identified based on their emission at TeV energies, and for which only faint synchrotron emission near the associated pulsars is seen in the X-ray band. The broadband spectrum of a PWN, along with the associated dynamical information provided by measurements of the pulsar spin properties, and the size of the PWN and its SNR, place very strong constraints on its evolution and on the spectrum of the particles injected from the pulsar. Combined with estimates of the swept-up ejecta mass, this information can be used to probe the properties of the progenitor star and to predict the long-term fate of the energetic particles in the nebula. Recent multiwavelength studies of PWNe, combined with modeling efforts of their evolution and spectra, have provided unique insights into several of these areas.

4 Case Studies A complete summary of recent results on PWNe is well beyond the scope of this paper. Below we discuss four distinct systems for which recent multiwavelength observations have begun to probe both the detailed structure and the underlying particle population in these nebulae.

4.1 3C 58 3C 58 is a flat-spectrum radio nebula (α ≈ 0.1, where S ν ∝ ν−α ) for which upper limits based on IRAS observations indicate a spectral break between the radio and infrared bands [21]. The PWN has often been associated with SN 1181 [41]; the low break frequency would then suggest an extremely large magnetic field (> 2.5mG) if interpreted as the result of synchrotron break. This has resulted in a number of different interpretations, including the suggestion that the pulsar in 3C 58 underwent a rapid decline in its output at some early epoch [21], the possibility that the low-frequency break is inherent in the injection spectrum from the pulsar, and the suggestion that 3C 58 is not actually associated with SN 1181, but is an older nebula [11, 5]. The X-ray emission from 3C 58 (Figure 4) is dominated by a power law component, typical of synchrotron emission. However, a faint thermal component is clearly detected in the outer regions of the PWN, and also contributes to the interior regions [17, 97, 22]. The temperature is ∼ 0.25 keV, and enhanced abundances of Ne and Mg are observed, indicative of ∼ 0.5M⊙ of ejecta that has been swept up by the PWN. This is much larger than the expected mass if the PWN is associated with SN 1181, and suggests a larger age for the system [11]. To investigate the evolution of 3C 58, we have carried out Spitzer observations using IRAC [38]. These observations reveal the PWN in both the 3.6 and 4.5 µm

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Fig. 4 Top: Chandra image of 3C 58. The pulsar is at the center, and is surrounded by a elongated compact nebula with a curved jet extending to the west. A softening of the spectrum with radius is observed – an effect resulting from both synchrotron aging of the electrons and the presence of a soft thermal shell. Bottom: Chandra image of the pulsar in 3C58, and its associated torus and jet (left) and the IRAC 8 µm image of the same region. The elliptical region indicates the torus, and has the same center and size in each image.

bands, representing the first detection of synchrotron emission from this important young PWN anywhere in the five decades of frequency separating the radio and X-ray bands. The morphology of the IR emission from 3C 58 is strikingly similar to that seen in the radio and X-ray bands. The emission extends all the way to the radio boundaries, indicating that no synchrotron loss breaks occur below the band, and some regions of enhanced or diminished emission match well with those seen in the other bands (notably the large cavity on the eastern side), suggesting that we are observing primarily synchrotron radiation. Optical filaments in 3C 58 [97, 33], which presumably originate from supernova ejecta overtaken by the expansion of the PWN, do not show a good spatial correspondence with the radio or IR structures, suggesting that the IR emission is not dominated by dust contributions. This is similar to results from Spitzer observations of the Crab Nebula [42], where emission in the IRAC band is also identified primarily with synchrotron radiation. The IRAC data also reveal emission from the torus surrounding the pulsar in 3C 58 [36] in all four bands (Figure 4).2 Optical emission from the torus is detected 2

We also show preliminary results from MIPS observations at 24 µm where we also detect the torus.

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Fig. 5 The flux of all of 3C 58 (upper) and its torus (lower), plotted from the radio to the X-ray band. While the torus is not detected in the radio band, the IR data require a flattening of the Xray spectrum when extrapolated back to the longer wavelength band. (From [38]. Reproduced by permission of the AAS.)

as well [35]. These observations provide new constraints on the evolution of the particles as they flow from the termination shock in 3C 58. There is little question that this emission is synchrotron in nature; there is insufficient dust in the environment of the pulsar termination shock to provide a shocked dust component to the emission. The spectrum (Figure 5) requires a break of some sort between the IR and X-ray bands, suggesting that the synchrotron loss break appears just above the IR band. Most importantly, these results indicate that the spectrum of particles injected into the PWN through the termination shock does not follow an unbroken power law. As a result, structure in the PWN spectrum is, at least in part, the imprint of structure from the injection region. From Figure 5, it is clear that additional observations of 3C 58, and particularly its torus, at longer wavelengths will be crucially important to understand the nature of the injected particles and the subsequent long-term evolution of the PWN. Deep observations of the central regions of other PWNe are clearly of importance as well.

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Fig. 6 ROSAT PSPC image of Vela SNR. The single contour represents the outer boundary of the radio nebula Vela X. The point source at the northern extreme of Vela X is the Vela pulsar and the box inside the PWN indicates the XMM MOS region of the cocoon shown in the inset.

4.2 Vela X Located at a distance of only 280 pc, the Vela SNR houses a young pulsar that powers the extended nebula Vela X. This nebula lies within a limb-brightened shell of thermal X-rays. The outer shell is cool, and the exceptionally low foreground absorption (NH ∼ 1 − 5 × 1020 cm−2 ) allows us to see strong emission lines from O, Ne, and Mg. In X-rays, the overall brightness asymmetry of Vela is evident (Figure 6). The SNR is much brighter in the northeastern hemisphere, toward the Galactic plane. This is apparently the result of large-scale inhomogeneities in the ISM, with n0 ≈ 0.06 cm−3 in the south [7], and n0 ≈ 1 cm−3 on the north side of the SNR [13]. Radio observations of the PWN [28] reveal a morphology concentrated to the south of the pulsar itself, suggesting that the nebula has been disrupted by the impact of the reverse shock which propagated more rapidly from the northeast due to the higher ambient density in this direction. Higher resolution radio images show a network of filamentary structure in the PWN [15], possibly formed by R-T instabilities in this interaction with the reverse shock. ROSAT observations of the Vela X region [27] reveal a large emission structure – the so-called “cocoon” – extending to the south of the pulsar. The region is characterized by a hard spectrum and ap-

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Fig. 7 XMM-Newton spectrum from the “cocoon” region in Vela X. The best-fit model, shown in black, is composed of two components – a thermal plasma with enhanced, ejecta-like abundances (light dashed curve) and a power law (dark dashed curve). (From [23]. Reproduced by permission of the AAS.)

pears to lie along a bright elongated radio structure. ASCA observations established a two-component X-ray spectrum with the hard component adequately described by either a power law or a hot thermal plasma [29]. The PWN is observed at energies up to ∼ 200 keV with BeppoSAX [26], and observations with H.E.S.S. [2] reveal extended VHE γ-ray emission with the brightest emission concentrated directly along the cocoon. Our initial studies of a small region along the cocoon [23] reveal a bright X-ray structure shown as an inset to Figure 6. The emission is concentrated into several distinct regions, at least some of which appear to be filamentary structures. The integrated emission from these regions is characterized by two distinct components – a power law with a spectral index of ∼ 2.2 and a thermal plasma with enhanced abundances of O, Ne, and Mg, presumably associated with ejecta that has been mixed into the PWN upon its interaction with the reverse shock (Figure 7). It is of particular interest that our broadband modeling of the nonthermal emission from this central region of Vela X indicates a disconnect between the radioemitting particles and those that produce the X-ray and TeV γ-ray emission [23]. A model with a single spectral break between the bands either underpredicts the radio flux or produces an incorrect radio spectral index (Figure 8), while a model with two breaks can satisfy the data. Treating the poorly-characterized low-energy electron component as a separate population of particles, de Jager, Slane, & LaMassa

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Fig. 8 Broadband spectral model consisting of synchrotron emission in the radio and X-ray bands accompanied by IC emission in the VHE γ-ray band. The upper panel shows a model with two spectral breaks in the electron spectrum. Models with a single break (lower panel) either underpredict the radio emission, or produce a radio flux whose spectral index does not agree with observations. (From [23]. Reproduced by permission of the AAS.)

[12] showed that enhanced IC emission from this component could be expected in the GeV band. This has now been confirmed with observations by AGILE [31] and Fermi [1]. Interestingly, a similar excess is observed in Fermi observations of HESS J1640−465 [39], another evolved PWN that appears to have undergone a RS interaction (see Section 4.4). The nature of the low-energy particle spectrum in Vela X is poorly understood, but the Fermi studies in particular suggest a difference in the cocoon emission from that of its surroundings; the LAT emission appears to be concentrated distinctly to the west of the TeV emission. Whether or not this emission component is somehow associated with the reverse shock interaction is not clear. An XMM-Newton Large Project to map a significant portion of Vela X is underway to investigate the distribution of nonthermal particles and thermal ejecta in the nebula.

4.3 G327.1−1.1 G327.1−1.1 is a composite SNR with a bright central PWN whose structure is complex in both the radio and X-ray bands. As shown in Figure 9, the SNR is character-

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Fig. 9 Composite radio (red and orange) and X-ray (blue) image of G327.1−1.1. The outer radio shell defines the SNR boundary, while the bright central nebula is the PWN. The compact source to the northwest of the nebula is the neutron star. It is embedded in a cometary-shaped structure accompanied by a tail of X-ray emission extending into the radio nebula, as well as prong-like structures (seen in inset) that appear to inflate a faint bubble in the northwest.

ized by a faint radio shell accompanied by a bright radio PWN. The PWN is offset from the SNR center, and a finger-like structure extends toward the west/northwest. The morphology is suggestive of a PWN that has been disrupted by an asymmetric reverse shock interaction that has arrived preferentially from the northwestern direction. Detailed Chandra observations [43] appear to confirm this scenario in detail.3 A compact X-ray source resides at the tip of the radio finger, and a trail of nonthermal X-ray emission extends from the source back into the radio nebula. The compact X-ray source itself is resolved, with possible evidence of a jet or torus structure, and the source is embedded in a cometary nebula whose structure is suggestive of a bow shock. A pair of prong-like structures originate from the vicinity of the compact core 3

See also the contribution by T. Temim in these Proceedings.

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and extend out to the west/northwest. Their axes are not aligned with the compact core, and they do not appear to be jets from the pulsar. The most unusual feature in G327.1-1.1 is a large bubble-like structure that extends out from the prongs. The bubble is very faint, but it is apparent in images taken with both Chandra and XMMNewton. The spectral index in the tail of X-ray emission that extends into the brighter radio PWN appears to vary from ∼ 1.8 to ∼ 2.1, although significantly better statistics are needed to map this fully. Faint loop-like structures, possibly associated with Rayleigh-Taylor filaments or magnetic loops, are evident in the southern part of the tail and they appear to extend from radio structures inside the relic PWN. Deeper X-ray observations are required to better characterize these and, more importantly, to study the detailed properties of the complex structures seen in the immediate vicinity of the pulsar, and to investigate the apparent upstream diffusion of particles that form the bubble-like structure. The overall X-ray morphology of the PWN in G327.1-1.1 presents several challenges. It appears clear from the displacement of the radio nebula that the PWN has undergone an interaction with the SNR reverse shock, and that this shock arrived earlier from the northwest, possibly as a result of pulsar motion in this direction. In such a scenario, we expect the ongoing pulsar wind production to begin forming a new PWN around the pulsar, shaped by the surrounding pressure conditions. Radio emission from the displaced relic nebula will persist, but the compression from the reverse shock will temporarily increase the magnetic field in the nebula, causing rapid synchrotron losses for the more energetic particles. The X-ray emission is thus expected to be concentrated closer to the pulsar, as observed. Spectral steeping of the X-ray spectrum in the direction of the relic nebula is expected if the synchrotron loss timescale is shorter than the particle flow timescale; mapping this spectral evolution along the extended X-ray tail thus constrains the conditions in the relic nebula. In the direction from which the reverse shock propagated, the structure of the medium is complicated. The density in the immediate post-shock region is enhanced, but declines downstream due to adiabatic expansion of the SNR. At least qualitatively, this could provide the environment in which freshly-injected wind from the pulsar inflates the observed bubble. The cometary feature surrounding the putative pulsar complicates the above picture. The morphology is suggestive of a bow shock that forms when the pulsar motion exceeds the sound speed in the the ambient medium, yielding a structure quite different from that of a static PWN. The wind termination shock in such systems is compressed in the direction of motion, and extended in the backward direction. X-ray emission is then observed between the termination shock and the contact discontinuity, and forms three distinct structures: the “head” that surrounds the pulsar; an enhanced region behind the pulsar, associated with the termination shock; and an elongated tail where the swept-back wind is concentrated [17, 9]. For G327.11.1, such a geometry would require a significant pulsar velocity component perpendicular to the plane of the sky, but the overall velocity that would be required (770 km s−1 ) is not unreasonable.

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Given the similarity between G327.1−1.1 and Vela, in the context of both being systems in which an interaction between the PWN and the SNR reverse shock has occurred, it is of considerable interest to determine whether or not G327.1−1.1, like Vela X, produces γ-rays. Preliminary investigation of Fermi-LAT data indicates faint emission that is positionally coincident with G327.1−1.1, but further analysis is required to assess this in detail.

4.4 HESS J1640−465 HESS J1640−465 (see Figure 10) is an extended source of very-high-energy γ-ray emission discovered with the High Energy Stereoscopic System (H.E.S.S.) during a survey of the Galactic plane [3]. Centered within the radio SNR G338.3−0.0 [34], the deconvolved TeV image of the source has an RMS width of 2.7 ± 0.5 arcmin [16]. HI measurements show absorption against G338.3−0.0 out to velocities corresponding to the tangent point, indicating a distance of at least 8 kpc [24], and thus implying a rather large size for the PWN (RPWN > 6.4d10 pc, where d10 is the distance in units of 10 kpc). X-ray observations with XMM-Newton [16] and Chandra [24] establish the presence of an accompanying X-ray nebula and an X-ray point source that appears to be the associated neutron star. The point source is offset from the center of the PWN, and both are offset from the center of the SNR, suggesting that an asymmetric interaction with the SNR reverse shock has occurred. We have investigated Fermi-LAT data acquired from the region surrounding HESS J1640−465 and detect the source with high significance [39]. The spectrum is well-described by a power law with Γ = 2.30 ± 0.09 and a F(> 100 MeV) = 2.8 × 10−7 photons cm−2 s−1 . We have modeled the emission assuming a 1-zone model in which particles are injected into the nebula with a simple power law distribution. We use a radius of RS NR ∼ 11.6d10 pc for G338.3−0.0, based on radio observations. The observed extent of HESS J1640−465 constrains the radius of the PWN to RPWN > 6.4d10 pc. As indicated in Figure 2, where a horizontal line indicates the radius of G338.3−0.0, reasonable values for the SNR and PWN parameters indicate that the SNR reverse shock has almost certainly begun to impact the PWN. The broadband emission model results are shown in Figure 11 where we plot the Fermi and H.E.S.S spectra along with the radio upper limit from GMRT observations [20] and spectral confidence bands derived from Chandra [24]. The black curves represent the model prediction for the synchrotron (left) and IC (right) emission that best describes the X-ray and TeV γ-ray spectra, similar to results from [24]; the parameters for the model are summarized in the caption. As seen in Figure 11, this model significantly underpredicts the observed Fermi-LAT emission. Our spectral fits can formally accommodate up to about ∼ 20% of the observed flux in a pulsar-like component characterized by a power law with an exponential cutoff energy between 1 and 8 GeV, and there are several known radio pulsars located within the error circle of HESS J1640−465 that could potentially produce observable γ-ray

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1FGL J1640.8-4634 20:00.0

Declination (J2000)

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J1640-465 centroid

MOST contours

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Right Ascension (J2000) Fig. 10 Fermi-LAT image of HESS J1640−465. The solid (cyan) circle indicates the uncertainty in the centroid of the Fermi-LAT source, the magenta dashed circle indicates the 95% encircled flux distribution of the H.E.S.S. image, and the white dashed circle indicates that for 3EG J1639−4702. The white contours outline radio emission from G338.3−0.0 while the black contours at the center outline extended X-ray emission observed with XMM-Newton. A compact X-ray source detected with Chandra resides within the X-ray contours. (From [39]. Reproduced by permission of the AAS.)

emission. Even in this case, however, the Fermi-LAT emission still greatly exceeds the predicted flux from HESS J1640−465. As described in Section 4.2, simple power-law models for the particles in Vela X, another evolved PWN, fail to reproduce the observed broadband spectrum. The presence of an excess population of low-energy electrons is inferred, and models for the IC scattering of photons from this population predict an excess of γ-rays in the GeV range. Motivated by these results from Vela X, we modified the evolved power law spectrum from our model for HESS J1640−465 by truncating the lower end of the power law and adding a distinct low-energy component. Based on results from simulations of shock acceleration [40], we chose a Maxwellian distribution for this population. Our resulting (ad hoc) particle spectrum is shown in the upper panel in Figure 11, and the resulting broadband emission is shown in the lighter (magenta) curves in the lower panel. Here we have adjusted the normalization of the Maxwellian to reproduce the emission in the Fermi-LAT band, which is produced primarily by upscattered infrared (IR) photons from local dust. We find a mean value of γ ≈ 2 × 105 for the electrons in the Maxwellian component, and roughly

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Fig. 11 Electron spectrum (upper) and broadband emission model (lower) for HESS J1640−465 assuming the evolutionary history described in the text. The black curves represent a PWN with an age T = 10 kyr, and B(T ) = 5µG, assuming E˙0 = 4 × 1036 erg s−1 and an injection spectrum with σ = 10−3 , γ = 2.5, and Emin = 115 GeV. The light curves represent the scenario with a lowenergy Maxwellian electron component replacing the low-energy portion of the electron powerlaw spectrum. The mean temperature for the IR and optical photon fields are 15 K and 5000 K, respectively, and the energy densities relative to the CMB are 4 and 1.15. The dashed curve in the upper panel represents the truncated portion of the power law that was replaced by a Maxwellian. The dashed curve in the lower panel represents a model for which all of the γ-ray emission results from pion decay. (From [39]. Reproduced by permission of the AAS.)

5% of the total electron energy in the power law tail, consistent with results from particle-in-cell simulations. Recent work by Fang & Zhang (2010) [14] uses a similar input distribution to successfully model the emission for several PWNe including HESS J1640−465. However, their results for HESS J1640−465 underpredict the observed GeV emission from this source, apparently due to use of a slightly lower bulk Lorentz factor and a larger fraction of the total energy in the power law tail than we have used in this analysis. An alternative scenario for the γ-ray emission is that it arises from the SNR itself, and not the PWN. The dashed blue curve in Figure 11 represents a model

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for the emission from the collision of protons accelerated in the SNR with ambient material, leading to γ-rays from the production and subsequent decay of neutral pions. Assuming a shock compression ratio of 4 and that 25% of the total supernova energy appears in the form of relativistic protons, an ambient density n0 ≈ 100 cm−3 is required to produce the model shown in the Figure. This is much higher than can be accommodated for the observed size of the SNR and the lack of observed thermal X-ray emission from the SNR. Such high densities are found in dense molecular clouds, suggesting that the γ-rays could be produced by particles that stream away to interact with high-density material outside the SNR. However, only the most energetic particles can escape the acceleration region, which is in conflict with the proton spectrum we require to match the data. Moreover, the observed TeV emission appears to originate from within the SNR boundaries, making such an escapingparticle scenario appear problematic. Based on this, along with the lack of a spectral cutoff that might suggest emission from a central pulsar, we conclude that the GeV γ-ray emission most likely arises from the PWN.

5 Summary The broadband spectra of PWNe provide information about both the structure and evolution of these objects. New multiwavelength observations have begun to probe PWNe from the sites of particle injection to the ejecta-laden outer boundaries, providing crucial input for modeling these systems. Observations in the γ-ray band have uncovered previously unknown systems in the late phase of evolution, while X-ray observations continue to provide detailed information about the geometry and the composition of the pulsar winds. These observations continue to inform theoretical models of relativistic shocks which, in turn, have broad importance across the realm of high-energy astrophysics. At the same time, these recent results have pointed the way to new and deeper observations of PWNe across the electromagnetic spectrum. Acknowledgements I would like to acknowledge the considerable contributions of many colleagues to the work described here, including Bryan Gaensler, David Helfand, Stephen Reynolds, Okkie de Jager, and Stefan Funk. In particular, I would like to thank Yosi Gelfand, Tea Temim, Daniel Castro, Stephanie LaMassa, and Anne Lemiere who, as students as postdocs, led much of the work described here. This work was supported in part by NASA contract NAS8-03060, NASA grants NNX09AT68G, and NNX09AP99G, and Spitzer RSA 1375009.

References 1. Abdo, A. A., et al. 2010, ApJ, 713, 146 2. Aharonian, F. A. et al. 2006, A&A, 448, L43 3. Aharonian, F. A. et al. 2006, A&A, 636, 777

Multiwavelength Observations of Pulsar Wind Nebulae 11. 5. 16. 7. 17. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 77. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 97. 38. 39. 40. 41. 42. 43. 44.

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Multi-wavelength Observations of Composite Supernova Remnants Tea Temim

Abstract Multi-wavelength studies of composite supernova remnants (SNRs) lead to a better understanding of their evolutionary development, the interaction of supernovae (SNe) and pulsar wind nebulae (PWNe) with their surroundings, particle injection and loss processes, nucleosynthesis, and the production and processing of dust grains in SNe. This paper summarizes the basic evolutionary development of composite SNRs and describes two unique systems in different stages of evolution; G54.1+0.3, a PWN in the early stage of evolution that is expanding into inner SN ejecta, and G327.1-1.1, a composite SNR in the late stage of evolution whose PWN has interacted with the SNR reverse shock. Both systems exhibit unique properties that have not been observed previously.

1 Introduction Composite supernova remnants (SNRs) are those for which we see distinct evidence of both a pulsar wind nebula (PWN) and an SNR shell [5]. While the basic theoretical framework for their origin and evolution has been developed [1, 12, 4], the details are still not well-understood. We still lack a detailed understanding of the phases of evolution in which the PWN interacts with the SNR reverse shock and what structures form during these interactions. Detailed knowledge about the evolution of composite SNRs is also crucial for the understanding of the injected particle spectrum in PWNe and the eventual escape of these particles into the Galaxy. Initially, the young PWN expands supersonically inside the remnant and drives a shock into the freely-expanding inner SN ejecta. At this stage, we expect to observe synchrotron emission from the expanding PWN, surrounded by a skin of shocked SN ejecta [97, 4]. The reverse shock eventually crushes the PWN and causes it to Tea Temim Smithsonian Astrophysical Observatory, 60 Garden Street, MS 21, Cambridge, MA 02138, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_33, © Springer-Verlag Berlin Heidelberg 2011

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reverberate. The interaction can result in complex filamentary structures and mixing of the PWN material with ejecta gas [1]. After the interaction with the reverse shock, the PWN continues to expand subsonically into the reheated SN ejecta. The evolution becomes more complicated if the pulsar has a high space velocity and displaces the PWN off-center from the SNR shell. In that case, the reverse shock interacts with the PWN asymmetrically, sweeping it off to one side and producing a relic PWN. A new PWN continues to form around the pulsar, and as the pulsar’s motion eventually becomes supersonic, this newly forming PWN deforms into a bow shock nebula and takes on a cometary morphology [1, 12]. Here, we summarize observational studies of two systems that exhibit the properties described above.

2 G54.1+0.3: Expansion into SN Ejecta G54.1+0.3 is a young PWN closely resembling the Crab for which no thermal emission has been detected in X-rays. The SNR blast wave is presumed to be undetectable because it is expanding into a low density cavity and has not interacted with enough ISM material [6]. The Spitzer 24 µm image of G54.1+0.3 shows that the PWN is surrounded by an IR shell that contains a dozen point sources arranged in a ring-like structure, and a bright extended region of emission that appears to be aligned with the pulsar’s jet [7, 11]. These features are shown in Figure 1. Spitzer IR spectroscopy of the shell provided the first evidence for SN ejecta in G54.1+0.3 [11]. A number of emission lines are present in the IR spectrum, including [ArII], [NeII], [ClII], [SIII], [FeII], and [SiII]. Several are broadened to velocities of ∼ 1000 km s−1, suggesting that the IR shell is composed of rapidly expanding SN ejecta. The pulsar’s jet appears to be driving a ∼ 25 km s−1 shock into the shell material and compressing it to produce a region of higher density. The spectra also

Fig. 1 Three-color image of G54.1+0.3. Chandra X-ray emission is shown in blue, Spitzer 8 µm emission in green, and Spitzer 24 µm emission in red and yellow. The PWN is surrounding by an IR shell, 2.4 arcminutes in diameter (4.3 pc a distance of 6.2 kpc), containing a dozen point sources and a bright extended region of a higher density that is aligned with the pulsar’s jet. X-ray: NASA/CXC/SAO/T.Temim et al.; IR: NASA/JPLCaltech/T.Temim et al.

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reveal an unidentified dust feature at 21 µm that is likely produced by the same dust species as the freshly formed dust in Cas A [11]. The Chandra X-ray and Spitzer IR observations of G54.1+0.3 are best described by a scenario in which the shell emission arises entirely from SN ejecta and freshly formed dust. The dust is likely being illuminated by the members of a young stellar cluster in which the SN exploded. The point sources in the IR shell are attributed to radiatively heated dust that is blowing past these stars (see Figure 1). A simple Dust model shows that such a scenario can reproduce the observed IR emission from the shell and the embedded point sources, and that approximately 0.1 M⊙ of dust would be required [11]. If this scenario is correct, we are actually observing unshocked SN dust, before it has been processed by the reverse shock.

3 G327.1-1.1: Interaction with the Reverse Shock G327.1-1.1 is a composite supernova remnant that has an unusual morphology consisting of a symmetric radio shell and an off-center non-thermal component, seen in Figure 2. A narrow ridge of emission extends from the PWN structure toward the northwest. Chandra X-ray images reveal a compact source at the tip of the ridge, embedded in a cometary structure that resembles a bow-shock nebula. Two pronglike structures originate near the compact core and extend into a large bubble (Figure 2). There is a trail of X-ray emission whose spectrum steepens with increasing distance from the pulsar and loop-like structures that coincide with structures inside the radio PWN (Figure 2). An XMM-Newton detection of a 0.3 keV X-ray thermal component that spatially coincides with the radio shell leads to an age estimate of ∼ 18000 yr, for an assumed distance of 9 kpc [10].

Fig. 2 Left: MOST 843 MHz radio image of G327.1-1.1 with the PWN radio contours overlaid. Right: Chandra ACIS image of G327.1-1.1 is shown in blue, and the ATCA 13 cm radio image of the inner PWN region in red.

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G327.1-1.1 is one of the best examples of a composite SNR whose PWN has been asymmetrically disrupted by the SNR reverse shock. This shock likely arrived earlier from the northwest, possibly as a result of a combination of the pulsar’s motion in this direction and a density gradient in the ISM. It swept the PWN to the side, producing a relic nebula seen in the radio. Filamentary radio and X-ray structures, seen in Figure 2, are likely a result of this violent interaction. The pulsar is presumably forming a new PWN, represented by the compact core and the cometary structure that appears to be a bow shock. The presence of prong and bubble structures complicate the bow shock scenario, since such structures are not expected to form beyond the confines of the shock. Deeper imaging is required to explain the nature of the observed structures and determine if the PWN in G327.1-1.1 has deformed into a bow shock.

4 Conclusions Multi-wavelength observations of composite SNRs offer a wealth of information about their properties and evolution. The study of the interactions between the PWN and the evolving SNR can provide important information about the SNR properties that may otherwise be unobservable. G54.1+0.3 is a system in early stage of evolution, comprised of a PWN expanding into the inner SN ejecta. The unique environment of G54.1+0.3 allowed us to detect and characterize the SN ejecta and freshly formed dust that has not yet been processed by the SNR reverse shock. The study implies that IR searches for SN ejecta and dust around PWNe in stellar clusters may be an effective way of studying SNR properties. G327.1-1.1 is an ideal object for the study of several aspects of the late stages of PWN evolution. Its unusual morphology may be giving us a unique view into the transitional phase of evolution in which the PWN deforms into a bow shock nebula, following an asymmetric reverse shock interaction.

References 1. Blondin, J. M., Chevalier, R. A., & Frierson, D. M. 2001, ApJ, 563, 806 2. Bucciantini, N. 2002, A&A, 387, 1066 3. Gaensler, B. M., van der Swaluw, E., Camilo, F., Kaspi, V. M., Baganoff, F. K., Yusef-Zadeh, F., & Manchester, R. N. 2004, ApJ, 616, 383 4. Gaensler, B. M., & Slane, P. O. 2006, ARA&A, 44, 17 5. Helfand, D. J., & Becker, R. H. 1987, ApJ, 314, 203 6. Hester, J. J. 2008, ARA&A, 46, 127 7. Koo, B.-C., et al. 2008, ApJL, 673, L147 8. Rho, J., et al. 2008, ApJ, 673, 271 9. Slane, P., Helfand, D. J., van der Swaluw, E., & Murray, S. S. 2004, ApJ, 616, 403 10. Temim, T., Slane, P., Gaensler, B., Hughes, J., & Van Der Swaluw, E. 2009, ApJ, 691, 895 11. Temim, T., Slane, P., Reynolds, S., Raymond, J., & Borkowski, K. 2010, ApJ, 710, 309

Multi-wavelength Observations of Composite SNRs 12. van der Swaluw, E., Achterberg, A., Gallant, Y. A., & T´oth, G. 2001, A&A, 380, 309

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Fermi-LAT Results on Pulsar Wind Nebulae after 1.5 year of Observations M.-H. Grondin & M. Lemoine-Goumard for the Fermi-LAT Collaboration and the Pulsar Timing Consortium

Abstract Prior to the Fermi Gamma-ray Space Telescope, only six pulsars and one associated pulsar wind nebula, the Crab Nebula, had been detected in γ-rays by EGRET. Since then, the Large Area Telescope (LAT) aboard Fermi has significantly increased the number of detected pulsars in the 100 MeV to 30 GeV energy range. The new pulsar population established by early LAT observations show that we are detecting many nearby young pulsars in addition to the population of millisecond ˙ from ∼ 3 × 1033 pulsars. All Fermi-LAT pulsars have high energy loss rate (E), −1 38 −1 erg s to 5 × 10 erg s . A large fraction of these pulsars are associated to pulsar wind nebulae candidates observed in the TeV energy range by Cherenkov telescopes. These pulsars are thus likely to power a PWN detectable by Fermi, as it has already been done for the Crab. Here, we will review the results obtained so far by Fermi-LAT after 1.5 year of observations.

1 Introduction The catalog of pulsars detected using only 6 months of Fermi-LAT observations included 46 sources [1] and this number is still increasing [35], [4]. Yet most of the pulsar spin-down luminosity is not observed as pulsed photon emission and is carried away as a magnetized particle wind. Indeed, the deceleration of the pulsardriven wind as it sweeps up ejecta from the supernova explosion generates a termination shock at which the particles are pitch-angle scattered and further accelerated to ultra-relativistic energies. The pulsar wind nebula (PWN) emission, including synchrotron and inverse Compton components, extends across the electromagnetic spectrum from radio to TeV energies [21]. In the TeV range, PWNe are the major M.-H. Grondin & M. Lemoine-Goumard Centres d’Etudes Nucl´eaires de Bordeaux Gradignan, CNRS-IN2P3, Universit´e Bordeaux I, Chemin du Solarium, BP120, 33175 GRADIGNAN Cedex, FRANCE e-mail: [email protected]; e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_34, © Springer-Verlag Berlin Heidelberg 2011

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class of Galactic sources. However, the study of PWNe is complex. First, at high energies (HE; 100 MeV - 100 GeV), the pulsed emission highly dominates the signal from the associated PWN. Second, these sources are often faint in the Fermi-LAT energy range. Third, PWNe can be extended with respect to the LAT point-spreadfunction [16]; their study thus requires an adapted analysis method. Several years after EGRET, the Large Area Telescope (LAT), aboard Fermi, offers the opportunity to study faint and extended gamma-ray sources. The LAT is an electron-positron pair conversion telescope, sensitive to γ-rays with energies between 30 MeV and 300 GeV, with improved performance (a large effective area, a broad field of view, and a very good angular resolution) [16] compared to its predecessor. Only gamma-rays in the Diffuse class events were selected to perform the analyses presented in the following (with the tightest background rejection), and from this sample, we excluded those coming from a zenith angle larger than 105◦ to the detector axis because of the possible contamination from Earth albedo photons. The spectral analysis of the gamma-ray emission was performed using a maximumlikelihood method [30] implemented in the Fermi SSC science tools as the “gtlike” code.

2 The Crab Nebula The Crab Nebula is powered by the Crab Pulsar, one of the most energetic pulsars known (E˙ = 4.6 × 1038 erg s−1 ). It is the remnant of the 1054 A.D. supernova explosion, located at a distance of 2 kpc. The γ-ray detection of the Crab Pulsar and Nebula was reported by the EGRET collaboration in 1993 but their spectral parameters derived after several years of observations had large uncertainties [27]. The improved sensitivity and unprecedented statistics obtained using 8 months of Fermi-LAT data enable precise measurement of the Crab Nebula s