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 (20