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EAS Publications Series, Volume 2, 2002

GAIA: A European Space Project

LES HOUCHES CENTRE DE PHYSIQUE

Les Houches, France, May 14-18, 2001 Edited by: O. Bienayme and C. Turon

17 avenue du Hoggar, PA de Courtaboeuf, B.P. 112, 91944 Les Ulis cedex A, France

First pages of all issues in the series are available at: http://www.edpsciences.org

Sponsored by European High-Level Scientific Conferences programme (HPCF-2000-00093) ESA CNES CNRS (Formation Permanente) PNG (Programme National Galaxies)

Figure explanation and credits The GAIA satellite project By the kind permission of ESA

ISBN 2-86883-597-X

EDP Sciences Les Ulis

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, re-use of illustrations, recitation, broad-casting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the French Copyright law of March 11, 1957. Violations fall under the prosecution act of the French Copyright Law. C5 EDP Sciences, Les Ulis, 2002 Printed in France

Foreword A Summer School dedicated to the GAIA satellite, a cornerstone of theEuropean Space Agency's science programme, was held in Les Houches (France), at the "Centre de Physiques des Houches", from 14 to 18 May 2001. It was aimed at engaging the curiosity, interest and participation of the next generation of astronomers to the GAIA mission, and at guiding young scientists through the huge scientific harvest expected from this highly exciting and challenging project. The GAIA mission will provide a stereoscopic and kinematic map of our Galaxy at micro-arcsec level accuracy, and will survey more than one percent of the Galactic stellar population with the precision necessary to unravel its composition, formation scenario and subsequent evolution. Additional scientific products include characterisation of tens of thousands of extra-solar planetary systems, stringent tests of general relativity, and a comprehensive survey of objects ranging from minor bodies in our Solar System, through galaxies in the nearby Universe, to some 500000 quasars. The GAIA mission will give access to extremely high accuracy on distances and kinematics, and will provide on-board radial velocities and multi-colour photometry, i.e. to the full six-dimensional phase-space distribution function, combined with astrophysical diagnostics, for one billion stars in our Galaxy and throughout the Local Group. A more complete description of the mission, and of its expected scientific products, is available at http://astro.estec.esa.nl/GAIA The lectures given in Les Houches reviewed the mission design and accuracy performance, and the impact of the GAIA mission on various fields of astrophysics: covering the history of the various stellar populations in our Galaxy and in our neighbouring galactic companions, but also covering stellar physics and evolution with characterisation of all types of stars, planetary formation and census of extra-solar planetary systems in the solar neighbourhood, fundamental physics with stringent tests of general relativity, etc. In each domain, the most recent results were presented, along with the major key steps forward expected from the GAIA data. Highlights of the presentations are summarised at http://astro.estec.esa.nl/GAIA/resources/leshouches.html This book presents the text of the lectures and presentations given during a week in Les Houches to the 70 participants. The main goal of this conference was to open this project to the full astronomical community, and to guide young scientists in the direction of the most promising and exciting project concerning the understanding of the history of the Universe from a complete survey and detailed sampling of its local populations. The many fold improvement in the number of stars and measurement accuracy will urge scientists to reconsider classical methodologies and to develop new tools in order to be prepared for the analysis of the future GAIA data.

IV

The scientific organization of the meeting was in the hands of the Scientific Organising Committee: O. Bieriayme, M.A.C. Perryman, C. Turon, A. Baglin, J. Binney, A. Coradini. P. Fayet, K. Freeman, G. Gilmore, A. Gimenez, M.T. Lago, M. Mayor, F. Mignard, H.W. Rix, and P.T. de Zeeuw. We wish to thank particularly warmly the Strasbourg Observatory and the Centre de Physique des Houches for ensuring that the School ran so smoothly. In this respect, we are especially indebted to the Local Organising Comittee members, and particularly to C. Bruneau and J. Pluet, and to the staff members of the Centre de Physique, and of the Strasbourg and Paris Observatories. We also wish to extend our gratitude to Cecile DeWitt-Morette who founded the Summer School at Les Houches, fifty years ago. In practice the meeting would not have been possible without strong local, regional, national and European support. We gratefully acknowledge the participation of the European High-Level Scientific Conferences programme (HPCF2000-00093), and of ESA, CNES, CNRS (and more specifically the "Formation Permanente"), Observatoire de Paris, Observatoire de Strasbourg, the Louis Pasteur University, and the "Programme National Galaxies". O. Bienayme Observatoire Astronomique de Strasbourg, France (O.B.) C. Turon Observatoire de Paris-Meudon, France, (C.T.)

Top line from left to right:

A. Brown, M. Spite, S. Piquard, D. Pourbaix, V. Belokurov, M. Haywood, D. Egret, F. Royer, M. Lattanzi, A. Siebert, J. Isern, C. Babusiaux, B. Famaey, C. Reyle, V. Zappala, C. Bruneau, A. Omont, C. Cacchiari, U. Munari, A. Baglin, O. Bienayme, X. Luri, J. Torra, J. Portell, S. Picaud, M. Mayor, J. de Bruijne, E. Massana, S. Klioner, N. Christlieb, A. Digby,..., A. Gontcharov, F. Mignard, V. Vansevicius, J. Knude, A. Kucinskas, D. Hestroffer, R. Ibata, D. Carollo, N. Robichon, F. Arenou, A. Robin. Bottom line from left to right:

A. Helmi, Y.-P. Viala, D. Katz, W. Gasti, C. Turon, A. Maeder, J.M. Carrasco, M. Vaccari, A. Vecchiato, M.-T. Crosta, E. H0g, S. Torres Gil, L. Eyer, A. Berdyugin.

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List of Participants Ansari Salim: ESTEC, Nordwijk, The Netherlands, [email protected] Arenou Frederic: Observatoire de Paris, France, [email protected] Babusiaux Carine: Inst. Astron., Cambridge, UK, [email protected] Baglin Annie: Observatoire de Paris, France, [email protected] Baraffe Isabelle: Ecole Normale Superieure, Lyon, France, [email protected] Barucci Antonella: Observatoire de Paris, France, [email protected] Belokurov Vasily: Theoret. Phys., Oxford, UK, [email protected] Berdyugin Andrei: Tuorla Obs., Turku, Piikkio, Finland, [email protected] Bertelli Gianpaolo: Univ. di Padova, Italy, [email protected] Bienayme Olivier: Observatoire de Strasbourg, France, [email protected] Binney James: Theoret. Phys., Oxford, UK, [email protected] Brown Anthony: Leiden Observatory, The Netherlands, [email protected] Bruneau Chantal: Observatoire de Strasbourg, France, [email protected] Cacciari Carla: Univ. di Bologna, Italy, [email protected] Carollo Daniela: Oss. Astron. Torino, Italy, [email protected] Carrasco Jose Manuel: Dept. Astron., Barcelona, Spain, [email protected] Christlieb Norbert: Hamburger Sternwarte, Germany, [email protected] Crosta Maria Teresa: Univ. Padova, Oss. Torino, Italy, [email protected] de Bruijne Jos: ESTEC, Noordwijk, The Netherlands, [email protected] Digby Andrew: Royal Observatory of Edinburgh, UK, [email protected] Egret Daniel: Observatoire de Strasbourg, France, [email protected] Eyer Laurent: Princeton University Obs., NJ, USA, [email protected] Fabricius Claus: Copenhagen Univ. Obs., Denmark, [email protected] Famaey Benoit: Universite Libre de Bruxelles, Begium, [email protected] Fulchignoni Marcello: Observatoire de Paris, France, [email protected] Gasti Wahida: ESTEC, Noordwijk, The Netherlands, [email protected] Gilmore Gerry: Inst. Astron., Cambridge, UK, [email protected] Gontcharov Alexander: Lund Obs., Sweden, [email protected] Grenon Michel: Observatoire de Geneve, Switzerland, [email protected] Haywood Misha: Observatoire de Paris, France, [email protected] Helmi Amina: MPI Astroph., Garching, Germany, [email protected] Hestroffer Daniel: Observatoire de Paris, France, [email protected] H0g Erik: Copenhagen Univ. Obs., Denmark, [email protected] Ibata Rodrigo: Observatoire de Strasbourg, France, [email protected] Isern Jordi: IEECS, Barcelona, Spain, [email protected]

VIII Katz David: Observatoire de Paris, France, [email protected] Klioner Sergei: Lohrmann Obs., Dresden, Germany, [email protected] Knude Jens: Copenhagen Univ. Obs., Denmark, [email protected] Kucinskas Arunas: Inst. Theor. Phys., Vilnius, Lithuania, [email protected] Lattanzi Mario: Osservatorio Astron., Torino, Italy, [email protected] Lejeune Thibault: Obs. Astron., Coimbra, Portugal, [email protected] Luri Javier: Dept. de Astron., Barcelona, Spain, [email protected] Maeder Andre: Observatoire de Geneve, Switzerland, [email protected] Masana Eduard: Dept. Astron., Barcelona, Spain, [email protected] Mayor Michel: Observatoire de Geneve, Switzerland, [email protected] Mignard Frangois: OCA/CERGA, Grasse, France, [email protected] Munari Ulisse: Inst. di Astron., Univ. di Padova, Italy, [email protected] Omont Alain: Institut d'Astrophysique de Paris, France, [email protected] Ferryman Michael: ESTEC, Noordwijk, The Netherlands, [email protected] Picaud Sebastien: Observatoire de Besangon, France, [email protected] Piquard Sandrine: Observatoire de Strasbourg, France, [email protected] Portell Jordi: Un. Pol. Catalun, Barcelona, Spain, [email protected] Pourbaix Dimitri: Universite Libre de Bruxelles, Belgium, [email protected] Reyle Celine: Observatoire de Besangon, France, [email protected] Robichon Noel: Observatoire de Paris, France, [email protected] Robin Annie: Observatoire de Besangon, France, [email protected] Roser Siegfried: ARI, Heidelberg, Germany, [email protected] Royer Frederic: Observatoire de Geneve, Switzerland, [email protected] Siebert Arnaud: Observatoire de Strasbourg, France, [email protected] Spite Monique: Observatoire de Paris, France, [email protected] Torra Jordi: Dept. de Astron., Barcelona, Spain, [email protected] Torres Santiago: Univ. Catalal., Barcelona, Spain, [email protected] Turon Catherine: Observatoire de Paris, France, [email protected] Vaccari Mattia: Dept. Astron., Univ. Padova, Italy, [email protected] Vansevicius Vladas: Institute of Physics, Vilnius, Lithuania, [email protected] Vecchiato Alberto: Univ., Padova, Italy, [email protected] Viala Yves: Observatoire de Paris, France, [email protected] Wyse Rosemary: John Hopkins Univ., Baltimore, USA, [email protected] Zappala Vincenzo: Osserv. Astron., Torino, Italy, [email protected]

Contents

Foreword Conference Photograph List of Participants

III V VII

Section I: GAIA: Unprecedented Performance GAIA: An Introduction to the Project M.A.C. Perryman

3

Photometric and Imaging Performance E. H0g

27

GAIA Spectroscopy and Radial Velocities U. Mimari

39

Overview of GAIA Data Reduction J. Torra, X. Luri, F. Figueras, C. Jordi and E. Masana

55

RVs' Radial Velocities Accuracy D. Katz, Y. Viala, A. Gomez and D. Morin

63

Performance of the GAIA Photometric Systems 1F, 2A & 3G V. Vansevicius, A. Bridzius and R. Drazdys

67

Space Astrometry Missions F. Mignard and S. Roeser

69

Section II: Fundamental Physics: General Relativity Relativistic Modelling of Positional Observations with Microarcsecond Accuracy S.A. Klioner Fundamental Physics with GAIA F. Mignard

93 107

X

White Dwarfs as Tools of Fundamental Physics: The Gravitational Constant Case J. Isern, E. Garcia-Berro and M. Salaris

123

Section III: Astrometric Impact on Stellar Astronomy GAIA and Physics of Stellar Interiors Y. Lebreton and A. Baglin

131

Importance of Very Accurate Luminosities for Stellar Formation and Evolution A. Maeder

145

Duplicity and Masses F. Arenou, J.-L. Halbwachs, M. Mayor and S. Udry

155

The Oldest Stellar Populations and the Age of the Universe C. Cacciari

163

Absolute Luminosities of Stellar Candles X. Luri, F. Figueras and J. Torra

171

Analysis of Huge Catalogues. New Methodologies for the Virtual Observatories D. Egret

179

Section IV: Sub-Stellar Objects: Brown Dwarfs and Exo-Planets Theory of Low Mass Stars and Brown Dwarfs: Success and Remaining Uncertainties I. Baraffe

191

Field Brown Dwarfs & GAIA M. Haywood and C. Jordi

199

The GAIA Astrometric Survey of Extra-Solar Planets M. Lattanzi, S. Casertano, A. Sozzetti and A. Spagna

207

Detection of Transits of Extrasolar Planets with GAIA N. Robichon

215

Section V: Structure, Formation and History of the Galaxy Dust and Obscuration in the Milky Way J. Knude

225

XI

A Complete Census Down to Magnitude 20: Stellar Population Properties A.C. Robin

233

Components of the Milky Way and GAIA J. Binney

245

Astrometric Microlensing with the GAIA Satellite V. Belokurov and N.W. Evans

257

Star Formation: On Going and Past G. Bertelli

265

Mapping the Galactic Halo Today and in the Future A. Helmi

273

Preparing for the GAIA Mission: Astrophysical Parameter Determination A.G.A. Brown

277

Section VI: Outside our Galaxy GAIA and the Stellar Populations in the Magellanic Clouds M. Spite

287

M 31, M 33 and the Milky Way: Similarities and Differences R.F.G. Wyse

295

Local Group Dynamics with GAIA R. Ibata

305

GAIA Galaxy Survey: A Multi-Colour Galaxy Survey with GAIA M. Vaccari

313

Multi-Colour Photometry with GAIA of the Diffuse Sky Background E. H0g and K. Mattila

321

Observations of QSOs and Reference Frame with GAIA F. Mignard

327

Section VII: The Solar System Revisited The Impact of GAIA in our Knowledge of Asteroids V. Zappala and A. Cellino

343

XII

Other Objects in the Solar System: Trojans, Centaurs and Trans-Neptunians M.A. Barucci, J. Romon, A. Doressoundiram, C. de Bergh and M. Fulchignoni

351

Preparing GAIA for the Solar System D. Hestroffer

359

Section VIII: Posters Further Processing of the Hipparcos Variability Induced Movers S. Detournay and D. Pourbaix

367

Potentials and Distribution Functions to Be Used for Dynamical Modelling with GAIA-like Data B. Famaey and H. Dejonghe

371

On the Kinematic Deconvolution of the Local Luminosity Function A. Siebert, C. Pichon, O. Bienayme and E. Thiebaut

375

Galactic Structure and Evolution from Stellar Dynamics A. Digby, J. Cooke, N. Hambly, I.N. Reid and R. Cannon

379

Stellar Populations in the Large Magellanic Cloud: The Impact from GAIA A. Kucinskas, A. Bridzius and V. Vansevicius

383

Section IX: Conclusion From Hipparcos to Gaia, and Beyond C. Turon

387

Index

395

GAIA: Unprecedented Performance

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

GAIA: AN INTRODUCTION TO THE PROJECT M.A.C. Perryman 1 Abstract. In October 2000, the GAIA astrometric mission was approved as one of the next two "cornerstones" of ESA's science programme, with a launch date target of 2010-12. GAIA will provide positional and radial velocity measurements with the accuracies needed to produce a stereoscopic and kinematic census of about one billion stars throughout our Galaxy (and into the Local Group), amounting to about 1 per cent of the Galactic stellar population. GAIA's main scientific goal is to clarify the origin and history of our Galaxy, from a quantitative census of the stellar populations. It will advance questions such as when the stars in our Galaxy formed, when and how it was assembled, and its distribution of dark matter. The survey aims for completeness to V = 20 mag, with accuracies of 10 ^as at 15 mag.

1

Introduction

Following the success of ESA's Hipparcos space astrometry mission, the GAIA project has been approved as an ambitious space experiment to extend highly accurate positional measurements to a very large number of stars throughout our Galaxy. GAIA's contribution to the understanding of the structure and evolution of our Galaxy is based on three complementary observational approaches: (i) a census of the contents of a large, representative, part of the Galaxy; (ii) quantification of the present spatial structure, from distances; (iii) knowledge of the three-dimensional space motions, to determine the gravitational field and the stellar orbits. Astrometric measurements uniquely provide model-independent distances and transverse kinematics, and form the basis of the cosmic distance scale. Complementary radial velocity and photometric information are required to complete the kinematic and astrophysical information about the individual objects observed. Photometry, with appropriate astrometric and astrophysical calibration, gives a knowledge of extinction, and hence, combined with astrometry, provides 1

Astrophysics Division, Space Science Department of ESA, ESTEC, 2200 AG Noordwijk, The Netherlands © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002001

GAIA: A European Space Project

4

intrinsic luminosities, spatial distribution functions, stellar chemical abundance and age information. Radial velocities complete the kinematic triad, allowing determination of dynamical motions, gravitational forces, and the distribution of invisible mass. The GAIA mission will provide all this information. GAIA will be a continuously scanning spacecraft, accurately measuring onedimensional coordinates along great circles in two simultaneous fields of view, separated by a well-known angle. The payload utilises a large CCD focal plane assembly, passive thermal control, natural short-term instrument stability due to the Sun shield and the selected orbit, and a robust payload design. The system fits within a dual-launch Ariane 5 configuration, without deployment of any payload elements. A "Lissajous" orbit at the L2 Lagrange point of the Sun-Earth system is the proposed operational orbit, from where about 1 Mbit of data per second is returned to the single ground station throughout the 5-year mission. A more detailed description of the project is given elsewhere [1], based on the extensive study conducted between 1998-2000 [2]. 2

Scientific Goals

This section gives a concise introduction to some of the scientific topics that can be addressed by performing astrometric measurements at the microarcsec level for very large numbers of stars. By way of introduction, it may be noted that GAIA is expected to observe, or discover, very large numbers of specific objects, for example: 105 — 106 (new) Solar System objects; 30000 extra-Solar planets; 200000 disk white dwarfs; 107 resolved binaries within 250 pc; 106 — 107 resolved galaxies; 105 extragalactic supernovae; and 500 000 quasars. Structure and Dynamics of the Galaxy: one of the primary objectives of the GAIA mission is to observe the physical characteristics, kinematics and distribution of stars over a large fraction of the volume of our Galaxy, with the goal of achieving a full understanding of its dynamics and structure, and consequently its formation and history (see. e.g.. [3-7]). The Star Formation History of our Galaxy: one central element the GAIA mission is the determination of the star formation histories, as described by the temporal evolution of the star formation rate, and the cumulative numbers of stars formed, of the bulge, inner disk, Solar neighbourhood, outer disk and halo of our Galaxy (e.g. [8]). Given such information, together with the kinematic information from GAIA, and complementary chemical abundance information, again primarily from GAIA, the full evolutionary history of the Galaxy is determinable (e.g. [9,10]). Determination of the relative rates of formation of the stellar populations in a large spiral, typical of those galaxies which dominate the luminosity in the Universe, will provide for the first time quantitative tests of galaxy formation models. Do large galaxies form from accumulation of many smaller systems which have already initiated star formation? Does star formation begin in a gravitational potential well in which much of the gas is already accumulated? Does the bulge pre-date, postdate, or is it contemporaneous with, the halo and inner disk? Is the thick disk a mix of the early disk and a later major merger? Is there a radial age gradient

M.A.C. Perryman: GAIA: An Introduction to the Project

5

in the older stars? Is the history of star formation relatively smooth, or highly episodic? Answers to such questions will also provide a template for analysis of data on unresolved stellar systems, where similar data cannot be obtained. Stellar Astrophysics: GAIA will provide distances of unprecedented accuracy for all types of stars of all stellar populations, even those in the most rapid evolutionary phases which are very sparsely represented in the Solar neighbourhood. All parts of the Hertzsprung-Russell diagram will be comprehensively calibrated, from pre-main sequence stars to white dwarfs and all transient phases; all possible masses, from brown dwarfs to the most massive O stars; all types of variable stars; all possible types of binary systems down to brown dwarf and planetary systems; all standard distance indicators, etc. This extensive amount of data of extreme accuracy will stimulate a revolution in the exploration of stellar and Galactic formation and evolution, and the determination of the cosmic distance scale (cf. [11]). Photometry and Variability: the GAIA large-scale photometric survey will have significant intrinsic scientific value for stellar astrophysics, providing basic stellar data (effective temperatures, surface gravities, metallicities, etc.) and also valuable samples of variable stars of nearly all types, including detached eclipsing binaries, contact or semi-contact binaries, and pulsating stars (cf. [12]). The pulsating stars include key distance calibrators such as Cepheids and RR Lyrae stars and long-period variables. Existing samples are incomplete already at magnitudes as bright as V ~ 10 mag. A complete sample of objects will allow determination of the frequency of variable objects, and will accurately calibrate period-luminosity relationships across a wide range of stellar parameters including metallicity. A systematic variability search will also allow identification of stars in short-lived but key stages of stellar evolution, such as the helium core flash and the helium shell thermal pulses and flashes. Prompt processing will identify many targets for follow-up ground-based studies. Estimated numbers are highly uncertain, but suggest some 18 million variable stars in total, including 5 million "classic" periodic variables, 2-3 million eclipsing binaries, 2000 - 8000 Cepheids, 60000 - 240 000 6 Scuti variables, 70000 RR Lyrae, and 140000 - 170000 Miras [13]. Binaries and Multiple Stars: a key scientific issue regarding double and multiple star formation is the distribution of mass-ratios q. For wide pairs (>0.5 arcsec) this is indirectly given through the distribution of magnitude differences. GAIA will provide a photometric determination of the ^-distribution down to q ~ 0.1. covering the expected maximum around q ~ 0.2. Furthermore, the large numbers of ("5-year") astrometric orbits, will allow derivation of the important statistics of the very smallest (brown dwarf) masses as well as the detailed distribution of orbital eccentricities [14]. GAIA is extremely sensitive to non-linear proper motions. A large fraction of all astrometric binaries with periods from 0.03-30 years will be immediately recognized by their poor fit to a standard single-star model. Most will be unresolved, with very unequal mass-ratios and/or magnitudes, but in many cases a photocentre orbit can be determined. For this period range, the absolute and relative binary frequency can be established, with the important possibility of exploring variations with age and place of formation in the Galaxy.

6

GAIA: A European Space Project

Some 10 million binaries closer than 250 pc should be detected, with very much larger numbers still detectable out to 1 kpc and beyond. Brown Dwarfs: sub-stellar companions can be divided in two classes: brown dwarfs and planets. An isolated brown dwarf is typically visible only at ages <1 Gyr because of their rapidly fading luminosity with time. However, in a binary system, the mass is conserved, and the gravitational effects on a main-sequence secondary remain observable over much longer intervals. GAIA will have the power to investigate the mass-distribution of brown-dwarf binaries with 1-30 year periods, of all ages, through analysis of the astrometric orbits. Planetary Systems: there are a number of techniques which in principle allow the detection of extra-Solar planetary systems: these include pulsar timing, radial velocity measurements, astrometric techniques, transit measurements, microlensing, and direct methods based on high-angular resolution interferometric imaging. A better understanding of the conditions under which planetary systems form and of their general properties requires sensitivity to low mass planets (down to ~10 M0), characterization of known systems (mass, and orbital elements), and complete samples of planets, with useful upper limits on Jupiter-mass planets out to several AU from the central star (e.g. [15,16]). Astrometric measurements good to 2 — 10 //as will contribute substantially to these goals, and will complement the ongoing radial velocity measurement programmes. Although SIM will be able to study in detail targets detected by other methods, including microlensing, GAIA's strength will be its discovery potential, following from the astrometric monitoring of all of the several hundred thousand bright stars out to distances of ~200 pc [17]. Solar System Objects: Solar System objects present a challenge to GAIA because of their significant proper motions, but they promise a rich scientific reward. The minor bodies provide a record of the conditions in the proto-Solar nebula, and their properties therefore shed light on the formation of planetary systems. The relatively small bodies located in the main asteroid belt between Mars and Jupiter should have experienced limited thermal evolution since the early epochs of planetary accretion. Due to the radial extent of the main belt, minor planets provide important information about the gradient of mineralogical composition of the early planetesimals as a function of heliocentric distance. It is therefore important for any study of the origin and evolution of the Solar system to investigate the main physical properties of asteroids including masses, densities, sizes, shapes, and taxonomic classes, all as a function of location in the main belt and in the Trojan clouds. The possibility of determining asteroid masses relies on the capability of measuring the tiny gravitational perturbations that asteroids experience in case of a mutual close approach. GAIA is expected to discover a very large number, of the order of 105 or 106 new objects, depending on the uncertainties on the extrapolations of the known population. It should be possible to derive precise orbits for many of the newly discovered objects, since each of them will be observed many times during the mission lifetime. These will include a large number of near-Earth asteroids. The combination of on-board detection, faint limiting magnitude, observations at small Sun-aspect angles, high accuracy in the instantaneous angular velocity (0.25 mas s^ 1 ), and confirmation from successive

M.A.C. Ferryman: GAIA: An Introduction to the Project

7

field transits, means that GAIA will provide a detailed census of Atens, Apollos and Amors, extending as close as 0.5 AU to the Sun, and down to diameters of about 260 590 m at 1 AU, depending on albedo and observational geometry. Extragalactic Science: GAIA will not only provide a representative census of the stars throughout the Galaxy, but it will also make unique contributions to extragalactic astronomy. These include the structure, dynamics and stellar populations in the Local Group, especially the Magellanic Clouds, M 31 and M 33, the space motions of Local Group galaxies, a multi-colour survey of galaxies [18], and studies of supernovae [19], galactic nuclei and quasars. The Radio/Optical Reference Frame: the International Celestial Reference System (ICRS) is realized by the International Celestial Reference Frame (ICRF) consisting of 212 extragalactic radio-sources with an rms uncertainty in position between 100 and 500 //as. The extension of the ICRF to visible light is represented by the Hipparcos Catalogue. This has rms uncertainties estimated to be 0.25 mas yr _ 1 in each component of the spin vector of the frame, and 0.6 mas in the components of the orientation vector at the catalogue epoch, J 1991.25. The GAIA catalogue will permit a definition of the ICRS more accurate by one or two orders of magnitude than the present realizations (e.g. [20,21]). The spin vector can be determined very accurately by means of the many thousand faint quasars picked up by the astrometric and photometric survey. Simulations using realistic quasar counts, conservative estimates of intrinsic source photocentric instability, and realistic intervening gravitational lensing effects, show that an accuracy of better than 0.4 //as yr–1 will be reached in all three components of the spin vector. For the determination of the frame orientation, the only possible procedure is to compare the positions of the radio sources in ICRF (and its extensions) with the positions of their optical counterparts observed by GAIA. The number of such objects is currently less than 300 and the error budget is dominated by the uncertainties of the radio positions. Assuming current accuracies for the radio positions, simulations show that the GAIA frame orientation will be obtained with an uncertainty of ~60 //as in each component of the orientation vector. The actual result by the time of GAIA may be significantly better, as the number and quality of radio positions for suitable objects are likely to increase with time. Sun's Absolute Velocity: the Sun's absolute velocity with respect to a cosmological reference frame causes the dipole anisotropy of the cosmic microwave background. The Sun's absolute acceleration can be measured astrometrically: it will result in the apparent proper motion of quasars. The acceleration of the Solar System towards the Galactic centre causes the aberration effect to change slowly. This leads to a slow change of the apparent positions of distant celestial objects, i.e., to an apparent proper motion. For a Solar velocity of 220 km s-1 and a distance of 8.5 kpc to the Galactic centre, the orbital period of the Sun is ^250 Myr, and the Galactocentric acceleration has the value 0.2 nm s~"2, or 6 mm s–1 yr"1. A change in velocity by 6 mm s–1 causes a change in aberration of the order of 4 /was. The apparent proper motion of a celestial object caused by this effect always points towards the direction of the Galactic centre. Thus, all quasars will exhibit a streaming motion towards the Galactic centre of this amplitude.

GAIA: A European Space Project

8

Fundamental Physics: the reduction of the Hipparcos data necessitated the inclusion of stellar aberration up to terms in (v/c)2, and the general relativistic treatment of light bending due to the gravitational field of the Sun (and Earth). The GAIA data reduction requires a more accurate and comprehensive inclusion of relativistic effects, at the same time providing the opportunity to test a number of parameters of general relativity in new observational domains, and with much improved precision. The dominant relativistic effect in the GAIA measurements is gravitational light bending, quantified by, and allowing accurate determination of, the parameter 7 of the Parametrized Post-Newtonian (PPN) formulation of gravitational theories. While the angular separation to objects observed by GAIA, X, is never smaller than 35° for the Sun (a constraint from GAIA's orbit), grazing incidence is possible for the planets. With the astrometric accuracy of a few /^as, the magnitude of the expected effects is considerable for the Sun, and also for observations near planets. The GAIA astrometric residuals can be tested for any discrepancies with the prescriptions of general relativity. Detailed analyses indicate that the GAIA measurements will provide a precision of about 5 x 10~7 for 7, based on multiple observations of ~107 stars with V < 13 mag at wide angles from the Sun, with individual measurement accuracies better than 10 ^.as. 3

Overall Design Considerations

The proposed GAIA design has arisen from requirements on astrometric precision (10 //as at 15 mag), completeness to V = 20 mag, the acquisition of radial velocities, the provision of accurate multi-colour photometry for astrophysical diagnostics, and the need for on-board object detection [22,23]. 3.1

Astrometry

A space astrometry mission has a unique capability to perform global measurements, such that positions, and changes in positions caused by proper motion and parallax, are determined in a reference system consistently defined over the whole sky, for very large numbers of objects. Hipparcos demonstrated that this can be achieved with milliarcsecond accuracy by means of a continuously scanning satellite which observes two directions simultaneously. With current technology this same principle can be applied with a gain of a factor of more than 100 improvement in accuracy, a factor 1000 improvement in limiting magnitude, and a factor of 10000 in the numbers of stars observed. Measurements conducted by a continuously scanning satellite are optimally efficient, with each photon acquired during a scan contributing to the precision of the resulting astrometric parameters. The over-riding benefit of global astrometry using a scanning satellite is however not efficiency but reliability: an accurate instrument calibration is performed naturally, while the interconnection of observations over the celestial sphere provides the rigidity and reference system, immediately connected to an extragalactic reference system, and a realistic determination of the standard errors of the astrometric parameters. Two individual

M.A.C. Ferryman: GAIA: An Introduction to the Project

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viewing directions with a wide separation is the fundamental pre-requisite of the payload, since this leads to the determination of absolute trigonometric parallaxes, and absolute distances, exploiting the method implemented for the first time in the Hipparcos mission. The ultimate accuracy with which the direction to a point source of light can be determined is set by the dual nature of electromagnetic radiation, namely as waves (causing diffraction) and particles (causing a finite signal-to-noise ratio in the detection process). For wavelength A and telescope aperture D the characteristic angular size of the diffraction pattern image is of order X/D radians. If a total of N detected photons are available for localizing the image, then the theoretically achievable angular accuracy will be of order (X/D} x N–1/2 radians. A realistic size for non-deploy able space instruments is of order 2 m. Operating in visible light (A ~ 0.5 um) then gives diffraction features of order X/D ~ 0.05 arcsec. To achieve a final astrometric accuracy of 10 /was it is therefore necessary that the diffraction features are localised to within 1/5000 of their characteristic size. Thus, some 25 million detected photons are needed to overcome the statistical noise, although extreme care will be needed to achieve such precision in practice. The requirement on the number of photons can be satisfied for objects around 15 mag with reasonable assumptions on collecting area and bandwidth. Quantifying the tradeoff between dilute versus filled apertures, allowing for attainable focal lengths, attainable pixel sizes, component alignment and stability, and data rates, has clearly pointed in the direction of a moderately large filled aperture (as opposed to an interferometric design) as the optical system of choice. The GAIA performance target is 10 /^as at 15 mag. Restricting GAIA to a limiting magnitude of 15 mag, or to a subset of all objects down to its detection limit, would provide a reduction in the down-link telemetry rate, but little or no change in the other main aspects of the payload design. These are driven simply by the photon noise budget required to reach a 10 /^as accuracy at 15 mag. The faint magnitude limit, the ability to meet the adopted scientific case, and the number of target objects follow from the accuracy requirement, with no additional spacecraft cost. 3.2

Radial Velocity Measurements

There is one dominant scientific requirement, as well as two additional scientific motivations, for the acquisition of radial velocities with GAIA: (i) astrometric measurements supply only two components of the space motion of the target stars: the third component, radial velocity, is directed along the line of sight, but is nevertheless essential for dynamical studies; (ii) measurement of the radial velocity at a number of epochs is a powerful method for detecting and characterising binary systems; (iii) at the GAIA accuracy levels, "perspective acceleration" is at the same time both a complication and an important observable quantity. If the distance between an object and observer changes with time due to a radial component of motion, a constant transverse velocity is observed as a varying transverse angular motion, the perspective acceleration. Although the effect is generally small, some

10

GAIA: A European Space Project

hundreds of thousands of high-velocity stars will have systematic distance errors if the radial velocities are unknown. On-board acquisition of radial velocities with GAIA is not only feasible, but is relatively simple, is scientifically necessary, and cannot be readily provided in any other way. In terms of accuracy requirements, faint and bright magnitude regimes can be distinguished. The faint targets will mostly be distant stars, which will be of interest as tracers of Galactic dynamics. The uncertainty in the tangential component of their space motion will be dominated by the error in the parallax. Hence a radial velocity accuracy of ~5 km s""1 is sufficient for statistical purposes. Stars with V < 15 mag will be of individual interest, and the radial velocity will be useful also as an indicator of multiplicity and for the determination of perspective acceleration. The radial velocities will be determined by digital cross-correlation between an observed spectrum and an appropriate template. The present design allows (for red Population I stars of any luminosity class) determination of radial velocities to <7V ~ 5 km s"1 at V = 18 mag (e.g. [24]). Most stars are intrinsically red, and made even redder by interstellar absorption. Thus, a red spectral region is to be preferred for the GAIA spectrograph. To maximize the radial velocity signal even for metal-poor stars, strong, saturated lines are desirable. Specific studies, and ground-based experience show that the Call triplet near 860 nm is optimal for radial velocity determination in the greatest number of stellar types. Ground-based radial velocity surveys are approaching the one million-object level. That experience shows the cost and complexity of determining some hundreds of millions of radial velocities is impractical. There is also a substantial additional scientific return in acquiring a large number of measurements, and doing so not only well spaced in time but also, preferably, simultaneously with the astrometric measurements (e.g. variables and multiple systems). 3.3

Derivation of Astrophysical Parameters

The GAIA core science case requires measurement of luminosity, effective temperature, mass, age and composition, in addition to distance and velocity, to optimise understanding of the stellar populations in the Galaxy and its nearest neighbours. The quantities complementary to the kinematics can be derived from the spectral energy distribution of the stars by multi-band photometry and spectroscopy. Acquisition of this astrophysical information is an essential part of the GAIA payload. A broad-band magnitude, and its time dependence will be obtained from the primary mission data, allowing both astrophysical analyses and the critical corrections for residual system chromaticity. For the brighter stars, the radial velocity spectra will complement the photometric data. For essentially every application of the GAIA astrometric data, high-quality photometric data will be crucial, in providing the basic tools for classifying stars across the entire HR diagram, as well as in identifying specific and peculiar objects (e.g. [25]). Photometry must determine (i) temperature and reddening at least for OBA stars and (ii) effective temperatures and abundances for late-type

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giants and dwarfs. To be able to reconstruct Galactic formation history, the distribution function of stellar abundances must be determined to ~0.2 dex, while effective temperatures must be determined to ~200 K. Separate determination of the abundance of Fe and a-elements (at the same accuracy level) will be desirable for mapping Galactic chemical evolution. These requirements translate into a magnitude accuracy of ~0.02 mag for each colour index. Many photometric systems exist, but none is necessarily optimal for space implementation. For GAIA, photometry will be required for quasar and galaxy photometry, Solar System object classification, etc. Considerable effort has therefore been devoted to the design of an optimum filter system for GAIA (e.g. [26,27]). The result of this effort is a baseline system, with four broad and eleven medium passbands, covering the near ultraviolet to the CCD red limit. The 4 broad-band filters are implemented within the astrometric fields, and therefore yield photometry at the same angular resolution (also relevant for chromatic correction), while the 11 medium-band filters are implemented within the spectrometric telescope. Both target magnitude limits of 20 mag, as for the astrometric measurements. 3.4

On-Board Detection

Clear definition and understanding of the selection function used to decide which targets to observe is a crucial scientific issue, strongly driving the final scientific output of the mission. The optimum selection function, and that adopted, is to detect every target above some practical signal level on-board as it enters the focal plane. This has the advantage that the detection will be carried out in the same wave-band, and at the same angular resolution as the final observations. The focal plane data on all objects down to about 20 mag can then be read out and telemetered to ground within system capabilities. All objects, including Solar System objects, variable objects, supernovae, and microlensed sources are detected using this "astrometric sky mapper", described in further detail in Section 4.3. 4 4.1

Payload Design Measurement Principles

The overall design constraints have been investigated in detail in order to optimise the number and optical design of each viewing direction, the choice of wavelength bands, detection systems, detector sampling strategies, basic angle, metrology system, satellite layout, and orbit [28]. The resulting proposed payload design (Fig. 1) consists of: (a) two astrometric viewing directions. Each of these astrometric instruments comprises an all-reflective three-mirror telescope with an aperture of 1.7 x 0.7 m2, the two fields separated by a basic angle of 106°. Each astrometric field comprises an astrometric sky mapper, the astrometric field proper, and a broadband photometer. Each sky mapper system provides an on-board capability for star detection and selection, and for the star position and satellite scan-speed

12

GAIA: A European Space Project

Fig. 1. The payload includes two identical astrometric instruments (labelled ASTRO-1 and ASTRO-2) separated by the 106° basic angle, as well as a spectrometric instrument (comprising a radial velocity measurement instrument and a medium-band photometer) which share the focal plane of a third viewing direction. All telescopes are accommodated on a common optical bench of the same material, and a basic angle monitoring device tracks any variations in the relative viewing directions of the astrometric fields.

measurement. The main focal plane assembly employs CCD technology, with about 250 CCDs and accompanying video chains per focal plane, a pixel size 9 um along scan, TDI (time-delayed integration) operation, and an integration time of -0.9 s per CCD; (b) an integrated radial velocity spectrometer and photometric instrument, comprising an all-reflective three-mirror telescope of aperture 0.75 x 0.70 m2. The field of view is separated into a dedicated sky mapper, the radial velocity spectrometer, and a medium-band photometer. Both instrument focal planes are based on CCD technology operating in TDI mode; (c) the opto-mechanical-thermal assembly comprising: (i) a single structural torus supporting all mirrors and focal planes, employing SiC for both mirrors and structure. There is a symmetrical configuration for the two astrometric viewing directions, with the spectrometric telescope accommodated within the same structure, between the two astrometric viewing directions; (ii) a deployable Sun shield to avoid direct Sun illumination and rotating shadows on the payload module, combined with the Solar array assembly; (iii) control of the heat injection from the service module into the payload module, and control of the focal plane

M.A.C. Perryman: GAIA: An Introduction to the Project

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assembly power dissipation in order to provide an ultra-stable internal thermal environment; (iv) an alignment mechanism on the secondary mirror for each astrometric instrument, with micron-level positional accuracy and 200 //m range, to correct for telescope aberration and mirror misalignment at the beginning of life; (v) a permanent monitoring of the basic angle, but without active control on board. The accuracy goal is to reach a 10 uas rms positional accuracy for stars of magnitude V — 15 mag. For fainter magnitudes, the accuracy falls to about 20-40 //as at V = 17-18 mag, and to 100-200 //as at V = 20 mag, entirely due to photon statistics. For V < 15 mag, higher accuracy is achieved, but will be limited by systematic effects at about 3—4 //as for V < 10—11 mag. Raw data representing the star profile along scan must be sent to ground. An integral objective of the mission is to provide the sixth astrometric parameter, radial velocity, by measuring the Doppler shift of selected spectral lines. Colour information is to be acquired for all observed objects, primarily to allow astrophysical analyses, though calibration of the instrument's chromatic dependence is a key secondary consideration. The astrometric accuracy can be separated into two independent terms, the random part induced by photo-electron statistics on the localisation process accuracy, and a bias error which is independent of the number of collected photons. The random part decreases in an ideal system as JV~ 0.5 , where N is the number of detected electrons per star; the bias part is independent of N, represents the ultimate capability of the system for bright stars, is limited by payload stability on timescales shorter than those which can be self-calibrated, i.e. shorter than about 5 hours. GAIA will operate through continuous sky scanning, this mode being optimally suited for a global, survey-type mission with very many targets, and being of proven validity from Hipparcos. The satellite scans the sky according to a predefined pattern in which the axis of rotation (perpendicular to the three viewing directions) is kept at a nominally fixed angle £ from the Sun, describing a precessional motion about the Solar direction at constant speed with respect to the stars. This angle is optimised against satellite Sun shield demands, parallax accuracy, and scanning law. Resulting satellite pointing performances are determined from operational and scientific processing requirements on ground. A mission length of 5 years is adopted for the satellite design lifetime, which starts at launcher separation and includes the transfer phase and all provisions related to system, satellite or ground segment dead time or outage. A lifetime of 6 years has been used for the sizing of all consumables. 4.2

Optical Design

The astrometric telescopes have a long focal length, necessary for oversampling the individual images. A pixel size of 9 um in the along-scan direction was selected, with the 50 m focal length allowing a 6-pixel sampling of the diffraction image along scan at 600 nm. The resulting optical system is very compact, fitting into a volume 1.8 m high, and within a mechanical structure adapted to the Ariane 5

14

GAIA: A European Space Project

Fig. 2. Operating mode for the astrometric field CCDs. The location of the star is known from the astrometric sky mapper, combined with the satellite attitude, a window is selected around the star in order to minimise the resulting read-out noise of the relevant pixels.

launcher. Deployable payload elements have been avoided. System optimisation yields a suitable full pupil of 1.7 x 0.7 m2 area with a rectangular shape. Optical performances which have been optimised are the image quality, characterised by the wave-front error, and the along-scan distortion, avoiding at the same time a curved focal plane in order to facilitate CCD positioning and mechanical complexity. The optical configuration is derived from a three-mirror anastigmatic design with an intermediate image. The three mirrors have aspheric surfaces with limited high-order terms, and each of them is a part of a rotationally symmetric surface. The aperture shapes are rectangular and decentered, while each mirror is slightly tilted and decentered.

M.A.C. Ferryman: GAIA: An Introduction to the Project

4.3

15

Astrometric Focal Plane

The focal plane contains a set of CCDs operating in TDI (time-delayed integration) mode, scanning at the same velocity as the spacecraft scanning velocity and thus integrating the stellar images until they are transferred to the serial register for read out. Three functions are assigned to the focal plane system: (i) the astrometric sky mapper; (ii) the astrometric field, devoted to the astrometric measurements; (iii) the broad band photometer, which provides broad-band photometric measurements for each object. The same elementary CCD is used for the entire focal plane, with minor differences in the operating modes depending on the assigned functions. The astrometric sky mapper detects objects entering the field of view, and communicates details of the star transit to the subsequent astrometric and broad-band photometric fields. Three CCD strips provide (sequentially) a detection region for bright stars, a region which is read out completely to detect all objects crossing the field, and a third region which reads out detected objects in a windowed mode, to reduce read-out noise (and hence to improve the signal-to-noise ratio of the detection process), and to confirm objects provisionally detected in the previous CCD strips, in the presence of, e.g., cosmic rays. Simulations have shown that algorithms such as those developed for the analysis of crowded photometric fields (e.g. [29]) can be adapted to the problem of on-board detection, yielding good detection probabilities to 20 mag, with low spurious detection rates. Passages of stars across the sky mapper yield the instantaneous satellite spin rate, and allow the prediction of the individual star transits across the main astrometric field with adequate precision for the foreseen windowing mode. The size of the astrometric field is optimised at system level to achieve the specified accuracy, with a field of 0.5 x 0.66 degrees. The size of the individual CCD is a compromise between manufacturing yield, distortion, and integration time constraints. The pixel size is a compromise between manufacturing feasibility, detection performances (QE and MTF: Modulation Transfer Function), and charge-handling capacity: a dimension of 9 /um in the along-scan direction provides full sampling of the diffraction image, and a size of 27 yum in the across-scan direction is compatible with the size of the dimensions of the point spread function and cross scan image motion. In addition, it provides space for implementation of special features for the CCD (e.g. pixel anti-blooming drain) and provides improved charge-handling capacity. Quantitative calculations have demonstrated that the pixel size, TDI smearing, pixel sampling, and point spread function are all matched to system requirements. The CCDs are slightly rotated in the focal plane and are individually sequenced in order to compensate for the telescope optical distortion. Cross-scan binning of 8 pixels is implemented in the serial register for improvement of the signal-to-noise ratio. At the apparent magnitude and integration time limits appropriate for GAIA most of the pixel data do not include any useful information. There is a clear trade-off between reading too many pixels, with associated higher read-noise and telemetry costs, and reading too few, with associated lost science costs.

16

GAIA: A European Space Project

This contributes to the choice of on-board real-time detection, with definition of a window around each source which has sufficient signal to be studiable, and determination of the effective sensitivity limit to be that which saturates the telemetry, and which provides a viable lower signal. Combining all these constraints sets the limit near V = 20 mag, resulting in an estimated number of somewhat over one billion targets. The broad-band photometric field provides multi-colour, multi-epoch photometric measurements for each object observed in the astrometric field, for chromatic correction and astrophysical analysis. Four photometric bands are implemented within each instrument. 4.4

Spectrometric Instrument

A dedicated telescope, with a rectangular entrance pupil of 0.75 x 0.70 m2, feeds both the radial velocity spectrometer and the medium-band photometer: the overall field of view is split into a central 1° x 1° devoted to the radial velocity measurements, and two outer 1° x 1° regions devoted to medium-band photometry. The telescope is a 3-mirror standard anastigmatic of focal length 4.17 m. The mirror surfaces are coaxial conies. An all-reflective design allows a wide spectral bandwidth for photometry. The image quality at telescope focus allows the use of 10 x 10 //m2 pixels within the photometric field, corresponding to a spatial resolution of 0.5 arcsec. The radial velocity spectrometer acquires spectra of all sufficiently bright sources, and is based on a slit-less spectrograph comprising a collimator, transmission grating plus prism (allowing TDI operation over the entire field of view) and an imager, working at unit magnification. The two lens assemblies (collimating and focusing) are identical, compensating odd aberrations including coma and distortion. The dispersion direction is perpendicular to scan direction. The array covers a field height of 1°. Each 20 x 20 //m2 pixel corresponds to an angular sampling of 1 arcsec and a spectral sampling of approximately 0.075 nm/pixel. The focal plane consists of three CCDs mechanically butted together, each operated in TDI mode with its own sequencing. 5

Spacecraft System

The spacecraft and orbit are characterised as follows: • orbit: Lissajous-type, eclipse-free, around L2 point of Sun/Earth system; 220 240 day transfer orbit; • sky scanning: revolving scanning with scan rate = 120 arcsec s""1, precession period = 76 days; • spacecraft: 3-axis stabilized; autonomous propulsion system for transfer orbit; electrical (FEEP) thrusters for operational attitude control; 6 deployable Solar panels, integrated with multi-layer insulation to form the Sun shield;

M.A.C. Ferryman: GAIA: An Introduction to the Project

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• science data rate: 1 Mbps sustained, 3 Mbps on down-link, using electronically steerable high-gain phased array antenna; • launch mass: 3137 kg (payload = 803 kg, service module = 893 kg, system margin (20%) = 339 kg, fuel = 1010 kg, launch adaptor = 92 kg); • power: 2569 W (payload = 1528 W, service module = 641 W, harness losses = 76 W, contingency (10%) = 224 W); • payload dimensions: diameter = 4.2 m, height = 2.1 m; • service module dimensions: diameter = 4.2 m (stowed)/8.5 m (deployed), height = 0.8 m; • launcher: Ariane 5, dual launch; • lifetime: 5 years design lifetime (4 years observation time); 6 years extended lifetime. 6 6.1

Accuracy Assessment Astrometric Accuracy

There are three main components involved in the improved performance of GAIA compared with Hipparcos. The larger optics provide a smaller diffraction pattern and a significantly larger collecting area; the improved quantum efficiency and bandwidth of the detector (CCD rather than photocathode) leads to improved photon statistics; and use of CCDs provides an important multiplexing advantage. The GAIA astrometric wavelength band G is fixed such that G ~ V for unreddened AOV stars. The approximate transformation from (V, V — /) to G can be expressed in the form:

which is valid (to ±0.1 mag) at least for -0.4 < V-I < 6. For -0.4 < V-I < 1.4 we have the convenient relation G — V — 0.0 ± 0.1 mag. Many models of the Galaxy are available, from simplified star-count models to complex evolutionary models. For present purposes we adopt a star-count and kinematic model (updated from [30]), probably satisfactory within 25%, and adequate until GAIA provides better data. The biggest uncertainty is perhaps the distribution of interstellar extinction. The model predicts that ~1.1 billion stars will be observable, corresponding to 1-2 per cent of the total stellar content of the Galaxy. The estimated number of stars according to the three Galactic populations (disk, thick disk and spheroid) shows that the main scientific goal, a representative census of the Galaxy, can be achieved. In addition, there are many rare objects of high astrophysical interest for which star count predictions cannot be obtained reliably from a Galaxy model. Details include globular clusters, double and multiple stars, high-density areas, and galaxies.

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GAIA: A European Space Project

The basic accuracy estimation proceeds from the details of image formation, taking into account the detector signal, precision of the location estimator, instrument stability and calibration errors, and propagation from one-dimensional (single-epoch) measurement errors to the final astrometric accuracy, estimated as:

where TV; = 2 is the number of instruments, r = LJ1/47T the (average) total time available per object and instrument, r\ is the integration time per CCD (s), L is the effective mission length (s), a^ is the angular precision in the scan direction from one CCD crossing (rad), ac&\ is the accuracy of the astrometric calibration, and pdet(G) the detection probability as function of magnitude. The factor g& relates the scanning geometry to the determination of the astrometric parameters. Numerical simulations of the scanning law are used to determine the mean values of g& for given mission parameters, and their large-scale variations with ecliptic latitude. The estimation of pdet is a complex problem, since it depends on many factors besides the brightness of the star. For the accuracy analysis an estimation of pdet as function of N, the total number of photoelectrons in the stellar image, was made by means of dedicated simulations. An explicit error margin of 20 per cent is added on the astrometric standard errors resulting from this analysis. For the faintest stars the accuracy estimates take into account that a given star may not be observed in all transits. They include the factor pdet(G}~1/2, where pdet(G) is the detection probability as a function of the G magnitude obtained from simulating star detection in the astrometric sky mapper using the robust APM algorithm. Since, by construction, the G magnitude yields a rather uniform accuracy as a function of spectral type, useful mean accuracies can be derived from a straight mean of the detailed calculations, and are given in Table 1. An approximate analytical fit to the tabular values for the parallax accuracy, (TTT, which also takes into account the slight colour dependence (due to the widening of the point spread function at longer wavelengths) is:

where z = 100.4^G 15). For the position and proper motions errors, <JQ and <7M, the following mean relations can be used:

The expected standard errors vary somewhat over the sky as a result of the scanning law. The number of stars whose distances can be determined to a certain relative accuracy can be estimated using a Galaxy model. For a given apparent magnitude and direction, the model provides the distribution of stars along the line of sight (in

M.A.C. Perryman: GAIA: An Introduction to the Project

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Table 1. Mean accuracy in parallax (0v), position (at mid-epoch, <JQ] and proper motion (
10

11

12

13

14

15

16

17

18

19

20

21

UTT (/Zas)

4 3 3

4 3 3

4 3 3

5 4 4

7 6 5

11 9 8

17 15 13

27 23 20

45 39 34

80 70 60

160 140 120

500 440 380

a0 (//as) CTM (uas yr"1)

a small solid angle), as well as their distribution in colour index at each distance. It is then simple to compute the fraction of stars having relative parallax accuracy below a certain limit R. Very good distance information (R = 0.1 or better) will be obtained for virtually all stars brighter than V = 15 and for significant fractions down to much fainter magnitudes, e.g. 10-50 per cent at V ~ 18, depending on direction. For G < 15 mag, more than 85 per cent of the stars will have tangential velocity errors smaller than 5 km s"1, and 75 per cent will be smaller than 2 km s-1. These figures worsen if all the stars with G < 20 mag are considered, but even in this case, for galactic latitudes higher than 5 — 10°, 40 per cent of the stars observed by GAIA will have tangential velocities accurate to better than 10 km s"1. 6.2

Photometric Accuracy

The photometric analysis cannot be separated from the astrometric analysis. The basic model for the pixel or sample values must be fitted simultaneously for the centroid coordinates £o, ??o and the photometric quantities b and N. Moreover, this fitting must be done globally, by considering together all the transits of the object throughout the mission, in which the centroid positions are constrained by the appropriate astrometric model. This procedure is referred to as "global PSF fitting". A simpler procedure, "aperture photometry", is used for the photometric accuracy estimation. Simple calculations for single-epoch accuracies including photon noise, readnoise arid sky background noise have been adopted, and corrected with an error margin of 20 per cent. The formal photometric precision reached at the end of the mission, typically by averaging n0bs ~ 50-100 observations, is on the level of one or a few millimag for the bright stars (~12 mag). Can this be calibrated to reach this accuracy? Photometric calibration of the CCD zero points can be achieved from standards. The photometric consistency can be derived from repeated observations of all non-variable stars, and assured to a very high degree. Photometric observations in a number of colour bands will be obtained for all stars detected. A quick photometric reduction will be carried out for each field crossing, providing rapid epoch photometry results for scientifically timecritical phenomena such as the detection of supernovae, burst, lensing, or other

20

GAIA: A European Space Project

Fig. 3. Left: errors on Teff derived from C47-57 (continuous line), C57-75 (dotted line) and C75-89 (dashed line) indices, for M dwarfs with Teff = 3500 K. Solid symbols correspond to the errors for a single observation, open symbols to the mission-average (100 observations). Right: errors on [Ti/H] derived from the TiO index, for Teff = 3500 K M dwarfs, for single observations (filled symbols) and for mission averages (open symbols).

transient events. Improved photometric reduction can be obtained later in the mission, when accurate satellite attitude, CCD calibration data, and astrometric information for each star become available. This accuracy has been simulated using the complete GAIA image simulation and the APM photometry package. The two astrometric telescopes provide photometry in a wide spectral band defined by the CCD sensitivity. This G band photometry from one single measure has a standard error of typically 0.01 mag for G ~ 18.5 mag. The two astrometric telescopes also provide broad-band photometry in four bands. The magnitudes resulting from averaging 67 observations obtained during a mission time of 4 years will have a precision of about 0.02 mag in the F63B band at V ~ 20.0 mag for all spectral types. The spectrometric telescope will collect photometry in 11 bands. The resulting average magnitudes will have a precision of 0.01 mag in the F57 band at V — 19 mag, and 0.02 mag in the F33 band for an unreddened G2V star. The photometric accuracies as a function of colour index can be converted into accuracies on astrophysical parameters. For example, Figure 3 (left) shows the uncertainty in effective temperature for G- and M-type dwarfs (Teff = 5750 and 3500 K respectively) as a function of magnitude, for single transit and missionaverage photometry, while Figure 3 (right) shows the uncertainty in [Ti/H] for M dwarfs. 6.3

Radial Velocity Accuracy

The radial velocity accuracy assessment has been derived from extensive numerical simulations, utilising observed spectra. Template spectra covering a wide range of astrophysical properties will be required. Global velocity zero points can be

M.A.C. Perryman: GAIA: An Introduction to the Project

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derived from the system geometry and astrometric positions of the target stars. The required accuracy is 1/40 pixel for 1 km s~l. Performance has been studied using simulations as well as real observations of the selected spectral region for a variety of stars. Simulations were performed by producing synthetic spectra with different atmospheric parameters in the Ca II region, degrading them to the resolution and signal-to-noise ratio of a single GAIA observation, and then determining the radial velocity by cross-correlation. The photon budget was computed from the basic instrument design, and in addition to Poisson noise both the total readout noise (3 e~) and the sky background (normalized to a Solar spectrum with V = 22.5 arcsec"2) were considered. For cool stars, the mission-aver age velocity accuracy is av ~ 5 km s"1 at V — 18, while for hot stars the performance is limited to crv ~ 10 km s"1 at V = 16 mag. 6.4

Summary of Measurement Performances

In summary, GAlA's measurement capabilities can be summarised as follows: Catalogue: ~1 billion stars; 0.34 x 106 to V = 10 mag; 26 x 106 to V = 15 mag; 250 x 106 to V = 18 mag; 1000 x 106 to V = 20 mag; completeness to about 20 mag. Sky density: mean density ~25000 stars deg~ 2 ; maximum density 6 2 ~3 x 10 stars deg~ . Median parallax errors: 4 //as at 10 mag; 11 //as at 15 mag; 160 //as at 20 mag. Distance accuracies: 2 million better than 1 per cent; 50 million better than 2 per cent; 110 million better than 5 per cent; 220 million better than 10 per cent. Tangential velocity accuracies: 40 million better than 0.5 km s"1; 80 million better than 1 km s"1; 200 million better than 3 km s""1; 300 million better than 5 km s"1: 440 million better than 10 km s"1. Radial velocity accuracies: 1 — 10 km s"1 to V = 16 — 17 mag. Photometry: to V = 20 mag in 4 broad and 11 medium bands. 7

Data Analysis

The total amount of (compressed) science data generated in the course of the fiveyear mission is about 2 x 1013 bytes (20 TB). Most of this consists of CCD raw or binned pixel values with associated identification tags. The data analysis aims to "explain" these values in terms of astronomical objects and their characteristics. In principle the analysis is done by adjusting the object, attitude and instrument models until a satisfactory agreement is found between predicted and observed data (dashed lines in Fig. 4). Successful implementation of the data analysis task will require expert knowledge from several different fields of astronomy, mathematics and computer science to be merged in a single, highly efficient system [31]. The global astrometric reductions must be formulated in a fully general relativistic framework, including post-post-Newtonian effects of the spherical Sun at the 1 //as level, as well as including corrections due to oblateness and angular momentum of Solar System bodies.

22

GAIA: A European Space Project

Fig. 4. Model of CCD data interrelations for an astronomical object. In principle, the data analysis aims to provide the "best" representation of the observed data in terms of the object model, satellite attitude and instrument calibration. Certain data and models can, from the viewpoint of the data analysis, be regarded as "given"; in the figure these are represented by the satellite orbit (in the barycentric reference system) and the relativistic model used to compute celestial directions. Other model data are adjusted to fit the observations (dashed lines). Processing these vast amounts of data will require highly automated and efficient numerical methods. This is particularly critical for the image centroiding of the elementary astrometric and photometric observation in the astrometric instruments, and the corresponding analysis of spectral data in the spectrometric instrument. Accurate and efficient estimation of the centroid coordinate based on the noisy CCD samples is crucial for the astrometric performance. Simulations indicate that 6 samples approximately centred on the peak can be read out from the CCD. The centroiding, as well as the magnitude estimation, must be based on these six values. Results of a large number of Monte Carlo experiments, using a maximumlikelihood estimator as the centroiding algorithm, indicate that a rather simple maximum-likelihood algorithm performs extremely well under these idealized conditions, and that six samples is sufficient to determine the centroid accurately. Much work remains to extend the analysis to more complex cases, including in particular overlapping stellar images. A preliminary photometric analysis, for discovery of variables, supernovae, etc, can be carried out using standard photometric techniques immediately after data delivery to the ground. In addition, more detailed modelling of the local background and structure in the vicinity of each target using all the mission data in all the passbands will be required. A final end-of-mission re-analysis may benefit from the astrometric determination of the image centroids, locating a well-calibrated point spread function for photometric analysis. Studies of these photometric reductions have begun. The high-resolution (radial velocity) spectrometer will produce spectra for about a hundred million stars, and multi-epoch, multi-band photometry will be obtained for about one billion stars. The analysis of such large numbers of spectra

M.A.C. Perryman: GAIA: An Introduction to the Project

23

and photometric measurements needs to be performed in a fully automated fashion, with no manual intervention. Automatic determination of (at least) the surface temperature Teff, the metallicity [M/H], and the relative a element abundance [cK/Fe] is necessary; determination of logg is, given the availability of parallaxes for most stars, of lesser importance. A fully automated system for the derivation of astrophysical parameters from the large number of spectra and magnitudes collected by GAIA, using all the available information for each star, has been studied, showing the feasibility of an approach based on the use of neural networks. In the classification system foreseen, spectra and photometric measurements will be sent to an "initial classifier", to sort objects into stellar and non-stellar. Specialist networks then treat each class. For example, stellar data sets are passed to an "automated stellar parameterization" sub-package. It is the physical parameters of stars which are really of interest; therefore the proposed system aims to derive physical parameters directly from a stellar spectrum and photometry. Detailed simulations of the automated stellar parameterization system have been completed using a feed-forward neural network operating on the entire set of spectral and photometric measurements. In such a system, the derived values for the stellar parameters are naturally linked to the models used to train the network. Given the extreme rapidity of neural networks, when stellar atmosphere models are improved, re-classification of the entire data set can be done extremely quickly: an archive of 108 spectra or photometric measurements could be reclassified in about a day with the present-day computing power of a scientific workstation. The computational complexity of the data analysis arises not just from the amount of data to be processed, but even more from the intricate relationships between the different pieces of information gathered by the various instruments throughout the mission. It is difficult to assess the magnitude of the data analysis problem in terms of processing requirements. Certain basic algorithms that have to be applied to large data sets can be translated into a minimum required number of floating-point operations. Various estimates suggest of order 1019 floating-point operations, indicating that very serious attention must be given to the implementation of the data analysis, and that this effort must start very early. Observations of each object are distributed throughout the mission, so that calibrations and analysis must be feasible both in the time-domain and in the object domain. Flexibility and interaction is needed to cope with special objects, while calibrations must be protected from unintentional modification. Object Oriented (OO) methodologies for data modeling, storage and processing are ideal for meeting the challenges faced by GAIA. 8

GAIA and Other Space Missions

The scientific capabilities and goals of GAIA and other proposed or approved space astrometric missions are summarised in Table 2. GAIA is a survey mission, essential for statistical analysis of the unknown, with broad applications to the Solar System, galaxies, large-scale structure, and primarily Galactic structure and

GAIA: A European Space Project

24

Table 2. Summary of the capabilities of Hipparcos and GAIA, along with those of the DIVA (Germany) and SIM and FAME (NASA) astrometric space missions. Numbers of stars are indicative; in the case of SIM they are distributed amongst grid stars and more general scientific targets. Typical accuracies are given according to magnitude where appropriate. Mission

Launch

No. of stars

Mag limit

Accuracy (mas) (mag)

Hipparcos DIVA

1989 2004

120 000 40 million

12

1

10

15

0.2 5

9 15

FAME

2004

40 million

15

9 15

SIM

2009 2012

10000 1 billion

20

0.050 0.300 0.003 0.003 0.010 0.200

GAIA

20

20 12 15 20

evolution. SIM (Space Interferometry Mission, [32]) is an interferometer, ideal for precise measurements of a small number of carefully pre-selected targets of specific scientific interest. The SIM target selection is yet to happen, but will be focussed towards searches for low-mass planets around a few nearby stars, calibration of the distance scale, and detailed studies of known micro-lensing events. FAME (Full-Sky Astrometric Mapping Explorer; [33]), selected by NASA in the MIDEX competition in 1999, and DIVA (Double Interferometer for Visual Astrometry; [34]), a small German astronomy satellite planned for launch in 2004, are essentially successors to Hipparcos, with an extension of limiting sensitivity, sample size and accuracy (statistical weight) by a factor of order 100 in each. DIVA and FAME will both provide an excellent reference frame, substantially improve calibration of the distance scale and the main phases of stellar evolutionary astrophysics, and map the Solar Neighbourhood to much improved precision. The difference between GAIA and these two missions is one of scale and comprehensiveness. GAIA exceeds these two missions in scale by a further factor of order 100, allowing study of the entire Galaxy, and only GAIA will provide photometric and radial velocity measurements as crucial astrophysical diagnostics. 9

Conclusion

GAIA will create an extraordinarily precise three-dimensional map of about one billion stars throughout our Galaxy and the Local group. It will map their space motions, which encode the origin and subsequent evolution of the Galaxy, and the distribution of dark matter. Through on-board photometry, it will provide the detailed physical properties of each star observed: luminosity, temperature,

M.A.C. Perryman: GAIA: An Introduction to the Project

25

gravity, and elemental composition, which encode the star formation and chemical enrichment history of the Galaxy. Radial velocity measurements on board will complete the kinematic information for a significant fraction of the objects observed. Through continuous sky scanning, the satellite will repeatedly measure positions and colours of all objects down to V = 20 mag. On-board object detection ensures a complete census, including variable stars and quasars, supernovae, and minor planets. It also circumvents costly pre-launch target selection activities. Final accuracies of 10 microarcsec at 15 mag will provide distances accurate to 10 per cent as far as the Galactic Centre. Stellar motions will be measured even in the Andromeda galaxy. GAIA's main scientific objective is to clarify the origin and history of our Galaxy, from a quantitative census of the stellar populations. It will advance fundamental questions such as when the stars in the Milky Way formed, when and how the Milky Way was assembled, and the distribution of dark matter in our Galaxy. In so doing, it will pinpoint exotic objects in substantial numbers: many thousands of extra-Solar planets will be discovered, and their detailed orbits determined; tens of thousands of brown dwarfs and white dwarfs will be identified; rare stages of stellar evolution will be quantified; some 100000 extragalactic supernovae will be discovered, and details communicated for follow-up groundbased observations; Solar System studies will receive a massive impetus through the detection of many tens of thousands of new minor planets; inner Trojans and even new trans-Neptunian objects, including Plutinos, may be discovered. GAIA will follow the bending of star light by the Sun and major planets over the entire celestial sphere, and therefore directly observe the structure of space-time-the accuracy of its measurement of general relativistic light bending may reveal the long-sought scalar correction to its tensor form. The PPN parameters 7 and /?, and the Solar quadrupole moment J2, will be determined with unprecedented precision. New constraints on the rate of change of the gravitational constant, G*, and on gravitational wave energy over a certain frequency range, will be obtained. GAIA is timely as it complements other major space and ground initiatives. Understanding and exploration of the early Universe, through microwave background studies (Planck) and direct observations of high-redshift galaxies (NGST, FIRST, ALMA), are complemented by theoretical advances in understanding the growth of structure from the early Universe up to galaxy formation. Serious further advances require a detailed understanding of a "typical" galaxy, to test the physics and assumptions in the models. Our Galaxy, a typical example of those luminous spirals which dominate the luminosity of the Universe, uniquely provides such a template. This introduction to the GAIA project is a summary of the paper [1] authored by the members of the GAIA Science Team for the Concept and Technology Study: M.A.C. Ferryman, K.S. de Boer, G. Gilmore, E. H0g, M.G. Lattanzi, L. Lindegren, X. Luri, F. Mignard, O. Pace and P.T. de Zeeuw.

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GAIA: A European Space Project

References [1] Perryman, M. A. C., de Boer, K. S., Gilmore, G., et al, 2001, A&A, 369, 339 [2] ESA 2000, GAIA: Composition, Formation and Evolution of the Galaxy, Technical Report ESA-SCI(2000)4 (scientific case on-line at http://astro.estec.esa.nl/GAIA) [3] Gilmore, G., Wyse, R. F. G., Kuijken, K., 1989, ARA&A, 27, 555 [4] Majewski, S., 1993, ARA&A, 31, 575 [5] Ibata, R. A., Wyse, R. F. G., Gilmore, G., Irwin, M., Suntzeff, N., 1997, AJ, 113, 634 [6] Wyse, R. F. G., Gilmore, G., Franx, M., 1997, ARA&A, 35, 637 [7] de Zeeuw, P. T., 1999, in B. K. Gibson, T. S. Axelrod, M. E. Putman (eds.), The Third Stromlo Symposium: The Galactic Halo: Bright Stars and Dark Matter, ASP Conf. Ser. 165 (Astronomical Society of the Pacific, San Francisco), 515 [8] Hernandez, X., Gilmore, G., Valls-Gabaud, D., 2000, MNRAS, 316, 605 [9] Freeman, K. C., 1993, in S. Majewksi (ed.), Galaxy Evolution: The Milky Way Perspective, ASP Conf. Ser. 49 (Astronomical Society of the Pacific, San Francisco), 125 [10] Gilmore, G., 1999, Baltic Astron., 8, 203 [11] Lebreton, Y., 2000, ARA&A, 38, 35 [12] Paczyriski, B., 1997, in R. Ferlet, J. P. Maillard, B. Raban (eds.), Proc. 12th ZAP Astrophysics Coll. 1996: Variable Stars and Astrophysical Returns from Microlensing Surveys (Editions Frontieres), 357 [13] Eyer, L., Cuypers, J., 2000, in L. Szabados, D. W. Kurtz (eds.), The Impact of LargeScale Surveys on Pulsating Star Research, ASP Conf. Ser. 203 (Astronomical Society of the Pacific, San Francisco), 71 [14] Soderhjelm, S., 1999, A&A, 341, 121 [15] Marcy, G. W., Butler, R. P., 1998, in R. A. Donahue. J. A. Bookbinder (eds.), Cool Stars, Stellar Systems and the Sun; Proceedings of the 10th Cambridge Workshop, ASP Conf. Series 154 (San Francisco), 9 [16] Ferryman, M. A. C., 2000, Rep. Prog. Phys., 63, 1209 [17] Lattanzi, M. G., Spagna, A., Sozzetti, A., Casertano, S., 2000, MNRAS, 317, 211 [18] Vaccari, M., 2000, GAIA Galaxy Survey, Master Thesis, University of Padova [19] H0g, E., Fabricius, C., Makarov, V. V., 1999b, Baltic Astron., 8, 233 [20] Feissel, M., Mignard, F., 1998, A&A, 331, L33 [21] Johnston, K. J., de Vegt, C., 1999, ARA&A, 37, 97 [22] Mignard, F., 1999, in D. Egret, A. Heck (eds.), Harmonizing Cosmic Distance Scales in a Post-Hipparcos Era, ASP Conf. Ser. 167 (Astronomical Society of the Pacific, San Francisco), 44 [23] Gilmore, G., de Boer, K. S., Favata, F., et al., 2000, in J. B. Brekinridge, P. Jakobsen (eds.), UV, Optical and IR Space Telescopes and Instruments, SPIE 4013 [24] Munari, U., 1999a, Baltic Astron., 8, 73 [25] Straizys, V., 1999, Baltic Astron., 8, 109 [26] H0g, E., Fabricius, C., Knude, J., Makarov, V. V., 1999a. Baltic Astron., 8, 25 [27] Munari, U., 1999b, Baltic Astron., 8, 123 [28] Merat, P., Safa, F., Camus, J. P., Pace, O., Perryman, M. A. C., 1999, Baltic Astron., 8, 1 [29] Irwin, M. J., 1985, MNRAS, 214, 575 [30] Chen, B., 1997, ApJ, 491, 181 [31] O'Mullane, W., Lindegren, L., 1999, Baltic Astron., 8, 57 [32] Boden, A., Unwin, S., Shao, M., 1997, in M. A. C. Ferryman, P. L. Bernacca (eds.), Hipparcos Venice 97, ESA SP-402 (ESA, Noordwijk), 789 [33] Triebes, K. J., Gilliam, L., Hilby, T., et al, 2000, SPIE 4013, 482 [34] Roser, S., Bastian, U., de Boer, K. S., et al, 1997, in M. A. C. Perryman, P. L. Bernacca (eds.), Hipparcos Venice 97, ESA SP-402 (ESA, Noordwijk), 777

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

PHOTOMETRIC AND IMAGING PERFORMANCE E. H0g1 Abstract. Three topics within GAIA photometry have been selected for discussion here. (1) The sampling scheme of the CCDs has been tuned to serve the various purposes: detection of stars, astrometry, broad- and medium-band photometry, and imaging of a small area around each detected star, but the tuning may not yet be optimal. (2) The calibration of CCD sensitivity is critical since we aim for millimagnitude accuracy, the spikes of the diffraction image are suited for an accurate calibration of the magnitude scale, and for extending the range of astrometry and photometry to very bright stars. (3) Finally the various photometric filter systems are illustrated.

1

Introduction

The multi-colour photometry with GAIA shall serve astrometric and astrophysical purposes. The broad-band photometry in four or five bands of wavelength in the focal planes of the two Astro telescopes shall especially give the spectral energy distribution of each star or quasar with an accuracy sufficient for the correction of chromaticity errors in the astrometry (see [1]). This photometry is also useful for astrophysical purposes. Astrophysical information for most of the one billion objects observed by GAIA would be missing unless it is provided by GAIA. Therefore all objects will obtain broad-band photometry in Astro and mediumband photometry in the Spectro telescope, cf. the bands in Section 4. An overview of GAIA photometry is given in various sections of [2] and [3], and some was presented at this meeting. The following sections go in more detail on some topics and introduce new possibilities, but they are basically consistent with these texts. Three topics of GAIA photometry have been selected here: the sampling scheme of the CCDs in Section 2, the photometric calibration and measurement of bright stars and double stars in Section 3, and an overview of the relevant photometric systems in Section 4. A fourth topic has been discussed recently in [4]: multi-colour photometry with GAIA of the diffuse sky background. 1

Copenhagen University Observatory, Juliane Maries Vej 30, DK 2100 Copenhagen 0. Denmark © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002002

28 2

GAIA: A European Space Project Sampling and Imaging

The CCDs of GAIA integrate the light from stars and background in time delayed integration, TDI mode, synchronized with the scanning motion of the satellite. At the angular rotation speed of 120 arcsec/s this results in 0.86 s integration time per CCD in the two Astro telescope fields and about 3 s per CCD in the Spectro field, cf. Section 3 of [2] for details. An average star will cross one of the Astro fields 67 times during a five year mission and the Spectro field 100 times. All point sources, mostly stars, are detected if they are brighter than a given limit using the read out from the whole area of the first CCD in the Astro and Spectro telescopes, i.e. respectively the first Astro sky mapper, ASM1 (not shown in Fig. 1) and the Spectro sky mapper, SSM. In the following CCDs only a window or patch centred on the position of the detected star is read out for analysis onboard and/or transmission to ground. This means that about 99.9 per cent of the pixels can be skipped since most of the sky contains no stars, even with a detection limit of G = 20 mag. This gives a lower read out noise and much less data to be transmitted to ground. The G magnitude is measured with no filter so that the whole CCD sensitivity range is utilized. This applies for all CCDs except those in the broad-band photometer, BBP, and the medium-band photometer, MBP, and the G magnitude is nearly equal to the V magnitude for most stars, cf. Section 6.4.2 of [2]. The charge content of the pixels is read out from the serial register of the CCD in samples where the charges of several pixels have been added or "binned". The sampling or binning in the GAIA telescopes is shown in Figure 1. The sampling is identical to that in Figure 3.7 of [2], except that a smaller sample is proposed in Astro-2 for multi-colour photometry of galaxies according to [5], and an error in the drawing of the SSM has been corrected. The patch of 25 samples from the third Astro sky mapper, ASM3, covers an area somewhat larger than the Airy disk. About 130 such patches for each detected star will result from a five year mission. Analysed together they will provide a mapping or imaging in a field of 1 arcsec diameter as indicated in the lower right of the figure. Imaging in an area about 2 arcsec diameter can be obtained with the patches from the CCD # 17 in the astrometric field, AF17. This imaging is obtained in white light, i.e. the whole sensitivity range of the CCD. The final analysis can assume that the positions of patches on the sky is known with sub-milliarcsec accuracy since a global astrometric and photometric analysis will be carried out, cf. Section 3.2. This is the reason why stars as faint as G = 23 mag can be detected, which is important because they could disturb the photometry and astrometry of the central star. When these stars are detected they can be taken into account either for a correction or rejection of the main star. All these stars will obtain broad-band photometry with the patches from Astro-1 and Astro-2. It is noted that the 16 samples in Astro-1 BBP1-4, the four CCDs for broadband photometry, are read out with 8 pixels length across scan as indicated in

E. H0g: Photometric and Imaging Performance

29

the figure. Before transmission the outer 10 samples are reduced to 4 samples by numerical addition of 2 or 3 samples, cf. Section 3.2. The samples in the Spectro telescope are shown at lower left. All pixels in the CCD of the SSM are read out and the samples are used for the detection. The 14 x 9 samples in a patch centred on the detected star are reduced to the 14 x 3 samples by additions as indicated in the figure. The 100 patches per star during the mission will be used for an imaging of an area of 7 arcsec diameter. Again, stars about G = 23 mag can be detected, and they can obtain mediumband photometry. The angular resolution will be about 0.5 arcsec, not as high as in the Astro telescopes. 2.1

Optimiza tion

The sampling shown in the figure is a compromise between the wish to get the best possible angular resolution and astrometric and photometric accuracy, and the constraints of read out noise and transmission rate. The development of the scheme during two years of the GAIA study is documented in about twenty technical reports from Copenhagen University Observatory, cited in [2]. This optimization was done mainly by simple considerations, it should be verified and possibly improved during the preparation phase of GAIA, e.g. by simulations of double and multiple stars. The mathematical formulation of the data analysis in [6] is a good starting point, though the detection of disturbing stars by means of ASM3, AF17 and SSM has not yet been implemented. An optimization on difficult cases of, e.g., very high star density, must not endanger the performance on the vast majority of objects, which are in fact single or double stars in a nearly empty sky. The difficult high-density areas cover perhaps so small a fraction of the sky that they could be observed by ground- or space-based instruments with a smaller field pointed for longer integration time. All instruments have certain limitations, even GAIA, but GAIA performs well at star densities up to 2 million stars per square degree brighter than G = 20 mag, cf. Figure 6.6 in [2]. The imaging performance on extended sources, e.g. quasars, compact galaxies, or in star forming regions deserves especial attention. An optimization of the sampling must take into account in a balanced way the whole scientific case of GAIA described in the 100 pages Section 1 of [2]. 3

Calibration of Sensitivity

The internal photometric calibration is discussed in Section 7.5 of [2] where it is shown that a calibration with sub-millimag accuracy should be possible. The calibration is not done from observations of "standard stars", i.e. stars with accurately known magnitudes and/or colour indices in some well-defined photometric system. Such standards will almost exclusively be used to define the overall zero points of the various magnitudes scales. Most of the calibration is done by means of anonymous stars, distinguished only by their (presumed, and eventually confirmed) constancy from one transit to the next, and that they are generally well-behaved,

30

GAIA: A European Space Project

Fig. 1. Sampling in the Astro and Spectro telescopes. The patches of samples are obtained from left to right, chronologically as a star crosses the field of view, but the star is at a fixed position in each patch. The sampling is identical to that in Figure 3.7 of [2], except that a smaller sample is shown here in Astro-2 for broad-band photometry of galaxies, according to the results in [5].

E. H0g: Photometric and Imaging Performance

31

e.g. not obviously double. Thus, literally millions of suitable calibration stars are available scattered over the whole sky. The transits of the same constant calibration star across two different CCDs, or along two different pixel columns on the same CCD, produces a condition equation relating to the photometric responses of the two CCDs or columns. The response of a CCD is not constant and not a linear function of the stellar flux. It varies with the position of the star on the CCD, and from one CCD to another, and it varies with time during the mission. It can also vary with the immediately preceding history, for instance if a very bright star has recently crossed the same part of the CCD, but this short-term after-effect is not discussed here. Nor is the effect of cosmic rays or blemishes. Thus, the CCD is here assumed to have a slowly varying and non-linear response. The sensitivity is essentially a one-dimensional function of the cross-scan position on the CCD since the other dimension is integrated by the TDI motion across the CCD. Defining /: observed count rate, and m: calibrated apparent magnitude, we have by definition where / is the calibration function to be determined for each band. We furthermore define j: number of the spectral band, k: number of CCD for the given spectral band, y: cross-scan coordinate on the CCD, and t: epoch of the observation. Photometric calibration then means to determine the functions g(j, k, y, t; m) and Ag(jf, m) in the equation

This requires iterations since the calibrated magnitude m appears as argument on the right hand side. Each iteration requires two steps, the first is to determine or improve the g function by use of the constant calibration stars in intervals of perhaps 1 mag size. In each of these intervals the constant stars will be used to derive the function g(j, fc, y, t; m). These functions must be derived for the central part of the stellar images and for the spikes as sampled by the patches described in the following section. The second step is to determine or improve the function Ag(j, m) by means of the spikes. The final iterated g function used in equation (3.2) will correct an observed count rate of a constant star to a magnitude which is independent of the time of observation and of where in the focal plane the observation took place. The Ag function will correct for an error of the magnitude scale. 3.1

The Spikes

The rectangular entrance pupil of the GAIA telescopes creates diffraction images of the stars with spikes which can be used in the calibration process. Circular pupils would have been unsuited for this purpose. An example of a point-spreadfunction is shown in Figure 2. We propose to use the vertical spikes for calibration

GAIA: A European Space Project

32

Fig. 2. The PSF in the Spectro telescope at 350 nm for a 40 nm (FWHM) filter (see [7]). The transverse motion of the star and the TDI smearing have been taken into account, curves of equal attenuation in [mag] are shown. The patch of 8 transmitted samples is indicated.

Table 1. Sampling in the medium-band photometer of Spectro. JVP is the number of patches per star taken for the proposed percentage of stars. Ns is the resulting number of star transits for which spikes are sampled, compared with the number of transits without spikes given in the last line. The last three columns give the approximate attenuation in the patches on the spikes at 940 nm. Attenuation G mag

Np patches

Percentage of stars

0-9 9 -14 14 -16 16 -20 12 -20

7 3 5 3 1

100 100 0.5

0.05 100

Ns

108 transits 0.1 12 0.5 0.5 without spikes: 1000

#1

#2 mag 5 7 5

5 5 -

7

#3 8

E. H0g: Photometric and Imaging Performance

33

Fig. 3. The running sum through the PSF when sampled by n x 4 pixels, versus the vertical offset of the image from the centre of the patch. Central wavelength and width in [nm] of the filter band are in (a): 350, 40, and in (b): 940, 20. It appears, e.g., in (a) that 0.025 mag, i.e. ~2.5 per cent of the light of a centred image at 350 nm falls outside the four central samples covering 4x4 pixels. This fraction is 0.065 mag at 940 nm according to (b).

purposes, but not the horizontal ones since the trailing spike can be affected by a bright central part. The profile along a horizontal line anywhere in the central image or in the vertical spike has the same form. Such profiles differ only by a shift of a certain magnitude which can be theoretically calculated from the entrance pupil, focal length, transmission of the filter, and CCD sensitivity. Naturally, the final calculation of the PSF must be based on a verification using comparison with real GAIA data to improve the theoretical formulae for this calculation. It is possible to use photometry of the spikes to determine the calibration functions Ag(j, ra) if the spikes are sufficiently sampled, and a realistic scheme is proposed here. The stars need not be constant for this part of the calibration but they should not be double. The vertical spikes are also useful for astrometry of bright stars, which is mainly relevant in the Astro telescopes.

34

GAIA: A European Space Project

Stars are always observed by the patch shown in the figure giving 8 samples to be transmitted to ground. It is proposed for some stars to take two more patches, one below and one above that shown in the figure. The attenuation in each patch is about 5 mag at 940 nm compared to the central patch, according to [7]. With an attenuation of a factor 100 per patch, the two patches together give a standard error in astrometry and photometry which is y^OO/2 ~ 7 times higher than of the central patch. For shorter wavelengths the attenuation is higher and the factor correspondingly higher. For bright stars it is proposed to take up to 3 pairs of patches on the spikes, i.e. 7 patches altogether. The sampling proposed in Table 1 serves three purposes: the calibration of magnitude scale, the measurement of very bright stars where the central parts will be saturated, and the measurement of double stars with large magnitude difference where the faint component may be well sampled by the extra patches. The resulting telemetry is obtained as Np x Ns. It thus appears that the proposed sampling would increase the telemetry from the medium-band photometry by about 4.0 per cent. It is useful for the various purposes of photometry to sample all stars to G = 14 mag with 3 patches as in the table, although for calibration it would be sufficient to go to 12 mag. Saturation sets in at G < 12 mag in the medium-band photometer according to Figure 8.9 in [2]. With the proposed sampling and the attenuations given in the last columns of the table it should be possible to extend photometric measurements to G = 3 mag, and to calibrate the magnitudes from G — 3 to 23 mag. A similar sampling should be introduced in the Astro instruments, perhaps with more than 7 patches for the brightest stars in order to obtain astrometry of them, even without the special CCD options for this purpose described in [2]. The patches on the spikes are always considered in pairs since the total flux in a pair is quite insensitive to a small decentering of the stellar image. This flux is shown in Figure 3 versus offset of the image which will mostly be less than 0.5 pixel, and will never exceed 1 pixel. The offset will be known with milliarcsec accuracy at the final photometric reduction and can therefore be taken into account. 3.2

P5F and Aperture Photometry

The photometric data analysis is carried out on the ground as outlined in Section 9.4.2 of [2]. A "local PSF fitting" is carried out on each of the patches, using the position of the star given by the star mapper. Such preliminary photometric data can be used for verification purposes and for scientific studies, e.g. of supernovae and other sudden events. The final photometric analysis applies "global PSF fitting" utilizing a known PSF, all astrometric information of the stars, and the satellite attitude so that only the magnitude of each star and the background is determined from the patches for the stars obtained during the mission. Also one or a few transits of a star may be analyzed in this way in order to obtain epoch photometry. A mathematical formulation is given in [6].

E. H0g: Photometric and Imaging Performance

35

Fig. 4. Overview of photometric systems. Each band is shown with its width at half maximum (FWHM).

36

GAIA: A European Space Project

Fig. 5. The three proposed photometric systems for GAIA photometry. Further studies shall lead to one optimal system to be implemented on GAIA. It should be noted that the term "PSF fitting" used here differs from that used in, e.g., DAOPHOT processing where a functional form of the PSF is defined from well-exposed stars on the exposure, and is then used for other fainter stars on the same exposure to determine the flux and the position of the image. In general, the fitting shall use the 10 or 8 transmitted samples for respectively BBP and MBP photometry as shown in Figure 1. It is however possible to add, e.g., the central transmitted samples, except the two outer ones, into one new sample, and then make PSF fitting with three samples: the new one and the two outer ones. This is called "aperture photometry". The advantage of aperture photometry is that an uncertainty in the assumed PSF, for instance because the star is double, will have less effect on the photometric result because nearly all the star light is contained in the new central samples of the patches for all stars brighter than G = 14 mag according to Table 1. For bright stars the two outer samples will be sufficient for the background determination. The curves in Figure 3 are provided for discussion of the proper size of the two outer samples in the on-board compression. With the present sampling they each contain two samples read out from the CCD, leaving a central sample of 10x 4 pixels for aperture photometry. The distance between the corresponding curve in the figure and that for 8x4 pixels is only 5 millimag at 940 nm (part 6 of the figure). This indicates that the proposed sampling is adequate. The disadvantage of aperture photometry is that stars in the surroundings will affect the new central samples. This can at least partly be taken into account by means of the result from a previous PSF photometry, or the particular result may be flagged as disturbed, or it may be rejected from further use.

E. H0g: Photometric and Imaging Performance

37

PSF and aperture photometry should be applied to all bright stars and can presumably give sub-millimag accuracies for many stars if they are relatively wellbehaved, for instance not double. 4

Photometric Systems

The choice of niters for GAIA photometry is extremely important considering that GAIA multi-colour photometry will be the only astrophysical information available for most of the brightest one billion stars on the sky during the next perhaps fifty years. No other project on ground or in space could presumably compete with GAIA with respect to all-sky photometry. Thus GAIA photometry seems to be as unique as GAIA astrometry. Figure 4 gives an overview of various photometric systems, UBVRCIC, Sloan, Geneva and the systems proposed for GAIA as of July 2001. At present three filter systems are proposed, shown in Figure 5. The IF system is the (provisional) baseline system described in [2]. The 2A and the 3G systems represent somewhat different basic ideas, and were proposed in respectively [8] and [9]. The medium bands in the 2G and 3G systems are identical and consist of three red bands plus the seven band Stromvil system which combines the Stromgren uvby and the Vilnius systems. The three systems in Figure 5 are now being compared within the GAIA Photometry Working Group (see [10]) in order to derive an optimal system which can best serve the GAIA mission. The optimal system will probably have five broad and about ten medium bands. References [1] Lindegren L., 2001, GAIA Chromaticity calibration and design of the Broad Band Photometry system. 44 pp., GAIA-LL-39, Technical Report from Lund Observatory [2] ESA 2000, GAIA: Composition, Formation and Evolution of the Galaxy, Technical Report ESA-SCI(2000)4 [3] Perryman M.A.C., et al, 2001, A&A. 369, 339 [4] H0g E. & Mattila K., 2002, EAS Publ. Ser., 2, 321 [5] Vaccari M., 2002, EAS Publ. Ser., 2, 313 [6] Brown A., 2001, Photometric Data Analysis for GAIA: Mathematical Formulation, 6 pp.. GAIA-AB-001, Technical Report from Leiden Observatory, and 2002, EAS Publ. Ser., 2, 277

[7] Fabricius F. & Lindegren L., 2001, Point spread function of Spectro, 7 pp., GAIA-CUO-085, Technical Report from Copenhagen University Observatory [8] Munari U., 1999, A modular and consistent photometric system for GAIA, Baltic Astron., 8, 123 [9] H0g E. & Straizys V., 2000, The 3G photometric system, GAIA-CUO-078, Technical Report from Copenhagen University Observatory [10] Vansevicius V., 2002, EAS Publ. Ser., 2, 67

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

GAIA SPECTROSCOPY AND RADIAL VELOCITIES U. Munari1 Abstract. GAIA spectroscopic and radial velocity performances are reviewed on the base of ground-based test observations and simulations. The prospects for accurate analysis of stellar atmospheres (temperature, gravity, chemical abundances, rotation, peculiarities) and precise radial velocities (single stars, binaries, pulsating stars) are colourful provided the spectral dispersion is high enough. A higher dispersions also favors a given precision of radial velocities to be reached at fainter magnitudes: for example, with current parameters for GAIA spectrograph, a 1km s–1 accuracy on individual epoch RVs of a KO star is reached at V ~ 13.0 mag with 0.25 A/pix dispersion spectra, at V ~ 10.3 mag for 0.5 A/pix, and V ~ 6.7 mag for 1 A/pix. GAIA radial velocities for single stars can match the ~ 0.5 km s—1 mean accuracy of tangential motions at V = 15 mag, provided the observations are performed at a dispersion not less than 0.5 A/pix.

1

Introduction

The giant leap that GAIA spectroscopy will lead us through can be sized by four basic considerations: (a) GAIA will record multi-epoch spectra for a magnitude complete sample of stars ~103 larger than any whole-sky existing database (e.g. HD survey, progressing Michigan project, etc.); (b) for each target, an average of 67 epoch spectra will be recorded over the five year mission lifetime; (c) the wavelength and flux calibrated spectra will be available in digital format to the community; (d) the foreseeable spectral dispersion (current baseline: 0.75 A/pix) is significantly higher that those of other whole-sky surveys. A review of GAIA spectroscopy has already been presented by Munari (1999a, hereafter M99a [1]). We will consider here mainly updates to the content of M99a [1] reflecting advancements in some areas over the last couple of years. Therefore, to cope with the generous but limited amount of space available to this review in its printed format, basic physics and overall considerations developed in M99a [1] 1

Osservatorio Astronomico di Padova, Sede di Asiago, 36012 Asiago (VI), Italy © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002003

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GAIA: A European Space Project

will not be discussed here again. Technical aspects connected to spacecraft optical and mechanical assembly, telemetry budgets, modus operandi, limiting magnitudes etc., are covered in the ESA's GAIA Concept and Technology Study Report (ESASCI-2000-4) and in abridged format in [2]. GAIA spectra will cover the 8490 — 8750 A wavelength range, centered on the near-IR Ca ll triplet and head of the Paschen series. The extension to 8750 A (the redder Call line laying at 8662.141 A) allows observation of remarkable #I #1 and 8 multiplets in hot stars and particularly strong Fe I, Mg I and Ti I lines in cool stars. GAIA wavelength range is the only spectral window in the near-IR which is not crunched by telluric absorptions (cf. Fig. 1 of M99a [1]), allowing uncontaminated ground-based preparatory and follow-up observations. Ca II triplet is by far the strongest line feature in the red/near-IR spectra of cool stars (cf. Fig. 1 of Munari & Castelli 2000 [3]; Jaschek & Jaschek 1995 [4]), being core-saturated even in metal-poor halo stars, thus allowing derivation of radial velocities on epoch-spectra of even the faintest and more metal deprived GAIA spectral targets. Cool stars will vastly dominate among the latter (with O and B stars barely traceable). GAIA wavelength range (restricted to A A ~ 250 A by optical and telemetry constraints) is placed toward peak emission in cool stars and lower interstellar extinction, with obvious benefits for the number of detectable targets. The number of GAIA spectral targets (approaching 108 in current estimates), will require fully automatic data treatment and analysis. Line intensities and ratios may be useful in pre-flight ground-based preparatory work and/or quick-look classification and re-direction along the reduction pipeline of actual GAIA data. However, it is clear that proper exploitation of GAIA spectra will required a smart spectral synthesis approach. Even if currently available synthetic models of stellar atmosphere (MARCS, ATLAS, Phoenix, etc.) and nebular regions (CLOUDY, etc.) will be probably quite improved by the time GAIA data will be available (and new families of models will probably be developed too), nevertheless they play a fundamental role right now in the current infancy of GAIA spectroscopy, by offering precious guidelines, ways to improve basic underlying physics (for ex. atomic constants) and unlimited databases for simulations. Most of GAIA performances will depend on the eventually adopted spectral dispersion. An example of how lowering the resolution affects spectral appearance of a KO III star a typical GAIA target - is given in Figure 1. On one side the race for fainter limiting magnitudes and smallest demand on telemetry push for mid to low spectral dispersions. On the other side, getting the best astrophysical return and the highest accuracy of radial velocities most decidedly ask for high dispersions. The best compromise will have to balance between them. The spectra presented in this review carry a 0.25 A/pix dispersion, at the high end of the 0.25—1.0 A/pix range currently considered, thus allowing the reader to guess the highest possible GAIA performances. In the following, effective temperatures and surface gravities for MKK spectral types are adopted from Strayzis (1992) [6].

U. Munari: GAIA Spectroscopy and Radial Velocities 2 2.1

41

Stellar Physical and Classification Parameters Temperature/Spectral Type

A temperature sequence spanning the MKK classification scheme is presented in Figure 2. M to F spectral types are governed by the CaII triplet, hotter ones by He I, NI and the hydrogen Paschen series. A rich forest of metal lines populates the GAIA wavelength range (cf. Fig. 3 in M99a [1]), which is dominated by Ca II, Fe I, Ti I atomic lines and CN molecular transitions. Relevant absorptions are also due to Mgl, Si I, CrI, NI, Col, Nil, Mnl, SI as well as TiO, with other elements and molecules contributing weaker spectral signatures. Such a harvest makes spectral classification over the AA ~ 250 A GAIA range nearly as much easy as it is for the AA ~ 1000 A classical MKK range (which extends from 3900 to 4900A). Only O and B stars perform less good, which is however of no concern given their barely traceable fraction among GAIA targets. Diagnostic line ratios useful for spectral classification purposes can be easily derived on GAIA spectra. Two examples of line ratios are illustrated in Figure 3. Near-IR Call over Paschen lines are highly effective in classifying late B, A and F stars, as it if for Ca II H and K over Balmer lines in optical spectra. Ti I 8674.7/FeI 8675.4 works very well in G, K and M stars, with the following expression giving

Fig. 1. The same KO III spectrum at different dispersions/resolutions. The number in the four columns give the dispersion (in A/pix), the resolution (in A, with FWHM(PSF) = 2 pix), the resolving power and the number of pixel required to cover the whole GAIA wavelength range.

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GAIA: A European Space Project

Fig. 2. Sequence of synthetic spectra (from [3. 5] Munari & Castelli 2000; Castelli & Munari 2001) illustrating the variations along the main sequence (Teff in K on the left and corresponding spectral type for luminosity class V on the right) for moderately metal poor stars ([Z/ZQ] =—0.5). All spectra are on the same ordinate scale, only displaced in their zero-points.

U. Munari: GAIA Spectroscopy and Radial Velocities

43

Fig. 3. Example of temperature diagnostic ratios (Boschi 2000 [8]; Boschi & Munari 2001 [9]) from real spectra (from Munari & Tomasella 1999 [10]). Left panel: hydrogen Paschen and Call lines in main sequence stars. Right panel: a powerful temperature diagnostic ratio for cool giants (requiring 0.25 A/pix dispersion spectra to resolve the lines).

the fitting curve in Figure 3 (right panel):

A AR = 4% error in the line ratio (typical for the observations in Fig. 3) corresponds to just ATeff =65K. It worth to mention that also GAIA photometry will (obviously) estimate the temperature of target stars (however with contamination from interstellar reddening, if present), providing independent data to be compared with spectroscopic findings. 2.2

Gravity/Luminosity Class

Figure 5 illustrates line behavior with luminosity class. With lowering surface gravity (increasing luminosity, decreasing pressure) the intensity of absorption lines goes up, as much as in classical optical spectra and required by physics. The equivalent width of Call lines shows a pronounced positive luminosity effect (collisional de-population of excited state less effective with decreasing pressure). Width of Paschen lines presents a negative luminosity effect (being pressure broadened, similarly to Balmer lines) as given in Figure 4. It is again worth noticing that surface gravities will be also quite effectively measured by GAIA combining astrometric distances with photometry (cf. Sect. 2.1 in Munari 1999b, hereafter M99b [7]).

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GAIA: A European Space Project

Fig. 4. Left: gravity effects on the profile of Call 8542 A for Teff = 5000 K (~G8 spectral type) and [Z/Z0] = —0.5 (synthetic spectra from Munari & Castelli 2000 [3]). Center: gravity effects on the profile of Paschen 14, 8598 A for Teff = 9750 K (~AO spectral type) and [Z/Z0] = —0.5 (synthetic spectra from Zwitter et al. 2001 [13]). Right: dependence upon gravity of the ratio (Si I 8728.0 + Fel 8729.1)/MgI 8736.0 (Boschi & Munari 2001 [9]) on G5 real spectra (from Munari & Tomasella 1999 [10]).

As for temperature/spectral type, it is easy to derive diagnostic line ratios highly sensitive to surface gravity/luminosity class. The steep behavior of (Si I 8728.0 + Fe I 8729.1)/(MgI 8736.0) in G5 stars is illustrated in Figure 4, with fitting curve given by:

A AR =3% error (typical for Fig. 4 data) corresponds to just A log g = 0.11. 2.3

Chemical Abundances

The intensity of absorption lines obviously correlates with the chemical abundances. Figure 6 presents spectra of two G5 III stars of widely differing metallicities ([Fe/H] = -2.65 and -0.02). Even at the lowest metallicities (like those found in the Halo and globular clusters), Ca II lines remain core-saturated while nearly all other metallic lines have gone, allowing accurate radial velocity measurements and fine rotational velocity estimates. The possibility to perform chemical analysis on the recorded spectra will depend on the spectral dispersion that will be eventually adopted for GAIA. Figure 1 is illuminating in this sense. At 0.25 A/pix hundreds of absorptions

U. Munari: GAIA Spectroscopy and Radial Velocities

45

Fig. 5. Gravity effects on G8 and A2 spectra (from Munari & Tomasella 1999 [10]).

Fig. 6. Examples of G5 III stars of quite different metallicities (from Marrese 2000 [11]). On cool stars, even at very low abundances, Call lines remain strong, allowing accurate radial velocity measurements, while nearly all other metallic lines have gone.

lines blossom over the whole GAIA range, tracing tens of different elements which individual chemical abundances can be derived as routinely done with high resolution optical spectra secured with ground-based telescopes. At 0.5 A/pix, lines from different elements merge into blends and individual chemical abundances can be derived (with a limited accuracy) probably only for Fel, Til and Mgl (tests are

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GAIA: A European Space Project

underway). At even lower dispersions, chemical analysis looks hopeless, with absorption lines washing into an unfeatured continuum. It is also worth to mention that GAIA narrow band photometry (M99b [7]; V. Vansevicius, M. Grenon, these proceedings) should estimate metallicity (a weighted average of individual chemical abundances) from colour indexes with a sensitivity comparable to best performing, existing ground-based photometric systems (Moro & Munari 2000 [12]). 3

Rotational Velocities

Projected rotational velocity (Vrot sin i) is another intrinsic property of stars that GAIA can measure with relevant confidence, provided the spectral dispersion is high enough. The impact of axial rotation on stellar evolution is only recently being appreciated and modelled (cf. Maeder, this volume; Maeder & Meynet 2001 and references therein). A sequence of rotationally broadened FO III spectra is presented in Figure 7. Call and Paschen lines perform equally well up to very high Vrot, offering bright prospects for measuring rotational velocities both in cool and hot stars, respectively. Other, weaker lines are useless at Vrot >40km s^ 1 , being washed out in the adjacent continuum. Rotational velocities of G-K-M stars (constituting the largest fraction of GAIA targets) are usually confined to Vrot < 15km s-1 (Glebocki et al. 2000 [14]). To effectively discriminate at so low values, a properly high spectral resolution is necessary. 0.5 A/pix spectra would not allow GAIA to distinguish Vrot sin i = 15 km s-1

Fig. 7. Rotational velocity sequence for FO III giants (spectra from Zwitter et al. 2001 [13]).

U. Munari: GAIA Spectroscopy and Radial Velocities

47

stars from non-rotating ones, i.e. rotational velocities will be undetermined for the majority of GAIA targets. Instead, 0.25 A/pix spectra can detect and measure rotational velocities to an accuracy of AV^-0t sin i — 5 km s-1, thus providing decent sensitivity to rotation for all GAIA targets. The rotational broadening of narrow lines may be expressed in term of the total half intensity width (HIW), in A, as

4 4.1

Radial Velocities Single Stars

Munari et al. (2001a, hereafter MOla [15]) have investigated in detail GAIA radial velocity performances as function of spectral resolution and signal-to-noise ratio, by obtaining 782 real spectra and using them as inputs for 6700 automatic crosscorrelation runs. MOla [15] have explored the dispersions 0.25, 0.5, 1 and 2 A/pix (compared to the current baseline: 0.75 A/pix) over S/N ranging from 12 to 110, carefully maintaining the condition FWHM (PSF) = 2 pixels. MOla [15] have investigated late-F to early-M stars (constituting the vast majority of GAIA targets), slowly rotating ( ( V r o t sin i) = 4 km s- 1 , as for field stars at these spectral types), of solar metallicity ({[Fe/H]) = —0.07) and not binary (target stars selected among IAU standard radial velocity stars). The results are accurately described by:

where a is the cross-correlation standard error (in km s l) and D is the spectral dispersion (in A/pix). Inserting 0.25, 0.5, 1, 2 for D in the above expression gives the four fitting curves in Figure 8. The spectral dispersion is the dominant factor governing the accuracy of radial velocities, with S/N being less important. Spectral mismatch affects the results only at the highest S/N. MOla [15] findings suggests that mission-aver aged GAIA radial velocities on non-variable, single stars can match the ~O.5 k m s - 1 mean accuracy of tangential motions at V = 15 mag, provided the observations are performed at a dispersion not less than 0.5 A/pix. Binary and/or fast rotating and/or pulsating and/or surface spotted stars will require higher accuracies (thus higher spectral dispersions) in order to disentangle perturbing effects from barycentric motion. The flattening of RV performances at the highest S/N in Figure 8 and equation (4.1) results from the spectral type mismatch between template and program stars in MOla [15] study (while metallicities and rotational velocities were instead pretty similar and therefore not influent). The large but however limited number of real spectra (782) and the extreme paucity of IAU RV standards sharing the same spectral classification, forced spectral type mismatch in MOla [15] investigation. Extensive simulations on huge numbers of synthetic spectra have been performed by Zwitter (2001) [16] to get rid of mismatches unavoidable with real spectra. His results confirm equation (4.1) and Figure 8 behavior at low and mid

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GAIA: A European Space Project

Fig. 8. The accuracy of radial velocities obtained via cross-correlation for late-F to early-M stars as function of S/N and spectral dispersion (Agnolin 2000 [17]; Munari et al. 2001a [15]). The results based on 782 real spectra and 6700 cross-correlation runs include the effect of mismatch between object and template stars (removing it would reduce the upward curvature at higher S/N). The V magnitude of unreddened G5 V stars producing epoch spectra of the given S/N is reported next to the points (computed for: mirror size = 75x70 cm; overall throughput — 35%; crossing time = 60.8 s; 9 2 1 1 = 520 photons cm^s"1 A"1; R.O.N^Se" 1 ; 7 ma g =o.o = i.i96xlO- ergcm- s~ A' 1 -1 dark = 0.01 e" s ; background /c = 21.5arcsec^ 2 ).

S/N. As expected, they do not show the upward curvature at the highest S/N induced in Figure 8 by the spectral mismatch (see also Katz, these proceedings, for additional results on GAIA radial velocities). MOla [15] and Zwitter (2001) [16] investigations argue in favor of increasing the spectral dispersion to get more accurate radial velocities, for a fixed photon budget (like in GAIA fixed exposure time observations). From the results with real spectra of Figure 8, with current parameters for GAIA spectrograph, a Ikms" 1 accuracy on epoch RVs of a KO star is reached at V ~ 13.0 mag with 0.25 A/pix spectra, at V ~ 10.3 mag for 0.5 A/pix, and V ~6.7 mag for 1 A/pix dispersion. The reason for this is quite obvious looking at Figure 1: at high dispersions all pixels carry RV information, even at low S/N, while at low dispersion only a few pixels carry RV information, no matter how high is the .

U. Munari: GAIA Spectroscopy and Radial Velocities 4.2

49

Binary Stars

Eclipsing stars represent the most astrophysically relevant type of binary stars GAIA will spectroscopically observe during its mission. They are a prime tool to derive fundamental stellar parameters like mass and radius, or the temperature scale. Moreover, their use as accurate, geometric distance indicators is rapidly growing (current best distances to LMC, dwarf spheroidals, globular clusters). Their study is by no means a simple task as evidenced by the fact that stellar parameters have been derived with an accuracy of 1% or better for less than a hundred objects. Scaling the Hipparcos results (0.8% of the 118218 stars surveyed turned out to be eclipsing), ~4 x 105 of all V < 15 mag GAIA targets should be eclipsing binaries, with a average G7 spectral type. It may be estimated that about 25% of the eclipsing binaries will be doublelined in GAIA spectral observations (cf. Carquillat et al. 1982 [18]), thus ~1 x 105 of all V < 15 mag GAIA targets. Even if for only 5% of them it should be possible to derive orbits and stellar parameters at 1% precision, this still would be

Fig. 9. V505 Per as an example of GAIA performance on eclipsing binaries (from Munari et al. 2001b). Upper panel: a sample of the recorded spectra to illustrate line splitting with orbital phase. Lower left panel: radial velocity curve and model fitting, Hipparcos Hp photometry and model fitting. Lower right panel: orbital and physical parameters as derived from modelling of radial velocity and photometric data.

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GAIA: A European Space Project

100 x what humanity have so far collected from devoted ground-based efforts during the whole last century (cf. Andersen 1991 [19]). That a 1% accuracy in orbital and physical parameters of eclipsing binaries is feasible within GAIA has been demonstrated by Munari et al. (2001b, hereafter MOlb [20]). 0.25 A/pix spectra over the GAIA range have been secured from the ground for 15 eclipsing binaries (mostly unstudied in literature and distributed among detached, semidetached, contact and intrinsic variable types) and combined with Hipparcos VT, BT, HP photometry to properly simulate GAIA data harvest. Example results from MOlb [20] for V505 Per are given in Figure 9. Semimajor axis, masses, surface gravities, effective temperatures, inclination, eccentricity, barycentric velocity, epoch and orbital period are in the 1% or better accuracy regime. Radii of individual components (and therefore individual bolometric magnitudes) however depends on how well the branches of eclipses are mapped. In the case of Hipparcos observations of V505 Per only three points cover the principal eclipse. Even if model solution can fit these three points to a formal accuracy of ~1% (cf. lower-right panel of Fig. 9), nevertheless the massive undersampling casts many doubts on the true accuracy of derived radii. In fact, high quality and massive ground-based observations of V505 Per by Marschall et al. (1997) [21] fully confirm GAIA-like solution of V505 Per as reported in Figure 9 for all orbital and physical parameters but individual radii. If the sum of them is R1 + R2 — 2.54 RQ for the GAIA-like solution and 2.55 for Marschall et al. (1997) [21], the individual values are 1.29 and 1.26 for the latter and 1.40 and 1.14 RQ for MOlb [20]. Numerical experiments however show that by just doubling the number of points covering the principal eclipses in the Hipparcos light curve would fix the result to a much higher degree of confidence and close to the Marschall et al. (1997) [21] findings. It is therefore of great relevance to the broadest stellar astrophysics that a minimum number of identical photometric bands is replicated in all the three viewing fields of GAIA, so to achieve maximum density of points in light curve mapping of eclipsing binaries (with obvious benefit to all other types of variable objects observed by GAIA). The high quality of the results on V505 Per shown in Figure 9 (typical of other cases investigated in MOlb [20]) is however definitively depending upon the adopted 0.25 A/pix spectral dispersion. At such a dispersion, lines from both components are easily resolved and measured, while at the coarser 0.75 A/pix dispersion currently baselined for GAIA the lines would merge into unresolved profiles that could even hide the binary nature of the object.

4.3

Pulsating Stars

Radial velocity mapping of pulsating stars add precious information to the effort of understanding their nature (cf. Bono et al. 1997 [22]). Non-radial pulsators manifest marked variations of line profiles that can be observed and modeled if the spectral resolution is high enough.

U. Munari: GAIA Spectroscopy and Radial Velocities

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Fig. 10. Radial velocity curves of representative pulsating stars. Spectra of template radially pulsating stars (RR Lyr, 6 Cep, o Cet) are presented in M99a [1]. The wealth of strong absorption lines, in particular Ca II, assures that accurate radial velocities can be obtained at even the lowest metallicities (RR Lyr itself has [Z/ZQ] = -1.37). Pulsation curves of representative cases are given in Figure 10. Shapes and details of such curves (e.g. the glitch in W Crt at phase 0.67, or BG Lac at phase 0.52), tell a lot about interior physics of these stars. It may be easily anticipated that GAIA spectroscopic monitoring of thousands of them (compared to the very few cases investigated from the ground) will loudly impact on our understanding of stellar radial pulsations, provided the accuracy of epoch radial velocities will be good enough. Semi-amplitudes for Lyrids are of the order of ARV ~ 40 k m s ~ l , ARV ~ 15 for Cepheids and ARV ~ 7 for Miras. So low amplitudes need high spectral resolution to be properly mapped: at 0.25 A/pix even glitches in the pulsation curves will be detected, while at 0.75 A/pix the pulsation curves of the majority of Miras will be unobservable. 5

Peculiarities

The 8480-8750 A GAIA wavelength range offers fine detection capabilities and diagnostic potential toward stellar peculiarities. Spectra of a few representative peculiar stars are presented in Figure 12 (for other types and examples see M99a [1]) and briefly commented hereafter. Be stars show strong and variable Paschen and He I emission lines, which profile trace conditions within the circumstellar disk. Hot mass-losing stars (P-Cyg type) present Paschen and He I lines with the characteristic emission/absorption profile that can be modeled to derive the mass-loss rate. Very wide and bright Call profiles (and usually weaker Paschen) trace the fast expansion of novae ejecta

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(FWHM = 1280 km s-1 in Nova Cyg 2001 #1), with sub-structures correlated to and tracing the inhomogeneities and clumps in the dispersing material. Either hot and cool pre-ZAMS objects well perform over the GAIA range. Herbig Ae/Be stars display both Ca ll and Paschen lines in strong emission, usually emerging from an absorption core. In cooler pre-ZAMS objects Call lines play the game, from the exceptional intensity in TTau (cf. the spectrum in M99a [1]) to the weak emission components in FU Ori. Active atmosphere/spot stars reveal their nature by a complex cool absorption spectrum and structured emission profiles. Major bright and active areas over the stellar surface correlates with individual, radial velocity displaced (by axial rotation) components in the spectrum, as in the BY Dra spectrum in Figure 12 where emission cores in Ca II separated by 74km s-l are paralleled by Fe I double absorption lines separated by an identical 74kms~ 1 . Spectra of interacting binary stars offer a fine and intriguing display over the GAIA spectral range. Symbiotic stars usually present strong Paschen, Call and weaker He I emission lines, while in some other case the naked absorption spectrum of the cool giant can be observed without contamination from the hot companion. The same Ca ll, Paschen and He I lines plus strong NI (multiplet #1 and #8) dominate spectra of the X-ray transient XTE J0421+560 in Figure 12, with complex line profiles indicating kinematically decoupled emitting regions. Wide, strong and multi-component, orbital-phase variable Call profiles stand out in the spectra of the recurrent nova RS Oph. Finally, the interstellar medium can manifest itself in GAIA spectra. Figure 11 show the spectra of three similar hot stars affected by different amount of reddening, where absorption by the diffuse interstellar band at 8620 A clearly stands out. The equivalent width of the latter correlates surprisingly well with reddening, offering interesting opportunities for GAIA diagnostic of the interstellar medium

Fig. 11. The diffuse interstellar band at 8620 A (marked by the arrow) on spectra of early type stars at different reddenings. Note the increase of DIB equivalent width with reddening (from Munari 2000 [23]).

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Fig. 12. Spectra of representative peculiar stars (from Munari et al. 2001c [24]).

(Munari 2000 [23]): Efforts are currently underway (cf. Moro & Zwitter 2000, [25]) to investigate the

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GAIA: A European Space Project

dependence of the slope coefficient (2.69) upon the intrinsic and tri-dimensional properties of the galactic interstellar medium (Ep-v — a(l,b,D) x E.W. (A)). References [I] Munari, U.:-1999a, in Proc. of "GAIA" ESA-ESTEC Workshop, V. Strayzis (ed.), Balt. Astron., 8, 73 (M99a) [2] Perryman, M.A.C., de Boer, K.S., Gilmore, et al, 2001, A&A, 369, 339 [3] Munari, U., Castelli, F., 2000, A&AS, 141, 141 [4] Jaschek, C., Jaschek, M., 1995, The behaviour of chemical elements in stars (Cambridge Univ. Press) [5] Castelli. F., Munari, U., 2001, A&A, 366, 1003 [6] Straizys, V., 1992, Multicolor Stellar Photometry (Pachart Pub. House, Tucson) [7] Munari, U., 1999b, in Proc. of "GAIA" ESA-ESTEC Workshop, V. Strayzis (ed.), Balt. Astron., 8, 123 (M99b) [8] Boschi, F., 2000, Degree Thesis, Dept. of Physics, Univ. of Milan [9] Boschi, F., Munari, U., 2001. AJ, to be submitted [10] Munari, U., Tomasella, L., 1999, A&AS, 137, 521 [11] Marrese, P.M., 2000, Degree Thesis, Dept. of Astronomy, Univ. of Padova [12] Moro, D., Munari, U., 2000, A&AS, 147, 361 [13] Zwitter, T., Munari, U., Castelli, F., 2001, A&A, in preparation [14] Glebocki, R., Gnacinski, P., Stawikowski, A., 2000, Acta Astron., 50, 509 [15] Munari, U., Agnolin, P., Tomasella. L., 2001a, Balt. Astron., 10, November 2001 issue, in press [astro-ph/0105167] (M0la) [16] Zwitter, T., 2001, A&A, to be submitted [17] Agnolin, P., 2000, Degree Thesis, Dept. of Astronomy, Univ. of Padova [18] Carquillat, J.M., Nadal, R., Ginestet, N., Pedoussaut, A., 1982, A&A, 115, 23 [19] Andersen, J., 1991, A&AR, 3, 91 [20] Munari, U., Tomov, T., Zwitter, et al, 2001b, A&A, in press [astro-ph/0105121] (MOlb) [21] Marschall, L.A., Stefanik, R.P., Lacy, C.H., Torres, G., Williams, D.B. and Agerer, F. 1997, AJ, 114, 793 [22] Bono, G., Caputo, F., Cassisi, S., Castellani, V., Marconi, M., 1997, ApJ, 477, 346 [23] Munari, U., 2000, in Proc. of "Molecules in Space and in the Laboratory", I. Porceddu & S.Aiello (eds.), Soc. It. Fis., 67, 179 [astro-ph/001027l] [24] Munari, U., Tomasella, L., Marrese, P.M., et al., 2001c, A&A, to be submitted [25] Moro, D., Zwitter, T., 2000, in Proc. of "Molecules in Space and in the Laboratory", I. Porceddu & S. Aiello (eds.), Soc. It. Fis., 67, 171

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

OVERVIEW OF GAIA DATA REDUCTION J. Torra1, 2, X. Luri 1,2 , F. Figueras1,2, C. Jordi 1,2 and E. Masana2

Abstract. GAIA will obtain, in a five-year mission, astrometric, photometric and spectroscopic data for more than a billion stars. The treatment of this huge amount of data is a challenge for the astronomical community, not only due to the database size, but also to the complex relationships existing between the different sets of data and with the instrumental and orbital parameters. The GAIA Data Analysis Study (GDAAS), under ESA's contract, aims to prove the feasibility of the data reduction scheme and to implement and test a prototype of such a large database. We present the main aspects that GDAAS addresses and review its present status.

1

Introduction

The GAIA mission [1] will provide positional, photometric and radial velocity data for a representative stellar sample of our galaxy as well as for some objects of the Local Group. At the end of the mission, a complete and unbiased sample up to V = 20 mag, with an estimated size of a billion objects, including variables, supernovae, lensing events, minor planets, etc. will be available. There are many challenging problems in an astrometric mission like GAIA, aiming to reach the 10 u-arcsec accuracy. Besides the ones related to the building and operation of the satellite itself, the most demanding problem is the data treatment, not only by the large amount of objects and data involved, estimated in some 10-100TB, but for the intricate relationships among different sets of data. For instance, chromaticity effects on the observed positions depend on the colour of the stars, and thus photometry is needed while it depends on the instrumental calibration. Therefore, an important feature of the GAIA mission is that the instrumental calibration and data analysis must be performed in a global manner since they are strictly related. On the other hand, at this level of accuracy, radial velocities are needed to determine the perspective acceleration, needed to reach 1 2

Departament d'Astronomia i Meteorologia, Universitat de Barcelona, Spain Institut d'Estudis Espacials de Catalunya, Spain © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002004

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the 10 /x-arcsec accuracy, and photometric data are needed to classify the objects before any use of data. In consequence, data processing is an essential part of the GAIA mission. The processing needs for this treatment have been estimated in about 1019 flops. This figure clearly shows that a specific effort is needed to evaluate the feasibility of data storage, treatment and data reduction in the GAIA context, verifying that the most problematic aspects can be solved. To cover this need, the European Space Agency (ESA) issued the GAIA Data Access and Analysis Study (GDAAS) contract, which was allocated to the consortium constituted by the Spanish company GMV, the University of Barcelona and the Centre de Supercomputacio de Catalunya (CESCA). We describe in the next sections the most important characteristics of the Data Management system developed in GDAAS. Section 2 describes the database system and Sections 3 to 5 describe the three processing steps: initial data treatment, core processing and shell processing (scientific data treatment). 2

The GAIA Data Base

Although there are other ongoing large databases projects related to astronomy (see [2]), the number and complexity of the operations to be applied to the GAIA data make the GAIA database a challenging project. O'Mullane & Lindegren (1999, [3]) tested the concepts for the GAIA data processing using Hipparcos Intermediate Astrometry data. The prototype was coded in Java and based in an object-oriented database. This prototype was run at CESCA facilities in single-node and multi-node environments. The results of this study lead to the concept of an object oriented framework and distributed database as main characteristics of the GAIA data management system. In a distributed database system the data are not stored in a single node but distributed across a set of nodes linked by a network. This distributed architecture is transparent for the database user that can query the database in a normal way, leaving the query optimisation task to the system. However, the distribution of the data, combined with an adequate processing strategy, allows to also distribute the data processing thus combining efficiency, accessibility and scalability. In the case of the GAIA database, a good design of the data distribution and processing strategy is a key issue. In the GDAAS context, the prototype database has been spatially distributed according to the HTM indexing [4] and its design will be tested using five million objects. The system is based in an object-oriented database system, has been coded in Java and designed using UML tools. Provisions have also been made to interface with Fortran and C routines. 3

Initial Data Treatment

The data gathered by the GAIA instruments are organized in telemetry packets and downloaded to ground. Once they are received, and before any data can be used, they have to undergo an initial treatment where they are decoded, ingested

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in the database, and submitted to some pre-processing that prepares them for scientific and data reduction purposes. In the context of GDAAS, telemetry data (including observations from the astrometric instruments and attitude data) is provided by the simulator described in [5]. 3.1

Telemetry Ingestion

The first step in the processing of the GAIA data is the ingestion of the telemetry into the database. Telemetry packets are read and decoded to obtain both the satellite housekeeping and attitude data, and the scientific data. The relevant data are formatted into database objects and stored as appropriate. These raw data will be permanently stored into the GAIA database and protected against accidental erasing or modification. The raw data objects related to observations are distributed using an HTM indexing, thus satisfying the need for fast positional and temporal access. 3.2 Cross-Matching When an observation is added to the database it is cross-matched with the objects already in it. New observations are matched with the sources already stored into the database: if a match is found, the observation is attached to the matching source, otherwise a new source is created. The cross-matching of observations requires a very efficient system, allowing a fast access to the sources stored in the database, and fast processing and ingestion of the incoming telemetry. This system should be able to process the daily telemetry in a few hours. On GDAAS, cross-matching is based only on spatial criteria, using an adaptation of the GSC-II cross matching algorithm developed at the Torino Observatory. However, the actual cross-matching algorithm for GAIA will use more observational data for the matching. Furthermore, during the actual GAIA data processing cross-matching will likely run several times as the calibration and data reduction advances. 3.3

Quick-Look

The purpose of the Quick-look processing is the detection in almost real time of transient events of astronomical interest. It runs in parallel with the crossmatching process and will include several specialised processes for special types of objects (i.e. NEOs), although for GDAAS it has been simplified to a bare minimum. 3.4

Classification

Before any scientific processing can be applied, an astronomical classification of sources (stars, galaxies, binary, etc.) is required, because specialised data reduction processes will be applied to each type of object. Classification has to be run

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continuously, updating results when new observations of an object are available. The requirements for classification will depend on the algorithms and associated criteria to be used but these processes are usually very CPU-time consuming, and therefore special provisions for fast execution are required. 4

Core Processing

As described in [1], the data analysis aims to give the best representation of the observed data in terms of the object model, the satellite attitude and the instrumental calibration plus some "given" data like the satellite orbit and the relativistic model used to compute celestial directions. It is important to bear in mind that all the GAIA calibrations, geometric and photometric, and the attitude determination must be derived from the same data used to obtain the astrometric and photometric parameters for the objects. To do that, one must assume that well-behaved objects, described by a simple fiveparameter astrometric model with no photometric variability, can be identified and, in addiction, that no sudden changes occur on the attitude and instrumental characteristics, thus smoothing and time-averaging are permitted. Under this hypothesis, an iterative process in which the selection of objects is improved at the same time that calibration and attitude can provide all the relevant parameters. This is the so-called core processing of the GAIA astrometric data. Once it is finished the data concerning calibration and attitude are available and can be used to solve for the astrometric parameters of more complex objects where specific object models are needed. 4.1

The Global Iterative Solution

The core processing can be formulated as the minimisation of the difference between the observed CCD data and the computed ones obtained from the physical model, the attitude model and the calibration model. The direct solution of the problem is not feasible even with powerful computers and thus an alternative approach, the Global Iterative Solution (GIS), is used. The GIS can be described as a cyclic sequence of three processes (left panel in Fig. 1) applied to four categories of data: Global parameters: parameters characterizing the instruments or coordinate transformations (i.e. the 7 relativistic parameter) which are constant all along the mission; Local parameters: attitude and instrument parameters that are functions of time. They are smoothed using functions of time; Elementary data: data describing the observation of a source. They are derived from the raw observations after some pre-processing (e.g. centroiding); Scientific data: astrometric and photometric data for the sources.

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Fig. 1. Left panel: first approximation to the GIS. Right panel: distributed GIS processing and database structure. In the first step, the scientific data and the global parameters are assumed to be known, and the comparison with the observed CCD data allows the improvement of the local parameters. The minimisation has to be performed for all the observations in a given interval of time because one wants to fit the local parameters. Thus, direct access by time to the elementary data stored into the database is needed. As the pointing of the instrument is determined by the scan law, it is possible to implement an efficient time-domain access, keeping the spatially organized structure for the database. The HTM (Hierarchical Triangular Mesh) partitioning is combined with an internal time-oriented structure of the containers as suggested in [1]. On the second step, local and global parameters are assumed to be known and source astrometric parameters are improved. Access to the database is now per source: for each source all its elementary data have to be retrieved, so appropriate pointers have to be included. Local parameters have to be retrieved by the time associated to each elementary data. The third step aims to improve the global parameters considering the whole set of observations, the science data for the sources and local parameters. 4.2

Core Processing: Execution Overview

The actual execution of the core processing does not necessarily follows the conceptual sequence described in the previous section. Depending on the needs and on the behaviour of the solutions the execution sequence can be altered.

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The processing can be described as: 1. Initialisation of well-behaved stars; 2. Iteration of the three steps, or some other suitable permutation until convergence; 3. End of processing: current values of data are the final values. The processing in each step is not sequential. It can be shared and parallelised: many processes can run on different parts of the database as can be seen in right panel of Figure 1. For example several Local Parameter (LP) processes can run under a LP coordinator, working each one in a time chunk TCI, TC2, ... TCk. On the other hand, an astrometry coordinator may distribute the work on several astrometry processors each one working on a source. On the same figure the needs of access to the different parts of the database (raw data layer, Source layer, local and global parameters) are described. 4.3

Core Processing: Present Implementation

The actual implementation of the core processing on the GDAAS has been made following the proposal by Lindegren, [6], who also has provided the appropriate Fortran routines. The model proposed is a simplified one, but it is enough to prove the feasibility of the core process and its implementation. A detailed schema of the processes involved in one of the steps, the attitude improvement, a part of the local parameters described in the previous sections, is presented in Figure 4. For each attitude interval the minimization of the differences between observed and computed positions is performed. To do that it is necessary to calculate the field angles (see [1]) for each elementary data (the result of a single CCD observation by one of the instruments), its derivatives and the proper direction to the source, for which auxiliary data (orbital data for the satellite and ephemeris) are needed. On the other hand, observed values are also transformed to field angles. A similar processing takes place for the calibration (second part of local parameters determination), the global parameters and the astrometric values updating. 5

Shell-Processing

Once the core-processing is finished, the final attitude and calibration data are available for further processing of the sources not entering the GIS. The treatment of this sources follows a more classical pattern in the sense that calibration data are applied to the observations to produce scientific data. Thus a great variety of specialised processing will be applied to the database. Two main steps are recognized: 1. A detailed classification of the sources into the relevant scientific categories for further processing using all the available information (astrometry, photometry, spectra). This classification has to be much more accurate that the one performed during the Initial Treatment;

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Fig. 2. Core processing: attitude updating. 2. Application of the calibrations to obtain the scientific data for all the objects in the database using the appropriate physical model for each kind of object including, for instance, the orbital motion in the astrometric model for binary stars. 6

Future Developments

Presently, the GDAAS project has completed its design phase and operational tests are underway. The final implementation will be ready next September and the battery of tests on the main processes described above is being prepared. Among them, and crucial for the GAIA success, the cross-matching and the coreprocessing. This last one will be run in a subset of one million stars; sequencing, effects of not well-behaved stars as well as computing time, storage will be extensively tested. The operational model will be delivered to ESA by the end of march 2002. References [1] ESA 2000, GAIA: Composition, Formation and Evolution of the Galaxy, Technical Report ESA-SCI(2000)4, (scientific case on-line at http://astro.estec.esa.nl/GAIA) [2] Egret, D., 2002, EAS Publ. Ser., 2, 179 [3] O'Mullane, W., Lindegren, L., 1999, Baltic Astron., 8, 57 [4] Kunzst, P.Z., Szalay, A.S., Csabai, I. ,Thakar, A. R., 2000, ASP Conf. Ser., 216, 141 [5] Luri, X., Masana, E., Jordi, C., Figueras, F., Torra, J., 2001, The GAIA simulator: reference document vl.O. In preparation [6] Lindegren, L., 2001, GAIA-LL-34

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

RVS' RADIAL VELOCITIES ACCURACY D. Katz 1 , Y. Viala1, A. Gomez1 and D. Morin1

1

Introduction

The resolution of the RVs instrument is, presently, not finalised. The foreseen values range from R = A/AA = 5000 to 20 000. Studies are now needed to establish the respective merits and drawbacks of the different possible configurations. As a first step in this direction, we have performed simulations to estimate the RVs' radial velocities (hereafter RV) accuracy, for a single observation, three different resolutions (R = 5000, 10000 and 20000), as a function of magnitude and for two different stellar types: two dwarfs (logg = 4.5) of solar metallicities and respective temperatures Teff = 5500 and 10 000K. A Monte-Carlo approach was used, repeating, for each stellar type, resolution and magnitude, 1000 times the following steps : (i) computation of an RVs synthetic spectra taking into account the resolution, the sampling, the overall efficiency of the instrument as well as some instrumental and astrophysical noise sources, (ii) derivation of the radial velocity, and therefore of the radial velocity error, by cross-correlation with a synthetic template. The RV accuracies were given by the dispersion of the 1000-point error distributions2. 2

RVs Spectra and RV Derivation

Kurucz [1] synthetic spectra, were used as "seeds" to compute RVs spectra. Table 1 lists some of the characteristics of those synthetic spectra and summarizes the 3 studied resolutions and the corresponding samplings (the samplings were chosen in order to get at least 2 pixels per spectral resolution element, all along the spectra).

1 DASGAL - Observatoire de Meudon, France e-mail: [email protected] 2 This approach is valid only because in the cases studied so far, systematic errors were negligible with respect to random errors.

© EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002005

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Table 1. Characteristics of Kurucz' atmospheric models and spectra (upper half) and studied resolutions and corresponding samplings (lower half).

a = l/Hp overshooting A range

0.5 none [8490, 8740] A

micro-turbulence macro-turbulence v smi

2 km s—1 2 km s—1 0 km s—1

Resolution Resolution Resolution

5000 10000 20000

Sampling Sampling Sampling

0.8 A per pix. 0.4 A per pix. 0.2 A per pix.

Table 2. RV accuracies (in km s—1) for the "late-type" (Teff = 5500 K) and the "earlytype" (Teff = 10 000 K) stars as a function of magnitude and resolution. The numbers in parenthesis are the samplings adopted for the different resolutions.

V 10 12 14 15 15.5

5000 (0.8 A) 0.66 1.74 4.80 8.98 13.70

Resolution 10000 (0.4 A) 0.36 0.88 2.87 6.15 15.62

20000 (0.2 A) 0.19 0.48 1.71 8.33 53.70

V 8 10 11 12 13

5000 (0.8 A)

1.28 3.47 5.75 9.54 21.38

Resolution 10 000 (0.4 A)

0.58 1.40 2.41 4.35 17.19

20 000 (0.2 A)

0.28 0.70 1.16 2.16 18.36

The first step of the transformation of the Kurucz synthetic spectra in RVs spectra was to re-sampled them to the desired pixel spectral size (as a function of the resolution: see Table 1). The central wavelength of the first pixel was randomly determined in order to account for the random positioning of the spectra with respect to the CCD: AQ = 8490 + (x — 1/2)) x £ A; where x is a random number in the range 0 and 1 and £ the sampling given in Angstrom per pixel. The fluxes were then converted in photon counts (using C. Jordi flux table), assuming an entrance pupil of 0.75x0.70 m2, a field of view of 1° x 1°, a transit time of 30.4 s3, a pixel angular size of 1 arcsec2 and a total efficiency of 35%. Photon and background noises were accounted for by a Poissonian distribution. For the latest, we only took into account the zodiacal light, assuming V = 22.5 mag arcsec~ 2 . A Gaussian readout noise of 3 e~ per pixel was also added to the spectra. The radial velocities were derived by cross-correlating the "RVs synthetic spectra" with a template "synthetic spectrum" of similar atmospheric parameters and resolution. 3

The foreseen size of the field of view has changed since we performed those simulations and will most likely be 1° X 2° for a transit time of 60.8 s.

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65

Results

Table 2 presents the RV accuracies obtained for the two stellar archetypes as a function of resolution and magnitude. Those results account for a single observation of 30.4 s exposure time. • On average on the 5-year duration of the mission, each star will be observed 200 times. As shown in Table 2, a "high" resolution (R = 20000) gives a better accuracy for bright (and moderately bright) stars, while a "moderate" resolution (R = 10000) gives better results for the very faint stars. This behaviour is more significant for the late-type star than for the early-type one.

References [1] R.L. Kurucz, http://cfaku5.harvard.edu

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

PERFORMANCE OF THE GAIA PHOTOMETRIC SYSTEMS IF, 2A & 3G V. Vansevicius1, A. Bridzius1 and R. Drazdys1 Three independent and very different photometric systems (PS) are proposed to date for the GAIA mission (IF [1], 2A [2] & 3G [3]). The aim of our paper is to compare these PS in term of their ability to derive basic stellar parameters, i.e., Teff, log g, [Fe/H], and EB-vThe bank of spectral energy distributions [4] is used as an input to the numerical GAIA machine developed by the Vilnius GAIA group for simulation of photometric observations of single stars [5]. The model of GAIA observations takes into account the following features: optical transmissions of the telescopes and filters; spectral sensitivity of the CCD chips; Poisson and read-out noise; realistic sampling; brightness of the sky background. The analysis of advantages and disadvantages of the photometric systems proposed for GAIA is based on 77600 stars (G < 20 m ), which are generated by the Galaxy model [6] in 19 directions (I, b) up to the distance of 5kpc. This star sample well represents the bulk of the Galaxy stellar populations which will be observed by GAIA. The performance of the PS is estimated for the entire sample of stars, i.e., the results are dominated by the main sequence F-K type stars residing in the thin disc. In order to make the comparison of the three PS on equal grounds, the minimum distance method for simultaneous determination of Teff, log g, [Fe/H], and EB-V is implemented in the 4-D stellar classification engine [7], which was applied for all PS under consideration. The idea of the 4-D classification procedure is rather straightforward - the model with minimum parameter Q (x2 criterion) among all the models in the bank of standards is to be found:

Here, d and Coi are adjacent colour indices, observed and taken from the bank of standards, respectively; n is equal to the number of colour indices used for Institute of Physics, Gostauto 12, 2600 Vilnius, Lithuania © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002006

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classification; Wi are the statistical weights defined to be equal to I/of, where erf are rms errors of colour indices. We find that performance of each individual GAIA PS is very much dependent on the magnitude range. For example, for the stars with G < 17m, PS 2A demonstrates the best performance, and the precision of the derived parameters is completely satisfactory for the main GAIA tasks. For the stars in the magnitude range 17m < G < 19m, PS 3G shows slightly better results in comparison with 2A system, however, the precision of derived parameters is marginally acceptable and should be improved. The PS IF, presently assumed as a baseline PS for GAIA [1], is the least precise in terms of derived stellar parameters over the whole magnitude range. To illustrate the performance of PS, we give rms errors of the determined stellar parameters for the sample of 41 500 stars (V < 19m) within a distance of 5 kpc from the Sun: cr(logT eff ) ~ 0.02;
References [1] ESA 2000, GAIA: Composition, Formation and Evolution of the Galaxy, Technical Report ESA-SCI(2000)4, (scientific case on-line at http://astro.estec.esa.nl/GAIA) [2] Munari, U., 1999, Baltic Astron., 8, 123 [3] Straizys, V., H0g, E., Vansevicius, V., 2000, GAIA-CUO-078, Technical Report from Copenhagen University Observatory [4] Lejeune, T., Cuisinier, F., Buser. R., 1997, A&AS, 125, 229 [5] Deveikis, V., Vansevicius, V., 2001, ApfcSS, submitted [6] Torra, J., Chen, B., Figueras, F., Jordi, C., Luri, X., 1999, Baltic Astron., 8, 171 [7] Bridzius. A., Vansevicius, V.. 2001, Ap&SS, submitted

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

SPACE ASTROMETRY MISSIONS F. Mignard1 and S. Roeser2

Abstract. The successful HIPPARCOS mission has brought, and proved the validity of, a new observational concept to achieve absolute measurements of star positions in space. Only five years after the final publication of the results there are now four astrometry missions scheduled for the next decade, three of which appearing as the natural heirs of this pioneering mission. Space astrometry missions share a certain number of common features imposed by their observational principles and their scientific goals. The first part of this paper attempts to show how the objectives put severe constraints on the design and that this can be investigated with a fairly general approach. The German mission DIVA is then detailed as an illustration (GAIA being considered elsewhere in this volume). In the last section few words are added about FAME and SIM followed by global comparisons of these missions and their scientific returns.

1

Introduction

1.1

The Renewal of Astrometry

Astrometry aims to determine the basic geometric parameters of celestial objects, like the position, distance and displacement, referred to a well defined reference frame. The making of accurate angular measurements is one of the key tasks of astronomical research and from ancient times to mid-nineteenth century the cataloguing of celestial positions was indeed what astronomy was all about. For centuries astronomers were primarily astrometrists, endlessly charting the sky for time-reckoning, providing tools to help seafarers in open seas navigation or mapmakers in their surveying of new coastlines. A second incentive, the search of the laws of the motion of the heavenly bodies, led to a close observation of celestial phenomena for centuries down to the present time. More recently much effort 1 2

OCA/CERGA, avenue Copernic, 06130 Grasse, France Astronomisches Rechen-Institut, Monchhofstr. 14, 69120 Heidelberg, Germany © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002007

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has been devoted to pinpoint the precise location of the stars and ascertain their distance to the Sun, the key to a deeper understanding of the Universe as a whole. Today the best wide-field astrometry from the ground is achieved by optical interferometers that can reach the milliarcsecond accuracy, but with a low productivity in term of number of sources observable. Narrow field astrometry may be ten times better on large telescope, but again remains limited by the available telescope time. Furthermore it is of little help to determine the absolute parallaxes of stars beyond ~1 kpc, as the uncertainty of the background reference stars becomes larger than the measurements errors, so that even the best observations will be useless due to the impossibility to correct them for the average parallax of the reference stars. Let this problem aside, nothing valuable can be expected from narrow field observations to set up a globally inertial frame, one of the major objective of astrometry. Ground-based astrometric surveys, like the US Naval CCD Astrograph Catalogue, can at best achieve 25 mas on few tens of million stars, far from the precision achievable from dedicated spaceborne instruments like HIPPARCOS. Despite the extreme care exercised in this undertaking, a ground based astrometry survey is always marred with zonal distortions due to the propagation of minute errors from the numerous overlapping fields needed to tile out the whole celestial sphere. The success of the HIPPARCOS mission in the early 1990s dramatically demonstrated the scientific interest of accurate global astrometry in space because of its major impact on many branches of astrophysics and, to a lesser extent, in fundamental physics. It was clear that the potential of this technique had only been glimpsed with the 1 mas accuracy for a sample of rather bright stars (V < 9) and that there was room for improvement, both in number of sources, brightness and accuracy, thanks to the advent of electronic digital detectors and the parallel increase of the computing power. Following this remarkable success and the availability of new technologies, several space astrometry missions have been studied and propounded to space agencies aiming to explore the //as (1 //as = 10~6 arcsec) world for much fainter sources. Regarding this endless race toward extreme precision, the unique situation of the present epoch can only be fully appreciated with an historical perspective encompassing the last two millennia, as sketched in Figure 1. Between the time of Hipparchus and 1980, the art of fixing stellar positions on the sky has progressed by about four to five orders of magnitude, from a precision of one third of a degree for the bright stars in the Almagest to something close to 0'/05 for the FK5 the last of a series of fundamental catalogues, published just before HIPPARCOS. At the horizon of 2015, when the GAIA and SIM missions are completed, astronomers will have definitely set foot in the realm of microarcsecond astrometry, something just unthinkable 30 years earlier. Again a progress of another four orders of magnitude will be accomplished, but this time in less than three decades instead of two millennia. This achievement will place the best ground based astrometry of the 1980s, still so common to most astronomers, just mid-way between Hipparchus and the state of the art of space astrometry! Accordingly, it is not

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Fig. 1. The Rebirth of Astrometry illustrated in an historical perspective with the three main epochs: naked eyed observations, telescopic sightings and space astrometry.

exaggerated to refer to this unique period we are living in as the New Golden Age of Astrometry, maybe even more exciting and promising than that experienced in the XVIIth century with the invention of the telescope and its adaptation to eyesight for precise astronomy. 1.2

Direct and Indirect Goals of Space Astrometry

A space astrometry mission has a unique capability to perform global measurements, such as positions, and changes in positions caused by proper motion and parallax. These directions are determined in a reference system consistently defined over the whole sky, for a very large numbers of objects. Four missions are now planned to be launched within the coming decade, two from the USA and two from Europe, GAIA being the most ambitious. These new space astrometry missions share common features both in objectives and, to a lesser extent, in design, as shown in Section 2. Astrometric missions produce virtually no usable data until the mission is over and all the data sets are analyzed. Typically the direct results from the processing of the raw measurements are: • Accurate positions, absolute parallaxes, proper motions for millions stars; • Multi-epochs photometry (50 to 400 observations) in several bands at the milli-magnitude level;

72

GAIA: A European Space Project • Radial velocity to few km s~l (GAIA); • Spectrophotometry in the near IR and UV; • High resolution imaging.

Not every mission is able to perform all this variety of observations. It depends on the instruments and detectors included in the payload, on the observation strategy and the on-board storage capacities. While astrometric measurements are the baseline, in particular with the direct measure of the absolute parallaxes, it remains nonetheless that the major support and main drive follow from the indirect results and applications to stellar and galactic physics. The list below bears witness of the extraordinary versatility of global astrometry which touches just about every aspect of astronomy: • Recalibration of the extragalactic distance scale (cepheids, RR Lyrae); • Determination of the age of the globular clusters; • Determination of the absolute luminosities of a wide range of spectral types; • Detections of companion stars, brown dwarfs, and giant planets; • Detailed study of the structure, content and kinematics of our galaxy; • Materialization an optical inertial reference frame; • Mapping of the interstellar matter; • Survey of minor bodies in the solar system; • Contribution to fundamental physics (GR testing). It happens that each of the above items would be nearly sufficient to build a well balanced proposal for a space program, and in fact there are such proposals or even approved mission, like the French (and ESA supported) COROT. Probably the most awaited and easily publicized question that Space astrometry may answer is the detection of companion stars either in the substellar range (<0.1 A40) or in the planetary range (<10 Mj). As appealing this topic may seem, one may consider the impact on galactic and extragalactic physics as deeper and more far-reaching, with a recalibration of the extragalactic distance scale and a high resolution study of the period-luminosity relation of the Cepheids. Fundamental physics as well, will also benefit from astrometry through the accurate observation of the light bending in the solar gravitational field. Again HIPPARCOS has open the way [1] by demonstrating convincingly the possibility to use observations at wide angle from the Sun to estimate the curvature of the spacetime. No doubt that new generation missions will confirm and strengthen this feat.

F. Mignard and S. Roeser: Space Astrometry Missions 2 2.1

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Overall Concept of a Space Astrometry Mission Overview

There are basically two ways of measuring star position in space, each setting strong instrumental constraints. Either one chooses to survey in a very systematic way the whole sky down to a limiting magnitude or one has the capability to point nearly at will a given region of the sky. In the first instance a scanning instrument will be the best and a nearly optimal option with each detected photon contributing to the final astrometric accuracy. This minimizes the dead time needed for the operation as the sky survey is carried out by following a predefined smooth scanning law. In addition, observing simultaneously in two widely separated viewing directions allows to carry out the instrument calibration and to construct a rigid network on the celestial sphere with only six degrees of freedom, that are frozen by including very distant extragalactic sources, virtually motionless. The price to pay to the survey by continuous scanning is the lack of flexibility of the observation program with no way to tailor the observation times to each source. The scanning law determines completely the total time devoted to each source, the epochs at which it is observed and the number of times it will cross the fields of view. 4-90

Fig. 2. Typical sky coverage obtained with a scanning satellite designed for an astrometry mission. The plot corresponds to the GAIA scanning law over 60 days. Some areas have already been observed several times while others have not yet been visited.

With a pointing mission, one must work on a preselected list of targets, and accept to loose precious time and fuel to point the instrument in the specified directions. This has the benefit of flexibility and offers the possibility to adjust the observing time according to the scientific interest of the sources. The precision on the targets may then be much higher than with a scanning system which

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distributes the available observing time nearly uniformly over every source observable. However this is not adapted to global astrometry because of the difficulty of linking together sources widely separated on the sky. The two principles appear complementary and do not compete with each other. In addition it is difficult to imagine a system able to apply both principles within the same payload. Among the four astrometry missions approved for the next decade, three are of the scanning type: DIVA a small German mission due for launch in early 2004, FAME the NASA-USNO mission of comparable performances and scheduled for 2004-05, GAIA the European mission scheduled for the end of the decade. On the other hand SIM is a pointing mission aiming at a very high accuracy over a limited number of high value scientific targets. It will not be launched before 2009 and is part of a major technological program to detect terrestrial planets. 2.2

Design

The instrument design arises from the constraints on astrometric precision, the completeness of the survey down to a certain limiting magnitude and the need to carry out photometric measurements, more or less simultaneously with the astrometry. An elementary analysis of the signal-to-noise ratio yields already interesting design elements. For a diffraction limited optics with aperture size D, the diffraction spot on the focal plane has a typical angular size of X/D. Then if a total of N photons is available for localizing the center of the image, the achievable accuracy is of the order of

To reach a final accuracy of a it is necessary to estimate the image location to within a factor a/(\/D} of the diffraction pattern, which can be termed as the astrometric power of the instrument. The larger the power, the more challenging the mission. Typical powers for the four scanning astrometry missions are listed in Table 1. The increasing power from HIPPARCOS to GAIA is much more challenging than simply to collect more photons: before all, this is a technical challenge to design, build and calibrate the optics and the detection chain and keep the geometry from changing over various timescales. Now for an integration time T over a source of photon flux <J> we have,

where 77 is the overall quantum efficiency of the system, including the optics transmission. This leads to the required integration time as,

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75

Table 1. Astrometric power and integration time needed for the astrometry missions.

D(m) \/D(mas) cr(^as)

V rj Power (Airy/cr) Collecting area (m 2 ) Integration(s)

HIP

DIVA

FAME

GAIA

0.20 600 1000 9 0.003

0.25 500 200 9 0.5

0.4 300 50 9 0.2

1.7 70 10 15 0.5

600

2500

6000

7000

0.04

0.02

0.04

500

150

500

1.2 2000

With $ = 4 x 104 ph. m 2 s 1 for a star of 15th magnitude, one gets the results listed in the bottom of Table 1. Regarding the overall efficiency 77, it was very low for HIPPARCOS because one relied on a photoelectric detection; we took 0.5 for the other missions using CCDs except for FAME which has 15 transmitting optical surfaces, in addition to the four reflecting's. Therefore the overall transmission over a wide band might be severely affected.

which yields for a sun-like star of 15th magnitude,

Therefore, for GAIA a typical star should be allocated about 2000 s of observation over the mission length to reach the targeted astrometric accuracy of 10 /zas. Now, if Q is the field size in square degrees and T the effective mission length, we have for the available observation time for a specific star,

which yields a strong constraint on the field,

76

GAIA: A European Space Project

Table 2. Scanning parameters and observation efficiency of the astrometry missions.

Basic angle (deg) Sun aspect angle (deg) Scan rate ("/s) Period (mn) Precession period (days) Field height (deg) Mission length (yr) Time efficiency factor

HIP

DIVA

FAME

GAIA

58 43 168 128 56 0.9 3

100 45 180 120 56

106 55 120 180 72

0.57 2

81.5 35 540 40 20 1.1 5

0.66 5

0.8

0.9

0.9

0.65

Number of crossings per FOV

60

34

600

65

Available time per crossing (s)

5

2.8

2

15

Total time available per star(s)

600

200

2400

2000

This ensures that for a uniform scanning of the sky, a star will be repeatedly observed during the mission so that the observation time will reach the targeted time. For GAIA this time will be distributed over an average of 130 observations of ~15 s scattered over the five years of the mission, allowing to sample the parallactic ellipse, the orbit of close binaries and the photometric signal of variable stars. More generally the average number of observations can be readily estimated from the scanning parameters. However, one needs first to make clear of what is meant by "an observation". This could be the crossing of a CCD (as adopted for FAME) since this constitutes the basic data acquisition and one centroid is computed at each such crossing. Another approach would be the number of times a star enters one of the FOVs of the instrument (solution used for GAIA), or, when a complex mirror is used to map two regions on a single detector, the number of times a star is imaged on the focal plane (as used in HIPPARCOS or now for DIVA). Quite as important for the astrometric solution are the number of different epochs at which a star is observed, since this will control the sampling of the astrometric signal. For the sake of simplicity we consider here that one observation is defined as the passage of either FOV in the direction of a star. So observations in the preceding and, few minutes later, in the following field of view are counted as two observations (but combined in Fig. 3). From this choice, it is easy to adapt to any other definition, once the layout of the focal plane is known.

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Fig. 3. Typical number of observations achieved with a scanning satellite designed for an astrometry mission in ecliptic coordinates. The plot corresponds to the GAIA coverage for the astrometric fields over 1500 days. The average number is ~130.

If the field height (normal to the scan motion) is h and the scan rate on the sky is uj, the area swept during the interval of time dt is then wh dt. Therefore for a mission of effective length T the total number of observations per FOV is,

that is to say the number of times the celestial sphere is scanned. The time available for observations depends on the structure of the focal plane and the precise layout of the CCDs. Computation, using an efficiency factor (to allow for dead time), for the different missions are given in Table 2. The efficiency factor for HIPPARCOS is the real one; for DIVA it follows from the possibility of downlink the data only 19 hours every day; the other two values are conservative. The typical variation of the actual number of observations with the ecliptic latitude is shown in Figure 3. The highest density is obtained at an ecliptic latitude equal to 90 — £, where £ is the Sun aspect angle. The GAIA instrument and its scientific mission are widely presented in different chapters of this volume and are not covered again here. Detailed information is available in the GAIA study report [2] and in a summary paper covering most of the aspects of the mission [3]. A detailed presentation of DIVA is now provided, while FAME and SIM are marginally covered later in this chapter.

78 3

GAIA: A European Space Project The DIVA Mission

DIVA has been selected as the next scientific mission within the German space program "Small Missions" by an independent scientific selection committee. DIVA is planned to measure parallaxes, positions, proper motions, magnitudes and colors of up to 40 million stars. In its overall performance DIVA can be regarded as an intermediate step between HIPPARCOS and GAIA. With a launch expected in 2004, DIVA will deliver high-quality scientific data in the near future. 3.1

The Observing Programme

DIVA is a survey mission that will perform 3 different kinds of surveys. Each of the surveys is defined by an extremely simple selection function: observe all objects on the whole sky above a well-defined signal-to-noise ratio (S/N) and detect these in real-time onboard. Survey 1: Observe all objects having S/N > 15 at single transit in the integrated light given by the transmission of the optics and the sensitivity of the CCD-detectors. This S/N corresponds to V — 15.3 for an AO star and 17.1 for an M5 star (unreddened). For all stars of this survey DIVA will provide: positions, proper motions, parallaxes and magnitudes, as well as rough colors derived from the shape of the images. Unbiased from any a priori knowledge, this survey will comprise some 35 to 40 million objects. Typical values for the accuracy of measured parallaxes for a K4 star are: at V = (9, 12, IS)^ = (0.18, 0.35, 1.5) mas. Details of the performance are given below. As a rule of thumb, DIVA will measure the parallaxes of stars five times as accurately as Hipparcos (at the same magnitude), or it will achieve the same accuracy as Hipparcos but five magnitudes fainter. Survey 2: Observe all objects having S/N > 15 at single transit in the dispersed light created by a grid in the ray-path giving a dispersion of 200 nm/mm. This S/N corresponds to V = 13.5 for an AO star and 15.9 for an M5 star (unreddened). This is a subset of Survey 1 and the additional observations are spectra with a resolution of A/AA = 20. The survey, unbiased from any a priori knowledge, will comprise some 12 million objects. These observations will be used to determine effective temperature, surface gravity and metallicity for all stars in the survey. At V — 12, Teff can be determined to better than 5% and log g to better than 0.15 dex. Survey 3: Observe all objects having S/N > 3.5 in two photometric channels in the UV defined by filters, one from 310 to 350 nm and the other from 370 to 400 nm. This survey will supply magnitudes in both bands. The survey

F. Mignard and S. Roeser: Space Astrometry Missions

79

unbiased from any a priori knowledge will comprise some 30 million objects in the UV long channel and 15 million objects in the UV short channel. The UV observations will strengthen the classification of stars together with the spectral information from survey 2.

3.2

The Science Programme

The unique combination of homogeneous astrometric and photometric data as obtained with DIVA is expected to have a huge scientific impact on many fields of astronomy and astrophysics. DIVA will recalibrate the cosmic distance scale by measuring trigonometric parallaxes of some 30 Cepheids with a relative accuracy better than 10%. It will give about 25 times as many significant parallaxes as Hipparcos, with important consequences on the luminosity calibration for a wide variety of object types. Due to multicolor observations of at least 12 million stars, DIVA will map interstellar extinction with unprecedented accuracy as a function of direction and distance up to about 1 kpc. It will measure the tangential velocity of a typical OB-star at 3 kpc to 3 — 4 km s~l. The photometry and the parallaxes obtained by DIVA will determine the accurate locations of half a million stars in the Hertzsprung-Russell diagram. Precise distances of many stars of different populations in the solar neighborhood allow an age determination of the galactic disk and of the globular clusters. DIVA will test some 10000 stars for the presence of Brown Dwarf companions. Within R = 15 pc, DIVA will detect all Red Dwarfs (My — 17, £iM9.5) and measure their parallaxes with relative accuracy better than 5%. This yields a unique determination of the local luminosity and mass functions. Tangential motions of pre-main-sequence stars in nearby star-forming regions will allow to accurately determine their birth-places. With DIVAS measurements of the tangential velocities of several hundred stars in the Magellanic Clouds a reliable dynamical mass determination as well as a determination of the rotation axis and the space velocity of the Magellanic Clouds will be possible. From the relativistic light deflection at the sun, DIVA will determine the PPN-parameter 7 to 10~4. 3.3

Mission Overview and Satellite

As was originally planned for Hipparcos, a geostationary orbit would be best suited for DIVA; an L2-orbit as in the case of GAIA does not fit into DIVA'S cost envelope. But even launch into a geostationary orbit is out of reach because of costs. The present concepts relies on affordable launchers like Rockot or Dnepr-1, which will inject DIVA into a low-earth-orbit, from which the kick-stage of the satellite will deliver DIVA into a highly eccentric geosynchronous one with a perigee height of 500 km and an apogee height of 71000 km. The kick-stage will be separated from the mission module (Fig. 4), when the final orbit is reached. The time of revolution in this orbit is 24 h. That allows the use of only one ground station for the data link, which is possible for 19 hours. The 30-m antenna of GSOC in Weilheim (Germany) will be used as ground station. An average data rate for the transfer

80

GAIA: A European Space Project

of scientific data of 700 kbit/s will be procured. The nominal mission length will be 2 years. The DIVA mission module consists of a cylinder with a diameter of 2.1m housing the service module and a truncated cone containing the pay-load module (see Fig. 4). It has a total height of 1.5 m and a total dry mass of 446 kg. With this shape the mission module is optimized for minimum perturbation by the torque exerted by solar radiation pressure. In orbit, the vector of the solar radiation pressure points to the center of gravity of the satellite. DIVA follows a scanning law similar to that of Hipparcos whose parameters are given in Table 2.

Fig. 4. The DIVA mission module. This is the view as seen from the cold space. The solar cells cover the bottom of the cylinder and are not shown here. The sun-shielded entrances of the main instrument and the UV-instrument are seen on the conical envelope.

4

The Main Instrument

DIVA uses the Hipparcos concept of a solid beam-combining mirror to assemble the two lines of sight (about 100 degrees apart) onto a single focal plane. For each viewing direction the apertures are two rectangles of 225 mm x 110 mm. The optical system is a three-mirror assembly with the addition of two flat folding mirrors to make the design compact. The effective focal length is 11.2 m. The lay-out is schematically shown in Figure 5. Spectral dispersion in a direction perpendicular to scan is enabled by a diffraction grating on the last folding mirror (bottom in Fig. 5). The grating has 10 lines/mm giving a dispersion of 200 nm/mm on the focal plane. The blaze wavelength is 750 nm in the first diffraction order. 4.1

Focal Plane Assembly

The grid on the last folding mirror affects only a part of the focal plane. This part, receiving dispersed light, houses the so-called spectroscopic CCDs (SCI and SC2).

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81

Fig. 5. Schematic lay-out of the DIVA telescope. For more description see text.

Outside this area, in undispersed light, two CCD mosaics, called Sky Mappers (SMI to SM2 with another one cold redundant) are mounted. This arrangement is shown in Figure 6. All mosaics are identical and each consists of 4 individual chips with 1024x2048 pixels of 13.5 micronxl3.5 micron. The CCDs are thinned, back-side illuminated for high quantum efficiency.

Fig. 6. Schematic lay-out of the DIVA focal plane (main instrument). See text for a description.

82

GAIA: A European Space Project

Due to the rotation of the satellite the stellar images are moving across the focal plane. To compensate for this motion, all CCDs are clocked synchronously with the actual rotation of the satellite, i.e. they are operated in the so-called time-delayed integration (TDI) mode. The actual rotation rate, nominally 180 arcsec/s, is determined in real-time to an accuracy better than 0.1 arcsec/s from the crossings of individual stars through SMI to SM2. The integrated exposure time per mosaic transit is 1.4 s. In scan direction the full width of the central "Airy" fringe in both the SMs and the SCs is about 1.4 arcsec or 6 pixels at a central wavelength of 750 nm. In crossscan direction it is 2 times larger. Because the main astrometric measurements are done along scan a four times larger pixel size in cross-scan direction is used. In the present concept, this is achieved via an on-chip binning of four pixels in cross-scan direction. So, read-out noise as well as on-board data rates are reduced. 4.2

The UV-lnstrument

The UV telescope has Cassegrain-like optics with two flat folding mirrors and one FOV. The aperture area has a size of 133 cm 2 . The focal length is 70 cm. The UV telescope is optically separated from the main instrument, but mechanically connected to it. The DIVA UV telescope uses a configuration of 2 identical CCD mosaics (one for short, 316 — 356 nm, and one for long, 370 — 400 nm, wavelength) each consisting of one Ikx2k CCD. 5

Performance

The combination of an undispersed and a dispersed field in the focal plane makes DIVA a unique instrument. Astrometric and spectrophometric measurements are made quasi-simultaneously. The astrometric measurements will be performed with the Sky Mapper (SM) CCDs exclusively whereas the SC CCDs in the dispersed light are meant for spectroscopy only. With a small exception described below, DIVA does not rely on an a priori available input catalogue. Due to the relatively slow rotation rate, onboard realtime detection of star images is possible. After detection in the CCDs of the first sky mapper (SMI) the onboard computer predicts the position of the stars in the continuous pixel stream of the other CCDs (SM2, SCI and SC2) and cuts out the windows surrounding the stars on all CCDs plus small background windows. Only these windows will be transferred to the ground. Additionally, from time to time from each CCD a full-chip window will be transmitted to the ground. This on-board detection facility makes DIVA independent of an input catalogue. For a comparable small number of objects windows will be cut out without detection according to a guest observer catalogue. Another small catalogue has to be permanently stored onboard for the purpose of attitude determination. With the given properties of the DIVA instrument images of stars with different spectral type have been simulated by use of the spectral atlas from

F. Mignard and S. Roeser: Space Astrometry Missions

83

Gimn & Stryker (1983). On the basis of these simulations we show in Figure 7 the limiting magnitudes of the DIVA Sky Mapper CCDs. These estimations have been derived using conservative assumptions on sky background (0.1 e~/pix/s on average), dark-current (5 e~/pix/s on average) and read-out noise (7 e~ on average). Du to the fact that the available data rate determines the number of objects to be observed, we had to set a signal-to-noise (S/N) ratio of 15 for the detection level. At this S/N ratio, on-board detection on SMI at a single transit yields a portion of false detections of much less than 1 percent. Cross-checking with the data at SM2 eliminates most of these, and also spurious effects caused e.g. by impacts of cosmic particles, from further processing.

Fig. 7. Limiting magnitudes for stars of different spectral types as observed with the DIVA instruments: SM - Sky Mapper, SC - Spectroscopic CCDs, UVs - UV instrument, short wavelength (316-356 nm), UV1 - UV instrument, long wavelength (370-400 nm). The limiting magnitude for on-board detection is set at a signal-to-noise ratio (S/N) of at least 10 yielding a negligible number -of false detections. A priori known objects can still be analysed on ground if S/N is larger than 1.5.

The constraints from the available data rate and it's consequence on the specification of the S/N ratio for the detection define the limiting magnitude of DIVA uniform sky survey. As seen from Figure 7, this limit means a completeness at least down to V = 15 and gives an observing programme of more than 30 million objects. The expected accuracy of the parallaxes at this magnitude (see Fig. 8) is limited by read-out noise and will be about 6 mas (or even better for late-type stars). As the shape of the diffraction image on the SM CCDs is different for stars with different spectral type, information on the color of the stars can be obtained in the undispersed field, too.

84

GAIA: A European Space Project

As mentioned above, the brighter portion of stars detected in SMI and SM2 will be observed in the dispersed field on the mosaics SCI and SC2. The raw pixel data in windows around all stars down to about V — 11.5 (some 2 million objects), which contain the full spectral information, will be transferred to ground. For another 10 million objects between V = 11.5 and V = 13.5 the spectra are downlinked as the central fringe and the marginal distributions of these windows in cross-scan direction. Detailed spectrophotometric information will thus be gained for the brightest 12 million survey stars. The basic observing programme outlined above can be augmented by an additional list of a few ten thousand stars in the range between a S/N = 1.5 and S/N = 15. Proposals from the wide astronomical community are encouraged for these objects of particular interest. For the brightest stars the astrometric performance is limited by unmodelled errors from attitude determination and instrument calibration. The analysis of the effect of perturbations on the attitude has shown that the contribution of attitude noise to the error budget is 0.5 mas along scan per single field-of-view transit. We estimate that another 0.5 mas must be admitted due to unknown residuals of the instrument calibration. As said above, only the measurements of the 2 SM CCDs contribute to the overall astrometric performance. In Figure 8 the mean errors of parallaxes, as averaged over the sphere, are plotted on the basis of a 2-years mission. The distributions of the mean errors of the stellar positions and proper motions follow the same dependance on brightness. Figure 8 shows that mean errors of the parallaxes better than 1 mas will be obtained for all stars brighter than V = 14. The accuracy achieved by Hipparcos is plotted for comparison. As a general rule, DIVA surpasses the Hipparcos performance by a factor of 5 at the same stellar magnitude, or reaches the same accuracy as Hipparcos but for stars 5 magnitudes fainter. DIVA is designed for a mission length of 2 years. In order to quickly supply new observations to the astronomical community, the observations of the first year will be combined with the Hipparcos measurements. So, in this quick look reduction the proper motions of Hipparcos stars will be improved by a factor of 10, enabling also the detection of astrometric double stars. Spectrophotometric observations of all 120000 Hipparcos stars will also be published. These data will be available about 2 years after launch. For further details and for information on the progress of the mission the reader is referred to http://www.ari.uni-heidelberg.de/diva/diva.html 6

The FAME Mission

The Full-sky Astrometric Mapping Explorer (FAME) is a project funded by the NASA explorer program. It is currently under construction and will be operate.^ by the United States Naval Observatory with several institutional collaborations. It belongs to the new generation of astrometric satellites that exploit the same basic principle of the scanning telescope and the simultaneous viewing of two

F. Mignard and S. Roeser: Space Astrornetry Missions

85

Fig. 8. Mean errors of DIVA parallaxes for typical Bl, K4 and M5 stars after two years of observations. The signal-to-noise ratio (S/N) of 15 is used for the survey. The astrometric performance is limited to about 0.2 mas due to unmodelled errors from attitude determination of the satellite and instrument calibration. For faint stars, the CCD readout noise becomes the dominant error source. The corresponding accuracy for Hipparcos is plotted for comparison. In general, DIVA surpasses the Hipparcos performance by a factor of 5 at the same stellar magnitude, or reaches the same accuracy as Hipparcos for stars 5 magnitudes fainter.

different regions of the sky similar to the Hipparcos project. Like HIPPARCOS and DIVA and unlike GAIA the instrument makes use of a beam combiner to image the two fields on a single focal plane having f^~10 astrometric CCDs arrays and two photometric CCDs. Its design specification have been recently (July 2001) rescoped to deal with cost. Its aim is to obtain astrometry, as well as photometry in two Sloan bands (r1 and i'} for « 4 x 107 stars down to R = 15. FAME will accurately measure, over a 5-year mission, the absolute trigonometric parallaxes, positions, and proper motions of stars brighter than R — 9 to an accuracy of 50 /^as, equivalent to a 10 percent error for distances within 2 kpc of the Sun. For fainter stars (9 < R < 15), the lower signal-to-noise ratio resulting from fewer photons will degrade the astrometric precision to 500 //as at the faint limit.

86

GAIA: A European Space Project

FAME scans the sky by rotating with a period of 40 min perpendicular to the aperture plane keeping its rotation axis at 35 degrees from the Sun. It observes as it smoothly rotates, reading out the CCDs in the focal plane in time delayed integration mode. FAME also smoothly precesses, with the solar radiation pressure on the Sun shield providing torque to precess the spacecraft. The FAME rotation axis will be initially aligned 35 degrees from the Sun; solar radiation pressure on the shield will result in precession of the rotation axis around the FAME-Sun line. Trim tabs at the edges of the Sun shield are adjusted to tune the precession rate to a nominal 20 days. Every 20 days the two FAME apertures will scan over the entire sky except for the regions within 55 degrees of the Sun and the anti-Sun point. The observing operations will be based on an input star list built by the ongoing project of the first all-sky CCD astrometric catalogue (UCAC, [4]) whose completeness will cover the needs of the FAME survey. Therefore the bias in the survey will be the same as the bias of the input catalogue, although it is likely to be small because of the 2 magnitude difference between the limiting magnitude of the UCAC (V\im = 17) and that of FAME. Additional sources, as the brightest QSO's will be added to the programme for specific purposes. 7

The SIM Mission

We would say few words about SIM since it differs considerably from the three others both in objectives and design, though, as a pointing mission it can be seen as complementary to the scanning missions. The Space Interferometry Mission is being developed by the Jet Propulsion Laboratory under contract with NASA and in close collaboration with two industry partners. Beyond the scientific motivation for such a mission, the technological side is also a major drive to test for the first time optical interferometry in space, a prerequisite for the future search of extrasolar terrestrial planets. SIM will be placed in an Earth-trailing solar orbit slowly drifting away from the Earth at a rate of approximately 0.1 AU per year, reaching a maximum communication distance of about 95 million kilometers after 5.5 years. In this orbit the spacecraft will receive continuous solar illumination, avoiding the eclipses which would occur in an Earth orbit. The performance of the SIM instrument is designed to a wide-angle, 5-yearmission accuracy of 4 /ias down to a limiting visual magnitude of 20. The instrument will be a Michelson interferometer operated with a maximum baseline of 10 m. and able to point sources for several hours if needed at the limiting magnitude. Over its narrow field of view (~1°) SIM is expected to achieve a mission accuracy of 1 //as. About one hour integration is needed to reach this accuracy for V = 10. In this mode SIM will carry out measurements of distances to nearby galaxies and will search for planetary companions to nearby stars. In the wide angle mode (~15°), a lower accuracy will be achievable (nominally 4 /ias) but the positions and parallaxes are aimed to be absolute. In this mode the number of sources will be very limited (<10000) compared to scanning missions and

87

F. Mignard and S. Roeser: Space Astrometry Missions

Table 3. Summary data for the space astrometry missions. Vnm is the limiting magnitude, Kcompl. is the magnitude of completion of the survey. R10% is the distance at which the relative accuracy of the parallaxes is 10%. The next to last entry refers to the use or the independence of an input catalogue. The last line indicates if radial velocities are measured. Parameter

Hipparcos

DIVA

FAME

SIM

GAIA

Type

Scanning

Scanning

Scanning

Pointing

Scanning

1989

04/2004

06/2004

2009

2011

3

2.5

5

4

5

1996

2007

2011

12

16 (KO)

15

20

20

7-9

15

14

-

20

Launch Operations (yrs) Results Mim

^compl.

2017

a-* (^as)

1000(V < 9) 200(y = 9) 50(V < 9) 4(V < 16) IQ(V < 15)

o> (^as/yr)

1000(y < 9) 250(V = 9) 50(V < 9)

2

5 (V < 15)

2 (V < 9)

25

10 (V < 15)

Y

N

R10% (kpc)

0.1

0.5

Survey

N

Y 7

7

Y 4

N Objects

10

3 x 10

4 x 10

2 x 10

109

Input Cat.

Y

N

Y

Y

N

K

N

N

N

N

Y

5

restricted to rather bright stars except for the addition in the programme of several tens of QSO's needed to tie the global frame to the ICRF. SIM will build its own reference frame by creating a network of relative positions over the entire sky. Stars belonging to a tile of about ~100 square degrees, will be observed together with a fixed baseline inertially locked. By tying together sets of relative measurements of star separations, one can create a rigid reference frame. Overview of science and opearations can be found in the SIM documentation or summarized in [5]. 8

Overall Comparison of the Missions

The main properties and measurement capabilities of the planned astrometry missions are summarized in Table 3, together with that of HIPPARCOS for the purpose of comparison. The difference in content between a scanning mission and a pointing one is conspicuous, with several order of magnitude between the size of the GAIA and SIM catalogue at mission completion, although they have comparable

88

GAIA: A European Space Project

Fig. 9. Comparison of recent and future stellar catalogues for stellar positions and proper motions. The impact of Hipparcos and that of the future space astrometry missions is clearly visible, both by the number of sources, the precision and the measurement of parallaxes.

faint limiting magnitude. The number of objects selected for SIM in each class of stars (subdwarfs, Cepheids, RR Lyr, HGB) and in different locations (disk, bulge, globular clusters, Magellanic clouds, etc.) will be very limited, raising questions about the depth of the impact of the mission in the understanding of the Galaxy and its capability to disentangle complex physical or dynamical processes.

F. Mignard and S. Roeser: Space Astrometry Missions

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Fig. 10. The cosmic distance ladder. The revolutionary impact of space astrometry is so conspicuous that one may wonder how so much astrophysics was possible with so scarce a knowledge of the stellar distances. However the efficiency of the small angle astrometry for planetary detection and that of the imaging system for protoplanetary disks and compact galaxies are assets undisputed by GAIA, let alone the smaller missions. To place the scientific return into perspective with the recent and current ground based efforts, the major relevant catalogues are shown in Figure 9 for the positions and parallaxes (left) and for the proper motions (right), by indicating for each program the size of the catalogue vs. its astrometric precision. The role of space astrometry is striking as it allows to produce very large catalogues (comparable in size to the largest surveys in the visible and infra-red) but with a precision which cannot be reached on the ground, in particular for the parallax. The global nature of the astrometry has also an advantage not visible in these plots regarding its homogeneity and its lack of systematic zonal errors, as it has been brightly demonstrated by HIPPARCOS. Finally, Figure 10 is probably the best illustration of the revolution brought about by space astrometry thanks to the survey of stellar parallaxes and its consequence on the construction of the distance scale of the whole Universe. Despite considerable efforts deployed from the ground the measurement of trigonometric parallaxes has remained confined to the nearest stars, with only few hundreds known with a relative accuracy better than 10 percent at the time of the HIPPARCOS launch. The change is dramatic with the advent of space measurements, as if a totally new field had been opened. Beyond the improvement in

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GAIA: A European Space Project

accuracy, the major impact visible in this diagram is the possibility of including a wide variety of stellar types in the range achievable with the geometric method, without any assumption on the physics of the sources. Clearly astrophysics will not be quite the same after the completion of the astrometry missions and in particular when the GAIA survey becomes available in the middle of the next decade. References [1] Froeschle M., Mignard F. & Arenou F. 1978. Proc. of the ESA Symp. "Hipparcos – Venice 97", ESA SP-402, 49 [2] ESA 2000, GAIA, Composition, formation and evolution of the Galaxy, ESA-SCI(2000)4 [3] Perryman, M.A.C., et al., 2001, GAIA: Composition, formation and evolution of the Galaxy, A & A, 369, 339 [4] Zacharias N., et al., 2000, Astron. Jal., 120, 1148 [5] Unwin S., Pitesky J. & Shao M., 1999, ASP Conf. Ser., 167, 38

Fundamental Physics: General Relativity

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

RELATIVISTIC MODELLING OF POSITIONAL OBSERVATIONS WITH MICROARCSECOND ACCURACY S.A. Klioner1

Abstract. The problem of relativistic modelling of GAIA observations is reviewed. Basic principles of the relativistic model and its overall structure are described in detail. All relativistic effects which may amount to 1 uas are revealed and discussed. It is argued that relativistic definitions of astrometric parameters (position, parallax, proper motion, radial velocity, etc.) consistent with an accuracy of 1 uas should be considered only within a well-defined algorithm of relativistic reduction of observational data.

1

Introduction

The accuracy of GAIA is expected to attain 4 uas for the stars with magnitude V < 12 mag and 10 uas for the stars of V = 15 mag. Therefore, the model used to process the observations should be accurate at the level of at least 1 uas. It is quite clear that such a high accuracy makes relativistic effects an important part of the whole model. Moreover, relativistic effects cannot be considered as small corrections to Newtonian model. The whole model should be formulated in a language compatible with general relativity. In such a relativistic framework many Newtonian concepts typical for Newtonian astronomy must be eliminated and the meaning of astrometric parameters such as position, parallax and proper motion of a star should be changed: all these parameters are defined by the whole relativistic model applied to process the observations. 2

General Structure of the Model

Let us first outline general principles of relativistic modelling of astronomical observations on which the model presented below is based. General scheme of relativistic modelling is represented in Figure 1. Starting from general theory of 1

Lohrmann Observatory, Dresden Technical University, 01062 Dresden, Germany © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002008

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GENERAL THEORY OF RELATIVITY

A SET OF ASTRONOMICAL REFERENCE SYSTEMS

RELATIVISTIC EQUATIONS OF MOTION

EQUATIONS OF SIGNAL PROPAGATION

RELATIVISTIC DESCRIPTION OF THE PROCESS OF OBSERVATION

RELATIVISTIC MODELS OF OBSERVABLES Coordinatedependent parameters ASTRONOMICAL REFERENCE FRAMES

OBSERVATIONAL DATA

Relativistically meaningful astronomical parameters

Fig. 1. General principles of relativistic modelling of astronomical observations.

relativity one should define at least one relativistic 4-dimensional reference system covering the region of space-time where all the processes constituting the observed astronomical event are located. Typical astronomical observation depicted in Figure 2 consists of four constituents, which should be modelled. The equations of motion of both the observed object and the observer relative to the chosen reference system should be derived and a method to solve these equations should be found. Typically the equations of motion are second-order differential equations and numerical integration can be used to solve them. The observer receives information about the object by analyzing electromagnetic signals coming from

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the object. Therefore, the equations of light propagation relative to the chosen reference system should be derived and solved. The equations of motion of the object and the observer, and the equations of light propagation enable one to compute positions and velocities of the object, observer and the photon (light ray) with respect to the particular reference system at a given moment of coordinate time, provided that the positions and velocities at some initial epoch are known. However, these positions and velocities obviously depend on the used reference system. On the other hand, the results of observations cannot depend on the reference system used for theoretical modelling. Therefore, one more step is needed: relativistic description of the process of observation. This allows one to compute a coordinate-independent theoretical prediction of the observables starting from the coordinate-dependent position and velocity of the observer and in some cases the velocity of the electromagnetic signal at the point of observation. observer

observation light ray

object Fig. 2. Four parts of an astronomical event: 1) motion of the observed object; 2) motion of the observer; 3) propagation of an electromagnetic signal from the observed object to the observer; 4) the process of observation. The mathematical techniques to derive the equations of motion of the observed object and the observer, the equations of light propagation and to find the description of the process of observation in the framework of general relativity are well known. These three parts can now be combined into relativistic models of observables. The models give an expression for each observables under consideration as a function of a set of parameters. These parameters should be fitted to observational data to produce astronomical reference frames, which represent sets of estimates of certain parameters appearing in the relativistic models of observables. For example, International Celestial Reference Frame (ICRF) represents a catalog of coordinates of extragalactic radio sources with respect to the Barycentric Celestial Reference System (BCRS), which is a well-defined relativistic 4-dimensional reference system recommended by the IAU [I].

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It is very important to understand at this point that the relativistic models contain parameters which are defined only in the chosen reference system and are thus coordinate-dependent. A good example of such coordinate-dependent parameters are the coordinates and velocities of various objects at some initial epoch. On the other hand, from a physical point of view any reference system covering the region of space-time under consideration can be used to describe physical phenomena within that region, and we are free to choose the reference system to be used to model the observations. However, some reference systems, in which mathematical description of physical laws is simpler than in others, are more convenient for practical calculations. Therefore, one can use the freedom to chose the reference system to make the parametrisation as convenient and reasonable as possible (e.g., one prefers the parameters to have simpler time-dependence). Recently the IAU [1] has adopted two standard relativistic reference systems which are especially convenient to model astronomical observations. These two standard relativistic reference systems are called Barycentric Celestial Reference System (ICRS) and Geocentric Celestial Reference System (GCRS). Coordinate time t of the BCRS is called Barycentric Coordinate Time (TCB). Coordinate time of the GCRS is called Geocentric Coordinate Time (TCB). Throughout the paper the spatial coordinates of the BCRS will be designated as x. The GCRS is a socalled local reference system of the Earth, that is a geocentric relativistic reference system where at the coordinate level the influence of external gravitational fields is effaced as much as possible and is represented by a relativistic tidal potential. The existence of such a reference system is closely related to the Strong Equivalence Principle, on which Einstein's general relativity is based. The GCRS is convenient to describe the physical processed which are spatially localized in the vicinity of the Earth (e.g., motion of an Earth's satellite or rotation of the Earth itself). The BCRS is convenient to describe the phenomena occurring in and outside the Solar system and not localized within a smaller spatial region (e.g., planetary motion relative to the barycenter of the Solar system or light propagation from the source to the observer). Depending on the orbit of the satellite one can use either the BCRS or the GCRS to model its motion. In case of GAIA the BCRS is preferable, although the use of GCRS is also possible. If the GCRS is used then the position and velocity of the satellite relative to the GCRS must be recomputed into its position and velocity relative to the BCRS. Below it is supposed that the position xs and velocity xs of the satellite in the BCRS are given for any moment of t = TCB. According to the general scheme described above, the relativistic model of positional observations described below consists of several subsequent steps which account for the following effects: (1) aberration (effects vanishing together with the barycentric velocity of the observer): this step converts the observed direction to the source s into the unit BCRS coordinate velocity of the light ray n at the point of observation s; xs1

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(2) gravitational light deflection for the source at infinity: this step converts n into the unit direction of propagation of the light ray infinitely far from the Solar system at t —> — w; (3) coupling of finite distance to the source and the gravitational light deflection in the gravitational field of the Solar system: this step converts a into a unit coordinate BCRS direction k going from the source to the observer; (4) parallax: this step converts k into a unit BCRS direction / going from the barycenter of the Solar system to the source; (5) proper motion: this step provides a reasonable pararnetrisation of the time dependence of l caused by the motion of the source relative to the barycenter of the Solar system. Note that all these vectors should be interpreted as sets of three numbers characterizing the position of the source with respect to the BCRS (with expect for s which represents components of the observed direction projected in the local tetrad of the satellite). All these vector would change their numerical values if some other relativistic reference system is used instead of the BCRS. 3

Aberration

The first step is to get rid of the aberrational effects related to the BCRS velocity of the observer. Let s denote the unit direction (s • s = 1) toward the source as observed by the observer. Let p be the BCRS coordinate velocity of the photon in the point of observation (p is directed from the source to the observer). The unit BCRS coordinate direction of the light ray n = p/\p can be computed as

where w(xs) is the gravitational potential of the Solar system at the point of observation. This formula contains relativistic aberrational effects up to the third order with respect to 1/c. Because of the first order aberrational terms (classical aberration) the BCRS coordinate velocity of the satellite must be known to an accuracy of 10~3 m/s in order to attain an accuracy of 1 //as. For a satellite with the BCRS velocity \xs\ ~ 40 km s"1, the first-order aberration is of the order of 28", the second-order effect may amount to 3.6 mas, and the third-order effects are ~1 //as. Note also that the higher-order aberrational effects are nonlinear

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with respect to the velocity of the satellite and cannot be divided into pieces like "annual" and "diurnal" aberrations as could be done with the first-order aberration for an Earth-bound observer. This is the reason why one needs a precise value of the BCRS velocity of the satellite. Equation (3.1) is equivalent to a Lorentz transformation with velocity xs (l + 2c~ 2 w(xs)') which is the velocity of the satellite as observed by an observer co-located with the satellite at a given moment of time and having zero velocity relative to the BCRS. 4

Gravitational Deflection

Next step is to account for the general-relativistic gravitational light defection, that is to convert n into the corresponding unit direction a of the light propagation infinitely far from the gravitating sources at t —> — oo (below it will be shown that the correction due to possible finite distance to the source is important only for the objects located in the Solar system). The equations of light propagation can be derived from the general-relativistic Maxwell equations. It is sufficient, however, to consider only the limit of geometric optics. Relativistic effects coming from finite wavelength of the light are much smaller than 1 //as (see, e.g. [2]). In the limit of geometric optics relativistic equations of light propagation can be written in the form

where to is the moment of observation, xp(to) is the position of the photon at the moment of observation (this position obviously coincides with the position of the satellite at that moment xp(to) = xs(to)), cr is the unit coordinate direction of the light propagation at past null infinity

and S x p ( t ) is the sum of all the gravitational effects in the light propagation (&Cp(£ 0 ) =0, lim 6xp(t) = 0). t—> — oo

The Solar system is normally assumed here to be isolated. This means that the gravitational field produced by the matter outside of the Solar system is neglected. This assumption is well founded if the time dependence of the gravitational fields outside of the Solar system is negligible. Otherwise the external gravitational field must be explicitly taken into account. Some of such cases are mentioned in Section 8. Coordinate velocity of the photon can be obtained by differentiating equation (4.1): xp = c(T+6xp and then normalized to give the unit coordinate direction of the light propagation at the moment of observation

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The largest contribution in 5xp and in Scr due to the Solar system gravitational field comes from the spherically symmetric components of the gravitational fields of the massive bodies. In the post-Newtonian approximation for this effect one has

where MA is the mass of body A, d& = a x (r^0 x °") is the impact parameter of the light ray with respect to body A, r^0 = xs(to) — XA, and XA is the position of the body. Hence one can easily derive the post-Newtonian angle of deflection due to the spherically symmetric part of the gravitational fields of each body A:

where I/JA is the angular distance between body A and the source. Depending on the accuracy of observations and the minimal possible angular distance between the source and the body a number of additional gravitational effects should be taken into account. Table 1 illustrates the three most important effects: the post-Newtonian and post-post-Newtonian gravitational light deflection due to spherically symmetric parts of the gravitational fields of the massive bodies, and the effect due to non-sphericity of the bodies. Beside the effects shown in Table 1, the light deflection due to translational and rotational motion of the gravitating bodies may become important [3-5]. At the level of 1 //as the only additional effect here which is practically important is the moment of time at which one should evaluate the position of the body XA in (4.5). The body is moving and its BCRS position is time-dependent. On the other hand, XA is taken to be constant in (4.5). As it was shown in [5] in order to minimize the errors caused by neglecting the motion of the body in (4.5) the position of the gravitating bodies should be taken at the moment of closest approach between the light ray and the corresponding body. If the position of the body were taken at the moment of observation, it would cause an error of up to 6 mas in case of Jupiter. Recently, a rigorous theory of light propagation in the gravitational field of moving bodies has been elaborated [6], where the retarded moment of time was used instead of the moment of closest approach. However, the difference between these two moments produces an effect smaller than 1 //as and can be neglected. It is interesting to note that a number of smaller bodies should be also taken into account. For a spherical body with the mean density p, the light deflection is larger than 6 if its radius

Therefore, at a level of 1 //as one should account for lo (31 //as), Europe (19 //as), Ganymede (35 //as), Callisto (28 //as), Titan (32 //as), Triton (10 //as). Pluto (7 //as) as well as Charon, lapetus, Rhea, Dione, Ariel, Umbriel, Titania, Oberon

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Table 1. Various components of the gravitational light deflection in //as: pN and ppN are the post-Newtonian and post-post-Newtonian effects due to the spherically symmetric field of each body. Q are the effects due to non-sphericity of the bodies. Symbol "—" means that the effect is smaller than 1 //as. The values in parentheses are the maximal angular distances between the body and the source at which the corresponding effect still attains f //as. The observer is supposed to be within 106 km from of the Earth. For the Earth and Moon two estimations are given: for a geostationary satellite and for a satellite at a distance of 106 km from the Earth. body

pN

Sun 1.75 x 106 Mercury 83 Venus 493 Earth 574 Moon 26 Mars 116 Jupiter 16300 Saturn 5800 Uranus 2100 Neptune 2600

Q

(180°) (9') (4.5°) (178°/124°) (9°/5°) (25') (90°) (18°) (72') (51')

-1 — — — — — 240 95 8 10

ppN

11 (53')

(152") (51") (4") (3")

— — — — — —

-

and Ceres (1-3 //as). The influence of the Galilean satellites attains 1 //as at the angular distances of 11-32", and that of Titan at a distance of 14". 5

Coupling of Finite Distance and Gravitational Deflection

Next step is to convert cr into a BCRS direction from the source to the observer. Let xs(t) is the coordinate of the satellite at the moment of observation t and X(T) is the position of the source at the moment of emission T = T(t) of the observed signal. Let us denote

Vector k is related to a as [4]

The only effect in 5xp to be accounted for here is the post-Newtonian gravitational deflection from the spherically symmetric part of the gravitational field of the Sun. The effect amounts to 10 uas for a source situated at a distance of 1 pc and

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observed at the limb of the Sun. One can check that the effect is larger than 1 uas if \X\ < 10 pc and the source is observed within 2.3° from the center of the Sun. If at least one of these conditions is violated (which is the case for GAIA due to the minimal Sun avoidance angle of 35°) one can put k = a. For the objects located within the Solar system equation (5.2) can be combined with (4.3, 4.4) to get

For the post-Newtonian effect of the spherically symmetric part of the gravitational fields of the bodies (this is the most important effect in 6k) one has

6

Parallax

Now we have to get rid of the parallax (that is to transform k into a unit vector l directed from the barycenter of the Solar system to the source):

Below definitions of both parallax and proper motion in the relativistic framework will be given. Starting from this point the mathematical appearance of the model becomes similar to Newtonian: we just operate with "vectors" in the space of spatial coordinates of the BCRS. Although the suggested definitions are quite natural, their interpretation at such a high level of accuracy is rather tricky. Parallax and proper motion are no longer two independent effects. Second-order effects due to parallax and proper motion as well as the effects resulting from interaction between these two effects are important. Moreover, parallax, proper motion and other astrometric parameters are defined in operational way and have some meaning only within particular chosen model of relativistic reductions. That is why the whole relativistic model of observations must be considered. It is also clear that in order to convert observed proper motion and radial velocity into true tangential and radial velocities of the observed object additional information is required. Since that information is not always available, the concepts of "apparent proper motion", "apparent tangential velocity" and "apparent radial velocity" are suggested. These concepts represent useful information about the observed object and should be distinguished from "true tangential velocity" and "true radial velocity". Definitions of all these concepts are discussed below.

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Let us here define several parameters. The parallax of the source is defined as

the parallactic parameter II is given by

and finally the observed parallactic shift of the source is defined as

With these definitions to sufficient accuracy one has

The second-order effects in (6.5) proportional to r2 are less 3 [aas if \X\ > 1 pc. The second-order terms can be safely neglected if X > 2 pc. 7

Proper Motion

Last step of the algorithm is to provide a reasonable parametrisation of the time dependence of l and TT caused by the motion of the source relative to the barycenter of the Solar system. The following simple model for the coordinates of the source is adopted here

where AT = T — TO, X0 = X(T0), and V is the BCRS velocity of the source evaluated at the initial epoch T0. This model allows one to consider single stars or components of gravitationally bounded systems, periods of which are much larger than the time span of observations. Depending on the parameters of the source, final accuracy and the time span of observations higher-order terms in (7.1) can also be considered. In more complicated cases special solutions for binary stars, etc. should be considered instead of (7.1). Substituting (7.1) into the definitions of l and TT one gets

The signals emitted at moments TO and T are received by the observer at moments to and t, respectively. The corresponding moments of emission and

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reception are related by the equations

and similar equation for to and T0. The relativistic effects in (7.4) can be shown to be negligible. Let us denote At = t—t0 the time span of observations corresponding the time span of emission AT. From (7.4) one can see that these two time intervals are related as

Equation (7.5) results from a Taylor expansion of (7.4). Which terms of such an expansion are important depends on many factors. For example, for a large time span of observations terms quadratic in AT may become important. Here the two most important terms are retained. The first term in (7.5) is linear with respect to AT. The second term represents a quasi-periodic effect with an amplitude of about 500 s, giving a quasi-periodic term in apparent proper motion of the source [5]. It is easy to see from (7.2) that time dependence of parallax TT can be used to determine radial velocity of the source. This question has been investigated in more detail in [7]. The "true" tangential and radial components of barycentric velocity V of the source can be defined by

Equations (7.2, 7.3) can be combined with (7.5) to get the time dependence of l and TT as seen by the observer. Collecting terms linear with respect to At we get the definition of apparent tangential velocityVaptanas appeared in the linear term in l(t), and of apparent radial velocityVapradas appeared in the linear term in TT(t):

With these definition the simplest models for r(t) and l(t) as seen by the observer read (the higher-order terms are neglected here):

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Apparent proper motion is denoted uap here. Factor (1 + c 1 Vrad) in (7.8, 7.9) has been discussed in, e.g. [5, 8]. This factor may become very large and is one of the possible explanations of the well-known problem of superluminal motions in quasars and active nuclei of galaxies. The amplitude of the third term in (7.11) is about 170 uas for the Barnard's star with its proper motion of 10 uas [3, 5]. In case of GAIA this effect exceeds 1 uas for all stars with the proper motion larger than ~50 mas/yr. This effect is closely related to the Roemer effect used in the 17th century to determine the light velocity. Analogous term is widely used in modern pulsar timing models. Its potential importance for astrometry was discussed in detail in [8]. The apparent radial velocityVapradcan be immediately used to restore the true radial velocity Vrad . If bothVaptanandVapradcan be determined from observations one can restore the "true" velocities Vtan and Vrad- However, even if it is not the caseVaptanis useful by itself. Note that the radial velocities as measured by Doppler observations are affected by a number of factors which do not influence positional observations (various Doppler and gravitational [red] shifts, which can only partially be calculated since the physical properties of the observed object are not always known). Therefore, the Doppler radial velocities do not coincide with either V ra d or Vaprad. 8

What is Beyond the Model

The relativistic model proposed above can be considered as a "standard model". This model allows one to reduce the observational data with an accuracy of 1 uas and restore positions and other parameters of the objects (e.g., their velocities) defined in the BCRS. The model properly takes into account the gravitational field of the Solar system, but ignores a number of effects related with the gravitational fields produced outside of the Solar system. Let us briefly review these effects. The first additional effect to be mentioned here is the so-called weak microlensing which is simply the gravitational deflection of the light coming from a distant source produced by the gravitational field of a visible or invisible object situated between the observed source and the observer near the light path. For the applications in high-precision astrometry one should distinguish between microlensing events and microlensing noise. Microlensing event is a time dependent change of position (and possibly brightness) of a source, which is large as compared to the accuracy of observations and clear enough to be identified as such. Microlensing events can be used to determine physical properties of the lens so that the undisturbed path of the source can be restored at the end (see, e.g. [9–11]). In this sense microlensing events represent no fundamental problem for the future astrometric missions. On the other hand, microlensing noise comes from unidentified microlensing events (the events which are too weak or too fast to be detected as such). The number of unidentified microlensing events is clearly much higher than the number of identified ones. The effect of microlensing noise is stochastic change of positions of the observed sources with unpredictable (but generally small) amplitude and to unpredictable moments of time. Therefore, microlensing

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noise can spoil the determination of positions, parallaxes and proper motions of the objects [12–16]. It is currently not clear to what extend the microlensing noise on the objects of our Galaxy can deteriorate the resulting catalogs of the future astrometric missions. To clarify this question realistic data simulations involving a model for microlensing with a reasonable model for the Galaxy would be of much help. In edge-on binary (or multiple) systems gravitational light deflection due to the gravitational field of the companion may be observable under favorable conditions. Although it is clear that for companions with stellar masses the inclination of the orbit should be very close to 90° for the effect to be observable at the level of 1 uas, a separate study of the effect is necessary in order to estimate the probability of observing such a system. Gravitational waves can in principle produce gravitational light deflection. Two cases should be distinguished here: 1) gravitational waves from binary stars and other compact sources and 2) stochastic primordial gravitational waves from the early universe. Gravitational waves from compact sources were shown to produce an utterly small deflection which is hardly observable at the level of 1 uas [17]. The influence of primordial gravitational waves was analyzed in [18, 19] and shown to produce certain patterns in apparent proper motions of the sources. Although initially applied for VLBI, the method of these papers can be directly used for optical astrometry. Finally, cosmological effects should be accounted for to interpret the derived parameters of the objects (e.g., the accuracy of parallaxes an = 1 uas allows one to measure the distance to the objects as far as 1 Mpc away from the Solar system; see [20] for a discussion of astrometric consequences of cosmology). It may be interesting here to construct metric tensor of the BCRS with a cosmological solution as a background and analyze the effects of background cosmology in such a reference system. References [1] IAU (January 2001): Information Bulletin, 88 [2] Mashhoon, B., 1974, Nature, 250, 316 [3] Brumberg, V.A., Klioner, S.A., Kopejkin, S.M., 1990, Relativistic Reduction of Astrometric Observations at POINTS Level of Accuracy, in Inertial Coordinate System on the Sky, J.H. Lieske, V.K. Abalakin (eds.) (Kluwer, Dordrecht), 229 [4] Klioner, S.A., 1991, Soviet Astron., 35, 523; 1991, Astron. Z., 68(5), 1046; also published as Communications of the Institute of Applied Astron., No. 12, 1989, in Russian [5] Klioner S.A., Kopeikin, S.M., 1992, AJ, 104, 897 [6] Kopeikin, S.M., Schafer, G., 1999, Phys. Rev. D, 60, ID 124002 [7] Dravins, D., Lindegren, L., Madsen, S., 1999, A & A, 348,

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[8] Stumpff, P., 1985, A & A, 144, 232 [9] H0g, E., Novikov, I.D., Polnarev, A.G., 1995, A & A, 294, 287 [10] Hosokawa, M., Ohnishi, K., Fukushima, T., Takeuti, M., 1993, A & A, 278, L27 [11] Hosokawa, M., Ohnishi, K., Fukushima, T., Takeuti, M., 1995, Gravitational Lensing by stars and MACHOS and the orbital motion of the Earth, in E. H0g, P.K. Seidelmann (eds.),

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[16] [17] [18] [19] [20] [21] [22]

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Astronomical and Astrophysical Objectivities of Sub-Milliarcsecond Optical Astrometry (Kluwer, Dordrecht), 305 Hosokawa, M., Ohnishi, K., Fukushima, T., 1997, AJ, 114, 1508 Sazhin, M.V., Zharov, V.E., Volynkin, A.V., Kalinina, T.A., 1998, MNRAS, 300, 287 Sazhin, M.V., Zharov, V.E., Kalinina, T.A., 2001, MNRAS, 323, 952 Zhdanov, V.I., 1995, The general relativistic potential of astrometric studies at microarcsecond level, in E. H0g, P.K. Seidelmann (eds.), Astronomical and Astrophysical Objectivities of Sub-Milliarcsecond Optical Astrometry (Kluwer, Dordrecht), 295 Zhdanov, V.I., Zhdanova, V.V., 1995, A & A, 299, 321 Kopeikin, S.M., Schafer, G., Gwinn, C.R., Eubanks, T.M., 1999, Phys. Rev. D, 59, 084023 Gwinn, C.R., Eubanks, T.M., Pyne, T., Birkinshaw, M., Matsakis, D.N., 1997, ApJ, 485, 87 Pyne, T., Gwinn, C.R, Birkinshaw, M., Eubanks, T.M., Matsakis, D.N., 1996, ApJ, 465, 566 Kristian, J., Sachs, R.K., 1965, ApJ, 143, 379 Doroshenko, O.V., Kopeikin, S.M., 1995, MNRAS, 274, 1029 Klioner, S.A., 2000, Possible Relativistic Definitions of Parallax, Proper Motion and Radial Velocity, in K.J. Johnston, D.D. McCarthy, B.J. Luzum, G.H. Kaplan (eds.), Towards Models and Constants for Sub-Microarcsecond Astrometry (US Naval Observatory, Washington), 308 Kopeikin, S.M., Gwinn, C., 2000, Sub-Microarcsecond Astrometry and New Horizons in Relativistic Gravitational Physics, in K.J. Johnston, D.D. McCarthy, B.J. Luzum, G.H. Kaplan (eds.), Towards Models and Constants for Sub-Microarcsecond Astrometry (US Naval Observatory, Washington), 303

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

FUNDAMENTAL PHYSICS WITH GAIA F. Mignard1 Abstract. The baseline of GAIA is the study of the formation and evolution of the Milky Way from astrometric and photometric measurements. The mission displays a remarkable versatility in its applications, including a significant impact in fundamental physics. In the following I will try to define the relationship between astrometry and fundamental physics, before considering in more detail the determination of the space curvature and the study of the non linearity of gravity from the astrometric measurements. It is shown that GAIA is perfectly at home to sense the bending of light-rays in the solar gravitational field and should be able to determine the PPN parameter 7 with a precision between 10-6 and 10- 7 , much better than any other determination expected by 2015. A favorable combination of distances and eccentricities on a handful of minor planets will permit to search for the relativistic perihelion precession. The parameter (3 should be ascertained to 10-3 —10- 4 provided the solar quadrupole moment is not solved simultaneously and constrained from other sources. This achievable accuracy rests also on assumptions regarding the reconstruction of orbits of minor planets from GAIA-only observations.

1

Introduction

The GAIA astrometry mission will allow to determine accurate positions and proper motions of point sources up to the 20th magnitude. The main goals of the mission have been presented in detail in the study report [1, 2] and include primarily the detailed study of our Galaxy thanks to accurate astrometry, photometry and spectroscopy. Aside from the main goals, fundamental physics is particularly appealing for GAIA with the possibility of probing the space curvature in the Solar System, testing the non linearity of gravitation from the perihelion shift of minor planets, investigating a possible variability of G with the white dwarfs and defining and materializing an almost perfect optical inertial frame with the observation of thousands quasars. In this particular field of fundamental physics GAIA 1

OCA/CERGA, avenue Copernic, 06130 Grasse, France © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002009

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stands alone among the other astrometric missions given its capability to provide very accurate measurements in a survey mode, that is to say by including a wide variety of sources. 2

Fundamental Physics with Astrometry

Each of the four astrometric missions under study (FAME, DIVA, GAIA, SIM) has a section or a chapter of its proposal related to its impact on fundamental physics, meaning that the proposers expect side results, not so directly related to the astronomical objectives. HIPPARCOS set a precedent by providing the best determination of the PPN parameter 7 made in the visible [3], just by repeating at large angular distance to the Sun and without eclipse the epoch-making measurement of 1919 [4]. Even with the accuracy of HIPPARCOS this determination was just short by a factor three of the radio determination and demonstrated conclusively the capability of astrometry in this field. This is to date the most conspicuous encroachment of space astrometry in the world of fundamental physics. With the increasing precision of astrometric measurements, it is not so obvious to delineate sharply scientific results as belonging to astronomy or to physics. Historically this distinction was a non sense with Natural Philosophy encompassing the modern mathematical, physical and astronomical sciences. It seems at first glance that there are clearer boundaries today. However the history of the Universe, the physics of the Big-Bang, the solar neutrino problem, the nature of the dark matter are just a list of topics for which astronomy and particle physics are deeply intermingled. To delineate the possible scope of this paper I will adopt my own list, which, as any selection, is not above criticism for personal bias. The following items illustrate the major impacts of astrometric and photometric measurements on areas which lie farther out the classical boundaries of astronomy and likely to arouse interests in a wider community of physicists. 1. Definition and realization of a quasi-inertial and rigid machian reference frame based on extragalactic sources. This is not treated in this paper but considered in detail in another chapter of these proceedings [5]; 2. Determination of the space curvature through the influence of the light deflection on the proper direction of the stars; 3. Investigation of the non-linearity of the gravitation which manifests itself in the precession of the perihelion of the minor planets; 4. Time change of the Newton constant (G) which can be determined from the cooling of white dwarfs over very long period of time; 5. Large scale structure of the Universe that can be investigated with the distribution of quasars and distant galaxies combined with the reassessment of the distance scale;

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6. Distribution of dark matter that can be tackled with microlensing, rotational motion of galaxies, space density of white dwarfs; 7. The age of the Universe as determined from the observations and the physics of the oldest stars seen in globular clusters. Distances, chemical composition and absolute luminosity are the basic tools to constrain within ~1 Gyr the age of the Universe [6]. Because of lack of space and of competence on several of theses topics and also to avoid redundancies with other chapters of this volume I will consider with some details in the following sections only the items 2 and 3. Item 1 and 4 have a dedicated chapter and the other topics are interspersed here and there.

3

The Space Curvature

The curvature of the spacetime is determined by the distribution of matter through the Einstein equations of relativity. The path of a photon depends on the actual geometry of the spacetime and can be computed from the equations of propagation combined with boundary conditions. Hence, the observation of the change of direction of the incoming photon in relation with the position of the Sun helps probe the curvature between the source and the observer, more deeply in region of stronger gravitational field as in the inner Solar System. The evidence of the tiny deflection being related to direction measurements, accurate astrometric observations are the ideal mean to carry out such an investigation.

3.1

Propagation of Light Rays

The first step into a relativistic modelling of the light path consists of determining the direction of the incoming photons as measured by an observer located in the Solar System, as a function of the barycentric coordinate position of the light source. Then space curvature can be determined from astrometric measurements from the careful monitoring of the path of the photons in the gravitational field of the Sun. In the vicinity of the Sun the spacetime metric can be reduced to,

where isotropic coordinates have been used. The two main PPN parameters are as usual Y and B. This form of the metric around a single spherical massive body is sufficient for the following introductory presentation. A more comprehensive formulation can be found in [7].

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The equation of propagation of the light ray is given by the geodesic equation

where KM = d x / d < r , is the spacetime tangent vector along the ray. Equation (3.2) can be made explicit as a function of the coordinates xu as,

By using t as parameter, one has for the three equations of the space variables,

Now the actual path is very close to a straight line and one can just consider the departure from this line with,

where cr is the unit vector of the light ray at infinite distance from the Sun (this is not exactly the same as the unit vector along the path at the position of the source, since the latter is located at finite distance). The details of the integration of equations (3.4, 3.5) can be found in [8] and yields the trajectory of the photon and its temporal description. 3.2

The Deflection and its Magnitude

This point has been addressed in several books and publications and will not be discussed here. Apart from second order aberration, the only other sizeable effect is linked to the bending of light rays in the gravitational field of Solar System bodies, planets and satellites. The relevant geometry and notations are shown in Figure 1. The star is located at very large distance compared to the Sun and x is the angular separation between the Sun and the star. With the space observations to be carried out by GAIA, x is not necessarily a small angle. In fact, it can be very small for the planets where grazing observations are feasible, but remains always larger than Xmin = 35 ° for the Sun. The impact parameter of the unperturbed ray is denoted by d and the distance between the observer (on the earth or spaceborne somewhere in the Solar System) is r. The deflector has a mass M and a radius R. To the first order in GM/c2 and by neglecting any departure from the spherical symmetry the deflection angle is given by,

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Fig. 1. Deflection of starlight by the sun or the planets.

When the angular separation x is << 1 this expression reduces to

Then it is convenient to introduce the grazing deflection for a ray just passing at the surface of the deflector, or equivalently when d = R, which yields the classical result,

Although one talks about light deflection or bending, there is no way to measure this effect directly since the initial direction is not known. In fact one have access to the proper direction in the observer frame, and only the variation of this proper direction with time, due to varying geometry with respect to the Sun, is accessible, which eventually permits to determine the deflection proper. The magnitude of the deflection is given in Table 1 for various observing conditions likely to occur with GAIA. Considering an astrometric accuracy in the range of few uas, the magnitude of the effect is considerable, even for the planets in grazing conditions. However the observations of a star nearly aligned with a giant planet will be a rare event, and while this must be allowed in the modelling, these observations will not be very useful to determine the space curvature. On the other hand, there will be numerous and regular observations at wide angle from the Sun, up to x = Xmax = 145°, carrying the signature of the deflection. Additional terms are needed to allow for gravitational effect on the light ray at the uas level [7]. The post-PPN term for grazing ray is no more than 11 uas

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Table 1. Amplitude of the light deflection by masses in the Solar System. Grazing rays refer to rays touching the limb of the sun or the planet. Columns xmin and xmax give results for the minimum and maximum accessible angle to GAIA.

Quadrupole

Monopole Grazing Xmin

Gaia X = 45° X = 90°

J2

Grazing x — 1°

Xmax

uas

mas

mas

mas

Sun

1750

13

10 mas 4. 1 mas

2.1

<10-7

0.3

Earth Jupiter Saturn

0.5 16 6

0.5 16 6

2.5 uas 1 1 uas 2.0 uas 0 7 uas 0.3 uas 0 1 uas

0 0 0

0 001 0 015 0 016

1 500 200

uas

7 x 10-5 3 x 10-6

for the Sun and could be modelled with the Einstein theory. The effect of the solar quadrupole is shown in Table 1 and will not be a problem. It is significant for Jupiter and Saturn, but falls off very rapidly with the angular separation and only a handful of observations are concerned. 3.3

Space Curvature Determination

Like HIPPARCOS, the astrometric observations of GAIA will be modelled by including the effect of the light deflection in the computation of the apparent direction. Even in the case of HIPPARCOS, the magnitude of the solar deflection at wide angle was large enough (4 mas at 90 degrees) to introduce the PPN parameter 7 as an additional unknown to be solved as a general parameter within the astrometric solution. Although the strong correlation between the deflection and parallactic displacement limited the precision, 7 was found in agreement with General Relativity within ±0.003 [3]. With GAIA the individual observations will be much more precise and the solar avoidance angle smaller, which at the same time increases the signal and decreases the correlation with the parallax. Scaling on the HIPPARCOS result, Table 2 shows that a determination of 7 better than one part in a million could be achieved with GAIA. The last column of the table gives the ratio of the standard deviation for each scaling factor. This estimate is based on the 3 x 106 stars brighter than the 13th magnitude for which the expected astrometric accuracy is better than 4 uas and a correlation of 0.85 has been considered between the zero point of the parallaxes and 7 (see below). Clearly astrometry missions are the ideal tool to investigate the light deflection because of the very principle of measurement. The current ground based techniques have shown that 7 must be within 0.002 (time delay on Viking) or 0.0003 (VLBI) of unity [9]. No major advances can be expected from VLBI on the ground

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Fig. 2. Comparative geometry for the light deflection (f01) and the parallactic effect (f0 2 ).

in the next decade and the progress in the determination of 7 will be marginal with this technique. Before GAIA the data processing of GPB (Gravity Probe B scheduled for launch in fall 2002) could provide an estimate of 7 to 3 x 10-5 although there remain many uncertainties on the way to control the accuracy [10]. The best chances rest on the astrometry missions FAME and DIVA that should achieve a determination of 7 in 2007 between 10-4 — 10-5, intermediate between HIPPARCOS and GAIA. The determination of 7 through the variation of the amplitude of the light deflection should not be considered independently of the parallactic effect, as illustrated in Figure 2. A star lying on the scan circle is observed and both the parallactic effect (f01) and the light deflection (fO2) shift the direction of the incoming light along the line joining the star to the Sun: the parallax toward the Sun and proportional to TT and the deflection away from the Sun in proportion of (1 + 7)/2. Quantitatively the complete expressions are given by

which shows that the dependencies on the solar elongation are quite similar. One should not forget that in the case of GAIA x lies in the interval 35° — 145°. Hence a

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systematic and unmodelled effect in the origin of the parallaxes could contaminate the determination of 7. On the other hand, in a full model allowing for a constant term TTQ common to all the stars, there will be a strong correlation between 7 and TTo, but no bias. What really matters are the projections of the shifts on the scanning direction, because of the ID measurement. With a little algebra one gets for the final equations,

in which fo1 is the parallactic effect on the abscissa 0 and f02 the same for the light deflection. The minimum angular distance between a star observed by GAIA and the Sun is e = 35° and gives rise to the largest deflection of light (Eq. (3.9)). But in this circumstance the shift occurs precisely in a direction normal to the scan circle, which means that there is no sensitivity to the effect on the measured abscissa, as checked with equation (3.11) by putting 0 = 0. The maximum sensitivity (largest projected deflection) occurs when o = ±e that is to say x = arccos(cos2 e) ~ 48°. As for the correlation between 7 and TTQ it can be evaluated by computing the diagonal and off-diagonal terms of the condition matrix and averaging over 0 to account for a uniform distribution of abscissas during the mission. There is no closed expression and one must resort to numerical quadrature. With the GAIA scanning parameters one gets prQ = —0.85 instead of —0.92 for HIPPARCOS with a smaller sun aspect angle (43° for HIPPARCOS and 55° for GAIA). The extreme accuracy of the astrometric measurements will allow to determine 7 to an unprecedented accuracy of few 10- 7 . However this rests upon the ability to determine global parameters affecting in more or less the same way all the observations on all the stars yielding an improvement with the square root of the number of observations. The difficulty is not to solve for 7, but to make sure that any other global parameter, not orthogonal to the subspace determined by the condition equations of 7, is properly accounted for in the model. Otherwise, the real meaning of the parameter so determined will be questionable. The real challenge to do better than 10-6 lies precisely here. 4

Non Linearity of Gravitation

GAIA will observe and discover many hundred thousands minor planets during its five year mission. Most of these will belong to the asteroidal main-belt comprising objects primarily located between Mars and Jupiter and having small to moderate eccentricities. However there are also other populations exhibiting much smaller semi-major axes and/or very large eccentricities. For example, planets of the Amor group have perihelia between 1 to 1.3 AU and approach or cross the orbit of the Earth. Provided the astrometric accuracy in position propagates without too much degradation into the determination of the orbital elements, a refined

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F. Mignard: Fundamental Physics with GAIA

Table 2. Determination of the PPN parameter 7 with space astrometry.

HIPPARCOS

GAIA

105 stars V < 10 2.5 x 106 abscissas a ~ 3 to 8 mas X>47°

8 x 106 stars V < 13 2.5 x 108 abscissas a ~ 10uas

^ x 10-3 ay - 3

ay

X > 35° _>3 ~ 5 x 10- 7

aW^c

=

10 400 3 12000

modelling of the motion will be needed, including relativistic effects, giving additional possibilities of testing. 4.1

Perihelion Precession

As well known the relativistic effect and the solar quadrupole moment cause the orbital perihelion of a planet to precess at the rate,

where A = (2r - B + 2)/3 is the PPN precession coefficient, a the semi-major axis and e the orbital eccentricity. The rates are given in radians per revolution. Inserting numbers one has for the relativistic precession in mas yr- 1 ,

and for the solar quadrupole,

where a is in AU. One should note that the dependence of the precession rates in a and e are similar but not identical. The solar effect drops off more quickly with the distance. For the main belt the relativistic precession is of the order of 3 mas y r - 1 that is to say a hundred times smaller than for Mercury. At the moment, only observations of Mercury are available to test the relativistic precession in the Solar System implying that there is no way to separate the quadrupole effect from the prediction of general relativity (binary pulsars display also considerable precession, but this is used the other way round: GR is assumed to be

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valid and the precession is used to determine the masses). With GAIA orbits should be improved or determined ab initio for a great many objects providing a sampling in semi-major axes and eccentricities. In principle two planets are sufficient! However, even with many planets, the precession will be significant only for the Apollo-Amor asteroids, all with similar orbital elements. So one may fears that a non negligible correlation will remain between the determination of A and that of the solar J2. So it may be wise to decide that GAIA is not able to improve J2 (a reasonable bet for 2010 after the completion of the Picard mission http://www-projet.cst.cnes.fr:8060/PICARD/Fr/Welcome.html) and solve only for A.

Fig. 3. Distribution of the known minor planets in the plane semi-major axis - eccentricity. The level curves give the relativistic perihelion precession rate in mas yr- 1 . Mercury would lie below the plot at a = 0.39 and e = 0.21 and a precession rate of 430 mas yr- 1 .

4.2

Solving for A and J2

The current list of numbered asteroids with good or approximate orbits totals more than 105 objects. Nearly 90 percent have a very small perihelion precession, less than 3 mas yr- 1 , that will not be usable for GR testing. However there are -300 with Aw > 20 mas yr-1 and a handful for which the precession rate is even larger than 100 mas yr- 1 (Fig. 3). Few cases of earth-crossing objects are

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117

Table 3. Perihelion precession due to general relativity and the solar quadrupole moment for Mercury, a typical main-belt object and relevant objects with large precession rate. The last column gives the absolute magnitude of the planet (visual magnitude at 1 AU from the Sun and from the Earth at zero phase).

BODY

Aw mas/yr

J2(= 10-6) mas/yr

H mag

0.21

430

1.24

-

2.70

0.1

3.4

0.001

-

1.08 0.83 0.84 1.27 1.08

0.83 0.44 0.45 0.89 0.82

101 76 74 102 101

0.30 0.12 0.12 0.41 0.30

16.9 16.0 19.2 14.6 17.0

a AU

e

Mercury

0.39

Asteroid (main belt) 1566 2100 2340 3200 5786

Icarus Ra- Shalom Hator Phaeton Talos

illustrated in Table 3 giving a very significant yearly precession, due to a favorable combination of distance and eccentricity. These objects are predominantly small (0.5 to 3 km in radius), so the accuracy should not be too much affected by their apparent diameter, but in some case they will be simply too faint to allow repeated observations with GAIA [11]. The main difficulty will be the evaluation of a correction to be applied to the astrometric positions for the phase effect to refer the position to the center of mass instead of the center of light and then to determine good orbital parameters from the GAIA observations. The observational conditions for this sample of minor planets must be investigated in detail to determine the fraction which are actually too faint when crossing the astrometric field of view of GAIA, making the orbital fitting difficult to achieve with the required accuracy because of limited or biased coverage. It is hard to provide a reasonable guess on the actual accuracy in the determination of A and J2 achievable with GAIA without relying on an extensive simulation that would include the determination of the orbital parameters of the Apollo-Amor. The observability is by itself very complex due to the change in apparent magnitude with the distance. A planet of absolute magnitude close to 20, will be seldom detected, and this will impact considerably on the orbital parameters. I have considered a much simpler approach, aiming to test the mere possibility to decorrelate A and J2. I assume that orbital parameters have been determined and try to solve by least squares the following models, • Full model with two unknowns:

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Table 4. Determination of the relativistic precession parameter A and the solar quadrupole moment J2. The columns give the expected precision and the correlation under various assumptions. The first three columns give the result when both parameters are fitted to the data and in the last column J2 is constrained and not fitted. 1 unknown

2 unknowns run

a(J 2 )

P

Weighted with magnitude 1

0.58 x 10"2 1.6 x 1(T6 -0.90

0.25 x 10~2

a(e8w] = 0.1 masyr" 1 at H = 16 0.58 x 10~3 1.6 x 10~7 -0.90

0.25 x 10~3

a(e8w] = 1 masyr" at H = 16

No magnitude weighing

a(eSw) = lmasyr~

1

<j(e8w] = 0.1masyr- 1

0.51 x 10~2 1.3 x 10~6 -0.89

0.23 x 10~2

0.51 x 10~3 1.3 x 10"7 -0.89

0.23 x 10~3

Reduced model with J^ constrained:

where the ai and bi are computed for every planets from equations (4.2, 4.3). Then it is possible to compute the covariance matrix by weighing the equations from the expected standard deviation of the left-hand side. This depends on the magnitude, but probably not strongly, and on the eccentricity. In fact, for a given magnitude one may consider that the parameter properly determined with a nearly constant variance is efw, since the perihelion is poorly determined for orbits of low eccentricity. Therefore a(5w] oc l/e. There are two weighting schemes for each model, one without magnitude effect and Wi = 0"o/e2 and the second which allows for magnitude dependence with Wi = <jQ/e2/10OA(H~16\ where aQ(e8w} is the reference standard deviation of the orbital elements for a planet with absolute magnitude H — 16. Again two cases are considered with <JQ = 1 masyr" 1 and <JQ = 0.1 masyr" 1 . GAIA should be somewhere in between for a typical planet. This latter assumption will not be confirmed (or found utterly optimistic) before a more ambitious simulation is completed. Orbital data are taken from the files maintained by Bowell including ^100000 planets (ftp.lowell.edu/pub/elgb/astorb.html). Only planets of absolute magnitude H < 18 mag have been considered, so that they are more or less regularly observed [11] with good prospect of improving the orbital parameters. In the sample there are 7 planets with relativistic precession rate >100 masyr" 1 , 30 with rate >50 masyr" 1 , 240 with rate >10 masyr" 1 . The contribution of the

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119

thousands planets with smaller precession rate, most in the main belt, was found to be negligible, despite their large number. 4.3

Results and Comments

The results of the runs are summarized in Table 4, with the 2- and 1-parameter solutions and two kind of weighting. In spite of the different running conditions, there is no big difference between the solutions. A determination of A with an accuracy of 10~3 is a reasonable goal with a value closer to 10~4 probably achievable with favorable statistics and additional planets that will be known by the time of the GAIA launch. A goal of 10~5 that was initially quoted from crude estimation seems impossible to reach. This will give a slight improvement to the current determination based on Mercury perihelion shift giving
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mission of five years. Simulations are not in a sufficiently advanced state at the moment to be more precise and one must be cautious as long as the orbit determination problem from GAIA short arc observations is not solved. Compared to the huge experience accumulated with ground-based observations, GAIA scientists must reformulate the problem of orbit determination, and to a lesser extent that of orbit improvement, nearly from scratch because the positional data will be one dimensional and very accurate but will cover at the beginning a very short timespan, of the order of few hours, from which one will have to compute a preliminary orbit. Then, when an object is identified at the next passes, the orbit will be refined with the best precision allowed by the observations. Because of the systematic search of NEOs today, it is likely that most of the population of interest for GAIA will have been observed from the ground before the launch, a situation that will ease considerably the burden of orbit determination. 5

Conclusion

Even if the above investigations are limited to only two aspects of the relationship between space astrometry and fundamental physics, the prospects are very exciting, all the more because this is a side objective of the mission. For the PPN parameter 7 this study confirms the figures given in the Study Report and the fact that there is no other foreseen measurements able to challenge GAIA in the next ten years. As for /?, a limited simulation with seemingly reasonable assumptions ends up with a precision not as good as the initial guesses used at the time of the study report. Despite that, it improves significantly on the best ground based determinations and will only be challenged by the Mercury mission by 2010. But real difficulties lie ahead to process the observations of the Solar System objects and get reliable orbital parameters. References [1] ESA, GAIA, ESA 2000, GAIA: Composition, Formation and Evolution of the Galaxy, Technical Report ESA-SCI(2000)4, (scientific case on-line at http://astro.estec.esa.nl/GAIA) [2] Ferryman, M.A.C., et al, 2001, A&A, 369, 339 [3] Frceschle, M., Mignard, F., Arenou, F., 1997, Proceedings of the ESA Symposium "Hipparcos - Venice 97", ESA SP-402 [4] Dyson, F.W., Eddington, A.S., Davidson, C.A., 1920, Determination of the Deflection of Light by the Sun Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919, Phil. Trans. Royal Soc., 220, 291 [5] Mignard, F., 2002, EAS Publ. Ser., 2, 327 [6] Carreta, E., Gratton, R., Clementini,G., Fusi Pecci, F., 2000, ApJ, 533, 215 [7] Klioner, S., 2001, Practical Relativistic Model of Mircoarcsecond Astrometry in Space, AJ submitted [astro-ph/0107457] [8] Will, C.W., 1993, Theory and Experiment in Gravitational Physics, 2nd Ed. (Cambridge University Press) [9] Eubanks, T., et al., 1999, Advances in Solar System tests of gravity, ftp://casa.usno.navy.mil/navnet/postscript/prd_15.ps

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[10] Everitt, F., 2001, personal communication [11] Mignard., F., 2001, Observations of Solar System objects with GAIA, A&A, submitted [12] Will, C., 2001, The confrontation between general relativity and experiment, 2001, Living Review in Relativity 2001-4 (http://www.livingreviews.org/) [13] ESA 2000, BepiColombo, A mission to the planet Mercury, ESA-SCI(2000)1 [14] Rozelot, J.P., Bois, E., 1998, Synoptic Solar Physics, ASP Conf. Ser., 140, 75 [15] Godier, S., Rozelot, J.P., 1999, A&A, 350, 310 [16] Paterno, L., Sofia, S., Di Mauro, M.P., 1996, A&A, 314, 940 [17] Pijpers, F.P., 1998, MNRAS, 297, L76

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

WHITE DWARFS AS TOOLS OF FUNDAMENTAL PHYSICS: THE GRAVITATIONAL CONSTANT CASE J. Isern1, E. Garcia-Berro2 and M. Salaris3 Abstract. In this paper we examine the effects introduced in the luminosity function of white dwarf stars by a change of the gravitational constant during the life of the Universe. A decrease of G induces the expansion of the star and accelerates its cooling. This effect has noticeable effects on the luminosity function and can be used to set upper bounds on the rate of change of G. Preliminary results indicate that G/G < 10~13 yr^ 1 . These values are the best ever obtained and will improve as the white dwarf luminosity function will improve.

1

Introduction

The value of the constant of gravitation, G, is relatively poorly known. The reason for this is the small strength of gravitational forces and the limited relevance of G to the rest of physics. The possibility of varying the gravitational constant was first considered by Dirac [1] on the basis of his large number hypothesis and later developed by Brans & Dicke [2] in their theory of gravitation. The idea of an expanding universe led to the idea of a gravitational constant evolving with it, its rate of variation being of the order of the Hubble time, i.e. G/G = O~HQ, where a is a dimensionless parameter that depends on the theory considered. Of course, in the standard General Relativity model a — 0. The attempts of quantization of the gravitational force have reopened the topic of varying fundamental constants. As a general result, modern theories predict that in the ordinary three-dimensional subspace, gauge couplings like the fine structure constant a or the gravitational constant G should vary as the inverse square of the mean scale of the extra dimensions. Hence, the evolution of the 1

IEEC/CSIC, E. Nexus, c/Gran Capita 2, 08034 Barcelona, Spain IEEC/UPC, Departament de Fisica Aplicada, c/Jordi Girona Salgado s/n, Modul B-4, 08034 Barcelona, Spain 3 Astrophysics Research Institute, Liverpool John Moores University, 12 Quays House, Egerton Wharf, Birkenhead CH41 1LD, UK 2

© EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002010

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scale size of the additional dimensions is related to the variation of fundamental constants [3-5]. Several constraints to the rate of change of the constant of gravitation have been obtained up to now using the observation of lunar occultations and eclipses, planetary and lunar radar-ranging measurements, the evolution of the Sun, gravitational lensing, Viking landers or data from the binary pulsar PSR 1913+16, which provided for many years the most reliable bound, G/G < —(1.10± 1.07) x 10~n yr"1 [6]. Later on, Garcia-Berro et al. [7] used the luminosity function of white dwarfs and obtained a similar bound in an independent way, G/G < — (1.0 ± 1.0) x 10~n yr"1. The best value has been obtained using helioseismological data: G/G < -1.6 x HT12 yr-1 [8] . Given the important role played by a time varying gravitational constant in the unification of gravity with other interactions, and the uncertainties associated with the different methods, it is worthwhile to try to refine the values obtained with white dwarfs. 2

The Role of G in White Dwarf Cooling

The evolution of a white dwarf is just a cooling process that can be roughly described as:

where E is the internal energy and 0 is the gravitational energy. If G is allowed to change with time, then

Therefore, when all the sources of energy are exhausted, the influence of any change in G will appear. Figure 1 displays the contribution of these two terms as a function of time. The luminosity function is denned as the number of white dwarfs of a given luminosity per unit of magnitude interval:

where / is the logarithm of the luminosity in solar units, M is the mass of the parent star (for convenience all white dwarfs are labeled with the mass of the main sequence progenitor), tcoo\ is the cooling time down to luminosity /, rcooi = dt/dMboi is the characteristic cooling time, Ms and M\ are the maximum and the minimum masses of the main sequence stars able to produce a white dwarf of luminosity /, IMS is the main sequence lifetime of the progenitor of the white dwarf, and T is the age of the population under study. The remaining quantities, the initial mass function, <J>(M), and the star formation rate, ^(t), are not known

J. Isern et al: White Dwarfs as Tools of Fundamental Physics

125

Fig. 1. Contribution of the two terms of equation (2.2) as a function of time for a 0.6 and a 1.0 M0.

a priori and depend on the astronomical properties of the stellar population under study. It is important to realize that the number of white dwarfs at each bin depends on the time that each star stays in the bin. Therefore, roughly speaking, the number of stars at each bin will be reduced as:

and the effects of a change in G would become evident in the distribution of dim white dwarfs. The first one to use these objects for such a purpose was Vila [9]. However, he could not arrive to any conclusion because of the uncertainties in both, the observational data and the cooling theory of white dwarfs. Moreover, at that time the low luminosity branch, the region of interest, was not available. The cooling sequences adopted here are those of Salaris et al. [10]. They include an accurate treatment of the crystallization process [11,12] and a careful computation of the envelope. The adopted envelopes were made of pure H layer (MH = 10~4Mwo) on top of a pure He layer (MHe = 10~2Mwo)- Therefore, this envelope is only representative of DA white dwarfs. These sequences, which have been computed down to log(L/L0) ~ —5.5 and extrapolated beyond this point, reproduce well the blue shift in the colour-magnitude diagram quoted by Hansen [13], but have longer cooling times (even when sedimentation is suppressed) than those found by this author. Table 1 provides a glimpse to them.

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GAIA: A European Space Project

Table 1. Cooling times (Gyr) for some white dwarfs. The delays introduced by the sedimentation induced by crystallization are represented within parenthesis.

-log(L/L 0 )

2.0 3.0 4.0 4.2 4.4 4.6 4.8 5.0

0.54 M0

0.61 M0

0.77 M0

1.00 M0

0.15(0.00) 0.68(0.00) 3.56(0.12) 6.25(0.43) 8.39(0.65) 10.26(0.67) 12.25(0.67) 13.59(0.67)

0.16(0.00) 0.74(0.00) 4.00(0.15) 6.83(0.80) 9.34(0.99) 11.40(1.00) 13.37(1.00) 14.50(1.00)

0.18(0.00) 0.87(0.00) 4.81(1.15) 7.15(1.21) 10.45(1.21) 12.27(1.21) 14.38(1.21) 15.20(1.21)

0.24(0.00) 1.33(0.00) 5.28(0.98) 6.63(1.02) 9.11(1.03) 11.80(1.03) 12.25(1.03) 13.43(1.03)

Fig. 2. The left panel displays the observed luminosity function obtained by different authors. The right panel displays the merging of all of these functions.

3

The Observed Luminosity Function of White Dwarfs

There are at present several determinations of the white dwarf luminosity function [14-19]. Since all of them are in qualitative agreement, it is meaningful to merge all of them into a single one using their error bars as a statistical weight. Table 2 shows the distribution obtained in this way. The horizontal error bar was obtained from the number of observed bins present at each luminosity interval. The result is also displayed in Figure 2.

J. Isern et al: White Dwarfs as Tools of Fundamental Physics

127

Table 2. Averaged white dwarf luminosity function.

-log(L/L Q )

logn (pc 3mag *)

logn sup

logn inf

gt

nbjn

1.26 1.68 2.12 2.46 2.76 3.24 3.62 4.01 4.36

-4.67 -4.00 -3.94 -3.75 -3.61 -3.33 -3.07 -2.82 -3.14

-4.54 -3.87 -3.80 -3.54 -3.48 -3.16 -2.92 -2.68 -2.94

-4.85 -4.32 -4.17 -4.22 -3.81 -3.67 -3.30 -3.06 -3.89

0.20 0.03 0.08 0.04 0.16 0.06 0.08 0.05 0.09

1 3 2 2 4 4 5 5 5

Fig. 3. The continuous line shows the white dwarf luminosity function obtained assuming G/G = 0. Dashed curves have been obtained in the same way but assuming that G/G = 10-14,10-13,10-12,10-11,10-10 yr-1 from top to bottom, respectively. 4

Results and Discussion

To see the effect of a hypothetical variation of G we have computed the luminosity function for G/G = 0,10~ 14 ,10~ 13 ,10 -12,10-11, and 10-10 yr-1, assuming a

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constant star formation rate per unit volume and an age of the galactic disk of 10 Gyr. Figure 3 displays the results. As expected, the luminosity function is extremely sensitive to the rate of change of G. As soon as white dwarfs are cool enough, any continued decrease of G immediately causes a noticeable decrease of the density of white dwarfs per luminosity bin. Figure 3 clearly shows that this property will allow to put bounds of the order of TG > 1013 yr to the characteristic time scale for changing of (7, a value that is one order of magnitude better than that obtained from helioseismology. Notice, however, that to improve the situation not only is necessary to increase the precision of the luminosity function beyond log(L/L0) < —3 and to improve the models of white dwarf cooling, but also to put additional constrains to the star formation rate and age of the Galaxy. This work has been supported by the MCYT grants AYA2000-1785, ESP98-1348 and by the CIRIT program SGR.

References [1] Dirac P.A.M., 1938, Proc. R. Soc. London, Ser. A, 165, 199 [2] Brans C., Dicke R.H., 1961, Phys. Rev. B, 124, 925 [3] Marciano W.J., 1984, Phys. Rev. Lett., 52, 489 [4] Barrow J.D., 1987, Phys. Rev. D, 35, 1805 [5] Damour T., Polyakov A.M., 1994, Nuc. Phys. B, 423, 532 [6] Damour T., Gibbons G.W., Taylor J.H., 1988, Phys. Rev. Lett., 61, 1151 [7] Garcia-Berro E., Hernanz M., Isern J., Mochkovitch R., 1995, MNRAS, 277, 801 [8] Guenther D.B., Krauss L.M., Demarque P., 1998, ApJ, 498, 871 [9] Vila S.C., 1976, ApJ, 206, 213 [10] Salaris M., Garcia-Berro E., Hernanz M., Isern J., Saumon D., 2000, ApJ [astroph/0007031] [11] Isern J., Mochkovitch R., Garcia-Berro E., Hernanz M., 1997, ApJ, 485, 308 [12] Isern J., Garcia-Berro E., Hernanz M., Chabrier G., 2000, ApJ, 528, 397 [13] Hansen B.M.S., 1999, ApJ, 520, 680 [14] Fleming T.A., Liebert J., Green R.F., 1986, ApJ, 308, 176 [15] Liebert J., Dahn C.C., Monet D.G., 1988, ApJ, 332, 891 [16] Evans D.W., 1992, MNRAS, 255, 521 [17] Oswalt T.D., Smith J.A., Wood M.A., Ilintzen P., 1996, Nature, 382, 692 [18] Legget S.K., Ruiz M.T., Bergeron P., 1998, ApJ, 497, 294 [19] Knox R.A., Hawkins M.R.S., Hambly M., 1999, MNRAS, 306, 736

Astrometric Impact on Stellar Astronomy

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

GAIA AND PHYSICS OF STELLAR INTERIORS Y. Lebreton1 and A. Baglin2

Abstract. Understanding the stellar interiors is an important issue for astrophysics, but also for fundamental physics. The physical description of the stellar material implies statistical physics as well as hydrodynamics. We give examples of unsolved physical problems and their consequences for predictions of stellar properties and evolution. It is shown that the accumulation of high-quality data like distances and photometry on a large variety of objects, as proposed by GAIA, will be very useful. During the same period, asteroseismology will develop both from the ground in velocimetry, and from space in photometry, providing for the closest stars, a direct insight into their interiors. This ensemble of new data will constitute the basis of the general physical description of stellar interiors.

1

Introduction

Understanding the internal constitution of stars is fundamental both for physics and astrophysics. The great success of stellar physics and evolution theory has been the qualitative understanding of the Hertzsprung-Russell diagram in the 50s, relating the luminosity and the surface temperature of stars. However, since then, a global quantitative agreement is still missing and it remains difficult to infer the internal properties from observed surface quantities. With temperatures ranging from ~103 K to a few 109 K and densities of ~10~4 to ~108 g cm~ 3 , stars offer the rare opportunity to study the properties of matter in conditions generally not accessible to laboratory experiments. Moreover, part of our knowledge of the Universe and of its constituent galaxies is based on what we know about stars, in particular on our ability to model them properly: "If we did not have confidence in our ability to understand the stars, at least in principle, we would worry about the enormous astrophysical edifice which has been built up to explain the large scale features of our Universe" (M. Longair [1]). 1 2

UMR 8633, DASGAL, Observatoire de Paris, 92195 Meudon, France UMR 8632, DESPA, Observatoire de Paris, 92195 Meudon, France © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002011

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But stars are quite complex systems. Even the Sun, that can be observed with the best spatial and spectral resolutions, is far from being understood thoroughly. From the atmosphere to the deep interior, there are many unsolved questions related for instance to the description of microscopic physics or hydrodynamics, in particular convection. To build a satisfactory representation of a star's internal structure and to predict evolution, we have to proceed in two steps: first use the well-known stars to check and validate the theory and then apply this knowledge to study large populations. Modern instrumentation gives access to the global parameters (luminosity, radius or effective temperature, mass or radius for binaries and the Sun) and to surface abundances with a high level of accuracy for an increasing number of stars. This provides valuable but still partial constraints for the models because global parameters do not allow to probe the deep interior unambiguously. On the other hand, the measurement of the frequencies and amplitudes of various kinds of oscillating stars has proved to be a very powerful tool to sound their interiors, but only if their global parameters are accurate enough. In this paper, we outline some of the remaining problems in stellar physics and discuss the progress that is expected combining and complementing data from GAIA with, on one hand, asteroseismic data from the ground and more extensively from the future space missions (COROT, MOST, MONS and EDDINGTON), and on the other hand, data from high resolution spectroscopy, photometry and interferometry. 2

Modelling Stellar Interiors, What Should Be Done?

As said by Eddington in 1926, in his famous book, The Internal Constitution of the Stars, "At first sight, it would seem that the deep interior of the Sun and Stars is less accessible than any other part of the Universe... What appliance can pierce through the outer layers of a star and test the conditions within?". The question is still there and, a few years ago, the 32nd Liege Colloquium was dedicated to that subject [2]. 2.1

The Required Physical Description

A star is a gaseous body, which maintains its identity by self gravitation. To model a star one has to solve the basic equations which govern this type of object, expressing conservation of mass, momentum, energy, in a fluid. The adopted geometry is usually spherical for sake of simplicity, but non spherical processes like rotation or magnetic fields, are often present. Because the variations of the abundances of the various chemical elements proceed on very different time scales, the resolution of the equations expressing the evolution of chemical composition constitutes a stiff problem. The global set of time dependent differential equations has to be complemented by initial and boundary conditions. The initial

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composition and mass are needed as inputs and a model atmosphere provides the external boundary conditions, i.e. the interface with the interstellar medium. The physical description of the state of the matter enters the game through both the microscopic and the macroscopic descriptions. The equation of state, nuclear reaction rates, radiative transport efficiency, microscopic diffusion of the elements with respect to hydrogen, are needed on the microscopic side. Large scale hydrodynamical processes like convection or angular momentum transport are present. The exchanges through the "surface", as mass loss or accretion also intervene. There is generally a unique solution -and a unique evolutionary sequence- for a given initial mass, chemical composition and physical description. 2.2

The Level of Knowledge

Recent theoretical developments improving the microphysics (equation of state, opacities) have now been checked in the range of parameters corresponding to the solar radiative zone using helioseismological constraints. Cepheids, and in particular bump cepheids, have pinpointed inconsistencies. Part of them have now been understood but difficulties remain for instance in the modelling of low metallicity cepheids [3]. Experimental data have long been of little help. But one should mention the extent of high pressure laboratory experiments toward the domain of brown dwarfs [4], and the possibility to reach stellar internal densities and temperatures with high power lasers (see [5,6]). On the other hand, our knowledge in macroscopic physics as convection, turbulence, mixing or angular momentum transport remains very poor. The observations that are presently limited to the Sun, are not yet sufficiently constraining to distinguish between different hydrodynamical models (see [7]), and it is still impossible to explain some of the discoveries of helioseismology, like for instance the tachocline. The physical conditions of deep stellar interiors are difficult to reach for numerical simulations, but 3D codes run on massive computers are now able to describe the interplay between the high non-linear turbulence of the solar convective zone and the differential rotation (see [8]). Very often stellar evolution calculations use phenomenological descriptions, based on extremely rough physics, also roughly calibrated on observations. So, results have to be taken with caution! And models still completely neglect processes (for instance magnetic fields) because the observations have not reached a level of accuracy sufficient to characterize them. 2.3

The Theory/Observation Confrontation in Two Steps

The major issue for stellar physicists is the understanding of the physical mechanisms at work during the different phases of stellar evolution. This understanding has direct impact on fundamental physics, and at the same time should allow to

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predict stellar evolution in most cases and to use these predictions for a general understanding of the Universe. It proceeds generally in two steps: 1. improve our understanding of physics by testing theoretical descriptions in comparing predictions and observations, on a few well-known objects, and/or on sufficiently large homogeneous samples. This includes the Sun, the closest stars, binaries, pulsating stars, and the closest clusters; 2. on the basis of this validation, and assuming the universality of the laws of physics, provide the necessary inputs for interpreting observations in less common and more remote objects where observations are incomplete and less accurate, with the aim to improve our global vision of the Universe. But, the problem is not so simple. Parameters intervene in the description of the stellar plasma (microscopic physics, convection, rotation, mixing etc.) as well as in the choice of the initial characteristics of the models (abundances, masses etc.) when these latter are not given by observations. The number of observational quantities that can be obtained for a given star is generally small while the number of parameters used to model it is large, so that the Observation/Theory confrontation, needed to fix the unknown physics, is often an undefined problem. In addition, the measured global parameters are generally very poor indicators of the physical state in the interiors. For instance, different inner distributions of chemical composition can correspond to the same set of surface parameters. Also, observed and/or theoretical input parameters can have the same signatures in the HR diagram, implying a degeneracy of the solution whereas the uncertainties in the conversion of colour and magnitude into luminosity and effective temperature enlarges the error bars. The problem is simpler when stars belong to groups, assumed to share similar properties, as stars in clusters or in binary systems which have similar age and initial chemical composition but different masses. Moreover, stellar masses can sometimes be measured in binaries. For such groups, the model calibration involve a reduced number of parameters. To improve the situation, there are several ways from the observational side: (1) increase the accuracy on the global parameters, (2) increase the size of the samples to allow more precise statistical studies, (3) increase the number of observables. GAIA will contribute to the two first items, while seismology and interferometry for instance will contribute to the third one. 3

What's More from GAIA

GAIA will provide a huge, complete and homogeneous set of astrometric, photometric and spectroscopic data covering all types of stars, even the rarest, located in every region of our galaxy and in its nearest neighbours (see this volume). This will give access to luminosities, surface temperatures, abundances, extinction, and in some cases masses. For rare classes, corresponding to very bright massive stars, to very faint stars, and to rapid stages of evolution, a limited sample will be observed, for the first

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time. For more common objects, which have already been nicely observed by Hipparcos, the sample will be richer and the bright stars will be observed with a much higher accuracy. In the following, we present a few examples to illustrate the expected impact of GAIA on stellar physics. 3.1

Open Clusters

It is commonly accepted that open clusters stars have same age, same initial chemical composition for masses spanning a large interval. They draw a isochroneline in the HR diagram. If several cluster stars, members of binary systems, can have their masses and radii determined, then the models are constrained both by the HR diagram and the mass-luminosity (M-L) relation. This case which implies a reduced number of free parameters for the modelling is presently encountered only in the Hyades, the closest open cluster. For ~100 secure Hyades members observed by Hipparcos and from the ground, the HR diagram accuracy is of ~0.05 mag in My and ~0.01 mag in (B — V] [9,10]. For 10 Hyades stars in binary systems, the masses are determined with accuracies in the range 1 — 25 percents (see [11,12] and references therein). The [Fe/H]value has been determined with an internal accuracy of 0.05 dex (35%) by detailed spectroscopic analysis of 40 dwarfs [13]. The Hyades HR diagram and M-L relation are plotted in Figure 1.

Fig. 1. The Hyades M-L relation and H-R diagram: fitting the observations with models, from [11]. The stellar helium abundance Y (in mass fraction) which cannot be derived from the spectral analysis can be constrained by an accurate M-L relation if the error on metallicity is small. For example, the Hyades Y can be estimated from the M-L relation defined by the vB22 system in the range 0.8 — 1.1 MQ [11].

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Table 1 lists the contributions to the y-error budget expected from the internal errors quoted above: clearly the weight of metallicity is important. Table 1. Uncertainty on the helium determination due to model inputs in the 0.8 — 1.1 MQ range. mass magnitude BC [Fe/H] input physics error 1% 0.05 mag 0.05 mag 0.05 dex EOS, convection, atmosphere, diffusion AF 0.005 0.005 0.005 0.010 0.002

As indicated in Figure 1, the shape and position of the isochrone in the HR diagram, depends on the characteristics of the stars and on various aspects of the physics of the models. • Turn-off. The Hyades turn-off correspond to A-type stars in the 5-Scuti instability strip. The turn-off stars had convective cores on their main sequence (MS) life and many of them rotate at high speed. Rotation affects photometric data (Fig. 2). Rotation and overshooting may be responsible for internal mixing; this effect is very poorly understood, but modifies the internal structure, the evolution and the position in the HR diagram (see Fig. 3). As a result, the age inferred from the turn-off location is uncertain by about 20%; • MS slope. The slope at low mass is sensitive to the treatment of convection in the envelope. For the Hyades, in the mixing-length theory framework, it indicates that the mixing-length parameter may decrease slightly with decreasing mass, in the 0.8 — 1.5 M0 range; • Lower MS. The study at very low mass requires accurate magnitudes (the Hipparcos limit is My ~ 8 mag) and well-chosen colours. Appropriate model atmospheres are needed [14]. GAIA will allow further investigations in the Hyades. It will reduce the size of the error box in the HR diagram, both horizontally and vertically. It will extend the lower MS toward fainter red dwarfs and give access to white dwarfs. It will improve the binaries data and give some masses. However, it will not improve drastically the present age accuracy, nor our knowledge of convection. As discussed in Section 3.3, seismology is the appropriate tool for that. In addition, it will be necessary to know the abundances of those elements that, in addition to iron, contribute to the so-called metallicity and that are presently uncertain (C, N, O) or unknown (Ne). Also, GAIA will bring about 120 clusters like Praesepe, closer than about 1 kpc, at the same or better level of accuracy than that reached by Hipparcos in the Hyades. Ten binary systems are expected to be observed in each nearby open

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Fig. 2. Modelling the Hyades turn-off: correction to apply to isochrone to account for effects of rotation on photometric data [11]. cluster. This will give a better understanding of the relation between helium and metallicity in the galactic disk. The few open clusters observed by Hipparcos have shown that particularities exist, which are not well understood. The large sample accessible to GAIA will shed some light on this still obscure questions. 3.2

Binaries

Stars in binary systems provide more constraints for the models than single stars when their mass (and eventually radius) can be measured accurately. The "calibration" of the components, under the reasonable assumption that they have same age and were born with the same chemical composition, consists in finding a solution that reproduces the observed positions in the HR diagram for the observed component masses. Depending on the mass and evolutionary state of the components, one can obtain the system age and/or helium content, and constrain the models input physics. The three examples discussed below show the variety of questions that can be addressed. • a Cen. The nearest visual binary was considered, until recently, to be wellknown and well modelled. New interest came with new determination of the components masses [15] and the recent clear detection of p-mode oscillations in a Cen A [16]. The astrometric masses which were thought to be well assessed (internal error of 1%) became doubtful when radial velocity measurements yielded spectroscopic masses higher by 6 — 7% [15]. But, on the other hand, the orbital parallax corresponding to the high-mass solution is smaller than and outside the error bars of both ground-based and Hipparcos parallax. The calibration of the system on the basis of the global

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parameters neither allows to choose between the masses determinations, nor between the physical hypothesis like e.g. convective transport [17]. Progress will come (1) from the analysis of the oscillation spectrum of a Cen A which should give constraints on the stars interiors and (2) from safer data for the parallax, masses and individual abundances (GAIA, spectroscopy). • 92 Tau. This system belongs to the Hyades and is located at the turnoff. Its calibration could provide direct information on its age and helium abundance (Sect. 3.1). But a reliable calibration needs a reduction of the mass errors bars (12 and 8% for components A and B respectively) so that we can determine whether the A-component is a MS star or a subgiant (Fig. 1). In addition, the system is composed of two rapidly rotating stars, lying in the instability strip. A rich spectrum composed of several oscillation modes has been recently detected from space [18]. Because of high rotation influencing the photometry [19], it is difficult to pinpoint the system precisely in the observed HR diagram. Moreover, we cannot provide safe models for the system because we do not yet understand the processes able to extend the mixing beyond the limits of the classical convective cores, such as rotation and overshooting [11,20]. Progress requires (1) seismological analysis in Astars to get constraints on the interiors, (2) improved model atmospheres including rotation, (3) a better description of the pulsational spectrum in rapidly rotating stars. • n Cas. It is one of the rare, rather well-known, metal deficient systems, located in the thick disk of our Galaxy, having component masses accurate to better than 10%. The calibration of such systems provides constraints on the helium content of old stars and therefore on the primordial helium and on the microscopic diffusion process which acted during the life of old stars (Sect. 3.4). /^ Cas A is a ~0.8 MQ star, with an excellent Hipparcos parallax and a precise position in the HR diagram [21]. Its iron abundance ([Fe/H] ~ 0.7 ± 0.1 dex) is uncertain: it has been shown that it is larger by ~0.15 dex if it is derived from model atmospheres that include NLTE effects [22]. Also, it is enriched in a-elements with respect to the Sun. Accurate masses and positions in the HR diagram of an enlarged sample of metaldeficient binaries, down to very low metallicities will help in understanding the helium-metallicity relation in metal deficient stars. GAIA will contribute to such studies. For instance, it will measure the masses in more than 104 systems with an accuracy better than 1%, including many G-K bright stars but also fainter ones. 3.3

Young Stars and Convective Cores

It has been stressed for a long time (see e.g. [23]) that the size of the convective cores is badly known and that it cannot be dictated only by the Schwarzschild criterion, which has important consequences for ages determinations and subsequent stages of evolution.

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Fig. 3. Influence of overshooting (left panel) and of rotationally induced mixing (right panel) on models [11,20].

The penetration of convective motions and of matter in the stable zones extends the size of the central mixed zone, where nuclear reactions take place. As illustrated in Figure 3, this effect induces an uncertainty amounting to ~25% on the ages of A stars around 2 Gyr. In these intermediate mass stars, rotation remains important on the MS, and the differential rotation creates turbulent instabilities, which also contribute to the outward transport of matter [11,20]. The influence of this effect on the evolutionary tracks is illustrated in Figure 3. In addition, the oblateness of the stellar surface due to rotation modifies the observed global parameters of the HR diagram, depending on the aspect angle, as seen in Figure 2. To disentangle these effects, and to test the hydrodynamics, a direct insight is necessary, and it will be provided by seismology [24]. But, this is possible only if stellar parameters are known accurately; for instance, the HR diagram of the Hyades, though very precise thanks to Hipparcos and accurate atmosphere detailed analysis, cannot help in fixing both the physics and the age [11]. 3.4

Microscopic Diffusion and Old Stars

Microscopic diffusion has long been proposed to explain several facts, as for instance the evolution of white dwarfs [25]. The long time scales, as well as the very low relative velocities of the elements cast doubts on the efficiency of this process. New support to the presence of this phenomenon in the Sun has been provided by helioseismology, the temperature distribution at the base of the convective zone being better reproduced when diffusion is included in the solar evolution calculation [26].

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Fig. 4. The interpretation of subdwarfs: the combined effects of microscopic diffusion and of the NLTE populations on abundance determination can explain their position in the HR diagram. Left: the position in the HR diagram, at 9 Gyr, of a 0.8 M0 subdwarf of initial [Fe/H] ~ —1.0 dex without (A) and with (C) microscopic diffusion of helium and metals [27]. Right: the modelling of u Cas A: dot-dashed line is the 12 Gyr isochrone calculated for the NLTE [Fe/H]-value and including microscopic diffusion [21].

As diffusion is a very slow process, its effects on the global parameters should become detectable directly only for very old objects. It has been shown that subdwarfs models including diffusion are shifted by —150 K in effective temperature with respect to standard models [27]. On the other hand, such a shift is required to explain the position in the HR diagram of the low metallicity stars of the solar vicinity very accurately observed both by Hipparcos and from the ground [21] (see Fig. 4). Today, very few objects have very accurate global parameters. GAIA will give access to a large number of old stars, for instance 4000 F-K stars with V < 13 and [Fe/H] < —1.0 are expected at d < 200 pc. This will allow more stringent tests of microscopic diffusion, with improvements on the knowledge of old stars, for instance in what concerns the datation of globular clusters and halo stars (see C. Cacciari, this volume). 3.5

Pulsating Stars and Advanced Stages

Large amplitude pulsators are present all along the giant stages, but they are quite rare, as the evolutionary time scales are short. If their global parameters are well known, in association with the pulsation properties, they can provide powerful tests of internal structure. Recent microlensing surveys have produced homogeneous sets of data on Cepheids, RR Lyrae and Long Period Variables. Difficulties remain, for instance

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Fig. 5. Blue loops in 3 M0 standard models cannot reproduce the OGLE2 cepheids [28]. to reproduce the bulk of OGLE2 cepheids by blue loops predicted by standard models (see Fig. 5, [28]). But, GAIA will first reach with a sufficient accuracy most of the Cepheids of the Galaxy, providing precise distances (mean parallax accuracy of 4 uas) and temperature and metallicity indicators. The precise location of the instability regions and their metallicity dependence are powerful tools to fix for instance the coupling processes between convection and pulsation. The precise statistical distribution of stars with different abundances along the giant branch will also be accessible with GAIA; it contains many information on the evolution, and in particular it can be used to understand the behavior of the central regions, and the dredge-up of core material to the surface [29]. 3.6

White Dwarfs

The understanding of the internal structure of white dwarfs (WD) is related to that of the physics of matter supported by the degenerate electron gas pressure. It is important because WD are (through their cooling curves) used as chronometers to infer a minimum age of various regions of the Galaxy, as the galactic disk or halo. The theory predicts that WD obey a mass-radius (M-R) relation. This relation has to be safely assessed as it serves to determine the masses of single WD and in turn the WD mass distribution and luminosity function. Distances from Hipparcos (for 22 WD among which 4 belong to binary systems) and high resolution spectroscopy allowed to better anchor the theoretical WD M-R relation, although a larger number of objects are needed to confirm the theoretical shape of that relation and smaller error bars are necessary to test fine details of

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the WD interiors (chemical composition, magnetic fields, thickness of the Henvelope in DA WD). With GAIA, the distances of ~200 000 WD will be available. The study of several pulsating WD with very good distances should permit to better characterize the internal energy sources (for instance the properties of weakly interactive particles) and to better determine the mass of the crystallized core.

Fig. 6. The white-dwarf theoretical mass-radius relation for various compositions compared to white dwarfs observed by Hipparcos [30].

Again, GAIA should have to be complemented. In particular, smaller errors on WD bolometric corrections and effective temperatures are needed. In that respect, Procyon B has recently been suspected to have an iron rich core: its photometric Teff (obtained with an internal accuracy of 200 K) made it too small with respect to its mass, see Figure 6 from [30]. However, from the recent analysis of HST STIS spectra, it has been found to be cooler by ~200 K, which should have implications for the iron core hypothesis [31]. 4

Conclusions

It has been shown by Lebreton [32] how the gain on the accuracy on distances by Hipparcos has been helpful in the understanding of stellar physics. But, it is also shown that samples are presently too scarce, that complementary parameters are often too imprecise, and that our present theoretical knowledge in hydrodynamics is definitely still too uncertain in the physical conditions of stellar interiors.

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The forthcoming years are very promising. Important progresses are expected from the theoretical side, in particular using massively parallel computing. Stellar seismology will enter a productive phase, with access to a wide sample of different stars. Large telescopes equipped with modern spectrographs and interferometers will produce more accurate data. But, we will have to wait for GAIA to have a complete set of observables, on sufficiently wide samples, to really probe stellar interiors, and to be able to predict most phases of stellar evolution with confidence. These firm results will grave in stone a major part of the history and evolution of the Universe. References [1] Longair, M., 1993, Inside the Stars., IAU Col. 137, W. Weiss, A. Baglin (eds.), ASP Conf. Ser., 40, 1 [2] Noels, A., Fraipont, D., Gabriel, M., Grevesse, N., Demarque, P., 1995, Stellar Evolution: What Should Be Done?, Proc. 32nd Liege International Astrophysical Colloquium [3] Buchler, J.R., Kollath, Z., Goupil, M.J., 1996, ApJ, 462, L83 [4] Saumon, D., Chabrier, G., Wagner, D.J., Xie, X., 2000, High Press. Res., 16, 331 [5] Chenais-Popovics, C., Merdji, H., Missalla, T., et al., 2000, ApJS, 127, 245 [6] Da Silva, L.B., Celliers P., et al., 1997, Phys. Rev. Lett., 78, 483 [7] Michaud, G., Zahn, J.P., 1998, Theor. Comput. Fluid Dynam., 11, 183 [8] Brun, S. and Toomre, Y., 2001, ApJ, submitted [9] de Bruijne, J.H.J., Hoogerwerf, R., de Zeeuw, P.T., 2001, A&A, 367, 111 [10] Dravins, D., Lindegren, L., Madsen, S., Holmberg, J., 1997, Hipparcos Venice '97, ESA SP-402, 733 [11] Lebreton, Y., Fernandes, J.. Lejeune, T., 2001, A&A, in press [astro-ph/0105497] [12] Torres, G., Stefanik, R.P., Latham, D.W., 1997, ApJ, 485, 167 [13] Cayrel de Strobel, G., Crifo, F., Lebreton, Y., 1997, Hipparcos Venice '97, ESA SP-402, 687 [14] Allard, F., Hauschildt, P.H., Alexander, D.R., Starrfield, S., 1997, ARA&A, 35, 137 [15] Pourbaix, D., Neuforge-Verheecke, C., Noels, A., 1999, A&A, 344, 172 [16] Bouchy. F., Carrier, F., 2001, A&A, in press [astro-ph/0107099] [17] Morel, P., Provost, J., Lebreton, Y., Thevenin, F., Berthomieu, G., 2000, A&A, 363, 675 [18] Poretti, E., Buzaci, E., Laher, R., Catanzarite, J., Conrow, T., 2001, Radial and non radial pulsation as probes of stellar physics, IAU Colloq. 185, C. Aerts, T. Bedding & J. Christensen-Dalsgaard (eds.), PASP in press [19] Perez-Hernandez, F., Claret, A., Hernandez, M.M., Michel, E., 1999, A&A, 346, 586 [20] Goupil, M.-J., Dziembowski, W. A., Pamyatnykh, A. A., Talon, S., 2000, Delta Scuti and Related Stars, ASP Conf. Ser., 210, 267 [21] Lebreton, Y., Perrin, M.-N., Cayrel, R., Baglin, A., Fernandes, J., 1999, A&A, 350, 587 [22] Thevenin, F., Idiart, T.P., 1999, ApJ, 521, 753 [23] Maeder, A. & Mermilliod, J.-C., 1981, A&A, 93, 136 [24] Lebreton, Y., Michel, E., Goupil, M.-J., Baglin, A., Fernandes, J., 1995, IAU Symp., 166, 135 [25] Schatzman, E., 1958 White dwarfs (North Holland Publ. Co., Amsterdam) [26] Christensen-Dalsgaard, J., Proffitt, C.R., Thompson, M.J., 1993, ApJ, 403, L75 [27] Morel, P., Baglin, A., 1999, A&A, 345, 156 [28] Cordier, D., Goupil, M.J., Lebreton, Y., Lejeune, T., Beaulieu, J.P., 2001, Observed HR diagrams and stellar evolution, Coimbra Coll., in press

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[29] van Eck, S., Jorissen, A., Udry, S., Mayor, M., Pernier, B., 1998, A&A, 329, 971 [30] Shipman, H.L., Provencal, J.L., 1999, 11th European Workshop on White Dwarfs, J.E. Solheim & J.E. Meistas (eds.), ASP Conf. Ser., 169, 15 [31] Provencal, J.L. Shipman H.L., Koester, D., Wesemael, F., Bergeron, D., 2001, AAS Meeting, 197, 8301 [32] Lebreton, Y., 2000, ARA&A, 38, 35

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

IMPORTANCE OF VERY ACCURATE LUMINOSITIES FOR STELLAR FORMATION AND EVOLUTION A. Maeder1

Abstract. We show that there is a wide range of problems, where high accuracy astrometry can bring new information in stellar evolution, not limited to the classical applications in the HR diagram, such as the determinations of the helium and metal contents and of the size of the convective core. In particular, we show some new applications to the study of star formation. The accurate measurement of the luminosity of the observed birthline in the HR diagram is a key information very sensitive to the mass accretion rates. These rates determine all the properties of the pre-MS models. For the evolution of massive stars with mass loss and rotational mixing, strong constraints can be obtained from the combination of astrometric data and abundance determinations obtained by high resolution spectroscopy. We also emphasize that a better knowledge of the luminosity distribution of WR stars is strongly constraining the final masses at the time of supernova explosions as well as the nucleosynthetic yields.

1

Introduction

Our knowledge of the internal stellar structure is now making giant steps forward with the progresses of high resolution spectroscopy and of asteroseismology. High resolution spectroscopy provides Li, CNO, Na and Ne abundances, which give indications on how much surface material has been destroyed or brought from the deep interior. These are key indications on the size of the core, on the depth of the external convective zone and on the possible internal mixing processes. However, in most analyses the poor knowledge of the absolute stellar luminosity is a great source of uncertainty in the study of stellar properties. Asteroseismology, recently with CORALIE and soon with COROT, MOST, MONS and EDDINGTON, etc. is also on the way to provide beautiful information on the large and small separations Av0 and dv 0 , which are major constraints on 1

Geneva Observatory, 1290 Sauverny, Switzerland © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002012

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the stellar masses, on the ages and on the internal physics of the stellar models. However, without an accurate knowledge of the absolute luminosity, all the tests of the models are losing most of their significance. The unprecedented accuracy of GAIA will also enable us to have distances for massive stars, for which the data are still very uncertain. Also, as shown by the GAIA Report, the calibrations of the distances will be greatly improved for the LMC, SMC and other galaxies of the Local Group. The massive stars in these metal deficient objects serve as template for studies in the distant universe; their luminosities and other properties need to be better known. In the line of the studies made on the results of the HIPPARCOS mission, it might be considered that astrometry would improve our knowledge of stellar evolution mainly from classical discussions of the HR diagram. These studies usually provide some indications on the helium Y and metal Z contents, or on the size of the stellar cores. These aspects are certainly interesting, but here I prefer to focus the interest on some new questions in star formation and in stellar evolution, which reveal how open these fields remain. 2

Star Formation

At present, there are 3 different scenarios for the formation of massive stars: 1) the classical models with constant mass from the Hayashi line to the zero age sequence. 2) the formation by collision of intermediate mass protostars (cf. Bonnell et al. [1]; Stahler et al. [2]). 3) the formation by continuous mass accretion during the preMain Sequence phase (Beech & Mitalas [3], Palla [4]). As shown by Norberg & Maeder [5] and by Behrend & Maeder [6], in order to form a massive star in the accretion scenario it is necessary to account for non-constant accretion rates, i.e. accretion rates growing with the stellar masses. Scenario 1) is not in agreement with the observation of accretion disks and is no longer reasonably supported. Scenario 2) generally requires too high star concentrations to operate in a reasonable time scale (Henning [7]). Concentrations as high as 104 stars • pc- 3 are needed, while some regions of O-star formation have concentrations an order of magnitude lower. Thus, this scenario does not seem to be the general one. In scenario 3), the accreting stars all initially follow the same track, the so-called birthline, as long as they are accreting mass at a sufficient rate. When accretion stops, which likely occurs progressively (but which we treat as a stepwise transition), the stars with masses lower than about 12 Mo leave the birthline and move nearly horizontally towards the Main Sequence. The birthline, which raises up in the diagram from right to left, forms an upper envelope of the tracks followed by the low and intermediate mass stars when the accretion process has stopped (cf. Fig. 1). The location of the birthline is extremely sensitive to the rate of mass accretion. An increase of this rate produces a shift of the birthline towards a higher luminosity; this is due to more deuterium burning. A decrease of the accretion rate by 40% makes the birthline 0.5 mag fainter (cf. Fig. 2). Accretion rates of the order of 10-5 Mo yr- 1 explain very well low mass stars (Palla [4]). But such values fail to describe the formation of massive stars, because

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Fig. 1. Pre-Main Sequence evolutionary tracks with mass accretion (Behrend & Maeder [6]). The accretion rates are growing with time according to the observations of mass outflows. The upper envelope is the birthline, i.e. the line followed by a star continuously accreting mass at a significant rate. The other lines indicate tracks after the end of the accretion process, the final mass in solar unit are given, as well as, at the top of the figure, the ages of pre-MS evolution in million years. with such rates the massive stars would need too long a time to be formed and they would have left the ZAMS (i.e. burned a significant part of their hydrogen) before being fully formed, as pointed by Nakano [8] and Norberg & Maeder [5]. A remarkable observational relation between the outflow mass rates Mout and the stellar bolometric luminosities L of the ultra-compact HII regions was found by Churchwell [9] over the luminosity range of 1 to 106 Lo and the outflow rates of 10-6 to 10-2 Mo yr- 1 . Independent observations by Henning et al. [10] confirm this relation. A polynomial fit of the observations by Churchwell [9] gives:

Unfortunately, there is at present no direct empirical relation for the accretion rates Maccr. Thus, we adopt Maccr = fMout and test various values of / as shown in Figure 2. This is a reasonable assumption, because it is likely that there is some proportionality relation between the amount of mass accreted and that

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Fig. 2. Birthlines with mass growing accretion for various values of /, compared to observations of pre-Main Sequence stars collected by Norberg & Maeder [5]. The parameter / is the ratio of the mass accreted by the star to the mass ejected in the polar outflows (cf. Churchwell [9]; Henning et al. [10]).

ejected into the outflows. Tomisaka [11], with numerical MHD-simulations of a low mass class 0 protostar, found that approximately 1/3 of the infalling material is accreted by the star (which corresponds to f = 0.5). Shu et al. [12] deduced a similar value with a model of X-wind magnetic configuration for a low mass star. From measurements of the far-infrared luminosity of a B star and the mass of its outflows, Churchwell [9] estimated a smaller value of the order of f ~ 0.15. The "best" value of / is presently unknown. However, we can estimate / from the location of the birthline in the HR diagram (cf. Norberg & Maeder [5]), as illustrated in Figure 2. We see that a value of f = 0.5 is well supported, which means that from the infalling material 1/3 is going onto the central star, while 2/3 are ejected in the outflows in agreement with some of the above theoretical estimates. However, smaller values like f = 0.3 are also possible. Interestingly enough, the very high accretion rates (10-3 to 10-2 M0yr-1) obtained in this way for the very massive stars above 30 Mo correspond to the region of the stable mass inflows (cf. Wolfire & Cassinelli [13]; Nakano [8]). Figure 2 shows the large error bars on the absolute luminosities of the pre-Main Sequence stars and this greatly inhibit the determination of the best birthline.

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Fig. 3. The HR diagram of massive stars with (solid line) and without rotation (dotted line). The tracks with rotation are made for an initial rotational velocity of 300 kms- 1 , which corresponds to an average velocity of about 220 kms- 1 on the Main Sequence. This correspondence depends on the stellar masses. Clearly, we stress that accurate distances of very young clusters combined with infrared spectra of the pre-Main Sequence stars could lead to a great accuracy in our knowledge of the pre-MS tracks. The location of the birthline is extremely sensitive to the value of the accretion rates, and in turn the accretion rates critically influence all the internal stellar properties as well as the pre-MS lifetimes. Thus, there is a high interest in obtaining accurate distances for pre-MS stars. 3

Evolution with Mass Loss and Rotation

Many observations show that rotation is a necessary ingredient of the models of massive stars (cf. Maeder & Meynet [14]). In particular, no fast rotating O-type star has a normal He-content (cf. Herrero et al. [15]). Also, the B- and A-type supergiants, particularly in the SMC, show large relative excesses of N/H up to a factor of 10 (Venn [16]). Such large differences with respect to the predictions of current models indicate that some additional effect has to be included in stellar models, and the most likely one is rotation. New stellar models with rotation are now being made in Geneva and these models show that all the current outputs of

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Fig. 4. Predictions of the N/C excesses for models with the average rotation for various stellar masses compared to the observed abundances for B- and A-type supergiants by Venn [20,21]. The dotted lines show the predictions of models without rotation, for which the enhancements only occur when the star becomes a red supergiant. stellar evolution are significantly influenced by rotation: tracks in the HR diagram, lifetimes, core sizes, surface chemical composition, yields, supernova explosions, final stages, etc. Figure 3 shows the tracks in the HR diagram for stars of different masses with zero rotation and with initial rotational velocities of 300 kms -1 on the zero age sequence. We see that the effects of rotation mimic the effects of core overshooting. This means that the current predictions about the amount of overshooting derived from the HR diagram must be regarded with suspicion. Accurate distances may allow us to disentangle the effects due to rotation from the effects due to convective overshooting. Figure 3 also shows the track for a 60 Mo with an initial rotation velocity of 400 kms- 1 (which corresponds here to an average velocity of about 220 kms- 1 ). Interestingly enough, the evolution proceeds bluewards, on a track which is close to the track of homogeneous evolution. The lifetimes of the hydrogen burning phase are increased by the internal mixing in rotating star by typically 25 to 30%, while the duration of the helium burning phase is less modified, i.e. by less than 10%. The resulting differences in the age determinations are not negligible: with appropriate isochrones from models with

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rotation, the ages obtained are larger by about 25% (Meynet & Maeder [17]). This may solve the problem set by the larger age found for the Pleiades, as derived from the study of Li destruction in brown dwarfs (cf. Martin et al. [18]). Simultaneously, the models with rotation predict significant N/H or N/C excesses (compared to the initial compositions) for stars more massive than about 9 Mo. Even for this mass, some moderate excesses are already present in rotating stars near the end of the MS phase and this in agreement with former observations by Lyubimkov [19]. In the B-and A-type supergiants, these excesses as observed by Venn [20, 21] are even larger and they are illustrated in Figure 4. We must emphasize that standard models without rotation do not predict the observed excesses, while as shown by Figure 4 the models with rotation have N/C excesses which are well in the observed range. We must emphasize that the observed excesses are even larger for the A- and B-type supergiants in the SMC, in agreement with recent models. The reasons for the stronger mixing in lower metallicity stars is due to the fact that the internal gradients of angular velocity O are larger in such stars, because of the smaller mass loss rates and the higher compactness of the stars. We have shown a few of the differences brought about by rotation. There are many more. All these effects which have important consequences need to be further tested. However, all the comparisons will be meaningful, only if we accurately know the luminosities of the observed stars. This is far from being the case at present. The uncertainties in the luminosities often are a most severe difficulty in the comparisons. In this respect, GAIA in combination with data from high resolution spectroscopy will allow us to put much stronger constraints on the models of massive stars. 4

WR Stars

WR stars are nowadays considered as bare cores left over from massive stars which have experienced huge mass loss and possibly internal mixing. Due to their high luminosities and conspicuous emission lines, WR stars are the stars for which the sample is the most complete in the Milky Way. Also, they are easily identifiable in nearby galaxies. Their contribution to the integrated spectrum of galaxies is conspicuous even for galaxies at cosmological distances. The problem is that the distances even of the close WR stars are uncertain and the same for their luminosities. This prevents us to know well which range of initial masses is leading to WR stars. A better knowledge of the WR star luminosities would be most valuable, since WR stars are tracers of star formation, in particular, they are used to estimate the intensity of the star formation rate, as well as the age of the HII regions and starbursts, where they are usually found. Not only the range of the initial stellar masses is of great concern, but also the values of the final stellar masses, which are relevant for the study of the pre-supernova stages and nucleosynthesis. Figure 5 shows some evolutionary tracks in the HR diagram for very massive stars leading to WR stars. These models are for metallicity Z = 0.02 and initial

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Fig. 5. Evolutionary tracks in the Hertzsprung-Russel diagram for rotating stars with initial masses between 40 and 120 Mo. The evolution during the pre-WR phases is represented by continuous lines. Shaded areas with slanted and vertical lines show the portions of the tracks during which the star is a WNL, WNE star respectively. We included the WN/WC phase in the WNE phase. The long dashed-dotted curves correspond to the WC phases. Short transition evolutionary stages are sketched with a dotted line. The limit of the distribution of stars in the HR diagram (Humphreys-Davidson Limit) is shown by a long-broken line.

rotational velocities of 300 kms -1, which correspond to an average velocity of about 200 km s0-1 in this range of masses. The model of 40 Mo becomes a WR star after the red supergiant stage. It goes through the stages WNL (L stands for late, E for early), WNE and WCL with a final luminosity of the same order as the initial one. In the case of the model of 60 M0, the mass loss and mixing are high enough to bring the star in the WR stage at the end of the MS phase. For the 120 MQ, the entering of the WR phase even occurs during the MS phase. Due to the strong mass loss rates in the WR stage, the stars end this phase with likely very low final masses, i.e. in the range of 5 to 10 MQ. We have a very interesting possibility with GAIA to test the values of the final stellar masses. Since the internal structure of WR stars is rather simple, there is a well defined massluminosity relation for WR stars with no hydrogen left (Maeder [22]). This means that from the distribution of WR luminosities we may estimate the distribution

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of the initial stellar masses as well as of the final stellar masses at the time of supernova explosions. Depending on the value of the final masses, the yields in chemical elements are very different. In particular, if the final masses are low, this implies that lots of He, C and N have been ejected before being turned to heavier nuclear products. On the contrary, for large final masses, the yields in oxygen and other a-elements is quite large. Thus, accurate determination of WR luminosities will have far reaching implications for the masses of the pre-supernova progenitors and for stellar nucleosynthesis. In the Milky Way, there are clear changes of the number ratios WR/O and WC/WN with galactocentric distances (Maeder & Conti [23]). This trend is even more pronounced if we consider the WR stars in the LMC and SMC. This shows that the properties of WR stars are changing with the local metallicity, this also concerns the initial masses, the lifetimes, the final masses, etc. Already in the accessible zone of the Milky Way, the changes of the WR/O and WC/WN are rather large. Thus, the determination of the luminosities of WR stars from GAIA appears as an astrophysical objective of a great importance. This is particularly true for the WR stars in very young clusters and associations. I express my best thanks to Dr. Georges Meynet for the fruitful collaboration, which has led to the above results.

References [1] Bonnell, LA., Bate, M.R., Zinnecker, H., 1998, MNRAS, 298, 93 [2] Stahler, S.W., Palla, F., Ho, P.T., 1998, in Protostars and Planets IV, Mannings V. et al. (eds.) (Univ. of Arizona Press, Tucson), 397 [3] Beech, M., Mitalas, R., 1994, ApJS, 95, 517 [4] Palla, F., 1998, in The Origin of Stars and Planetary Systems, Lada C., Kylafis N. (eds.), NATO Sci. Ser. 540 (Kluwer), 375 [5] Norberg, P., Maeder, A., 2000, A&A, 359, 1025 [6] Behrend, R., Maeder, A., 2001, A&A, in press [7] Henning, Th., 2001, in Modes of Star Formation and the Origin of Field Star Populations, Grebel E., Brandner W. (eds.), ASP Conf. Ser., in press [8] Nakano, T. 1998, ApJ, 345, 464 [9] Churchwell, E., 1998, in The Origin of Stars and Planetary Systems, Lada C., Kylafis N. (eds.), NATO Sci. Ser. 540 (Kluwer), 515 [10] Henning, Th., Schreyer K., Launhardt R., Burkert A., 2000, A&A, 353, 211 [11] Tomisaka, K., 1998, ApJ, 502, L163 [12] Shu, F., et al., 1998, in The Origin of Stars and Planetary Systems, Lada C., Kylafis N. (eds.), NATO Sci. Ser. 540 (Kluwer), 193 [13] Wolfire, M.G., Cassinelli, J.P., 1987, ApJ, 319, 850 [14] Maeder, A., Meynet, G., 2000, ARA&A, 38, 143 [15] Herrero, A., Kudritzki, R.P., Vilchez, J.M., et al., 1992, A&A, 261, 209 [16] Venn, K., 1999, ApJ, 518, 405 [17] Meynet, G., Maeder, A., 2000, A&A, 361, 101

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Martin, E.L., Basri, G., Gallegos, J.E., et al., 1998, ApJ, 499, L61 Lyubimkov, L.S., 1996, Ap&SS, 243, 329 Venn, K., 1995a, ApJ, 449, 839 Venn, K., 1995b, ApJS, 99,659 Maeder, A., 1983, A&A, 120, 113 Maeder, A., Conti, P., 1994, ARA&A, 32, 227 Schaller, G., Schaerer, D., Meynet, G., Maeder, A., 1992, A&AS, 96, 269

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

DUPLICITY AND MASSES F. Arenou 1 , J.-L. Halbwachs2, M. Mayor3 and S. Udry 3

1

Introduction

Duplicity is a key question in astrophysics, and there is no doubt that the Milky Way would look entirely different if stars were single. Binaries provide direct measurements of stellar or galactic quantities and several astronomical phenomena occur only in binary systems. The binary rate, the distribution of mass ratio between components inform on stellar formation in relation with the place of formation. Stellar physics needs masses, luminosities and radii obtained through the studies of binaries. Galactic physics benefits also from this studies, e.g. the galactic potential can be tested using wide binaries, and the chemical evolution depends on binaries through the supernovae la process. Remembering the large number of doubles detected or suspected by Hipparcos, so large that the need of an adequate classification emerged - five different categories in the Double and Multiple Stars Annex - one could simply consider that GAIA will rescale the number of double stars to a Catalogue of one billion stars. But there is something more important, and what will be learned from GAIA may be easily summarized: GAIA will be a complete on-orbit observatory since it will provide homogeneous astrometric, photometric, and spectroscopic measurements; GAIA will at last provide large and unbiased samples of all kind of binaries, for an extremely large range of periods and mass ratios, at all evolution stages. Some of the questions which will be solved with GAIA may be mentioned. First, the parallaxes and proper motions will allow to distinguish between optical doubles and physical binaries. The binary rate will be known down to low mass companions, and in particular may allow to study the low mass companion rate at large separation. The mass ratio distribution will be found either as a random distribution or as a formation product. The formation of close versus wide binaries will be better known. For large separations, the mass ratio distribution and binary rate will allow to know the evolution process of such systems. For multiple system, 1 2 3

Observatoire de Paris, UMR 8633 du CNRS, France Observatoire Astronomique de Strasbourg, UMR 7550 du CNRS, France Observatoire de Geneve, 51 chemin des Maillettes, 1290 Sauverny, Switzerland © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002013

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the hierarchy and relative inclination will be accessible. For contact binaries, the accurate knowledge of the masses will allow to address the question of mass transfer, evolution and space distribution... The GAIA study report [1] describes largely the science case concerning binaries. After a brief remainder from this report concerning the general GAIA capabilities, we will mention a few complementary applications. 2

GAIA Capabilities

GAIA will discover about 60 million binaries, that is 3/4 of the nearby binaries brighter than 20m, and about 35% of them at 1 kpc. The final mission product could be more than 107 astrometric binaries, 106 eclipsing binaries, 106 spectroscopic binaries, 107 resolved binaries within 250 pc and 10000 stars with masses within 1%. Due to the huge number of detected binaries, even short-lived evolution stages will be reachable. And the duplicity will be studied in the field, in clusters or star-forming regions, where a majority of young stars are in binary systems [2]. Even at large separations, the high precision of the obtained three-dimensional velocity will permit to locate easily "common proper motion" pairs. Orbits of nearby visual binaries can be recovered up to 40 yr periods, and precise masses will be obtained for short enough periods, with the astrometry alone or in combination with the spectroscopic data. This will allow to put severe constraints on stellar evolution models, where a 2% precision on masses is needed [4]. The impressive number of expected astrometric binaries is due to the extreme GAIA sensitivity to non-linear proper motions. As an example, a pair of one solarmass stars with a 1000yr period would have an acceleration of 10uas yr- 2 (i.e. significant for the brightest stars) at 300 pc [3]. 3

On-Board Double Star Detection

The small angular size (37 mas) of the pixels in the GAIA astrometric focal plane, with a PSF of FWHM = 2.2 pixels, will allow to easily detect close (0.1") visual binaries. In the Astrometric Sky Mapper (ASM) where the on-board detection takes place, the sample size is 2 x 2 pixels, and the readout noise higher than in the astrometric field [5], but the detection of double stars in ASM is of interest for at least two reasons: a) the detection defines the patches which are observed in the astrometric field, and an undetected duplicity would render the astrometric and photometric data reduction much harder if the patches are too small; b) a subsample of well-behaved (single) stars will be needed for the data reduction. Figure 1 shows the minimum separation between components for which a duplicity detection could be done, and it also shows where larger patches would be needed. This theoretical minimum separation will most probably not be reached by the on-board detection algorithm. Moreover spurious double star detection may

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Fig. 1. Detection limit of double stars in the Astrometric Sky Mapper, from [6].

occur since the PSF is larger for a red star, and this may be attributed to duplicity as nothing is known about the star's colour when it enters the sky mapper.

4

Photocentric Binaries

Apart from the 16 CCD dedicated to astrometric measurements, each GAIA astrometric instrument also includes 4 broad-band photometers (BBP) primarily used for chromaticity corrections. However, these BBPs could also be useful for the duplicity detection: the photocentre of an (unresolved) double pair will not be identically positioned in each of these BBP, provided that the two companions do not have the same color. GAIA could then introduce a new category of photocentric or "color-induced" binaries in the terminology of [7,8]. Using only the BBPs of the Astro 1 instrument, where the along-scan resolution is the same as in the astrometric fields, the expected precision in one BBP will then be about \/2 x 16 less precise than the final astrometric precision. Assuming this precision for a G-type primary, and projecting randomly the separation between components for each of the 67 transits expected on the average during the mission, main-sequence secondaries of various periods and magnitude differences have been simulated in [9] for different distances. Then the separation p, position angle, magnitude and color of each components have been recovered by least-square. As may be seen in Figure 2, where are indicated the solutions with p > 3crp, GAIA may be able to resolve the brighter binaries down to the milliarcsec level, provided that the magnitude difference is in the range 1 to 3 mag.

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Fig. 2. Simulation of 3r detection of main-sequence binaries in the BBP, for a lm magnitude difference between components (left) and 6m (right). The oblique line is a empirical fit, and gives approximately the minimum detectable separation between components as a function of the apparent magnitude of the primary. 5

Mass Ratio Distribution with GAIA Spectroscopic Binaries

Thanks to its spectroscopic measurements, GAIA will obtain radial velocity curves up to about magnitude 17. In what follows, we will assume that GAIA will achieve a 2.3 kms- 1 precision per field transit at G = 14. This is slightly lower than what is predicted by [10] for a 0.5 A/pix dispersion spectrum for late-F to early-M stars. From our experience in orbit computation, we assume that an orbit will be obtained for the single-lined spectroscopic binaries (SB1) with

if this orbit is well covered by the observations (where K\ is the semi-amplitude of the radial velocity, e the eccentricity and i the orbital inclination). In practice, if the primary is GOV, the reflex orbit due to a MOV secondary of period smaller than 1.5 year will be computable; at the transition between brown and red dwarfs (M-2 = 0.08), the orbit will be obtained if the period is smaller than 3 days. For double-lined binaries (SB2) with components with nearly equal brightness, the condition above is no more valid since the spectral lines are blended; in practice, the limit in K\ is six times larger than for SB1, giving the condition K1 > 69 kms- 1 . In what follows we will study how GAIA will contribute to the knowledge of the mass-ratio distribution. Many binary studies suffer from biases, since the definition of an unbiased sample is far from obvious. The situation will radically change with GAIA. If we consider solar type stars brighter than 14, the volume from which a complete sample can be extracted is limited by the apparent magnitude, not by

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the astrometric precision on distance. This limiting distance is about 500 pc for G stars, while it will be 150 pc for K stars, neglecting the interstellar extinction. In order to compute how many stars are included in this volume, one may extrapolate what is known from the solar neighborhood. The Gliese Catalogue contains 10 spectroscopic binaries of period smaller than 4 years, closer than 21.7 pc with declination above —15°. Half of these are F7-G, the other being K stars. Thus, for each of these two categories, the density is about 1.85 x 10-4 SB/pc3 whether we assume a constant volume density or 0.0054 BS/pc 2 for a constant surface density. This would give between 4240 and 96 900 G-type SB of period less than 4 years within 500 pc, and between 380 and 2620 K-type SB within 150 pc. For a given mass-ratio g, a small inclination of the orbit implies a smaller K1. Assuming isotropic orientations of the orbit, half of the inclinations are above 60°, so half of our SB sample will have

and the limiting period corresponding to a 50% detection rate will be

For each limiting period P(0.5), the proportion of binaries with P < P(0.5) in our sample is computed. A constant distribution of log P is assumed, from 3 days until 4 years. We consider a 0.8 MQ primary, at the transition between G and K, and we assume that q will be directly known for the SB2, when q > 0.7, provided that the radial velocity curves of both components can be obtained. For q < 0.7, the mass-ratio will be obtained in combination with the astrometric orbit, although it could be deduced from the mass function using the iterative method from [11]. The astrometric orbit will have a minimum reflex semi-major axis a1(D) = P(0.5)days x 13.3 x 103/(212.9 x Dpc x 365.2S2/3) mas at the limiting distance D = 150 or 500 pc. Getting an astrometric orbit will easily be obtained with GAIA if a1 > 10<7w ~ 0.1 mas. The results are indicated in Table 1. The largest achievable periods, for q near the SB1 SB2 transition, is larger than 1 year. For q > 0.2, there will be enough stars to get a good determination of the mass ratio distribution, provided that the selection effects are corrected (as may be seen from the variations of P(0.5) with q). For mass ratio of the same order of the flux ratio, the astrometry will prove less useful, since the motion of the photocentre will be small. Then, above q > 0.7, the determination of the mass-ratio will effectively depend on the GAIA capability of deconvolving the primary and secondary spectra. Assuming this will be possible, the mass ratio distribution for q > 0.2 will be obtained using the GAIA spectroscopic capabilities, which will allow to study its variation as a function of spectral type, population, formation place, etc. Now, below q = 0.2, the mass-ratio will hardly be known through astrometry of resolved components, since a magnitude difference between components larger than 10 mag

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Table 1. Half-sample limiting period, proportion of stars and limiting semi-major axis as a function of mass ratio for GAIA spectroscopic binaries.

q P(0.5) days prop(P) % ai(150pc) mas ai(500pc) mas

0.1 2.7

0.02 0.006

0.2 18 29 0.15 0.045

0.3 52 46 0.43 0.13

0.4 107 62 0.87 0.26

0.5 182 66 1.49 0.45

0.6 277 73 2.26 0.68

0.7 389 79 3.18 0.95

1.0 3.8

(corresponding to q < 0.1) will hardly be observed. Smaller mass ratios will be obtained with the astrometric binaries, though here an assumption on the mass of the primary will be needed. 6

Eclipsing Binaries and Light-Time Travel Effects

One unexpected result of Hipparcos has been the number of new eclipsing binaries, even bright (7 m ) ones, showing that the completeness of eclipsing and contact binaries was not assured. Concerning GAIA, several million eclipsing binary light curves will probably be obtained. The multi-epoch photometry (between 60 to 300 measurements) and the individual precision will be of the order of 0.001 mag at G = 14 to 0.05 mag at G = 20. Combining the G band measurements to the 4 broad bands and the 11 medium bands and to the spectroscopic measurements will allow to obtain masses and radii to better than one per cent for thousands of binaries [10]. The colour and fundamental parameters (luminosity, temperature) will be obtained for total eclipses. Short periods eclipsing binaries are especially of interest for contact binaries, and more generally for interacting binary systems. As the GAIA sample will be unbiased down to faint magnitudes, W UMa-type or Algol-type contact binaries will be common, and their mass distribution, structure, evolution, kinematics and distribution in space will be better known, combining the radial velocity measurements with the astrometric measurements. Another kind of duplicity detection may be done using eclipsing binaries (or other variable stars with stable short-period variations) which host a long period companion. In this case, the reflex motion of this "clock in orbit" can be detected through a light-time travel effect. An example of the combination of the Hipparcos astrometric data with the Hipparcos photometric data and ground-based times of minima may be found with R CMa [12]. Compared to the radial velocity method, this method is sensitive to long periods (Fig. 3) and returns the same orbital elements (ai sin i, P, T, e, w), which would give the full orbital elements when combined with the astrometric data, and the mass of the companion if the primary mass is assumed. The detection would

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Fig. 3. Maximum amplitude for light-time travel (plain, left) and radial velocity (dash, right) as a function of period, for a one solar mass primary, and a secondary of 1, 0.1 and 0.01 solar mass. be obtained if an acceleration term is present both in the astrometry and in the light curve, possibly complemented by ground-based light curves. In the GAIA Catalogue, a light-time travel effect could then be tested for a 10 Jupiter-mass companion of period larger than 11 yr on more than 105 stars [13]. References [1] ESA 2000, GAIA: Composition, Formation and Evolution of the Galaxy, Technical Report ESA-SCI(2000)4, (scientific case on-line at http://astro.estec.esa.nl/GAIA) [2] Ghez, A.M., Neugebauer, G., Matthews, K., 1993, A&A, 106, 2005 [3] Mignard, F., Ecole de Goutelas #23, D. Egret, J.-L. Halbwachs & J.-M. Hameury (eds.), 101 [4] Andersen, J., 1991, A&A, 3, 91 [5] H0g, E., 2002, EAS Publ. Ser., 2, 27 [6] Makarov, V.V., Arenou, F., 2000, SAG-CUO-80, Gaia technical report [7] Wielen, R., 1997, A&A, 325, 367 [8] Tokovinin, A., 1999, in 1'astrometrie pour 1'astrophysique et 1'astrodynamique (Atelier Gaia, Grasse) [9] Arenou, F., Jordi, C., 2001, GAIA-FA-02, Gaia technical report [10] Munari, U., 2002, EAS Publ. Ser., 2, 39 [11] Mazeh, T., Goldberg, D., 1992, in Binaries as Tracers of Stellar Evolution, A. Duquennoy & M. Mayor (eds.) (Cambridge Univ. Press), 170 [12] Ribas, I., Arenou, F., Guinan, E., 2001, AJ, in preparation [13] Arenou, F., 2001, GAIA-FA-01, Gaia technical report

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

THE OLDEST STELLAR POPULATIONS AND THE AGE OF THE UNIVERSE C. Cacciari1

Abstract. The study of the oldest stellar populations in the Galaxy provides important cosmological information (e.g. a lower limit to the age of the Universe) and helps constraining models of galaxy formation. The most commonly used stellar age indicators are reviewed and discussed, and the impact of GAIA on these topics is estimated.

1

Introduction

The main purpose of this contribution is to estimate the impact of GAIA on the study of the oldest galactic stellar populations (Pop. II). The determination of the age of the oldest objects in the Galaxy provides a lower limit to the age of the Universe, and this in turn can be used to constrain cosmological models and parameters, as well as models of galaxy formation. The oldest stellar components in the Galaxy are mainly related with the halo, which was the first component to take shape when the Galaxy formed, about 1 — 2 Gyr after the Big-Bang. These are the metal-poorest halo field stars and the metal-poor halo globular clusters. Parts of the galactic bulge/disc may be as old as the halo: these can be used for cosmological age determinations once they are identified (by metallicity and kinematics); reddening problems, however, may be worse than for the halo. Also, parts of the halo may be younger because of merging and/or accretion events: these can be identified by metallicity and kinematics, and are not suitable for cosmological age determinations. Until quite recently, cosmological ages derived from different methods, e.g. high redshift (cosmic microwave background), intermediate redshift (SNe) and low redshift (clusters and Pop. II stars) measurements, displayed a large range of values. The past few years, however, have seen signs of improvement in the accuracy of the individual age determinations and a tendency to converge towards 1

Osservatorio Astronomico, Via Ranzani 1, 40127 Bologna, Italy © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002014

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a common value. Bahcall et al. [1] suggest that the best agreement with current observations is provided by a ACDM model with cosmological parameters Om = 1/3, OA = 2/3, oK = 0 and age ~14 Gyr. On the other hand, the most recent estimates of Galactic globular cluster ages are 13.0 ± 2.9 Gyr (from 5 clusters with [Fe/H] < -1.5; [2]), 13.0 ± 1.0 Gyr (from 12 clusters with [Fe/H] < -1.5; [3]), and 13.0 ± 2.5 Gyr (from 47Tuc and NGC 6752; [4]). Perfect agreement! Is this the end of the story? Not quite... the individual age determinations are still affected by significant errors and uncertainties, and the goal will be to understand them and reduce them to the bare minimum. GAIA's contribution for Pop. II stars and stellar systems will be fundamental in this respect. 2

Clock Identification

Stellar evolution and nucleosynthesis provide some possible "clocks", that are here identified and commented for their advantages and shortcomings. 2.1 Turnoff Stars The luminosity (i.e. Mv in the observational plane) of main sequence turnoff (TO) stars, that can be obtained from the HR diagram (i.e. Colour-Magnitude diagram CMD) of the globular cluster or halo field stars, is related to age via the following equation [5]: logt 9 ~ -0.41 + 0.37Mv(TO) - 0.43 Y - 0.13 [Fe/H] where tg is the age in Gyr units, My (TO) the absolute visual magnitude of the main sequence turnoff, Y the helium abundance, and [Fe/H] the iron abundance in standard notation. This relation is based on isochrones [6]. For Y = 0.23 and ages older than several Gyr, a relation can be approximated between age and the TO (B-V) colour [7]: log t9 ~ -1.016 + 3.234 (B - V)TO - 0.8774 [M/H] - 0.1753 [M/H]2 where [M/H] = [Fe/H] for solar scaled elemental abundances. The use of TO stars is presently the most accurate and reliable of all dating methods for Pop. II stars available and described here. It will be commented in more detail in Section 3. 2.2

The White Dwarf Luminosity Function

The faint end of the White Dwarf (WD) cooling sequence in a stellar population is a function of the stellar mass hence age [8-11]. Therefore, the WD luminosity

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function (WDLF) cutoff can be used as age indicator provided extremely faint luminosities can be reached with good photometric accuracy (completeness is essential in order to identify the cutoff). For an old population (e.g. age = 12 Gyr) the faint end of the WD cooling sequence (corresponding to a mass ~0.8 MQ) occurs at Mv = 17.7 [8]: HST+WFPC2 is ~3 mag short in detecting such a feature even in the nearest globular cluster NGC6397 (~2 kpc). Only the ACS on HST will possibly be able to reach the faint end of the WD cooling sequence in a globular cluster, and wide-area very deep surveys will be required to detect a sizeable sample of old field halo WDs. We note that a survey with Vlim ~ 25 will sample as far as ~250 pc for the WDLF cutoff, and GAIA with Vlim ~ 20 will sample as far as 25 pc. Therefore, the WDLF cutoff for Pop. II stars is beyond GAIA 's possibilities.

2.3

The Horizontal Branch

The morphology and luminosity of the Horizontal Branch (HB) are in first approximation related to the metallicity and age of the stellar population, in the sense that red (blue) HBs have a tendency to be metal-rich (metal-poor) and/or young (old), and brighter (fainter) HBs are younger (older) (see [12] for a recent review on this topic). However, the HB morphology depends on other (still unidentified) parameters in addition to metallicity and age (the so-called "second-parameter effect"). These may be: helium abundance, [CNO/Fe], rotation, magnetic field strength, peculiar surface abundances due to mixing during the RGB phase, diffusion or sedimentation, some other yet unknown factor that affects mass loss efficiency or a combination of any of these. The HB luminosity also depends on some of the above parameters (helium abundance, rotation, mass loss) in addition to e.g. the equation of state (EoS). We conclude that the HB is not a reliable and accurate age indicator, at least until the "second-parameter effect" has been fully understood.

2.4

Nucleochronology of Radioactive Elements

Radioactive dating using lines of 232Th and 238U can be performed in extremely metal-poor stars. This potentially very promising technique has recently led to a very interesting result, a stellar age of 12.5 ± 3 Gyr [13]. However, even the strongest 238U line, which is a more precise age indicator than 232Th because of its shorter half-life time, is extremely faint and requires the use of high resolution (R ~ 70000) and very high S/N spectroscopy. Therefore, radioactive dating is no job for GAIA (except perhaps for providing suitable metal-poor candidates for high-resolution spectroscopic follow-up).

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After the isochrones by [6] quoted in Section 2.1, several other sets of isochrones have become available in the last few years [14-19]. These new isochrones: • use updated input physics, e.g. opacities (OPAL [20,21] vs. Los Alamos), EoS (including the effect of Coulomb interactions, e.g. [22]), nuclear reactions and neutrino cooling rates; • use different assumptions with respect to, e.g. treatments of convection (classical Mixing Length Theory [23] vs. Full Spectrum of Turbulence [24]), overshooting, a-element enhancement, helium diffusion; • are calibrated to the (revised) Sun, and possibly Gmbl830. Uncertainties in any of the above theoretical items affect the coefficients of the analytical formulae, i.e. the clock running, and lead to systematic errors on age. Errors in any of the observable items affect the clock reading and lead to additional random errors on age. 3.1

The TO Colours

The colours of the TO stars are afflicted by severe uncertainties due to a) the treatment of convection and the helium gravitational and thermal settling/diffusion in the convective atmosphere; b) theory/observation interface, such as the colour-Teff conversion (empirical calibrations, model atmospheres, chemical abundance); and c) the observables i.e. photometry, abundances, reddening. Errors in items a) and b) affect the coefficients of the analytical fits and lead to systematic errors by more than 30% in age [25] (but [18] have a more optimistic view...) Errors in item c) affect the observable parameters of the analytical fit and lead to random errors, e.g.: A(B — V) ~ 0.02 mag corresponds to At/t ~ 15%, and A[Fe/H] - 0.10 dex corresponds to At/t ~ 20%. We definitely share the concern expressed by [26]: "all of these factors lead me to prefer techniques that make the least use of colour, and I avoid those that rely on absolute colour like the plague"... although there may be some useful application of this technique, in the end (see Sect. 4). 3.2

The TO Absolute Magnitude

The absolute magnitude of TO stars is sensitive to input physics and assumptions that affect the radiative core energy production and size, and may lead to a systematic error on age. These are: a) radiative opacities, EoS, nuclear reaction and neutrino cooling rates, helium diffusion, [Fe/H] and [a/Fe]; and b) theory/observation interface such as bolometric corrections. The effect of these items can be minimized in properly calibrated models.

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Table 1. Error (rms) budget on absolute age determination.

Input Quantity

a(t)/t

*(IQ)

a(t}/t %

0.85c7(Vro) 0.85o-(mod) 2. 64 a (redd) 0.99 a(Y) 0.300-QM/H])

±0.10 ±0.15 ±0.03 ±0.02 ±0.20(*)

8.5 12.8 7.9 2.0 6.0

IQ VTQ mod redd

Y [M/H]

(*) Relative errors on metallicity determinations can be much smaller, i.e. <0.10 dex [27,28], but the zero-point (i.e. the calibration on the Sun) is still uncertain by 0.10 dex or more, the temperatures are uncertain by a few hundred degrees, several gf values are still poorly known.

With respect to the old models, i) the use of the new EoS and inclusion of helium diffusion decreases the age by about 2 Gyr [25,29]; and ii) the effect of [a/Fe] > 0 on age can be mimicked by the use of higher metallicity models that keep the same total mass-fraction abundance, Z. Comparison of the various most recent My (TO) vs. age relations indicates an intrinsic - hence systematic - theoretical error of ~5% in the age determinations, quite an improvement with respect to the estimate made by [5] of 2 Gyr (~15%). We conclude that My (TO) is the best clock that stellar evolution theory can provide for Pop. II stars.

What about random (observational) errors? We recall that the basic formula used to derive the age is: logtg ~ -0.41 + 0.37My(TO) - 0.43Y-0.13[Fe/H]. Following [30] we summarize in Table 1 the total rms error budget assuming the smallest errors realistically achievable at present on the absolute values of the individual quantities. We note that the biggest error comes from distance determinations (mod), that presently need the use of intermediary standard candles, e.g. HB stars (RR Lyrae), local subdwarf stars with known parallaxes for main sequence fitting, the tip of the red giant branch, WDs. The total random error on absolute age determinations sums up to ~18%, that becomes no less than 20% with the addition of the systematic errors.

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On the theoretical side, predictable improvement will come from: • statistically representative LFs in the HR diagram region from the TO to the sub-giant branch (SGB). In these evolutionary phases the input physics (opacities, diffusion, mixings, etc.) has the strongest effect on evolutionary rates (hence the clock running) and can be revealed by accurate LFs; • very accurate distances of globular clusters, hence accurate fitting of cluster loci to isochrones. This will provide information on the T e fj and shape of the TO, hence on all parameters (i.e. convection, diffusion, etc.) affecting the convective envelope. Here we can recover the technique discussed in Section 3.1 by applying it the other way around, i.e. not to derive the age but to obtain precise information on the physical assumptions underlying the models. GAIA will provide essential contribution in this respect, and we can expect to achieve a systematic accuracy At/t < 5%. On the observational side: • high-resolution spectroscopy on Sm-class telescopes will allow to derive absolute values of [M/H] with errors
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4.1

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The Contribution of GAIA on Halo Field Stars

Some models of galaxy formation suggest that the halo field stars were actually the very first to form, even before globular clusters, therefore are the oldest population in the Galaxy. These are faint objects and can be easily confused with a younger and more numerous disc population. The criteria to unequivocally identify a pure halo population are metallicity and kinematics, in addition to absolute magnitudes and colours. Presently, ages have been estimated for a small sample of local halo subdwarf and subgiant stars in the metallicity range from — 1.2 to — 1.8 and with Hipparcos parallaxes with UTT/TT < 0.125 [31]. The resulting age, 14 Gyr, although attractively similar to other independent estimates, is however very uncertain being critically dependent on only two subgiant stars. GAIA's Vlim = 20 will allow to sample TO stars as far as ~10 kpc. Individual distances will be less accurate than the mean distances derived for globular clusters, but for the first time a very large sample of true halo stars will be available, and accurate CMDs will be made at various metallicities and compared to those of globular clusters. It will be possible to derive the absolute age of the oldest halo components hence the age of the Universe, as well as the relative ages of various halo components hence constraints on Galaxy formation models. If we compare briefly with other similar space missions that will be operational in the near future, only SIM will compete with GAIA and obtain the same results a few years earlier, albeit on a small subsample of globular clusters. As far as the halo field stars and galactic structure are concerned, however, no other project will be up to GAIA in terms of statistical significance and accuracy of the results. References [1] Bahcall, N.A., Ostriker, J.P., Perlmutter, S., Steinhardt, P.J., 1999, Science, 284, 1481 [2] [3] [4] [5]

Carretta, E., Gratton, R.G., Clementini, G., Fusi Pecci, F., 2000, ApJ, 533, 215 VandenBerg, D.A., 2000, ApJS, 129, 315 Zoccali, M., et al., 2001, ApJ, 553, 733 Renzini, A., 1993, Ann. NY Acad. Sci., 688, 124

[6] VandenBerg, D.A., Bell, R.A., 1985, ApJS, 58, 561 [7] Straniero, O., Chieffi, A., 1991, ApJS, 76, 525 [8] Richer, H.B., Hansen, B., Limongi, M., et a/., 2000, ApJ, 529, 318 [9] Hansen, B.M.S., 1999, ApJ, 520, 680 [10] Wood, M.A., 1995, in White Dwarfs, D. Koester & K. Werner (eds.) (Springer), 41 [11] Isern, J., Garcia-Berro, E., Hernanz, M., Mochkovitch, R., Torres, S., 1998, ApJ, 503, 239 [12] Carney, B.W., in Star Clusters, 2001, L. Labhardt & B. Binggeli (eds.) (Springer), 39 [13] [14] [15] [16]

Cayrel, R., et al, 2001, Nature, 409, 691 Straniero, O., Chieffi, A., Limongi, M., 1997, ApJ, 490, 425 Girardi, L., Bressan, A., Bertelli, G., Chiosi, C., 2000, A&AS, 141, 371 Ventura, P., Zeppieri, A., Mazzitelli, L, D'Antona, F., 1998, A&A, 334, 953

[17] Salasnich, B., Girardi, L., Weiss, A., Chiosi, C., 2000, A&A, 361, 1023 [18] VandenBerg, D.A., Swenson, F.J., Rogers, F.J, Iglesias, C.A., Alexander, D.R., 2000, ApJ, 532, 430

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[19] [20] [21] [22] [23] [24] [25]

Cassisi, S., Castellani, V., degl'Innocenti, S., Salaris, M., Weiss, A., 1999, A&AS, 134, 103 Rogers, F.J., Iglesias, C.A., 1993, ApJ, 412, 752 Alexander, D.R., Ferguson, J.W., 1994, ApJ, 437, 879 Rogers F.J., Swenson F.J., Iglesias, C.A., 1996, ApJ, 456, 902 Bohm-Vitense, E., 1958, Z.Ap., 46, 108 Canuto, V.M., Mazzitelli, I., 1991, ApJ, 370, 295 D'Antona, F., 2000, in The Galactic Halo: from Globular Clusters to field stars, 35th Liege Astrophysics Coll. Rood, R.T., 1989, in Astrophysical Ages and Dating Methods, Vangioni-Flamm et al. (eds.) (Ed. Frontieres), 313 Gratton, R.G., et al., 2001, A&A, 369, 87 Thevenin, F., et al., 2001, A&A, 373, 905 Castellani, V., Ciaio, F., degl'Innocenti, S., Fiorentini, G., 1997, A&A, 322, 801 Renzini, A., 1991, in Observational Tests of Cosmological Inflation, T. Shanks et al. (eds.) (Kluwer), 131 Cayrel, R., Lebreton, Y., Perrin, M.N., Turon, C., 1997, in Hipparcos Venice '97, ESASP402, 219

[26] [27] [28] [29] [30] [31]

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

ABSOLUTE LUMINOSITIES OF STELLAR CANDLES

X. Luri 1 , 2 , F. Figueras1'2 and J. Torra1'2

Abstract. Stellar candles are the basic tools to determine the extragalactic distance scale. Its use relies on some given fundamental relation that allows to estimate the absolute magnitude of an object from observable parameters and from that its distance. The Hipparcos mission greatly contributed to the refinement of these fundamental relations, but even with its milliarcsecond-precision data, the uncertainties in the calibration of Stellar Candles are still high. To improve these results larger samples and higher astrometric precision are needed. GAIA, with its microarcsecond, one-billion objects catalogue, will provide all the necessary data for this task.

1

Stellar Candles

Stellar candles are objects of known absolute magnitude that can be used to calculate extragalactic distances. Essentially, a given fundamental relation is available for these objects, relating their (not directly measurable) absolute magnitude with some observable parameters. This relation is determined using a sample of well studied stars (typically galactic objects) and then applied to objects of the same type (typically extragalactic objects) to determine their absolute magnitudes.

1 2

Dept. Astronomia, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain Institut d'Estudis Espacials de Catalunya, Spain © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002015

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Using the observed values and the fundamental relation, the absolute magnitude can be calculated and, combined with the apparent magnitude and the interstellar absorption, the distance to the object can be derived. The Stellar Candles are thus used to determine galactic and extragalactic distances, allowing for instance the determination of the distance to the Magellanic Clouds and Hubble constant. One of the most important types of Stellar Candles are the Cepheid variables. In good approximation3 the average (along the variation cycle) absolute magnitude of a Cepheid is linearly related to the logarithm of its period: (Mv)=A + BlogP. This relation is one of the main tools used for the calculation of the distance to the Large Magellanic Cloud (LMC), first step in the establishment of the extragalactic distance scale. However, even after the Hipparcos contribution, the present knowledge of this relation still maintains a somewhat large uncertainty in the determination of the LMC distance module. After an analysis of the available determinations of the Cepheid PL relation and the associated uncertainties, Groenewegen &; Oudmaijer (2000) [I] make the following estimate:

3

Actually, the average luminosity also depends on the colour of the star and the metallicity.

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It is clear that for further improvements in this determination one would need better data but also a better knowledge of the physical basis of this relation. RR-Lyrae variables constitute another important type of Stellar Candle. The average (along the variation cycle) absolute magnitude is, in good approximation, the same for all the RR-Lyrae at a given metallicity. However, the uncertainties in the determination of this absolute magnitude are still large. For instance, Popowski & Gould (1999) [2] give the compilation of RR-Lyrae absolute magnitude determinations presented in Table 1. Table 1. Determinations of RR-Lyrae absolute magnitudes at [Fe/H] = —1.6, from Popowski & Gould (1999) [2]. Method (ordered by robustness) Statistical parallax Trigonometric parallax Cluster kinematics Baade-Wesselink Theoretical models Main sequence fitting to GC White dwarf sequence fitting to GC

< Mv >

0.77 ±0.13 0.71 ±0.15 0.67 ±0.10 0.45-0.70

0.45 - 0.65 0.45 ±0.04

0.67 ±0.13

Again, a precise determination of the absolute magnitude of RR-Lyrae variables would require better data, but also a better knowledge of the dependence of this absolute magnitude with the metallicity. The present limitations due to the scarcity of precise data are well illustrated in Figure 1. This figure compiles the determinations of the LMC distance modulus published after the release of the Hipparcos catalogue. The published values are found in a range of 0.6m, showing that there is still much work to do on the subject. 2 2.1

The GAIA Contribution Case Study: The Cepheid PL Relation

The examples given in Section 1 show that the uncertainties in the precision of the absolute magnitudes or distances obtained from the use of Stellar Candles are essentially due to the scarcity of precise data for these objects: • The effects of some of the factors in play (for instance metallicity) cannot be evaluated and corrected with precision; • The determinations of the relations themselves are not precise. This can be illustrated by studying the determination of the Cepheid PL relation from trigonometric parallaxes using Monte-Carlo simulations. Firstly, we have

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Fig. 1. Compilation of published determinations of the LMC distance modulus using Hipparcos data. Adapted from [3]. generated a simulated sample of 200 Cepheids: the periods and distances were generated using realistic distributions for galactic Cepheids and the absolute magnitudes were generated using an idealized PL relation (perfectly linear and with a small intrinsic dispersion of 0.05m). The distribution of the individual absolute magnitudes of this simulation is depicted in Figure 2a. Using the simulated distances we calculated the parallaxes of these stars and assigned Hipparcos-like errors to them to obtain "observed" parallaxes. If the stars with cr^/Tr < 0.25 are then selected, only a few stars remain (Fig. 2b). These "observed" parallaxes can be used to reconstruct the PL relation, but the scarcity of data does not allow a precise determination (Fig. 2c). This simulation is quite representative of the real situation for Cepheids: • There are about 200 Cepheids observed by Hipparcos; • Only 5 of them have CT^/TT < 0.25; • As a consequence, the available data does not allow a precise determination of the slope of the PL relation for galactic Cepheids. The slope is fixed a priori using the value observed in the Magellanic clouds and only the zero point of the PL relation is determined.

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Fig. 2. Monte-Carlo simulation of Hipparcos galactic Cepheids. (a) Individual absolute magnitudes of the simulated sample of Cepheids according to an idealized PL relation, (b) "Observed" parallaxes (with Hipparcos-like errors) versus "true" (simulated) parallaxes for stars with OV/TT < 0.25. (c) Reconstruction of the PL relation using these parallaxes.

We can now analyze what will be the GAIA contribution using these simulations. Assuming again an idealized PL relation, we have simulated a sample of 800 Cepheids (roughly the number of known galactic Cepheids because GAIA will observe all of them) and calculated their "observed" parallaxes with GAIA-like errors. In this case, all the relative errors in parallaxes are well below 25% (Fig. 3a) and can be used to reconstruct the PL relation (Fig. 3b). In this case, the PL relation can be reconstructed with good precision. However, the example shown was generated using an idealized PL relation and assuming a perfect knowledge of the interstellar absorption. In a real case there will

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Fig. 3. Monte-Carlo simulation of GAIA galactic Cepheids. (a) "Observed" parallaxes (with GAIA-like errors) versus "true" (simulated) parallaxes for stars (b) Reconstruction of the PL relation using these parallaxes. be more factors in play: • The PL relation is a simplification. The luminosity of a Cepheid does not only depend on the period but it is also affected by the colour index of the star and the metallicity; • The PL relation is not unique: Cepheids can pulsate on overtones and in this case follow a different PL relation; • A precise knowledge of the interstellar absorption is necessary for a proper reconstruction of the PL relation. These effects have been introduced in our simulations. In Figure 4a a simulation including the effects of the dependence of the luminosity on the colour index and metallicity is depicted, showing that the dispersion of the PL relation is increased. In Figure 4b the PL relation for Cepheids pulsating in the first overtone is included. When these effects are introduced in the simulations and an error of 15% in the estimation of the interstellar extinction is assumed, the reconstructed PL relation takes the shape depicted in Figure 4c. 2.2

Luminosity Calibrations in the GAIA Context

The last figure in the Cepheid case study may seem discouraging because no clear PL relation is seen but, on the contrary, it contains a huge amount of information. GAIA will provide enough data to disentangle the various effects in play, leading to precise relations and thus allowing the determination of Cepheid luminosities.

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Fig. 4. Monte-Carlo simulation of GAIA galactic Cepheids. (a) The dependence of luminosity on colour index and metallicity increases the dispersion of the PL relation, (b) PL relations for fundamental and first overtone Cepheids. (c) Reconstructed PL relation (15% in interstellar extinction assumed). The previous example illustrates how GAIA will bring a radical change in the calibration of Stellar Candles. The comparison of Figure 2c (present situation with Hipparcos data) with Figure 4c (GAIA data) gives a feeling of the possibilities that GAIA will open to the detailed study and improvement of the presently used calibration relations. However, it is important to bear in mind that the GAIA contribution will not be restricted to more and better parallaxes (as in the example). GAIA will bring: • Parallaxes • Proper motions

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- Used in Bayesian methods; — Kinematical discrimination. • Photometry and spectra: physical characterization — Metal abundances; - Multiband light curves; - Individual determination of interstellar absorption. To make a full an efficient use of all this information, the physical basis of the Stellar Candles calibration have to be improved. The fundamental relations used can be adapted and improved to produce better luminosity estimations using all the available data. At the same time, better calibration methods should be applied to take full advantage of the size and quality of the GAIA samples, avoiding unnecessary simplifications or approximations, adopting unbiased statistical methods adapted to each case and using all the available data for a global fit.

Finally, GAIA will also provide direct distances to the LMC Cepheids and mean distances to the closest galaxies. This will allow the first check of the universality of the new relations. References [1] Groenewegen, M.A.T., Oudmaijer, R.D., 2000, A&A, 356, 849 [2] Popowski, P., Gould, A., 1999, "Post-Hipparcos cosmic candles", A. Heck &; F. Caputo (eds.) (Kluwer Acad. Pub.), ASpSc Library, 237, 53 [3] Ferryman, M.A.C., 2000, private communication

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

ANALYSIS OF HUGE CATALOGUES. NEW METHODOLOGIES FOR THE VIRTUAL OBSERVATORIES D. Egret1 Abstract. We present, in a first part, a short review of existing and planned large catalogues and surveys. In a second part, we present the current plans for building the Virtual Observatories of the future. Finally we give a few examples of emerging methodologies for the analysis of huge catalogues.

1 1.1

Large Catalogues and Surveys Introduction

Huge (or very large) catalogues can be described as observational catalogues with a number of entries larger than 10 millions. This last figure is, in fact, a subjective limit, sensitive to hardware and software resources required for managing the catalogue. Modern catalogues can also be much more complex than simple tables and imply the management of a series of datasets. A major source of huge catalogues is constituted by the sky surveys: these are views of the complete sky (or of a large fraction of the sky) performed at a given time, and with a given instrument collecting observations at a given wavelength. During a long time, the photographic plate has been the privileged medium for sky surveys: hence the success of the Palomar Observatory Sky Survey (POSS), and Southern extensions by ESO and SERC using the Anglo-Australian Schmidt telescope. These plates are now digitized and distributed on-line at several places (Digitized Sky Survey, DSS). In a second step, very large catalogues of extracted sources have been produced by identifying point sources on the digitized images of the survey. Recent examples of such catalogues are USNO-A and GSC-II. Modern surveys now use electronic cameras to numerically record the images. DENIS, 2MASS, and Sloan Digital Sky Survey are the first of these new generation surveys to become (up to now, only partially) available. CDS, Observatoire astronomique de Strasbourg, UMR 7550, France © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002016

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In the following we will also consider the very large catalogues to be produced by the wide field cameras which collect deep and repeated observations of smaller regions of the sky. Access to the results of these sky surveys is becoming critical for many studies: new or rare categories of objects, statistical studies over complete samples of objects, spatial distribution, references for new kinds of observations, etc. Building an efficient access to these data cleaarly constitutes the primary reason for building a Virtual Observatory. 1.2

Currently Available Very Large Catalogues

The most important currently available large catalogues include: • The Guide Star Catalog (Lasker et al. 1990). This catalog has been digitized at the Space Telescope Science Institute for the specific needs of the Hubble Space Telescope. It provides 25 million positions for about 19 million objects (about 15 million being classified as stars). Limiting magnitudes in B and V are around 16. Astrometric reduction of GSC version 1.2 has been based on the Tycho catalogue (see below). The typical absolute position error of a GSC entry is 1 arcsec. It can be significantly larger on plate edges; • The Tycho survey used star mappers onboard Hipparcos satellite to continuously map the sky during the 2.5 years of the mission. The resulting catalogue (H0g et al. 1997) provides accurate astrometry and B and V magnitudes for one million stars. A new reduction of the same observational material, performed a few years later (H0g et al. 2000) conducted to a deeper catalogue of 2.4 million stars (Tycho-2) which is currently the most accurate star survey available. Typical limiting magnitude is V = 12. Typical position error is 30 mas; • The USNO A2 catalog (Monet et al. 1998) utilizes DSS plates digitized at Flagstaff Observatory with the Precision Measuring Machine to produce a very large catalogue of 526 million entries, identified on both B and R plates. Limiting magnitudes are around B = 20 and R = 22, with a typical error on position of 0.24 arcsec. The planned USNO B catalogue will include proper motions derived from the use of multiple plate epochs; • The GSC-II catalog is a second generation of the GSC catalog mentioned above, currently being released. Again a result of the extraction of point sources from digitized plate images, the GSC II is expected to list, when completed, two billion objects identified in at least two of the three B, R, I bands. Proper motions will eventually be derived with a nominal accuracy of 30 mas/year.

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New Surveys

The developments of new detectors, and of powerful data reduction techniques, have given a new impulse to the production of sky surveys, and of deep wide field observations, resulting in the production of catalogues in the billion object range. 1.3.1

Near-Infrared Surveys

The first new observational sky surveys, directly produced from electronic cameras, are the near-infrared surveys DENIS and 2MASS, currently under completion. • The DEep Near Infrared Survey of the Southen Sky (DENIS) will provide I, J, Ks magnitudes for stars below a declination of +2.5°. A few percent of the sky have already been released (Epchtein et al. 1999); • The 2 Micron All Sky Survey (2MASS) undertaken by the University of Massachussets and NASA (Skrutskie 1998) will provide a full coverage of the sky, from two telescopes, one in the North at Mt Hopkins, the other in the South, at Cerro Tololo. The wavelength range are those of J, H, and Ks filters. The complete point source catalogue, expected to be released at the end of 2002, will contain about 500 million objects, and will be produced out of a database including some 24 Terabytes of data. 1.3.2

The Sloan Digital Sky Survey

The Sloan Survey is expected to map in detail one-quarter of the entire sky, determining the positions and absolute brightnesses of more than 100 million celestial objects. Five colours will be measured, up to a limiting magnitude of approximately R = 23 mag. The SDSS will also measure the redshifts of more than a million galaxies and quasars. The volume of data to be released is announced to be about 15 Terabytes. 1.4

Deep Field Projects

Beside the major projects undertaking to map the entire sky, or large fractions of it, there exists a category of projects which are also heavy producers of huge amounts of data: these are the deep field projects, which use wide field cameras targetted to a small number of selected fields, observed repeatedly and/or up to an important depth in magnitude. A very successful example of this strategy is the Hubble Deep Field which was an essential tool to bring us new lights on galaxy formation and evolution. A number of such projects are being prepared or have already started. Here are a few examples: • The CFHT MegaPrime project hosted by the CFH 3.60 m Telescope will use a wide field camera equipped with arrays of CCD. A lot of developments have been invested in the data processing (Terapix, Bertin 2001) in order

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that features of very small amplitude affecting, e.g. the galaxy distribution, can be discovered; • The ESO VLT Survey Telescope will use a quite similar camera to map selected fields and identify candidate targets for the VLT; • The VISTA project aims at installing a 4 m telescope at Paranal with a a wide field Visible and Infrared camera WFCAM; • Another quite different example of survey is the 2DF Galaxy redshift survey recently started on the Anglo-Australian Telescope. 1.5

Multi-Wawelength Astronomy

The previous sections were concentrated on visible and near-infrared astronomy. Much developments also concern other wavelengths, and our understanding of the Universe nowadays relies largely on multi-wavelength approaches. In the present section we simply want to mention a few of the current or future projects that will provide complete or wide views of the sky in different spectral ranges: • ROSAT, XMM-Newton, Chandra, in the X-Ray; • Integral, in the gamma-ray; • ISO, SIRTF, in the Infrared; • MAP, Planck, Herschel, Alma, in the millimeter or submillimeter range; • GALEX in the Ultraviolet;

• etc. Multispectral cross-identification is a crucial step for the interpretation of many astronomical phenomena. Tools are being devised allowing massive cross-matching of large datasets. An example of results obtained from the cross-matching of optical and X-ray surveys can be found in Guillout et al. (1999), where young red stars (detected by both ROSAT and Tycho) are found to follow a specific ring structure in the Milky Way. 2 2.1

Virtual Observatories Introduction

The Virtual Observatory is a response to the deluge of information produced by the advent of very large telescopes and large scale surveys. It aims at providing access to all kinds of information resulting from digitized observations of the sky, eventually collected at many different wavelengths and epochs, and organized as on-line distributed archives, and higher level information services.

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The science case for the Virtual Observatory includes: • understanding large scale structures of the Universe; • formation and evolution of galaxies; • the Digital Galaxy; • discovery of rare objects (brown dwarfs, extrasolar planets);

• etc. 2.2

The Projects

The coordinated efforts known under the name of Virtual Observatories are quite recent, although there already exists a solid base with a network of interconnected data centres, archives, and information systems. But the challenge of the coming surveys and large telescopes imposes to go far beyond the existing resources.

2.2.1 The US NVO The US National Virtual Observatory (NVO) was recommended in early 2000 by the National Academy of Sciences as a "small mission" to be supported within the US NAS decadal survey. The general framework has been described in a preliminary White Paper (NVO 2001), and a first international meeting called at Caltech in June 2000 (Brunner et al. 2001) was the opportunity to bring forward science cases, and to start discussing international cooperation on standards and interoperabiliy tools. The first NVO contract was awarded by the National Science Foundation (NSF) in October 2001. 2.2.2

AVO

In the same time, a consortium of European institutes and institutions, coordinated by the Opticon network (Gilmore 2001), submitted a proposal to the European community for a prototype phase demonstrating the features of the future Astrophysical Virtual Observatory (AVO). The AVO has recently started (November 2001 )2 with a European funding, for an initial 3-year effort. The consortium includes the European Southern Observatory (ESO), the European Space Agency (ESA), the UK ASTROGRID consortium, the Centre de Donnees Astronomiques de Strasbourg (CDS), the TERAPIX astronomical data centre at the Institut d'Astrophysique in Paris, and the Jodrell Bank Observatory. 2

http://www.eso.org/avo/

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2.2.3 AstroVirtel AstroVirtel is also a European program, conducted by ESO and ST-ECF, which started in early 2000. The idea is to support each year half a dozen of selected science programs asking extended access to ESO or ESA archives. The experience gained in this exercise is to be used to improve the overall access of scientists to European astronomical archives. 2.2.4 VO in Practice In more practical terms, the advantages we should expect from the current developments of Virtual Observatories are the following: - an inventory of existing observational data sets; - a coherent and coordinated network of archives, surveys, information services and reference dictionaries; - normalized modes of access to the original data; - coordinated efforts for deriving innovative data analysis and data mining tools. 2.3

The CDS

As mentioned above, a coordinated network of interoperable astronomical services already exists, although at a smaller scale than it is becoming necessary. A short description of the present status of the Strasbourg astronomical Data Center (CDS; Genova et al. 2000) will help to illustrate the current state of the art in terms of access to reference astronomical data. As a service to the astronomical community, the CDS develops specific tools for managing and making accessible published data from sky surveys, deep fields, or very large catalogues at any wavelength; and for helping cross-identification, and validation of data from new surveys. Among all the services available at CDS3, those decribed below are more specifically designed for approaching survey data. 2.3.1 VizieR The VizieR service (Ochsenbein et al. 2000) provides access to the most complete astronomical library of published catalogues and data tables, including key catalogues and surveys, such as, for example, Hipparcos and Tycho catalogues, GSC and USNO Al.O catalogs, 2MASS point sources, etc. 2.3.2 SIMBAD The SIMBAD database is the reference database for identification and bibliography of astronomical objects (Wenger et al. 2000). It contains millions of crossidentifications of sources for objects referenced in the literature. 3http://cdsweb.u-strasbg.fr/

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Aladin

The ALADIN interactive sky atlas provides access to reference images from the large Schmidt surveys (DSS I and DSS II, completed with high resolution MAMA scans), and, more recently from the 2MASS survey, as well as a set of tools to help source diagnostic and identification, including the capacity of overlaying information from VizieR or Simbad (Bonnarel et al. 2000). Interoperability between these services, and external services such as the NASA/IPAC Extragalactic Database (NED), the NASA High-Energy Astronomy Archive Center (HEASARC), or the NASA/ADS service for bibliography, is the first step towards creating a network of all major complementary interconnected resources. 3 3.1

Emerging Methodologies Management of Large Catalogues at CDS

The Strasbourg astronomical Data Center (CDS), in close coordination with the data producers has started to develop specific tools for: (1) managing and making accessible published data from sky surveys, deep fields, or very large catalogues at any wavelength; (2) helping cross-identification, and validation of data from new surveys, through cros-matching tools. Specifically, original dedicated management techniques have been developed for compressed coding, indexing, and fast coordinate access to very large catalogues such as GSC (of size ~20 million objects), USNO A (500 million objects), or DeNIS and 2MASS. The VizieR catalogue service at CDS contains many reference catalogues and surveys, of smaller size, for example, currently: Hipparcos, Tycho, IRAS, VLA FIRST, etc. and allow respectively sampling (complex queries over any catalogue column) and full retrieval of the catalogues over the network. While VizieR generally uses a commercial relational database management system, catalogues of size larger than 20 million objects (currently: GSC, USNO A, DeNIS, and 2MASS) are managed through customized tools for which the performance has been optimized as much as possible by data compression and efficient indexing. The SIMBAD database already contains a few millions of cross-identifications of sources for objects referenced in the literature. Impact of an increase of the size of the data base by one (or several) order(s) of magnitude is currently being assessed. Solutions for a very large database management system, fully object-oriented, potentially storing several kinds of large catalogues together, with fast multicriterion access, are being explored: object-oriented commercial packages are being tested in the context of astronomical specifications. These studies are being done in close contact with groups having similar needs: Sloan Digitized Survey, Space

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Telescope Science Institute, European Southern Observatory, European Space Agency, etc. In the context of the VLT scientific environment, data mining tools including an automatic cross-referencing engine for catalogues is being investigated in the framework of a collaboration between ESO and CDS. While queries have been, up to now, mainly optimized for access by coordinates, new methods are being investigated to allow optimized access to queries based on all or part of the catalogue columns (object type, colours, distances, etc.), using multivariate analysis technique for the optimized indexing. All these projects, which will be interfaced in the future, will allow CDS to provide convenient access and data mining tools for large survey catalogues such as DENIS, 2MASS, Sloan DSS, TERAPIX, XMM-Newton, Planck, or, later on, GAIA. The experience with existing catalogues shows that it is already possible to support efficiently on-line queries to very large catalogues. Although the GAIA catalogue will be much more complex (especially with a large diversity of information collected), it can be reasonably anticipated that the resources available at the time of GAIA data production will make possible the support of on-line access to the core catalogue in the major astronomical data centers. 3.2

New Methodologies for Data and Image Analysis

A lot of developments is expected in the field of data processing and image analysis, in order to cope with the increasingly large volumes of data. Conferences such as the yearly ADASS Conference4 help to be kept informed about on-going efforts. This concerns the pipeline and data processing, the multispectral and multi-scale approaches, and more generally the new data mining techniques devised to explore peculiar features or groups of objects among huge datasets. An illustration of these new methodologies can be found in the recent contribution by Starck (2001) about combined transform methods for extracting relevant information from astronomical images. In order to extract information from point source catalogues it may be crucial to use powerful Bayesian inversion methods, as described, e.g., by Pichon et al. (2001) in order to constrain the parameters of underlying models (see also the contribution by A. Siebert in these Proceedings). The reader may refer to the recent publication of the proceedings of the Conference "Mining the Sky" for the latest developments in terms of catalogue and archive analysis (Banday et al. 2001). 4

Conclusion

The coming avalanche of new data is a real challenge for data processing and data analysis: innovative solutions will have to be found in order to be able to produce 4http://www.adass.org/

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the expected results of the endeavour: namely, possible answers to some of the major astronomical questions currently facing us. Huge comprehensive catalogues will provide the elements for a new global approach for solving scientific puzzles. This will help us understand the Universe at diverse scales and wavelengths. But, in a first step, this will require new tools, new methodologies, and probably a completely new science environment. Glossary ADASS AVO CDS CFHT DeNIS DSS GSC NVO POSS SDSS TERAPIX USNO A VLT 2DF 2MASS

Astronomical Data Analysis and Software Systems Astrophysical Virtual Observatory Centre de Donnees astronomiques de Strasbourg Canada Prance Hawaii Telescope Deep Near Infrared Survey of the Southern Sky Digitized Sky Survey Guide Star Catalog (all-sky digitization of photographic Schmidt surveys for Hubble Space Telescope) National Virtual Observatory (U.S.) Palomar Observatory Sky Survey Sloan Digital Sky Survey Pipeline processing of MegaPrime deep field images (project of Canada-France-Hawaii Telescope) US Naval Observatory catalogue (all-sky digitization of photographic Schmidt surveys) Very Large Telescope (ESO) Galaxy Redshift Survey (Anglo-Australian Telescope) 2 Micron All Sky Survey (Univ. Massachussets)

References [I] Banday A.J., Zaroubi S., Bartelmann M., 2001, Mining the Sky, ESO Astrophysics Symp. XV (Springer) [2] Bertin E., 2001, in ADASS XI Conf., in press (Terapix) [3] Bonnarel F., Fernique P., Bienayme O., et al, 2000, A&AS, 143, 33 (Aladin) [4] Brunner R., Djorgovsky S.G., Szalay A.S., 2001, Virtual Observatories of the Future, ASP Conf. Ser., 225 [5] Egret D., 2001, in "Mining the Sky", ESO Astrophys. Symp., XV, 656 [6] Epchtein N., Deul E., Derriere S., et al, 1999, A&A, 349, 236 (DENIS catalogue) [7] Genova F., Egret D., Bienayme O., et al, 2000, A&AS, 143, 1 (CDS) [8] Gilmore G., 2001, in "Mining the Sky", ESO Astrophys. Symp., XV, 689 [9] Guillout P., Schmitt J.H.M.M., Egret D., et al, 1999, A&A, 351, 1003 (RasTyc) [10] H0g E., Bassgen G., Bastian U., et al., 1997 A&A, 323, L57 (Tycho) [11] H0g E., et al, 2000 A&A, 357, 367 (Tycho-2) [12] Lasker B.M., Sturch. C., McLean B.J., et al, 1990, AJ, 99, 2019 (GSC) [13] Monet D., et al, 1998, The PMM USNO A2.0 Catalog, US Naval Observatory, Flagstaff Station

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[14] NVO Interim Steering Committee, 2001, in "Virtual Observatories of the future", ASP Conf. Ser., 225, 353 (White Paper) [15] Ochsenbein F., Bauer P., Marcout J., 2000, A&AS, 143, 23 (Vizier) [16] Pichon C., Vergely J.-L., Rollinde E., 2001, MNRAS, 326, 597 [17] Skrutskie M., 1998, in "The impact of near-infrared surveys on galactic and extragalactic astronomy" (Kluwer Publ.), ASSL, 230, 11 [18] Starck J.-L., 2001, in "Astronomical Data Analysis", SPIE Conf., 4477, 131 [19] Wenger M., Ochsenbein F., Egret D., et al., 2000, A&AS, 143, 9 (Simbad)

Sub-Stellar Objects: Brown Dwarfs and Exo-Planets

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

THEORY OF LOW MASS STARS AND BROWN DWARFS: SUCCESS AND REMAINING UNCERTAINTIES I. Baraffe

Abstract. Important progress has been made within the past few years regarding the theory of low mass stars (m < I MQ) and brown dwarfs (ra < 0.075 MQ). The main improvements concern the equation of state of dense plasmas and the modelling of cool and dense atmospheres, necessary for a correct description of such objects. These theoretical efforts now yield a better understanding of these objects and good agreement with observations regarding colour-magnitude diagrams of globular clusters, mass-magnitude relationships and nearIR colour-magnitude diagrams for open clusters. However uncertainties still remain regarding synthetic optical colours and the complex problem of dust formation in the coolest atmosphere models. We will present a review of the current success and uncertainties of the theory of these objects, which may guide forthcoming projects with GAIA.

1

Improvement of the Theory

Very low mass (VLM) stars and brown dwarfs (BD) are dense and cool objects, with typical central densities of the order of 100 — 1000 gr cm~ 3 and central temperatures lower than 107 K. Under such conditions, a correct equation of state (EOS) for the description of their inner structure must take into account strong correlations between particles, resulting in important departures from a perfect gas EOS (cf. [1]). Important progress has been made in this field, in particular by [2] who developed an EOS specially devoted to VLM stars, BD and giant planets. Since the EOS determines essentially the mechanical structure of these objects, and thus the mass-radius relationship, it can be tested against observations of eclipsing binary systems. Unfortunately, we only know two systems which can offer such a test (cf. Fig. 1 and [3]). Figure 1 displays also the data from the white dwarf- M dwarf binary system GD 448 (cf. [4]). Although the radius determination of the M-dwarf is model dependent, it provides an interesting case to test the very Ecole Normale Superieure de Lyon, CRAL, 46 allee d'ltalie, 69364 Lyon, France © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002017

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Fig. 1. Mass-radius relationship for VLM stars down to the BD regime. The solid curves are models from [1] for solar metallicity [M/H] = 0 and different ages. The two eclipsing binary systems CM Dra [6] and YY Gem [7] are indicated. The VLM star component of the binary system GD 448 (but not eclipsing) is also shown [4].

bottom of the Main Sequence. These type of binary systems are urgently required to test the theory in the brown dwarf regime. This EOS has been also successfully confronted to recent laser-driven shock wave experiments realized at Livermore, probing the complex regime of pressure-dissociation and -ionization (cf. [5]). Another essential physical ingredient entering the theory of VLM stars and BD concerns the atmosphere modelling. VLM stars or M-dwarfs are characterized by effective temperatures from ~5000 K down to 2000 K and surface gravities log g ~ 3.5—5.5, whereas BDs can cover a much cooler temperature regime, down to some 100 K. Such low effective temperatures allow the presence of stable molecules (H2, H2O, TiO, VO, CH4, NHs, ...), whose bands constitute the main source of absorption along the characteristic frequency domain. Such particular conditions are responsible for strong non-grey effects and significant departure of the spectral energy distribution from a black body emission. Finally, recent discoveries revealed two classes of objects requiring new spectral classifications. On one hand, a family of objects shows very red infrared (J — K, H — K) colours while the signature of metal oxides (TiO, VO), whose band strength index is used to classify Mdwarf spectral types, and hydrides (FeH, CaH bands) disappear gradually from the spectral distribution, as observed e.g. in GD 165B. Several of these so-called "L" dwarfs, have been discovered by the near-IR surveys DENIS and 2MASS. On the other hand, more than a dozen of objects with properties similar to GL229B have

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Fig. 2. CMD for NGC 6397 in the WFPC2 optical filters observed by [16]. The isochrone is from [15] for a metallicity [M/H] = —1.5. See [15] for distance modulus and reddening correction.

been recently discovered with 2MASS, SDSS and the VLT. The IR spectrum of these objects is characterized by the unambiguous signature of methane absorption in the H, K and L bands, the predicted dominant equilibrium form of carbon below a local temperature T w 1300 — 1500 K in the P w 5 — 10 bar range. This yields blue near-infrared colours, with J — K < 0 but I — J > 5. These cool dwarfs are identified as "methane" dwarfs, sometimes called also "T-dwarfs" (see [8] for a review). Tremendous progress has been made within the past years to derive accurate non-grey atmosphere models by several groups over a wide range of temperatures and metallicities [9-13]. A detailed review of the recent progress in the field is given in [14]. Another difficulty inherent to cool dwarf atmospheres is due to the presence of convection in the optically thin layers. This particularity is due to the molecular hydrogen recombination (H+H —» £[2) which lowers the adiabatic gradient and favors the onset of convective instability. Since radiative equilibrium is no longer satisfied in such atmospheres, the usual procedure based on T(r) relationships to construct grey atmosphere models and to impose an outer boundary condition for the evolutionary models is basically incorrect (cf. [I]). An accurate surface boundary condition based on non-grey atmosphere models is therefore required for evolutionary models. As shown in [1,8], the use of grey outer boundary conditions, like the well known Eddington approximation, overestimates the effective

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Fig. 3. Mass-magnitude relationships in different filters: standard V and / filters (solid lines), compared to GAIA F57 and F89 filters respectively (dashed lines), and for different ages. From up to down: isochrones for 1 Myr, 100 Myr and 1 Gyr. The vertical line show the transition star/brown dwarf at 0.075 MQ. temperature for a given mass and yields higher hydrogen burning minimum mass (HBMM). 2

Comparison with Observations

Evolutionary calculations based on such improved physics have led to a much better representation of the observed properties of M-dwarfs. The accuracy of the theory is demonstrated by several facts. For metal-poor stars, models based on the interior models of [1] and the atmosphere models of [13] reproduce accurately the observed main sequences of different globular clusters observed with the HST in the optical (WFPC2 camera) and the near IR (NICMOS camera), which correspond to metallicities ranging from [M/H] = —2.0 to —1.0, down to the bottom of the Main Sequence [15] (cf. Fig. 2). The models are also in excellent agreement with the observationally-determined mass-magnitude relationship [17,18] both in the infrared and in the optical [19] and reproduce accurately colour-magnitude diagrams (CMD) in the near IR colours of disk field stars and open clusters [19,20]. Predicted Mass - magnitude relationships are shown if Figure 3 in standard filters and GAIA filters for different ages. 3

Remaining Uncertainties and Next Challenges

Problems still remain in the optical colours for solar metallicity models, which are significantly too blue for objects fainter than My ~ 10 (see Fig. 4). The source of

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Fig. 4. CMD for disk field stars: the data are from [23] (full squares) and [24] (full circles). The isochrones are from [19] for metallicities [M/H] = —0.5 (dashed line) and [M/H] = 0 (solid line) for an age of 5 Gyrs. Masses are indicated by open circles in the solid curve.

this discrepancy is analysed in [19] and may stem from a missing source of opacity below 1 /im, due to possible shortcomings in the TiO line list. New calculations of this line list are under progress and will hopefully solve this problem. Moreover, below Teff ~ 2800 K, grain formation starts to affect the outer layers of the atmospheres, and could possibly be responsible for the discrepancy found at magnitudes fainter than My ~ 16 [21]. More direct evidence for the presence of grains can be found by analysing spectra of very-late type objects and their IR colours. Indeed, the first results obtained by the DENIS/2MASS surveys reveal several BD candidates showing extremely red (J — K) colours. Observed values of (J — K) > I cannot be reproduced by current grainless atmosphere models. Atmosphere models taking into account the effect of grain condensation can reproduce such a trend of very red IR colours (cf. [22]). Figure 5 shows evolutionary models based on grainless atmosphere models, labeled NEG [19,25], atmosphere models including grain formation but with no contribution to the opacity, labeled COND, and dusty models including the dust contribution to the opacity, labeled DUSTY (cf. [21] for details). Comparison of such models with observations in a (J-K)-MK CMD confirms the necessity to take into account grain formation and their opacity in order to explain the reddest objects now observed (e.g., Kelu 1, LHS102B, GD165B, etc.). Interestingly enough, GL229B is better explained by the COND models, which

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Fig. 5. CMD for the near-IR colour (J — K). Theoretical models correspond to various isochrones: on the right, dashed and solid lines: DUSTY models for 0.1 and 1 Gyr respectively; on the left, dashed and solid lines: COND models for 0.1 and 1 Gyr respectively; dash-dotted line: NEG dust-free models for 1 Gyr. Masses (in MQ) and Teff are indicated on the 1 Gyr DUSTY isochrone by open circles. Crosses on the COND 1 Gyr track indicate masses in MQ and Tefi in K. Some identified BDs are indicated by diamonds: Kelu-1; GD165B; LHS102B. See [21] for details.

omit grain opacity. This very likely reflects gravitational settling of the grain species below the photosphere. Although encouraging, these first results show the complexity of including grain formation in the atmosphere models. This problem represents certainly the next challenge for the theory to complete our understanding of cool BDs. References [1] Chabrier, G. & Baraffe, I., 1997, A&A, 327, 1039 [2] Saumon, D., Chabrier, G. & Van Horn, H.M., 1995, ApJS, 99, 713 [3] Chabrier, G. & Baraffe, I., 1995, ApJ, 451, L29 [4] Maxted, P.F.L., Marsh, T.R., Moran, C., Dhillon, V.S. & Hilditch, R.W., 1998, MNRAS, 300, 1225 [5] Collins, G.W., Da Silva, L.B., Celliers, P., et al., 1998, Science, 281, 1178 [6] Metcalfe, T.S., Mathieu, R.T., Latham, D.W. & Torres, G., 1996, ApJ, 456, 356 [7] Leung, K.C. & Schneider, D., 1978, AJ, 83, 618 [8] Chabrier, G., Baraffe, I., 2000, ARA&A, 38, 337 [9] Plez, B., Brett, J.M., Nordlund, A., 1992, A&A, 256, 551

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Saumon, D., Bergeron, P., Lunine, L.I., Hubbard, W.B. & Burrows, A., 1994, ApJ, 424, 333 Brett, J.M., 1995, A&A, 295, 736 Allard, F. & Hauschildt, P.H., 1995, ApJ, 445, 433 Hauschildt, P.M., Allard, F. & Baron, E., 1999, ApJ, 512, 377 Allard, F., Hauschildt, P.H., Alexander, D.R. & Starrneld, S., 1997, ARA&A, 35, 137 Baraffe, I., Chabrier, G., Allard, F. & Hauschildt, P., 1997, A&A, 327, 1054 King, I.R., Anderson, J., Cool, A.M. & Piotto, G., 1998, ApJ, 492, L37 Henry, T. & McCarthy, D.W. Jr., 1993, AJ, 106, 773 Delfosse, X., Forveille, T., Beuzit, J.L., Udry, S., Mayor, M., Perrier, C., 1999, A&A, 344, 897 Baraffe, I., Chabrier, G., Allard, F. & Hauschildt, P., 1998, A&A, 337, 403 Burrows, A., et al., 1997, ApJ, 491, 856 Chabrier, G., Baraffe, I., Allard, F., Hauschildt, P.H., 2000, ApJ, 542, 464 Allard, F., Hauschildt, P.H., Alexander, D.R., Tamanai, A., Schweitzer, A., 2001, ApJ, in press Monet, D.G., et al., 1992, AJ, 103, 638 Dahn, C.C., Liebert, J., Harris, H.C. & Guetter, H.H., 1995, in The bottom of the mainsequence and below, C. Tinney (ed.) Allard, F., Hauschildt, P.H., Baraffe, I. & Chabrier, G., 1996, ApJ, 465, L123

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

FIELD BROWN DWARFS & GAIA M. Hay wood1 and C. Jordi 2

Abstract. Because of their very red colours and intrinsic faintness, field brown dwarfs will represent a small but valuable subset of the GAIA catalogue. The return of the astrometric satellite is expected to be important because of the inherent difficulty of obtaining good parallaxes in general and for this class of objects in particular. Our first estimates show that, due to the photometric sensitivity of the astrometric CCD (ASM1) towards relatively blue objects, GAIA is unlikely to detect field brown dwarfs that have not been already seen is previous near-IR surveys, to the notable exception of the galactic plane region. The real advantage of GAIA over ground-based surveys will be the very accurate (to within a few percents) astrometric data for a few thousands brown dwarfs. These data should permit a detailed mapping of the transition region between stellar and substellar regimes, together with the kinematical and density patterns of the youngest brown dwarfs in our neighbourhood. 1

Introduction

The last decade has seen an important development in the field of brown dwarfs, with either theoretical or observational breakthrough (see [1,2] for reviews). However the brown dwarf population in the solar neighbourhood is still lacking a quantitative description in its different aspects (density, kinematics, mass and age properties), and in most cases these must be extrapolated from the stellar regime. This is the method used here to assess the possible number of brown dwarfs GAIA is likely to detect. We first give a brief description of the HR diagram and GAIA magnitudes, then we describe our estimates of the expected counts and comparison with ongoing surveys/projects, and comment on the main scientific interests. 1 GEPI, Observatoire de Paris, 92195 Meudon, France e-mail: [email protected] 2 Departament d'Astronomia i Meteorologia, Universitat de Barcelona, Avda. Diagonal 647, 08028 Barcelona, Spain e-mail: [email protected]

© EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002018

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Fig. 1. Left: general view of the bottom HR diagram with the G magnitude scale calculated from the V — I colour index. Evolutionary tracks & isochrones from [4]. Right: typical L dwarf spectra from [5]. Flux scale is arbitrary to show spectral features with respect to the medium band niters F75, F78, F82 and F89 (solid lines). 2 2.1

Detection and Photometry of Brown Dwarfs with GAIA Brown Dwarfs HR Diagram

Although great progress has been made in the study of field brown dwarfs, presenting an observational HR diagram for these objects is difficult. Preliminary parallaxes for a few late M and L dwarfs are available [3], with much complementary data from the web page of N. Reid. Because these objects are usually not measured in V and / bands, the calculation of the G magnitude is not possible but for a few objects. Figure la is a general view of the bottom of the HR diagram, including some of the few L dwarfs for which parallaxes exist (and for which V — I colour is available). The HR diagram is scaled with G magnitude calculated from the V — I colour index. The onset of methane formation in the atmosphere of these objects, which is the distinctive feature for the classification in the two separate spectral types that are currently proposed and discussed [6,7], happens atV-I « 7. One of the main feature of brown dwarf evolution is that they cool at a relatively fast pace towards faint magnitudes, with a faster decrease for lower mass BDs. An object of 0.08M0 looses 6 magnitudes within the first Gyr, a 0.04M0 looses more than 10 magnitudes. 2.2

Detection &. Photometry

The astrometric CCD has maximum sensitivity at 3500-4000 A and is not optimized for the detection of very red and faint objects such as brown dwarfs (Fig. Ib). However, the capabilities of the astrometric instrument should permit the detection of a few thousands genuine brown dwarfs. Most of these objects will be within

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Fig. 2. Estimated medium band magnitudes precision at the end of the mission as a function of G using atmosphere models by [8]. a few hundred parsec, which implies a determination of the astrometric parameters to very good precision. For example, objects detected brighter than G = 21 within 100 pc will have a relative precision on parallax less than 6%. Due to the larger integration time (3 s) and better sensitivity of the Spectro instrument at longer wavelength, it is expected that the reddest medium bands give accurate and useful photometry (Fig. Ib). Figure 2 shows that precisions of a few hundredths of a magnitude are attainable for objects with G = 20. 3

Estimates of Brown Dwarf Counts and Characteristics

Since no distance estimate exist for a complete sample of BDs, direct estimates of the local density of these objects does not exist, and it must be evaluated from fitting a model to the observed counts of BDs [9] and/or extrapolation of stellar counts to the substellar regime. The total number of known L and T dwarfs to date is still very small (just above a hundred objects in May 2001), and the total number of confirmed brown dwarfs is even smaller. The known L and T dwarfs distribution on the sky in galactic coordinates is shown in Figure 3, with the detected objects largely following the

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Fig. 3. Spectroscopically confirmed L and T dwarfs, mostly discovered with DENIS, 2MASS, and Sloan. The gray area represents the 2MASS coverage in the 2nd incremental release (May 2000).

present status of the 2MASS survey, and with the galactic plane being noticeably depleted. The only 2 regions of the sky which can be considered as providing a complete sample of L and T dwarfs are those studied by [10] and [7]. Brown dwarf counts have been estimated with a model based on evolutionary tracks from [4]. The G magnitude has been calculated from the theoretical V — I colour. Since the colours and intrinsic absolute magnitudes of brown dwarfs vary with age and mass, it is necessary to assume a given initial mass function and star formation rate. To date, there is no indication of the nature of these two functions for field brown dwarfs. Given our very limited knowledge on these objects, all that can be said is that (1) the IMF can be assumed continuous over the stellar/substellar limit and has a power form (dN/dM oc m~ a ), with no apparent contradiction with available evidences, (2) the age distribution can be assumed as uniform, that is the SFR is taken as constant. Finally, we assumed uniform space density. However, it should be mentioned that, due to the very small ages of the brown dwarf population GAIA is expected to detect, this assumption is to the least a very rough one. The result of the model are given in Table 1. The table gives the number of brown dwarfs assuming different slopes for the IMF and different limiting magnitude of the GAIA survey. The stellar IMF at low masses is believed to be around a w 1.1, which would imply of the order of 5000 brown dwarfs at G < 20. If such estimate is correct, it implies that there are two times as much stars than brown dwarfs in the solar neighbourhood. Also, the last column gives the number of brown dwarfs per square degree within the limits defined by the survey in [7].

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Limiting distances of GAIA brown dwarf sampling comparison with 2MASS, VISTA

Fig. 4. Relative limiting distances at the limiting magnitudes of the 2MASS survey, GAIA project and for a faint K band project such as Vista, as a function of age and mass. In all cases, the relative precision on GAIA parallaxes will be better than 4% for brown dwarfs brighter than G = 20 within 200 pc.

Table 1. Estimates of the number of brown dwarfs as a function of the limiting magnitude of the GAIA survey and assuming different slopes for the IMF.

Magnitude limit G < 20 G < 21 G < 22 # BD pc~ 3 J - K > 13 & J < 14.5 IMF slope a = 0 IMF slope a = 1 IMF slope a = 2

4

408 580 700 0.0032 3800 6700 8600 0.04 \ 22400| 380Qp| 5QOOo| 0.4

|

0.002 0.023 0.2

Comparison with Other Surveys

Most presently known L and T field dwarfs have been discovered with the near IR surveys 2MASS and DENIS. Figure 4 shows the limiting distance to which GAIA is expected to sample brown dwarfs compared to the 2MASS survey or the VISTA project. The VISTA project is given here as the kind of typical next

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Fig. 5. Simulated mass-Log (age) distribution, assuming a limiting magnitude in different bands. The line separates T and L dwarfs. It is seen that the limiting magnitude of the 2MASS survey at K — 14.5 reaches a few solar neighbourhood T dwarfs, while they are virtually undetectable in the ASM1. The right plot shows the comparison with the result of medium deep near infrared surveys, such as the Vista project, which could be available on similar time scale as GAIA. generation near-IR survey that are foreseen for the next decade. It is seen that only for the youngest objects (a few tens of million years), GAIA should be able to reach distances comparable to that of 2MASS. It is improbable that GAIA could find brown dwarfs much older than 1 Gyr in any significant amount. GAIA could observe a few objects just below the hydrogen burning limit around 1 Gyr and within a few parsecs from the sun. In crowded regions such as the galactic plane where brown dwarfs are significantly more difficult to detect from ground based surveys, GAIA will detect all brown dwarfs to the limiting magnitude of the survey. Figure 5 gives another view of the types of objects within the reach of each of these surveys. It shows that T dwarfs will remain undetectable for GAIA, while a few units can be (and have been, see [11]) detected with 2MASS. Deep near-IR surveys should be able to sample old very low mass brown dwarfs. 5

Brown Dwarf Science with GAIA

Since most BDs observed by GAIA will probably have been already discovered in ground based surveys, most of these objects will benefit from complementary ground based photometric data. Also, all BDs in the GAIA catalogue will be nearby objects, with astrometric parameters determined to very good precision, of the order of a few percent on both parallaxes and proper motions. There are two fields for which we would expect GAIA to bring a major contribution. The first is the calibration of the stellar/substellar limit. GAIA parallaxes should in particular allow the measurement of age and mass for very young brown dwarfs by theoretical sequence fitting in the HR diagram.

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The second is the mapping of the spatial and kinematical young brown dwarf population in the solar vicinity, and its connection to the stellar component. References [1] Chabrier, G., Baraffe, I., 2000, ARA&A, 38, 337 [2] Basri, G., 2000, ARA&A, 38, 485 [3] Dahn, C., et al., 2000, ASPC Conf. Ser., 212: From Giant Planets to Cool Stars, 74 [4] Chabrier, G., Baraffe, I., Allard, F., Hauschildt, P., 2000, ApJ, 542, 464 [5] Tinney, C.G., Delfosse, X., Forveille, T., Allard F., 1998, A&A, 338, 1066 [6] Martin, E. L., Delfosse, X., Basri, G., et al., 1999, AJ, 118, 2466 [7] Kirkpatrick, J.D., et al., 1999, ApJ, 519, 802 [8] Allard, F., Hauschildt, P.M., Alexander, D.R., Tamanai, A., Schweitzer, A., 2001, ApJ, 556, 357 [9] Reid, I.N., et al., 1999, ApJ, 521, 613 [10] Delfosse, X., Tinney, C.G., Forveille, T., et al., 1999, A&A, 344, 897 [11] Burgasser, A.J., Kirkpatrick, J.D., Brown, M.E., et al., 1999, ApJ, 522, L65

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

THE GAIA ASTROMETRIC SURVEY OF EXTRA-SOLAR PLANETS M.G. Lattanzi 1 , S. Casertano2, A. Sozzetti3'1 and A. Spagna1 Abstract. The ESA Cornerstone Mission GAIA, to be launched prior to 2012 and with a nominal lifetime of 5 years, will improve the accuracy of Hipparcos astrometry by more than two orders of magnitude. GAIA high-precision global astrometric measurements will provide deep insights on the science of extra-solar planets. The GAIA contribution is primarily understood in terms of the number and spectral type of targets available for investigation, and characteristics of the planets to be searched for. Several hundreds of thousands of solar-type stars (FG-K) within a sphere of ~200 pc centered on our Sun will be observed. GAIA will be particularly sensitive to giant planets (Mp ~ Mj) on wide orbits, up to periods twice as large as the mission duration, the potential signposts of the existence of rocky planets in the Habitable Zone. Thousands of new planets might be discovered, and a significant fraction of those which will be detected will have orbital parameters measured to better than 30% accuracy. By measuring to a few degrees the relative inclinations of planets in multiple systems with favorable configurations, GAIA will also make measurements of unique value towards a better understanding of the formation and evolution processes of planetary systems.

1

Introduction

The present catalogue of candidate extra-solar planets discovered by radial velocity surveys (see for example [1]) totals today 66 objects having minimum mass Msinz < 13 Mj (where Mj is the mass of Jupiter), the so-called deuteriumburning threshold. Orbital periods span a range between a few days and ~7 years, but ~80% of these objects revolves around the parent star on orbits with semimajor axis a < 1 AU, well outside the ice condensation zone. Orbital eccentricities 1 2 3

Osservatorio Astronomico di Torino, 10025 Pino Torinese, Italy Space Telescope Science Institute, Baltimore, MD 21218, USA University of Pittsburgh, Dept. of Physics &; Astronomy, Pittsburgh, PA 15260, USA © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002019

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are usually higher than in our Solar System, up to ~0.9 for HD 80606 [2]. Seven stars harbour multiple systems, formed by either two or three planets [3-6], or a planetary mass object and a probable brown dwarf [7-9]. Except for the case of HD 209458 [10], all low-mass companions to solar type stars having Mp < 13 Mj have been classified as extra-solar planets solely on the basis of their small projected masses, and thus, under the reasonable assumption of randomly oriented orbital planes on the sky, small true masses. But, some of them may not be planets at all, as ~l/5 of them have Ms'mi > 5 Mj. As a matter of fact, today the true nature of these objects is still matter of ongoing debates among the scientific community: for example, planet (and brown dwarf) candidates, and stellar binaries have remarkably similar orbital elements distributions [11], but the mass functions in the two cases are strikingly different [12]. Clearly, our present understanding of the origin of planetary systems is still limited, and more measurements will be needed in order to be able to discriminate among models. To go beyond a simple Catalogue of extra-solar planets, Classification will have to be made on the basis of the knowledge of their true masses, shape and alignment of the orbits, structure and composition of the atmospheres. The dependence of planetary frequencies with age and metallicity will have to be understood. Finally, important issues on planetary systems evolution, such as coplanarity and long-term stability, will have to be addressed. But, the big picture will not be complete without crucial New Discoveries. The existence of giant planets orbiting on Jupiter-LIKE orbits (4-5 AU, or more) will have to be established. Such objects are the signposts for the discovery of rocky planets orbiting in regions closer to their parent stars, maybe even inside the star's Habitable Zone (for its definition, see Sect. 2.2). The proof of the existence of Earth-LIKE planets would be an extraordinary step towards the ultimate goal of the discovery of extra-terrestrial life. 2

The Role of GAIA

GAIA's ability in detecting and measuring planets is twofold, it will impact both future planet discoveries as well as provide information of great value for a compute classification of planetary systems and overall assessment of the correct theories of planet formation and evolution. In particular, the uniqueness of the GAIA contribution to the science of extra-solar planets is better understood in terms of 1) the size of the GAIA sample of potential systems which might be discovered and measured, 2) GAIA's ability in revealing the existence of a possibly large number of systems which might be bearing rocky, perhaps habitable planets, and 3) the impact of GAIA's coplanarity measurements in multiple-planet systems on the theoretical models of formation and evolution of planetary systems. 2.1

The Size of the GAIA Sample

In our earlier work [13], we considered in the simulations single giant planets, in the mass range 0.1 < Mj < 5, orbiting 1-M0 stars with periods up to twice

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Table 1. Number of giant planets that could be revealed by GAIA (-/Vd), and fraction of detected planets having accurate orbital elements determined (-/Vm), as a function of increasing distance from the Sun (Ad). A uniform frequency distribution of 1.3% planets per 1-AU bin is assumed.

Ad (pc)

N*

Aa (AU)

7Vd

Nm

0-100

~61000

1.3-5.3

>1600

>640

100-150

~114000

1.8-3.9

>1600

>750

150-200

~295000

2.5-3.3

>1500

>750

the mission duration, and placing the systems at increasing distances from our Sun. We parameterized our results in terms of the astrometric signal-to-noise ratio a/cr^p between the astrometric signature a and the single measurement error, which we set to a^ = 10 /^as (implying a final accuracy of 4 //as), value which applies to stars brighter than V = 13. In practice, this choice for the mass of the parent star encompasses the spectral class range from ~FO to early K type dwarf stars, whose masses are within a factor of ~1.5 that of the Sun. This, in combination with the V < 13 magnitude limit, translates into a distance cutoff for detection and accurate orbit estimation of ~200 pc. To this distance, F-G-K type dwarfs dominate the star counts at bright magnitudes, and within this horizon modern galaxy models [14] predict some 3-5 x 105 solar-type dwarfs available for investigation. Knowing the stellar content in the solar neighbourhood and the planetary frequency distribution, we can extrapolate a number of potential planetary systems within GAIA's detection horizon. Early estimates [15] yield an integral planetary frequency of ~3-4% for giant planets in the mass range 0.55 Mj orbiting within 3 AU from the parent star. By assuming a uniform planetary frequency distribution with orbital semi-major axis [16], then we can derive a lower limit to the number of giant planets GAIA would detect and measure at a given distance d (in pc). In Table 1 we summarize the results. The values of N^ at different distances correspond to actual new detections, once the fractions of detected giant planets in common with the overlapping semi-major axis regions at lower distances have been properly subtracted. Therefore, the total number of giant planets GAIA could discover orbiting around normal stars within the distance limit of 200 pc from the Sun is then greater than 4700, and roughly 50% of the detected planets would have orbital parameters and masses good to 20-30%, or better. The statistical value of such a sample (comparable in size to that of the observing lists of the largest ground based surveys) would be instrumental for critical testing of theories on planet formation and evolution.

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GAIA and the Habitable Zones

With the current payload design [19], the range of planetary masses between 1 Earth-mass and a few Earth-masses (Neptune-class planets) will only be marginally accessible to GAIA's all-sky survey. Its astrometric accuracy will be sufficient to address the issue of their existence only around a handful of the closest stars, within 5-10 pc from the Sun. Nevertheless, GAIA's contribute to the search for rocky, possibly habitable planets will be significant. Theory, in fact, provides us with two important concepts: Habitable Zone and Exclusion Zone. The Habitable Zone [17] is defined by the distance from a given star at which the temperature is such that water can be present in the liquid phase. The center of the Habitable Zone (whose distance depends on the mass of the central star) can be roughly identified by the formula P/P® = (M/M0)1'75. The Exclusion Zone [18] is defined by the dynamical constraint PQ > 6 x PR, which states that for a rocky planet to form in the Habitable Zone of a star then a giant planet must form on an orbital period PQ at least six times larger than the period PR of the rocky planet. In Figure 1 we show these two concepts as they have been realized in our Solar System and in the only other interesting candidate known to-date, the 14 Her planet-star system. All those systems GAIA will discover harbouring a giant planet on a sufficiently wide orbit (a > 3 AU) would immediately be added to the list of targets for the next generation of missions which will search the Habitable Zones of such systems for evidence of the existence of terrestrial planets.

Fig. 1. Upper half: comparison between the Solar System's Habitable Zone (in green) and Exclusion Zone (in red). Jupiter's orbital period is sufficiently large that the entire Habitable Zone of the Sun is available for formation of rocky planets. Lower half: the same comparison in the case of the 14 Her system, the only one known to-date to bear a giant planet on a sufficiently large orbit for at least part of the Habitable Zone (in blue) to be able to host in principle a rocky planet.

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GAIA and the Planetary Systems

The observational evidence of the first extra-solar planetary systems, whose unexpected orbital configurations are very unlike the Solar System's, has immediately raised crucial question regarding their formation and evolution. Are the orbits coplanar? Are the configurations dynamically stable? Radial velocity measurements cannot determine either the inclination i of the orbital plane with respect to the plane of the sky, or the position angle Q of the line of nodes in the plane of the sky. General conclusions on the architecture, orbital evolution and long-term stability of the newly discovered planetary systems cannot be properly assessed without knowledge of the full set of orbital parameters and true mass values. GAIA will be capable of detecting and measuring a variety of configurations of potential planetary systems. Utilizing as a template the two outer planets in the v Andromedse system, we have found [20] how a 60-pc limit on distance holds for detection and measurement accurate to 30%, or better, of planetary systems composed of planets with well-sampled periods (P < 5 yr), and with the smaller component producing a/a^ > 2. Also, accurate coplanarity tests, with relative inclinations measured to a few degrees, will be possible for systems producing a/a^ > 10 [20]. The frequency of multiple-planet systems, and their preferred orbital spacing and geometry are not currently known. Based on star counts in the vicinity of the Sun extrapolated from modern models of stellar population synthesis, constrained to bright magnitudes (V < 13 mag) and solar spectral types (earlier than K5), we should expect ~13000 stars to 60 pc [16]. GAIA, in its high-precision astrometric survey of the solar neighbourhood, will observe each of them, searching for planetary systems composed of massive planets in a wide range of possible orbits, making accurate measurements of their orbital elements and masses, and establishing quasi-coplanarity (or non-coplanarity) for detected systems with favorable configurations. 3

How Can GAIA Achieve This?

Two major issues can be singled out at the moment of defining the crucial steps which must be undertaken in order for GAIA to fully accomplish the scientific goals in the field of extra-solar planetary systems which have been outlined in the previous sections. First, specific requirements on the instrument performance must be met, and secondly it will be essential to identify the most robust and reliable procedures of analysis of the actual observational data. 3.1

The GAIA Instrument

In order to fulfill the expectations for ground-breaking results in field of planetary science, the GAIA instrument [19] must meet the stringent requirement of 4 /^as final astrometric accuracy on positions, proper motions, and parallaxes for bright targets (V^ < 13). In fact, in order to keep the ratio a/a^ = const., an increase

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Fig. 2. Number of solar-type stars available for planet searches with GAIA, as function of the final accuracy on positions, proper motions, and parallaxes. If the final astrometric error is 8 yuas instead of 4, then the size of the sample decreases by an order of magnitude (~2 x 104 vs. ~3 x 105). In the limiting case of final astrometric accuracy equal to that of DIVA and FAME on bright objects, then the number reduces to some 150 stars.

in the measurement error implies an increase in the astrometric signature due to the planet. In particular, the same type of system (same stellar mass, same planet mass, same orbital period), as a^ increases, would be detectable at increasingly smaller distances. In Figure 2 we show how the number of stars available to GAIA for astrometric planet searches would decrease as a function of the increasing final error accuracy, assuming that the number of objects scale with the cube of the radius (in pc) of a sphere centered around the Sun. If a^ is increased by a factor 2 the number of stars available for investigation would already be reduced by an order of magnitude. In the limit for final astrometric accuracy equal to the one foreseen for DIVA and FAME on bright objects (50 //as), only some 150 stars would probably fall within GAIA's horizon. The size of the sample would be so reduced that extra-solar planets would completely disappear from the GAIA science case.

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213

Modeling the Observations

In order to quantify the scientific impact of GAIA global astrometry measurements in the field of extra-solar planets extensive simulations have been used during the last few years [13,16,20]. Future work will concentrate on: a) refinements of the models of observations and observables. In particular, the science object position as defined in the satellite's reference frame will be expressed as function of all possible kinematic and dynamical parameters and of all astrophysical effects which contribute to a significant motion of the stellar photocenter, at the level of the single-measurement error. To this aim, more realistic galaxy models will be used, together with detailed models of specific environments, which will be needed for example in the case of the search for planets in stellar associations; b) as new knowledge is obtained from continuous improvement in the understanding of the instrument errors and performance before launch, a more realistic error model for GAIA observations will be implemented, which includes all possible sources of instrumental and astrophysical systematic errors, and their correlations; c) for a proper assessment of the effectiveness of the overall search and optimization strategy, the analysis tools will have to be refined in order to obtain a realistic estimation process, which involves the implementation of refined models for global search and optimization strategies of starting guesses for the orbital parameters. To this end, actual ground-based (or simulated) spectroscopic data could be used jointly with the simulated astrometric dataset, to improve orbital solutions and determine the full three-dimensional motion of the analyzed systems. References [1] Butler, R.P., Marcy, G.W., Fischer, D.A., et al., 2000, in Planetary Systems in the Universe: Observation, Formation and Evolution, IAU Symp. 202, A. Penny, P. Artymowicz, A. M. Lagrange & S. Russell (eds.), in press [2] Naef D., Latham D.W., Mayor M., et al., 2001, A&A, 375, L27 [3] Butler, R.P., Marcy, G.W., Fischer, D.A., et al, 1999, ApJ, 526, 916 [4] Mayor, M., Naef, D., Pepe, F., et al., 2000, in Planetary Systems in the Universe: Observation, Formation and Evolution, IAU Symp. 202, A. Penny, P. Artymowicz, A. M. Lagrange & S. Russell (eds.), in press [5] Marcy, G.W., Butler, R.P., Vogt, S.S., et al., 2001, ApJ, submitted [6] Fischer, D.A., Marcy, G.W., Butler, R.P., et al., 2002, ApJ, to be published [7] Udry, S., Mayor, M., Queloz, D., 2000, in Planetary Systems in the Universe: Observation, Formation and Evolution, IAU Symp. 202, A. Penny, P. Artymowicz, A. M. Lagrange and S. Russell (eds.), in press [8] Marcy, G.W., Butler, R.P., Fischer, D.A., et al., 2001, ApJ, submitted [9] Els, S.G., Sterzik, M.F., Marchis F., et al., 2001, A&A, submitted [10] Henry, G.W., Marcy, G.W., Butler, R.P., et al., 2000, ApJ, 529, L41 [11] Stepinski, T.F., Black, B.C., 2001, A&A, 371, 250 [12] Mayor, M., Udry, S., Halbwachs, J.L., et al., 2001, in Birth and Evolution of Binary Stars, IAU Symp. 200, ASP Conf. Proc., B. Reipurth & H. Zinnecker (eds.), in press [13] Lattanzi, M.G., Spagna, A., Sozzetti, A., et al., 2000, MNRAS, 317, 211 [14] Bienayme, O., Robin, A.C., Creze, M., 1987, A&A, 180, 94

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[15] Marcy, G.W., Cochran, W.D., Mayor, M., 1999, in Protostars and Planets IV, V. Mannings, A.P. Boss & S.S. Russell (eds.) (University of Arizona Press, Tucson), 1285 [16] Lattanzi, M.G., Sozzetti, A., Spagna, A., 1999, in From Extra-solar Planets to Cosmology: The VLT Opening Symposium, J. Bergeron & A. Renzini (eds.) (Springer-Verlag, Berlin), 479 [17] Kasting, J.F., Whitmire, D.P., Reynolds, R.T., 1993, Icarus, 101, 108 [18] Wetherill, G.W., 1996, Icarus, 119, 219 [19] Ferryman, M.A.C., de Boer, K.S., Gilmore, G., et al., 2001, A&A, 369, 339 [20] Sozzetti, A., Casertano, S., Lattanzi, M.G., et al., 2001, A&A, 373, L24

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

DETECTION OF TRANSITS OF EXTRASOLAR PLANETS WITH GAIA N. Robichon1

Abstract. Extensive simulations of planetary transits in the epoch photometry of the future space astrometry mission has been performed. Thousands to tens of thousands of transiting planets should be detected with GAIA. 1

Introduction

At present, about 60 extrasolar planetary systems have been detected (see [1] for an updated list). From the size of the star sample surveyed for searching extrasolar planets, Marcy et al. [2, 3] estimate that about 4% of solar type stars have a planetary system. With GAIA, this proportion represents millions of stars. The question is then: will GAIA be able to detect them? The present paper studies the capability of GAIA to detect those who will transit their parent stars. The relative luminosity drop ^ of a planet transiting its star is given by the square of the ratio of the planet diameter by the star diameter. For a solar diameter, it is 10~4 for an Earth-like planet, 0.01 for a Jupiter-like planet. The individual accuracy of a GAIA epoch photometry observation as a function of apparent magnitude is given in Figure 1. It has been computed by C. Jordi (private communication) on the basis of the last satellite and CCD configuration. To be conservative, 1 millimagnitude has been quadratically added to this accuracy to take account of any eventual systematic errors. The adopted individual epoch accuracy per field is about 1 millimagnitude for the brightest stars and increases to a few hundredths for the faintest stars. Planets much smaller than Jupiter will then be out of reach with GAIA (at least as far as transit detection is concerned). If .R*, TT, M* and P are respectively the radius, the parallax, the mass of a star and the period of a planet orbiting this star, the transit duration is given by: (1.1)

1

DASGAL-CNRS/UMR 8633, Observatoire de Paris, France © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002020

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Fig. 1. Epoch photometric accuracy of the GAIA G band as a function of the apparent G magnitude. for a circular orbit and neglecting the planet radius over the stellar radius. It is 0.15% of the period for the Earth, 0.013% for Jupiter and 3.2% for the planet orbiting around HD 209458 which has a period of about 3.5 days. The number of GAIA individual epoch photometry observations will be between 100 and 300 for most of the stars. This means that planets with periods shorter than only a few days will have a chance to exhibit several transits in the GAIA epoch photometry. Among the 60 known stars with a planetary system, a quarter are orbited by "hot Jupiters" having a period shorter than 15 days. For these stars, the probability that the inclination of the planet orbit makes it transiting is of a few percents while it is only 0.5% for the Earth around the Sun and less than 0.05% for Jupiter. On the other hand, the minimum observed period known for extrasolar systems is around 3 days which probably corresponds to a real limit under which the planet just cannot exist for stability or temperature reasons. 2

Simulation

In order to have a quantitative idea of the number of stars with transiting planets, an extensive Monte-Carlo simulation has been done. This simulation uses the Galaxy model of Haywood (private communication) which is derived from the Besangon model of population synthesis (see for example [4]): in a given field, this model can simulates star counts with observable properties such as magnitudes in any band, proper motions, radial velocities... following any observational constraints (censorships in magnitude...). Star counts in the model have been normalized such as they reproduce quite well several star catalogues such as Hipparcos, Tycho, 2MASS...

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Interpolating counts in several fields of one square degree all over the sky, the model gives the density 3 days) and about a quarter of them have periods smaller than 20 days. The probability density of solar type stars with hot Jupiters has then been chosen to be proportional to l/P and normalized to represent 1% of all stars (a quarter of 4%). The probability of a given number of false detections follows a binomial law and depends on the number of observations and on the ratio of the depth of the transits by the photometric accuracy of a single observation. Therefore, it depends on the radii of the star and the planet and on the apparent magnitude of the star (which drives the photometric accuracy). For example, the probability of having randomly 5 observations out of 200 deviating by more than 3 sigmas is smaller than 5 x 10~7 but is about 0.002 for 2.5 sigmas. Knowing the probability distributions described above, the number of detected planets has been simulated in bins of ecliptic latitude (10° bins), apparent and absolute magnitudes (1 mag bins) and period (0.5 day bins). In each bin,

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Fig. 2. Left: GAIA simulation of the folded light curve of HD 209458 for two different values of the time origin of GAIA. Upper. 6 observations occur during transits. Lower, no points are observed. Right: probability distribution of the number of observations during transits for a planet with a 3-day period orbiting a star at (3 = 35° (filled histogram) and a planet with a 10 day period around a star at j3 — 5° (hatched histogram).

Fig. 3. Distribution of the periods of the 60 known extrasolar planets.

the number of false detections has also been computed and the detected planets have been counted only when the ratio of false detections over detected planets is smaller than 10%.

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Results

Simulations have been performed under several hypotheses concerning the mission duration, the size of the planet and the number of observations during transits needed to recover the period. The mission, as it is defined now, includes 4 full years of observation. An increase of 1 year is not unrealistic at this stage of the mission definition if strong arguments can be exhibited in favour of it. Anyway, if the satellite is still alive after 4 years of observation, an extension would seem reasonable. Two different planet radii have been used: 1.0 and 1.3 Jupiter radius (the radius of the planet orbiting HD 209458). This range of radii should cover most of "hot Jupiter" [5,6]. Recovering the value of the planet period from GAIA photometric observations would deserve a separate study. Obviously, at least three different transits must be observed which correspond to at least 5 GAIA observations during transits since, most of the time, GAIA observations are coupled: the preceding and following fields are separated by less than an hour. In the following, a planet is considered as detected if it is observed more than 5 times during transits. To be conservative, a more stringent limit of 7 observations during transits has also been considered. In fact, observing only one transit of a planet is theoretically enough to detect it and this would dramatically increase the number of detections. But no information would be available on the period and the photometric following of the stars would be much too time consuming since stars should be observed continuously to detect new transits. On the contrary, observing 3 or 4 different transits would reduce considerably the possible numbers of the period values and would then allow to predict the times for reobserving transits with a pointing instrument (on ground or in space). In this context, a detected planet is defined as a planet for which the period can be known to some extent. The following table gives the predicted number of extrasolar planets detected by transits under these different hypotheses. This number varies from 4000 to 40000 planets, with less than 10% of false detections. Table 1. Predicted number of detected planets under several hypotheses on the planet radius, the required number of observations during transits and on the mission duration.

duration of the mission -i Rp •Otfjup A^pts /transit = 1 Rp •3jRjUp TVpts/transit = 1. Rp •QRjup A?"pts/transit RP = 1•3-RjUp ^pts/transit

> > > >

5 5 7 7

4 years 9400 25500 3700 10100

5 years 13700 36300 6900 17800

5/4 +46% +42% +85% +76%

Extending the planet radius from 1 to 1.3 Jupiter radius triples the number of detections. Most of "hot Jupiters" probably having a radius in this range [5,6],

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the real number of detections should be in between the numbers obtained using 1 and 1.3 Jupiter radius. Choosing 7 observations during transits (equivalent to observing at least 4 different transits) instead of only 5 (3 different transits observed) reduces the number of detections by a factor of 3. This question of the detection algorithm needs then to be studied further. Extending the mission by one year would increase the number of detection by 40 to 85%. Figure 4 shows the detailed numbers of detected planets as a function of its period and of the absolute magnitude of its parent star. Extended mission of 5 years. At least 5 observations during transits.

period in days

Nominal mission of 4 years. At least 7 observations during transits.

period in days

Fig. 4. Number of detected planets in period bins of 0.5 day and for different values of the absolute magnitude of the parent star: from top to bottom MG = 4 to MG > = 11.

The vast majority of the detected planets will have a very short period of 3 to 5 days. This is the combination of the chosen period distribution with the geometric probability of having a transit and with the proportion of time spent during transits which all decrease when the period increases. Nevertheless, tens to hundreds of planets will be detected with periods larger than 10 days. Most of the detected planets orbit quite bright dwarfs although the proportion of "hot Jupiters" has been taken to 1% whatever the mass of its star is and although the distribution number of dwarfs in GAIA increases with the absolute magnitude. This is just due to the fact that intrinsically bright stars are also statistically apparently bright and then have a better photometric accuracy. Most of the planets will then be detected around solar type stars. This reinforces the validity of the numbers given in this study since it is around this type of stars that the planet number statistics are presently known. On the other hand, tens

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to hundreds of planets will be detected around K or M dwarfs if these stars hold planetary systems. 4

Conclusions

Realistic simulations of extrasolar planet transits observed by GAIA show that 4000 to 40000 Jupiter-like planets with known periods will be detected. The majority of these planets have a period of 3 to 5 days and orbit Sun-like stars. It is also shown that a 1-year extension of the mission would increase the number of planet detected by 40 to 85%. These simulations have to be refined in several ways: - The Galaxy model used here has to be checked. - The simulations must be extended to intrinsically brighter stars. - The detection algorithm i.e. the number of observed transits needed to recover the periods has to be improved. But these refinements shouldn't change the predicted numbers by orders of magnitude. Few statistics are available concerning extrasolar planet properties needed in such simulations. Proportion of stars with planetary systems as a function of spectral type or mass, radius distribution and minimum period of planets are not presently known. These statistics will be available in the next years and the models will be improved consequently. No study has been done here to estimate the importance of other physical effects which can mimic planetary transits. Star spots in cool dwarfs should produce periodic decreases of star flux and a way has still to be found to differentiate them from real transits. Grazing eclipsing binaries produce light curves very similar to those of planetary transits. Fortunately, they also produce a signature in radial velocity which should be detectable with the spectroscopic instrument of GAIA for most of them. Finally, an unbiased way of recovering the real distribution of planets as a function of period, planet mass, parent star mass... from the future distribution which will be observed by GAIA is still to be done. References [1] Schneider. J., Catalogue of extrasolar planets, http://www.obspm.fr/encycl/catalog.html [2] Marcy, G.W.. Cochran. W.D.. Mayor, M., 2000. in Protostars and Planets IV, V. Mannings, A.P. Boss. S.S. Russell (eds.) (University of Arizona Press, Tucson). 1285 [3] Marcy, G.W., Butler, R P., 2000, PASP, 112, 137 [4] Haywood, M., Robin, A., Creze, M., 1997, A&A, 320, 440 [5] Saumon, D., Hubbard, W.B., Burrows, A., et ai, 1996, AJ, 460, 993 [6] Burrows, A., Guillot, T., Hubbard, W.B., et a/., 2000, ApJ, 534, L97

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Structure, Formation and History of the Galaxy

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

DUST AND OBSCURATION IN THE MILKY WAY J. Knude1 Abstract. A detailed knowledge about the galactic extinction is mandatory to obtain the astrophysical/kinematical parameters time variation outside the solar neighbourhood. One may hope that the GAIA photometry itself will contribute to colour excess determinations for most of the sample otherwise the extinction must be deduced from external sources. 3D galactic models where the dust distribution is an integral part seems a viable solution.

1

Introduction

Since GAIA is an astrometric/photometric/spectroscopic mission aiming mainly at understanding the composition, formation, evolution and gravitational potential of the Galaxy the astrophysical requirements to the medium band photometry are quite severe. In order to model the Galaxy's evolution metallicities, effective temperatures and ages must be known with accuracies better than a few tenths of a dex, a few hundred degrees Kelvin and some hundred million years, respectively. Colour indices must accordingly be observed with a precision better than f^0.02 mag and the transformation to intrinsic indices (classification), ideally for any stellar type, to the same level of accuracy. This implies almost perfect correction for interstellar extinction. The amount and location of the obscuring interstellar material is best known in the immediate solar vicinity but only for the most diffuse part of the medium (Ay < 2 mag) much less is known about the galactic distribution of the extinction taking place in the molecular clouds (Ay > 2-3 mag). We review some recent extinction data and 3D modelling of the extinction distribution and propose a new simple method applying the GAIA parallaxes that possibly may be used to provide a coarse 3D extinction map. This may be useful since a result from the preliminary discussion of the accuracy of the photometric systems suggested for GAIA indicates that even a coarse limitation of the reddening range improves the accuracy of the remaining parameters, Vancevicius [1]. 1

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Dust on Different Scales

In Table 1 of Ferryman et al. [2] the primary galactic kinematic tracers are listed together with the relevant range of visual extinctions expected. From this table we note the expected range of Ay is 0-10 mag. Extinction determinations on the required accuracy level include correction for varying chemical composition and gravity implying that high quality photometry in the ultraviolet and violet bands must be available. This may be a serious problem for the high extinctions Ay > 2-3 mag. Consequently it could be necessary to introduce alternative, probably less precise methods to correct for large extinctions. If the inversion techniques applied to reconstruct the density field from the distance column density data can be refined to reproduce even small spatial features, 0 ~ 0.5 pc, one could hope that the parallax together with the reconstructed 3D field may provide extinctions of a sufficiently high quality even for interesting peculiar stars. The main source for the extinction should of course be the GAIA photometry itself and the photometric determination of the reddening is not a trivial matter, Vancevicius [1]. A photometric 8 band system proposed for FAME is claimed to estimate effective temperature and extinction with a precision of 1-2%, Oiling [3]. To have an overview of various external extinction indicators we briefly address the following items listed in the table below: (1) An example of the use of the dust emission in the IRAS bands for an all sky extinction determination may be found in Schlegel et al. [4], we get the, well known impression that dust seems ubiquitous. Recently Drimmel & Spergel [5] presented a new 3D model for the Galaxy where the dust distribution was modeled from far and near infrared emission from the COBE/DIRBE instrument. The "galactic" dust distribution introduced by Spergel and Drimmel indicates the high degree of sophistication that must be included in models of the diffuse, virtually continuous part of the galactic dust. Before launch of the GAIA mission we may probably expect rather detailed information on the all sky local dust emission from the various FIR - mm bands included in the MAP and Planck missions. Column densities from the cosmic background missions may provide a good comparison to the optical extinction resulting from GAIA. In addition to the smoothly varying galactic models based on the galactic structure parameters any model must also account for local deviations. There is a long tradition to derive structure parameters by comparing deep CCD photometry to model predictions. These Galaxy models include a dust distribution, Bienayme et al. [6]. A major challenge is how to account for local deviations to the double exponentional often applied, see [7]. The DENIS and 2MASS surveys are also quite useful for studying the galactic dust. Ruphy et al. [8] applied a smooth dust distribution to correct the DENIS J and KQ counts for a comparison to a model of the predicted infrared point source counts. Ojha [7] used 2MASS data for a study of the galactic thin and thick disk and assumed the smooth diffuse dust distribution to be like the young thin disk but also introduced individual absorption features.

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(2) An early investigation of the extinction's distribution over several kpc is given by Neckel & Klare [9], resulting maps may also be found in Hakkila et al. [10] a synthesis of published studies. Open clusters often have well determined distances and extinctions, facts used by Chen et al. [11] to reproduce the 3D Ay/pc field within ^2 kpc and at low galactic latitudes. The density field is determined with an inverse method. Given the rather small number of open clusters the spatial resolution in the density field is limited. Chen et al. also present an extinction - distance law for every 10 degrees along the galactic plane. J0nch-S0rensen [12] have presented Eb-y vs. distance diagrams for about ten small regions. The data are based on uvbyfi CCD photometry of A, F and G type stars brighter than V ~ 19 mag. Most of the directions observed penetrate the galactic dust disk but the data probably only pertain to the more diffuse part of the interstellar medium, Ay < 2-3 mag. GAIA results are expected to be of similar or better accuracy than the uvbyfi results. Better since the parallax is determined independently and because the GAIA photometry will be useful for a wider spectral type range than uvbyfi, see Vancevicius op.cit.

(1) The Galaxy

(a) infrared continuum emission: IRAS, COBE/DIRBE, MAP, Planck (b) optical stars counts (c) infrared stars counts

(2) The galactic plane (a) O and B stars (b) galactic clusters (c) CCD data of faint A, F and G stars (3) The galactic bulge (a) broad band CCD data (4) Molecular clouds

(a) USNO-PMM counts (b) broad band CCD colour counts (c) H, J, K photometry

(5) The solar vicinity (a) Hipparcos parallaxes and Nal D absorption (b) parallaxes and uvbyfi measurements (c) parallaxes, Tycho photometry and MK classification (6) The galactic poles (a) A and FG stars (7) gas emission

(a) 21 cm emission/absorption (b) HI and molecular gas

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(3) Discussion of the Galaxy's bulge requires very deep photometry and even the windows with the least extinction has Ay « 2 mag. Ng & Bertelli [13] present a discussion of the possible distribution of the extinction. Similar considerations may apply for GAIA data on the inner regions of the Galaxy. (4) Star counts may probably be used to derive extinctions through molecular clouds. Cambresy [14] used the USNO-PMM catalogue for star counts and a wavelet decomposition to derive the extinctions. Maximum extinctions beyond Ay ~ 25 mag are indicated for some molecular cores. Due to the sharp distribution of near infrared colours of dwarf stars a fairly straightforward determination of the near infrared colour excesses is possible for molecular clouds, Lada et al. [15], but V and / counts may probably also be used as shown by Thoraval et al. [16]. Due to the large ratio EAv « 16 the demands to the precision of the H, J, K photometry are extreme for correction of individual field stars. (5) The solar vicinity is of particular importance not least since it may represent a low density cavity. Local extinction measurements are preoccupied with defining the edge of this cavity and to search for possible clouds inside it. Sfeir et al. [17] have combined Nal D absorption lines with Hipparcos parallaxes to construct isocolumn density contours. Similar data were used by Vergely et al. [18] but with an inversion method to establish the density field within a few hundred parsecs. It is interesting to note that virtually none of the structures identified by Vergely et al. are present in Chen et a/.'s density map but also that nearby features like the Chameleon clouds are missed by their grid. If some classification may be provided, it need not be perfect and could come from Q — Q diagrams, the distance to extinction discontinuities may be identified. Knude & H0g [19] showed that even with Michigan classification, Tycho photometry and Hipparcos parallaxes distances to nearby molecular clouds could be estimated. (6) Last, we mention the rather complex colour excess distribution towards the NGP. This high latitude extinction is caused by matter closer than ^200 pc, it seems that only about 1/3 of the polar cap is screened by clouds with excesses exceeding about £&-y = 0.030 (Ay ~ 0.1 mag), Knude [20]. The local bubble may accordingly not have a completely coherent confinement, an impression one might get from the Nal D iso-contours, Sfeir et al. [17]. The reality of the isolated, low colour excess clouds, at high and intermediate latitudes, are confirmed from observations at UV and infrared wavelengths, see e.g. Haikala et al. [21] and Berghofer et al. [22]. (7) A further complication may have arisen with the recent revelation of a hitherto rather unnoticed population of HI clouds by the 1 arcmin beam survey of the galactic plane (Gibson et al. [23]). Some of the clouds showing HI absorption are proposed to have diameters ~0.5 pc and the majority has no CO emission counter parts, a rather peculiar combination. It is essential to investigate the frequency of these clouds both for the sake of extinction correction but also for understanding the structure of the Galaxy's extinction distribution. It seems important to put some emphasis on investigating the linear scales on which the extinction displays major variation.

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With a known gas/dust ratio and the known gas distribution Ay may be estimated at any (/, 6, d(pc)), Ortiz & Lepine [24]. 3

Inversion Models

A substantial fraction of the GAIA targets will have accurate parallaxes, mainly the brighter part of the sample, but it is assumed that even the faintest stars will have acceptable photometric parallaxes, ^ < 20-30%. The astrometry may, however, be of such high quality that the trigonometric parallax is more precise than the photometric parallax, even at the survey limit. We will thus have a very detailed combination of extinctions and distances which may be used to establish a 3D distribution of some parameter measuring the interstellar volume density. Recently there has been some papers presenting the results of inverting the column density - distance information to a 3D density field (Chen et al. [11], Arabadjis & Bregman [25], Vergely et al. [18]). In particular the maximum entropy reconstruction by Arabadjis and Bregman seems to be promising, their method have not been tested on real data so far. Chen et al. present a galactic extinction law for the Galaxy's plane, to which their extinction probes are confined, that may be compared to independent data. This comparison emphasizes the importance of a good angular resolution, apparently rather local molecular densities are missed by the model - this stresses the need to have a good knowledge of the model opacity Pop (I, b, r] and the different scale heights of the distribution of diffuse and molecular material (120-140 and 40-50 pc respectively). The opacity pop(l,b,r}, or po cm~ 3 (or Ay/pc) for the diffuse medium will vary with position as may be seen in Figure 12 in J0nch-S0rensen [12]. The extinction tracers in the GAIA sample on which emphasis should be put could be chosen from considering their ability to determine the input parameters for the inversion codes - like /QO> ^z and h^. This request could influence the choice of medium band filters. Are the information obtainable from O. B and A stars adequate or must stars with higher spatial densities, G and K, be preferred? 4

Extinction from Two Broad Bands and GAIA Parallaxes

The 3D mapping of the interstellar density is facilitated by the large number of stars per square degree resulting from the GAIA mission. Within 5 degrees from the galactic plane we may expect more than 5000 stars per square degree. We may probably define solid angles (rather small indeed) so that significant parts of the main sequence may be populated at most distances. We may chose two wide bands, e.g. like V and /, and form a representative main sequence (V — I)Q — My relation, could be done with unreddened GAIA data. We then select a distance d pc (parallax) and include all stars in the range d ± O.lOrf pc. We may then investigate if any stars at d ± O.ld have a common extinction Ay. If this is the case they must be located on a locus: the main sequence relation shifted by

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V - Mv = Av - 5 + 5 logo? and the colour shift given by A(V - /) = EV-I = Ay(\ — -^-} implying that the extinction law must also be known. The distance error from such fits are 10-20%. Stars at a common distance and with a common extinction must be located on a shifted main sequence relation, just like clusters. So this is "main sequence fitting" to field stars. Contours with a 3a separation Ay ~ 0.2 mag may be expected from such a method, almost meeting the requirements for studying the Galaxy's evolution. We have applied a similar method to the CG 30 complex of cometary globules and to the Lupus 2 cloud (Knude & Nielsen [26,27]). And we have performed sort of a test in the vicinity of the very local molecular cloud MBM 12 , 13, 14 with the Tycho-2 photometry, H0g et al. [28], and Hipparcos parallaxes, ESA [29], Knude & Fabricius in preparation:

Fig. 1. Tycho-2 photometry and Hipparcos parallaxes. The figure is a two colour diagram for the region 012000 = 40.0-51.0 (deg), £2000 = 14.0-23.0 (deg) covering the three molecular clouds MBM 12, 13 and 14. The curve is the (£?T — VT)O vs. MVT relation shifted to 75 pc with AVT ~ 0.15 mag. Diamonds indicate stars also in the Hipparcos Catalog and with (£?T — VT) within ±0.030 mag from the shifted main sequence.

Figure 1 is the Tycho-2 colour - magnitude diagram covering these three nearby molecular clouds. In the diagram we see features resembling main sequences protruding to the blue and bright part of the diagram. It is checked whether the features are due to known clusters in the region under study. If not we try to

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fit the features with the (B^ — VT)O vs- MyT relation established from nearby, presumably unreddened stars common to the Tycho-2 and Hipparcos catalogs. As for clusters the fit provides the distance d(pc) and the absorption AyT (mag). A fit to a feature is indicated by the solid curve in Figure 1. Now a fraction of the bright Tycho-2 stars is in the Hipparcos Catalog and we extract those that furthermore have (BT — VT) within ±0.03 mag from the fit in Figure 1, these stars are shown as diamonds in Figure 1. The main sequence fit suggest a distance of 75 pc and AVT ~ 0.15 mag. 19 stars fulfill the criteria mentioned above, their mean parallax is 11.44 ± 4.93 mas ranging from 3.09 to 20.24 mas. The mean implies a distance of ~87 pc. These stars are of course a mixture of dwarfs and giants, for our fit we assumed they were all dwarfs. The giant contamination may not be too serious because the colours of most of the stars fitted are bluer than (B^ — VT) ~ 0.8, about where the unreddened giants starts showing up. For the GAIA sample the parallax is known for all stars! If we exclude stars more than one standard deviation from the mean, 12 stars remain with a mean TT = 11.92 mas and the error of the mean is 0.70 mas. A common distance d ~ 84±5 pc is thus suggested. The median parallax of all 19 stars is 11.17 mas corresponding to 90 pc. Within the errors the two distance estimates are identical. For MBM 12 Hearty et al. [30] find a distance range 58-90 pc from a combination of Nal D spectroscopy and Hipparcos parallaxes. The lower distance limit just indicates the most distant star in front of MBM 12 not showing measured Nal D absorption. The upper distance limit from this study is identical to our suggested distance. This means that choosing a constant parallax, the GAIA stars with a given absorption must lie on a shifted main sequence and their location on they sky will trace the corresponding absorption contour. Combining these contours for varying distance may probably provide a coarse 3D dust distribution. One must necessarily study the reddening and distance effects of the main sequence width and the influence of metallicity on the intrinsic main sequence relation. References [I] Vancevicius, V., 2001, Performance of the GAIA photometric systems IF, 2A, 3G, 67 [2] Ferryman, M.A.C., de Boer, K.S., Gilmore, G., et al., 2001, A&A, 369, 339 [3] Oiling, R., 2001, A Proposal For Additional Photometric Bands. Astrometric and Photometric Accuracies, preprint USNO/USRA [4] Schlegel, D.J., Finkbeiner, D.P., Davis, M., 1998, ApJ, 500, 525 [5] Drimmel, R. & Spergel, D.N., 2001, ApJ, 556, 181 [6] Bienayme, O., Robin, A.C., Creze, M., 1987, A&A, 180, 94 [7] Ojha, D.K., 2001, MNRAS, 322, 426 [8] Ruphy, S., et al., 1997, A&A, 326, 597 [9] Neckel, Th., Klare, G., 1980, A&AS, 42, 251 [10] Hakkila, J., Myers, M.M., Stidham, B.J., Hartmann, D.H., 1997, AJ, 114, 2043 [II] Chen, B., Vergely, B., Valette, B., Carraro, G., 1998, A&A, 336, 137 [12] J0nch-S0rensen, H., 1994, A&A, 292, 92

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Ng, Y.K., Bertelli, G., 1996, A&A, 315, 116 Cambresy, L., 1999, A&A, 345, 965 Lada, C.J., Lada, E.A., Clemens, D.P., Bally, J., 1994, ApJ, 429, 694 Thoraval, S., Boise, P., Duvert, G., 1997, A&A, 319, 948 Sfeir, D.M., Lallement, R., Crifo, F., Welsh, B.Y., 1999, A&A, 346, 785 Vergely, J.-L., Freire Ferrero, R., Siebert, A., Valette, B., 2001, A&A, 366, 1016 Knude, J., H0g, E., 1998, A&A, 338, 897 Knude, J., 1996, A&A, 306, 108 Haikala, L.K., Mattila, K., Bowyer, S., et a/., 1995, ApJ, 443, 33 Berghofer, T.W., Bowyer, S., Lieu, R., Knude, J., 1998, ApJ, 500, 838 Gibson, S.J., Taylor, A.R., Higgs, L.A., Dewdney, P.E., 2000, ApJ, 540, 851 Ortiz, R., Lepine J.R.D., 1993, A&A, 279, 90 Arabbadjis, J.S., Bregman, J.N., 2000, ApJ, 542, 829 Knude, J., Nielsen, A.S., 2000, A&A, 362, 1132 Knude, J., Nielsen, A.S., 2001, A&A, 373, 714 H0g, E., Fabricius, C., Makarov, V.V., et a/., 2000, A&A, 355, L27 ESA 1997, The Hipparcos and Tycho Catalogues, vols. 1 - 17, ESA SP-1200 Hearty, T., Fernandez, M., Alcala, J.M., Covino, E., Neuhaser, R., 2000, A&A, 357, 681

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A COMPLETE CENSUS DOWN TO MAGNITUDE 20: STELLAR POPULATION PROPERTIES A.C. Robin1

1

GAIA, a Deep Scrutiny Inside Galaxy Formation and Evolution

The GAIA mission will provide an unprecedented view on galaxy evolution aspects. For the first time one will have accurate distances over a major part of the Galaxy, giving access to populations far towards the galactic centre. The aim of the mission is also to get reliable abundances estimates, effective temperature, gravity and ages for most of the survey stars, as well as accurate kinematics over the 3 axes. This will allow to constrain galactic evolution using together the chemical and dynamical aspects, keystones for building a self-consistent scenario of galaxy formation and evolution. The Galaxy may be described through the concept of stellar populations. First attentions being paid to the stellar populations were in the 40's when Baade discovered that similarities exist between populations of the Milky Way bulge and the one of M 31. Then he defined the concept of stellar population: a family of stars with common characteristics such as the space distribution, abundances, kinematics and the age. This stellar population concept is applicable to all galaxies and has been a good help for investigating the formation and history of galaxies. It is usually admitted that the Galaxy contains four major stellar components: the bulge, the thin disc, the thick disc and the halo. In the following sections, I shall describe the main characteristics of these four populations and explain how they are linked with the formation scenario of the Galaxy, with the star formation history, and how GAIA will improve this knowledge. 2

Bulge and Central Regions

One should distinguish the spatial region which is called the bulge (roughly a longitude between —10 and +10 and latitudes —5 to +5) and the bulge stellar population. The bulge region is a really complex region of the Galaxy. The stellar density is high and the observation is difficult at optical wavelengths due to 1

CNRS-UMR 6091, Observatoire de Besangon, France

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interstellar extinction, not only in the bulge but also in the disc behind it. When extrapolating the other populations towards the galactic centre they all superimpose (disc, thick disc and halo) but a distinct population is also present which dominates at near-infrared wavelength. This population has different characteristics which allow to identify it on a statistical basis but not quite on a star by star basis. The very central region of the Galaxy (I and b less than 0.5 deg or so) is called the inner bulge. It has a very high stellar density, with rich clusters, including a young population of high metallicity [1] and probably a massive black hole. This central region will not be observed in detail with GAIA because of high extinction in the visible and crowding. The outer bulge is a rather old population. It extends to probably about 10 or 15 degrees in longitude, a few degrees in latitude. It appears clearly boxy or peanut-shaped in the COBE-DIRBE data and shows triaxiality. However, while many authors assimilate the triaxial bulge to the bar, they could be two different structures [2]. At the present time, it seems that the bulge as traced by M giants is an old population, with a large range of metallicities (—1.6 to 0.55 dex in [Fe/H] [3]) with a mean slightly under solar (—0.3 dex). Their abundance in [a/Fe] is enhanced compared to solar, indicating that these stars have been formed before a large number of SNI, which are the main source of iron peak elements, have exploded. This is compatible with a formation nearly at the same time as the stellar halo, but with a faster enrichment probably due to the higher density. The metallicity gradient is still controversial. The velocity dispersions in the bulge range from 60 to 110 km s^1 from several kinematical studies using various tracers (see [4] for an overview). The rotation varies with galactic longitude, the maximum being at about 100 km s"1 at I = 10 as found by [4] from a sample of planetary nebulae, but results vary from a sample to another due to varying metallicities of tracers. With the available accuracy of kinematical data, the stellar kinematics in the Baade's window is compatible with the bulge being an isotropic oblate rotator, in spite of the fact that one clearly sees in photometry and gas kinematics that the bulge is not axisymmetric [5]. One need to consider velocity distributions on large scales rather than in a single window in order to recover a self-consistent view of the bulge and its origin. Remaining open questions concern mostly the link between the bulge and the other populations, specially with the bar (if there is one distinct from the outer bulge) and the discs (thin and thick). Kinematics as well as metallicity and distance determinations are key points to determine the overall scheme: one expects, from studies of external galaxies, a bulge to be formed at early times, when the galaxy was young, probably by a rapid evolution (high star formation rate, high enrichment) of the central part of the halo, or eventually by residuals of merging events of smaller galaxies into a bigger one (or both). The bar is formed from a disc by perturbations due to gravitational instabilities. With these two scenarios in mind one should be able to distinguish a bar from a bulge by their kinematics.

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The GAIA photometric bands are not probably the best for seeing the bulge due to extinction. However, with GAIA distances with a 10% accuracy up to the galactic centre will be available. It will allow to distinguish the foreground from the central region and even from the background disc. It can be shown from a realistic model of the stellar populations that at bright magnitudes in the visible, down to about magnitude V — 16, the bulge is not dominant over the disc in star counts, which has caused misleading results in the past (however this is no more true in the near infrared). With GAIA going deep to magnitude 20, a large number of bulge stars will have accurate distances and proper motions, a smaller number will also have radial velocities. This should give a detailed description of the kinematics, giving access to dynamics, potential, as well as on a measurement of the central mass. Metallicities and (less accurate) ages will also be available and used to constrain the chemo-dynamical model of formation, metallicity gradients being a prediction of models of dissipational collapse, but are still observationally controversial. 3

The Thin Disc

A simple description of the thin disc can be made as follows. It is flat (at least within the solar circle and for relaxed populations), its density in the plane is exponentially decreasing radially with a scale length of the order of 2.5 kpc, comparable with what is seen in most spirals of the same type [6]. The scale height varies with ages from 60 to about 250 pc. The maximum age of the disc is estimated to about 10 Gyr, from the white dwarf luminosity function, old open clusters or Hipparcos sample (see [7] for a detailed analysis of these determinations). But the disc is still forming stars, giving a broad distribution of ages. In the mean the star formation has remained roughly constant over these 10 Gyr, despite inhomogeneities in time and space. It seems that in the outer part the disc has a cut-off: the exponential is truncated at about 11 to 15 kpc [6,8,9]. In the inner side, there is no evidence for a hole in the disc: the disc seems to continue all the way to the centre, superimposed on the bulge population [10,11]. Past this crude description, the disc has large scale as well as small scale inhomogeneities. Among the first ones are the ring, the spiral structure, probably a bar, a warp and a flare. It has smaller structures like open clusters, associations, groups, and special local structures like the Goult Belt and a local arm. 3.1

Star Formation and Small Scale Inhomogeneities

The small scale inhomogeneities cover different realities depending of their size, with structures stable over several Gy for highly gravitationally bound clusters, and smaller structures limited to young stars. It has been estimated that the mixing time in the Galaxy should be of the order 1 Gyr [12], the time to complete a revolution around the Galaxy being about 250 Myr. This is true for unbound stars, not for groups, associations or clusters. [12,13] have estimated the degree of homogeneities of the solar neighbourhood at different scales in the phase space

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from the Hipparcos survey. They conclude that less than 7% of their A-F stars are in clusters, but up to 63% are in (Eggen's type) superclusters of large velocity dispersion (6 km s""""1). The probable scenario is that most stars form in groups, from bursts separated by quiescent periods. A fraction of initial groups is gravitationally bound and forms open clusters. GAIA will widen the point of view on the disc structure to inner and outer regions of the plane allowing a better understanding of the link between inhomogeneities and larger scale structures, like the spiral arms, the Gould belt (a local structure which is present only in young stars) or the ring. At the present time there is some evidence of variation of the mean star formation with time in the solar neighbourhood, while it appears that over 10 Gyr the SFR has stayed roughly constant in the mean [14,15]. No direct information about the global variations, specially variations with the galactocentric distances, are so far available. A more physical view of the star formation regulation processes (roles of spiral structure, gas density, metallicities and magnetic fields) will be obtained using ages estimated from the GAIA spectroscopic survey and intermediate band photometry, as well as from abundances and kinematics. 3.2

Large Scale Structures

3.2.1 Spiral Structure The spiral structure is difficult to trace because of the position of the sun close to the mid-plane. By studying the position of HII regions which have reliable distance estimates, [16] found evidence for a spiral structure best fitted by a 4-arm logarithmic spiral. This result has been confirmed by [17,18]. Observations of the dust emission at 240 microns favor a 4-arm spiral (as do radio and optical data), while K band emission of stars which does not suffer too much from dust extinction follows a 2-arm pattern [19]. Those assertions are preliminary, being based only on a description of the spatial distributions of matter. Understanding the dynamics through 3 -D models [20,21] is a necessary step towards the description of a realistic spiral structure, as well as the knowledge of the physical processes ongoing there (star formation, inter-relations between different phases of the interstellar material and interactions with the stars, role of magnetic fields).

3.2.2 The Bar The bar has been first discovered in the analysis of the gas dynamics [22]. It is only recently that a stellar component of the bar has been identified, in IRAS data [23], in COBE-DIRBE mission at 24 microns [24], but also by tracing the distribution of variables from microlensing experiments [25]. But this is not always clear if the authors refer to a triaxial bulge or a distinct bar. JV-body simulations of bars adjusted on available data generally agree with each other on a bar pointing towards us in the first quadrant with an angle of the order of 20 to 40 degrees, associated with a corotation radius at about 3-5 kpc, at the inner edge of the spiral structure [20,26-28]. From star count analysis of the DENIS and 2MASS

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near-infrared surveys, [29,30] show also evidences for the existence of a bar in the galactic disc, clearly distinct from a triaxial bulge population. The parameters are comparable with the ones obtained from models and gas dynamics, with a half-length of 3.9 kpc and an angle of 40 degrees. 3.2.3 The Warp The warp is a deformation of the mid-plane of the Galaxy in the external parts: the disc is no more flat but is rather made up of a number of annular rings, each of which is tilted with respect to the others. The warp has clearly been identified from HI data [31,32]. The node line is aligned with the centre-anticentre directions (within 10 degree error). Published values of the warp parameters show a considerable scatter. The galactocentric radius of the warp start ranges between 6.5 to 11 kpc and the slope is generally cited as being between 0.06 and 0.31 [33]. From HI data there is a clear asymmetry between the north and the south, the maximum height of the plane reaching in the north nearly 3 kpc, but only 1.5 kpc in the south (see Fig. 2 from [31]). From star count data, the warp has been identified even in rather old stars [9,34,35], with characteristics similar to the gaseous warp, although more sophisticated analysis of dust emission led [36] to conclude that the dust warp may have larger amplitudes than the stellar warp. It may suggest that hydrodynamic or magnetohydrodynamic forces are important. One mechanism to form a shortlived warp would be interaction with companions which would cause a different response in the gas and in stars. Local kinematical data [37] also implies the existence of a stellar warp but seems to favor a warp starting beyond the solar circle. At the present time distances of stars in the warp are rather difficult to obtain. To get a reasonably large sample one need to reach several kiloparsecs. Parallactic distances will be made available by GAIA, as well as good proper motion estimations, and radial velocities for the brightest. In simulations the difference between north and south star counts in the warp appear significant at about magnitude V = 16, giving a chance to GAIA to have full space velocities for a number of tracer stars in the warp. Obtaining the true distances and kinematics for warped stars would be of tremendous interest for understanding the origin of this structure, its dynamical time, and its relation with potential perturbations by galaxy satellites. 3.2.4 The Flare The galactic disc seems to undergo another deformation, called the flare, when the scale height grows with galactocentric distance. In CO, the scale height grows from 100 pc at R = 10.5 to 180 pc at 12.5 kpc [38]. In molecular clouds, [39] find an even stronger flare, with an increase of the scale height up to 800 pc at R = 19 kpc. In neutral hydrogen, [40] estimate the scale height at R = 24 kpc to be 3 kpc.

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This flare could be explained by the weakening of the Kz force with galactocentric distances. The flare has been detected in stellar population by [35] in the DENIS survey and in DIRBE data by [36]. GAIA will certainly detects the flare in star counts but more importantly will allow to measure the Kz force as a function of galactocentric distance and to check for the flare dynamical origin. 4

The Thick Disc

This population, still questionable some ten years ago, is now well established. The favorite scenario is nowadays the scenario of accretion of a satellite galaxy on the Milky Way, early after the formation of a thin disc, which was heated at this occasion by dynamical friction [41]. The probable characteristics of the thick disc are: a scale height of 850 pc, scale length similar or slightly larger that the thin disc (about 2.5 to 3 kpc), a local density relative to the thin disc of about 6% [42]. Metallicity estimates from in situ spectroscopic determination [43] or remote colour star counts [41,44], all conclude to a mean value of —0.7 dex iron abundance, with alpha elements enhanced and no vertical metallicity gradient. Most recent extensive investigation of chemical abundances in the thick disc [45] shows that the thick disc has a distinct chemical history from the thin disc, but similar to the metal rich halo and to the metal-poor bulge. They conclude from the detailed analysis of 9 elements that the thick disc stars formed over the course of >1 Gyr, ruling out most dissipational collapse scenarios formation for the thick disc. However some authors mention a low metallicity tail (—1.7 < [Fe/H] < —1.0) which is not yet understood [46,47]. Counts, abundances and kinematics determinations come from quite local data, at distances of less than 2 kpc from the sun. GAIA will allow to explore the thick disc in remote regions, then to assess its scenario of formation: the centre, where one could expect to find for example debris of satellite galaxies and external regions where kinematical signatures exist. The expected theoretical signatures of a merging event will be confronted with the GAIA data, especially kinematics versus abundances versus galactocentric positions. Simulations [48] of a satellite accretion show for example that the vertical velocity dispersions should be significantly higher in the external parts than in inner regions. The thick disc turnoff is accessible at visual magnitude around 15 at high galactic latitudes. At deeper magnitudes, the number of main sequence thick disc stars is high and well identified in star counts, even in a single colour index (but the B — V which is degenerated in the red). Because these stars are seen further away than the disc and in a larger volume (for a given area on the sky) they become dominant over the thin disc. GAIA will see a lot of them giving access to the thick disc density distribution in a very large volume. Thick disc giants will be seen even further away. They will be identified in the spectroscopic survey by their abundances and by their astrometry. Their kinematics will also allow to separate their contribution from the spheroid giants. Are there abundance or kinematical gradients? How are these two age estimators correlated? These questions will be

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answered by GAIA, hopefully ending with a clear conclusion about the scenario of formation of this particular structure. 5

The Stellar Halo

In the literature the stellar halo is usually called the spheroid. A priori it does not constitute a significant part of the dark matter halo, its local density being very small (about 0.5% of the theoretical dark halo in local mass density). But evidences from microlensing experiments of a significant density of red dwarfs or white dwarfs have led to controversies. I distinguish here the spheroid population from the hypothetic ancient white dwarf population of the halo. 5.1

The Spheroid Population

It is probably the oldest population of the Galaxy, age estimated to 11 to 15 Gyr from globular cluster diagram fitting. It is nearly non rotating with a velocity less than 50 km s –1 . The velocity ellipsoid has been estimated to (130:105:85) [47], but the orientation of the U axis (towards the centre or towards the symmetry axis of the Galaxy) is still uncertain. It has probably been formed during a rather short period of star formation (less than 2 Gyr) but the abundances range from about —4.5 to —1.5 dex in [Fe/H], with abundances enhanced in alpha elements compared to the sun, as in the bulge and the thick disc. Abundance gradients are still controversial. The density law is thought to follow a power law with an index between 2.5 and 3 [49, 50], and slightly flatten (axis ratio in the range 0.5 to 0.8). The local density is estimated from remote star counts to 1.6 x 10–4 stars per cubic parsec [50] in good agreement with local estimations [51] which however suffer from the small size of the sample. From a sample of RR Lyrae detected in the SDSS commissioning data, [49] find evidences that the spheroid density drops abruptly at R$$$50–60 kpc from the galactic centre. It may well be the external edge of the stellar halo. Because they are intrinsically bright, RR Lyrae are detected at magnitudes brighter than 20–21, even at 100 kpc. Thus GAIA is able to scan the totality of the Galaxy with RR Lyrae, allowing to confirm the result and to check the shape of this edge in various directions. Moreover this huge number of standard candles, having two independent distance estimates (parallaxes and period-luminosity relation) will allow to check the primary distance scale and to correct eventually for yet unknown biases. Noticeable inhomogeneities have been recently discovered in this population [49, 52-54]: relics of possible accretions of small galaxies (the dwarf Sagittarius galaxy, among others), residuals from globular clusters tidal tails, these structures are a key to constrain the scenario of formation of galactic halos: fast dissipational collapse [55] or accretions of small sub-halos [56], the truth could well be in between. GAIA will allow accurate distances for a large part of the spheroid, with kinematics, allowing a search for debris of satellites in the phase space.

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At high galactic latitudes, the spheroid main sequence appears to dominate the counts of blue objects at magnitudes fainter than 18. Giants are seen brighter but should be identified spectroscopically, to select them among thick disc giants. From the distribution of the kinematics, versus abundances, versus age, one should be able to check for galactocentric gradients, inhomogeneities, hence to constrain the scenario of formation of the spheroid, from dissipational collapse or from accretion of smaller elements. Are the globular clusters part of the spheroid population is another question. An unknown proportion of the spheroid can have been formed in globular clusters, as tidal tails have been identified. However the overall abundance distribution of GC is sensibly different from the one of the spheroid population. A better determination of abundances in large areas of the Galaxy, a good estimate of the kinematics of the globular clusters (which have inaccurate proper motions at present), a search for tidal streams and relics of globular cluster destructions in the phase space, will clarify the role of the globular clusters in the spheroid formation. 5.2

White Dwarfs as Relics of Early History of the Galaxy

Many people are looking for the ancient halo white dwarf (WD) population in order to give constraints on the fraction of dark matter halo in form of WD. This population could explain the detected microlensing events in the halo if their local density is high enough. While [57] claim to have detected several high proper motion white dwarf in the HDF, a third epoch has not confirmed the candidates (Ibata, private communication) . Although several high proper motion white dwarf candidates detected on photographic plates have been confirmed spectroscopically [58, 59], it is difficult to assess their membership to the thick disc or to the halo. We have shown [60] that these WD most probably belong to the normal thick disc and that the fraction of dark halo made of ancient WD may well drop below 1%, if the halo is 12 Gyr old. The difficulty is here that the number of ancient WD that can be found in such surveys depend on the assumed age of the halo. Most recent cosmological models give ages of the order of 13 Gyr for H0 = 70 km s–1 Mpc – 1 , $$$b = 0.3, A = 0.7 [61], which would give a good chance to see the ancient white dwarfs if they exist. If there age is 14 Gyr then they would be much more difficult to observe, being fainter. Advances will be done on this subject before GAIA using planned multi-epoch deep surveys, such as the SNAP satellite, the MEGAPRIME survey at CFHT or the ACS camera for the HST. The GAIA mission could extend such surveys on a much larger area and will contribute to the accurate determination of their density, luminosity function and kinematics in the solar neighbourhood. However at the GAIA magnitudes distinction between halo and thick disc white dwarfs will be difficult. Moreover the GAIA survey is probably not deep enough to conclude if the local density of ancient halo WD is low: if the dark halo is made of only 1 % of ancient white dwarfs, assuming an ad hoc IMF for the progenitors according

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to [62], one expect about 36 such stars in the GAIA survey to magnitude 20 if the halo is 12 Gyr old, and only 12 for a 14 Gyr old halo. 6

Universality of the Initial Mass Function

The mass distribution of stars at their birth is called the initial mass function (IMF). While this function may evolve with time in dense environment (by mass segregation, ejections or stellar mergers in clusters for example), the present day mass function allows in the field or after corrections of these effects to determine the IMF. It has often been suggested that the IMF is universal. [63] argues that the uncertainties on the determinations are of the order of the measured variations. On the contrary [64] find evidences that star formation in higher metallicity medium appears to produce more low mass stars. If this effect is confirmed one should expect shallower IMF slopes in the thick disc and halo than in the thin disc and the bulge. GAIA will allow to accurately measure the IMF in very different environments, in the field and in clusters, and at various galactocentric distances. It will be a clue for understanding the physical processes underlying the star formation in galaxies. 7

Conclusion

The main advances from the GAIA mission will be to get highly accurate distances on the major part of the Milky Way, as well as (less accurate) ages, two major parameters which are the most difficult to determine so far from the ground. It will allow to have a clear description of the correlations between age, metallicity and kinematics, all key parameters to establish a scenario of galactic evolution. This will be a huge amount of data for which multivariate analysis will be really challenging. One expects to be able to infer a detailed scenario of formation and evolution of the Galaxy. Various methods are being explored, from population synthesis to inverse methods. This last approach looks promising since for the first time the density, accuracy and the large number of observables in the sample should allow an inversion of multi-dimensional data [65] (see also Siebert et al. this conference). Obviously, the optimal method is still to built and will require creativity and a huge amount of work. References [1] Van Loon, J. Th., for the ISOGAL Collaboration, 4th Tetons Summer Conference on Galactic Structure, Stars and the Interstellar Medium, ASP Conf. Ser., in press [astro–ph 0009471] [2] Hammersley, P.L., Garzon, F., Mahoney, T.J., Lopez-Corredoira, M., Torres, M.A.P., 2000, MNRAS, 317, L45 [3] Rich, R.M., McWilliam, A., 2000, Proc. SPIE, 4005, 150, Discoveries and Research Prospects from 8- to 10-Meter-Class Telescopes, Jacqueline Bergeron (ed.) [4] Beaulieu, S.F., Freeman, K.C., Kalnajs, A.J., Saha, P., Zhao, H., 2000, AJ, 120, 855 [5] Kuijken, K., 1995, ApJ, 446, 194

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[6] Robin, A.C., Creze, M., Mohan, V., 1992, A&A, 265, 32 [7] Mendez, R., Ruiz, M., 2001, ApJ, 547, 252 [8] Freudenreich, H.T., 1998, ApJ, 492, 495 [9] Djorgovski, S., Sosin, C., 1989, ApJ, 341, L13 [10] Bertelli, G., Bressan, A., Chiosi, C., Ng, Y.K., Ortolani, S., 1995, A&A, 301, 381 [11] Kiraga, M., Paczynski, B., Stanek, K.Z., 1997, ApJ, 485, 611 [12] Chereul, E., Creze, M., Bienayme, O., 1998, A&A, 340, 384 [13] Chereul, E., Creze, M., Bienayme, O., 1999, A&AS, 135, 5 [14] Binney, J., Dehnen, W., Bertelli, G., 2000, MNRAS, 318, 658 [15] Haywood, M., Robin, A.C., Creze, M., 1997, A&A, 320, 440 [16] Georgelin, Y.M., Georgelin, Y.P., 1976, A&A, 49, 57 [17] Ortiz, R., Lepine, J.R.D., 1993, A&A, 279, 90 [18] Russeil, D., 1998, Ph.D. Thesis, Universite de Marseille, France [19] Drimmel, R., 2000, A&A, 358, L13 [20] Englmaier, P., Gerhard, O., 1999, MNRAS, 304, 512

[21] Fux, R., 1997, A&A, 327, 983 [22] de Vaucouleurs, G., 1964, in IAU Symp., 20, The Galaxy and the Magellanic Clouds, F.J. Kerr & A.W. Rodgers (eds.) (Sydney: Australian Academy of Science), 195 [23] Nakada, Y., Onaka, T., Yamamura, I., et al., 1991, Nature, 353, 140 [24] Blitz, L., Spergel, D.N., 1991, ApJ, 379, 631 [25] Minniti, D., et al., 1997, Amer. Astron. Soc. Meet., 191, 1910 [26] Binney, J., Gerhard, O., Spergel, D., 1997, MNRAS, 288, 365

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

COMPONENTS OF THE MILKY WAY AND GAIA J. Binney1 Abstract. The GAIA mission will produce an extraordinary database from which we should be able to deduce not only the Galaxy's current structure, but also much of its history, and thus cast a powerful light on the way in which galaxies in general are made up of components, and of how these formed. The database can be fully exploited only by fitting to it a sophisticated model of the entire Galaxy. Steady-state models are of fundamental importance even though the Galaxy cannot be in a steady state. A very elaborate model of the Galaxy will be required to reproduce the great wealth of detail that GAIA will reveal. A systematic approach to model-building will be required if such a model is to be successfully constructed, however. The natural strategy is to proceed through a series of models of ever increasing elaborateness, and to be guided in the specification of the next model by mismatches between the data and the current model. An approach to the dynamics of systems with steady gravitational potentials that we call the "torus programme" promises to provide an appropriate framework within which to carry out the proposed modelling programme. The basic principles of this approach have been worked out in some detail and are summarized here. Some extensions will be required before the GAIA database can be successfully confronted. Other modelling techniques that might be employed are briefly examined.

1

Introduction

GAIA will provide at least 5 and often 6 phase-space coordinates for 109 stars. The challenge is to make astrophysical sense of this vast dataset. Studies of external galaxies have convinced us that galaxies are best understood as being made up of a series of "components": a bulge or "spheroid" and perhaps a bar; a thin disk and perhaps a thick disk; a massive halo and perhaps a metal-poor halo. We must somehow use all those phase-space data to learn about the components of 1

Oxford University, Theoretical Physics, 1 Keble Road, OX1 3NP, UK © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002023

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the Milky Way: how big are they? how old? what are their radial profiles and shapes? did they form slowly or suddenly? did some give rise to others? Nearly all galaxies have a disk and a bulge, though the relative importance of these two components can vary greatly and largely determines the galaxy's Hubble type. It is probable but not certain that nearly all galaxies have dark halos. A significant proportion of galaxies possess either a bar or a thick disk. Understanding how the different components of galaxies were formed, and why their relative prominence varies from galaxy to galaxy, are clearly central questions in the current drive to understand why there are galaxies at all, and the relationship of galaxies to the rest of the matter in the Universe. To answer these questions we need to have the most complete picture possible of what individual components are, how they function dynamically, and how they fit together. The Milky Way, which is a prototype of the galaxies that are responsible for most of the luminosity in the Universe, is known to possess all the components listed above, and kinematic mapping of these with GAIA offers a unique opportunity to clarify some of the fundamental questions of contemporary astronomy. Interpreting the GAIA database in terms of components is a thoroughly nontrivial task because components are coextensive at many locations, both in real space and in theoretical spaces in which a kinematic or chemical datum is used as a coordinate. So it will often be impossible to assign unambiguously an individual star to this or that component: at best we will be able to give probabilities for its belonging to one or another component. Moreover, in the assignment of these probabilities we encounter the chicken-and-egg problem: until we have assigned stars to components, we will have a very imperfect knowledge of each component's chemical composition and dynamics and we will not be in a position to say how a star's membership probability varies as a function of its chemical and kinematic data. For these reasons a major intellectual and computational effort will be required to pass from the GAIA database to a knowledge of the structure and dynamics of the Galaxy's components. 2

The Steady-State Approximation

All components are held together by the Galaxy's gravitational potential$$$,which is currently extremely ill-determined at points away from the Galactic plane. A successful attempt to model the various components will inevitably yield, almost as a spin-off, a good knowledge of$$$throughout the visible Galaxy. Taking the Laplacian of$$$and subtracting the mass densities of the visible components, we will finally determine unambiguously the distribution of Galactic dark matter. The physical principle that will enable us to determine$$$is that the Galaxy is in an almost steady state. This assumption, which is only approximately valid, merits a moment's consideration. We think the Galaxy should be in an approximately steady state because throughout the visible Galaxy the dynamical time is orders of magnitude shorter than the Hubble time, and we have no reason to suppose this is a particularly exciting moment in the Galaxy's life, such as the climax of

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a major merger. However, various processes that are incompatible with a steady state should be detectable. One factor is the bar: deviations from steadiness will be significant unless we refer everything to the bar's rotating frame. The pattern speed of this frame is not exactly known, although Dehnen [1] gives a reasonably precise value. The bar is almost certainly losing angular momentum to other components, with the result that it is slowing down and the other components are heating up. Since bars such as the Galaxy's are extremely common in disk galaxies, these processes are probably slow and lead to only small violations of the steady-state principle. The violations are likely to be detectable, however. Spiral structure must be redistributing angular momentum within the disk, and heating it. This process should lead to small but detectable violations of the steady-state principle. The Galaxy is accreting angular momentum that is not aligned with its current spin axis. This accretion is in the long run expected to lead to significant reorientation of the spin axis [2], and in the shorter term probably generates the Galactic warp [3], whose kinematic signature Hipparcos reliably detected for the first time [4]. Finally, the Galaxy is constantly tidally stripping small fry that come too close and the debris of such stripping will not be in a steady state [5, 6]. Notwithstanding these process that violate the stead-state approximation, the latter is a vital tool in the determination of $$$. To see why, consider the consequence of modelling the GAIA database with a potential that is much less deep than the true potential. In this case, when the equations of motion of stars are integrated from the initial conditions that GAIA provides, the Galaxy will fly apart into intergalactic space. Similarly, if the adopted potential is too deep, integration of the equations of motion will result in the Galaxy contracting on a dynamical time, and if the potential's flattening towards the plane is incorrect, the halo and thick disk will change shape in the first dynamical time. The true potential is the one that make the observed stellar distribution pretty much invariant under integration of the equations of motion. The idea just described, of integrating the equations of motion forward from the initial conditions that GAIA will provide, illustrates the physical idea behind potential estimation, but it is not likely to be useful in practice. The main reason is that obscuration will prevent GAIA from observing the entire Galaxy. Moreover, stars less luminous than the horizontal branch will not be picked up throughout the Galaxy. If we take the correct potential and integrate the equations of motion from initial conditions yielded by such an incomplete survey, the star distribution will not be invariant: many of the low-luminosity stars that GAIA sees near the Sun will wander off and will not be replaced because the stars that should replace them were initially too far away to be seen by GAIA; stars will move into obscured zones, and gaps in the observed regions will open because they will not be replaced by stars moving out of obscured zones. Some more sophisticated procedure is going to be required to test whether the GAIA data are compatible with the steady-state approximation in a given potential.

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The Torus Project

Similar problems arise in accentuated form when one tries to model ground-based data. Some years ago my group in Oxford started work on a way of modelling the Milky Way that promises to overcome these problems [7]. Our work was interrupted by the arrival of the first Hipparcos data and is only now resuming. It will be disappointing indeed if the project has not been completed by the time GAIA flies, so I will outline it. We start from the premise that for any trial potential $$$ we should have a strictly steady-state dynamical model of each component. We recognize that real components will not be in exactly steady states, but argue that the best method of identifying the effects of unsteadiness in the data is comparison with the bestfitting steady-state model. Moreover, we hope to be able to model unsteadiness by perturbing our steady-state model. Jeans' theorem tells us that a steady-state model of a component may be generated by taking the component's distribution function (DF) fa to be an arbitrary non-negative function of the potential's isolating integrals. If the potential were "integrable" it would possess just three functionally independent isolating integrals, and the DF would be a function of three variables. That is, each component would correspond to a particular distribution of stars in a three-dimensional space, and the observed distribution of stars in six-dimensional phase space could in principle be read off from the function of three variables, just as a living organism can be constructed from its DNA sequence. Several practical difficulties have to be overcome before we can exploit this dramatic simplification. One is that isolating integrals are by no means unique: a function of two or more isolating integrals is itself an isolating integral. If we are to talk intelligently about the differences between the DFs of different components, or the DFs of the same component in different trial potentials, we must standardize our isolating integrals. This is readily done by using only action integrals (e.g., Sect. 3.5 of [8]). For an integrable potential these suffer only from a trivial degree of ambiguity, which is readily eliminated. For an axisymmetric potential our standard actions are the radial action JR, the latitudinal action J\ and the azimuthal angular momentum J$$$. The space that has these actions for Cartesian coordinates we call "action space". In addition to being unambiguously defined for any integrable potential, actions have the desirable property of faithfully mapping phase space into action space, in the sense that the volume of phase space occupied by orbits with actions in the action-space volume d3J is (2$$$)3d3J. Consequently, the DF of a component may be considered to be the density of stars in action space [up to a factor (2$$$)–3] as much as it is the density of stars in phase space. Unfortunately, a generic potential will typically not admit three global isolating integrals, and even if it does, we will not have analytic expressions for the functions Ji(r, r) that relate phase space to action space. Over a number of years my group has developed solutions to this problem [9-13]. In an integrable potential, the surfaces in phase space on which actions are constant are topologically 3-tori. On

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these surfaces the Hamiltonian is constant, and all surface integrals of the form2 $$$ dp.dq vanish, so they are called "null-tori". Stars move over these null-tori in a rather special way - each torus admits three variables, the "angle variables" $$$i, that are canonically conjugate to the actions that label the tori, and these angles increase uniformly in time: 9i(t] = $$$ i (0) + wit. Unless the frequencies wi are commensurable, it follows that in a steady-state model the phase-space density of stars is constant over a torus: this is the origin of Jeans' result that the DF of a steady-state model does not depend on the $$$i. It turns out that if all phase space can be foliated by such null 3-tori, and the given Hamiltonian H is constant on them, then H is integrable, and its actions label the tori by giving the magnitudes of their three independent cross-sectional areas, Ji = (2$$$)–1$$$ip.dq. We have developed a technique for foliating phase space with null tori on which a given H is nearly constant. These tori can be used to define a integrable Hamiltonian H that differs from H by only a small amount. 3.1

Resonances & Perturbation Theory

A real galactic potential is exceedingly unlikely to be integrable in the sense that it admits a global set of angle-action variables. Consequently, the integrable Hamiltonian H will surely differ from the true Hamiltonian H at some level. Since $$$H==H — H is small compared to H, stars integrated in H and H from the same initial condition will stay close to one another for a few orbital times. In fact, the motion in the true Hamiltonian H can be considered to be the result of perturbing the integrable Hamiltonian H by$$$H= H — H. The astronomical significance of this perturbation will depend on the age of the system measured in dynamical times and whether orbits of interest lie near a resonance of H: if the initial conditions lie on a resonant torus, even the small perturbation$$$Hcan cause the orbit in H to deviate significantly from that in H if you wait long enough. Consequently, the phenomena occurring in H can differ significantly from those occurring in H, and it may be necessary to obtain a better approximation to the true dynamics than H provides. The torus programme offers two ways of improving on the model provided by H. The left panel of Figure 1 illustrates one method by showing part of a surface of section. The figure's dots are the consequents of eight orbits in a barred gravitational potential. These orbits all admit an isolating integral in addition to H because their consequents lie on smooth curves. Six of these curves have the characteristic shapes of the invariant curves of box and loop orbits (e.g., Figs. 38 in [8]), which are associated with a global system of action-angle coordinates (Sects. 3-5 of [8]). Just inside the outer-most invariant curve, the invariant curves have a different structure, forming part of what would be a chain of six islands if the whole surface of section were plotted. The torus machinery has been used to draw three dashed curves through the region occupied by the islands: one curve goes through the middle of the islands, while flanking curves pass either side of 2

Here p, q are arbitrary canonical coordinates.

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Fig. 1. A surface of section for motion in a barred potential. Dots show consequents of numerically integrated orbits. In a band towards the outside of the figure, these delineate a chain of islands. At left three dashed curves through these islands show cross sections of tori of the underlying integrable Hamiltonian H. At right the full curves that accurately delineate the islands are obtained by treating SH as a perturbation on H (from [14]).

Fig. 2. One of the 2:3 resonant box orbits that generate the chain of islands in Figure 1. The orbit shown at left was generated by direct integration, while that at right was generated by applying perturbation theory to the integrable Hamiltonian H. The full curve is the underlying closed orbit (from [14]).

them. These curves are invariant curves of H, which admits global action-angle coordinates and therefore supports only boxes and loops. The right panel of Figure 1 shows the same surface of section, but now with the islands delineated by full curves. These curves are generated by treating $$$H as a perturbation of H. Since $ $ $ H / H is small, the agreement between the numerical consequents and the invariant curves from first-order perturbation theory is

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Fig. 3. A surface of section in a barred potential in which most orbits are resonant boxes ("boxlets"). The curves in the left panel shows the tori generated if all orbits are assumed to be non-resonant boxes. The curves in the right panel shows the tori obtained when orbits are assumed to be resonant (from [14]). excellent3. Figure 2 shows that in real space one cannot distinguish between the orbits obtained by direct integration and perturbation theory. Figure 3 shows an alternative approach to resonant orbits, which is appropriate when the resonance is powerful, and therefore$ $ $ H / His not small. The left panel again shows invariant curves of H ploughing through the resonant region, which is now associated with non-negligible stochasticity near the seperatrices. The right panel shows excellent agreement between consequents for a series of resonant orbits and invariant curves obtained by generating a new integral hamiltonian H' for the resonant region. This Hamiltonian is obtained by assuming that tori have the general structure required for libration about the closed resonant orbit, and then deforming them so as to make H as nearly constant over them as possible. These examples show that the torus programme can, in principle, provide an extremely accurate description of regular orbits, no matter what their structure. The ability of the programme to give a good account of stochastic orbits has not been so completely explored. I anticipate, however, that it will prove powerful in this area also, since, as Figure 3 illustrates, it can provide a system of action-angle variables in which the stochastic region is bounded by particular tori. Let us call the values taken by J on these tori the "critical actions". It is likely that over time the DF will tend to a function of energy only in the region of action space that is bounded by the critical actions. 3.2

Galaxy Modelling with Tori

Our procedure for interpreting a data set such as GAIA will produce is as follows. We start with a trial potential $$$(r). We foliate phase space with 3-tori on which 3 To exploit fully the smallness of $ $ $ H / H , Kaasalainen [14] had to develop an extension of standard first-order perturbation theory.

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H =1/2r2+ $$$(r) is nearly constant. This foliation establishes a system of actionangle coordinates for an integrable Hamiltonian H that differs from H only slightly. Routines are then available to pass between these action-angle coordinates and the ordinary Cartesian coordinates for phase space, (r, r). Next, for each component a of the Galaxy we choose a simple analytic DF f a (J). Because the actions are unique and physically well-motivated variables, it is easy to understand the relationship between the form of fa and the observables of the component, such as its flattening, characteristic spin and the typical eccentricity of its stellar orbits [15]. Finally, for each component we choose an Initial Mass Function and a star-formation history, which together enable us to predict the distribution in colour and absolute magnitude of the component's stars. We now have a steady-state dynamical model of each component in the given $$$. This model predicts the probability of observing a star of a given component at any phase space location. By convolving this probability distribution with the assumed colour and absolute-magnitude distributions of the component, and summing over components, we convert these probabilities into the probability of finding a star of given colour and My at any point in phase space. Finally, these probabilities are convolved with the selection functions in colour and phase space of any given survey. This final probability distribution is then evaluated at the location of each catalogued star and the resulting numbers are multiplied together to give the likelihood of the catalogue given the current Galaxy model. We propose to maximize this likelihood by adjusting a suitably parameterized form of the Galactic potential$$$(r)as well as the functions that characterize each component: the function of three variables f Q (J), the IMF and the star-formation history. This maximization is likely to be a computationally challenging task, but not one that is out of proportion to the other computational challenges that GAIA inherently poses. Notice that the final model will encode not only the current state of the Galaxy, but much information about its past. Some more detail and sample calculations can be found in [7]. 4

Other Modelling Techniques

It is not self-evident that the approach just described to modelling the GAIA database will be the most important one in practice, but it does contain a number of elements that any viable technique is likely to include. First, I believe it is essential to produce a steady-state model of the Galaxy. Such a model is an unrealized ideal, but a key step both in the determination of the Galactic potential, and in deducing what features in the data are symptomatic of unsteady dynamics. Second, one has somehow to extrapolate the stellar distribution from the parts of the Galaxy that are observed, to those that are not. The strategy suggested above for doing this is three-fold. First Jeans' theorem is used to argue that if I observe the stellar density at one point in phase space, I know the density at all other points in phase space at which the isolating integrals take the same values.

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For hotter components, such as the halo and the thick disk, this argument allows one to determine even from observations confined to the solar neighbourhood, the value of the DF through a surprisingly large part of phase space [16]. For more luminous stars, GAIA's coverage will be so extensive that this principle will be very powerful indeed. Second, the theory of stellar evolution and nucleosynthesis is used to connect the phase-space densities of faint stars to those of their more luminous brethren. Finally, the uniqueness of the action integrals is used to reduce the DF of each component to an analytic function of the actions that depends on a small number of parameters. This reduction not only simplifies the computational task of optimizing the DFs, but also facilitates astrophysical interpretation of the results. 4,1

Schwarzschild's Modelling Technique

A widely used technique for modelling external galaxies is that of Schwarzschild [17, 18] and it is interesting to examine the possibility of using this to model the GAIA database. In Schwarzschild's method one again starts with a trial potential $$$, but one integrates a large number of orbits in it instead of constructing tori for it. Then, instead of choosing a DF fa for each component, one chooses a set of weights Wa for each orbit i. The merit of the method is that orbit integration is computationally simple, and uses routines that are completely independent of the nature of the orbits: whether they are tube or box orbits, regular or stochastic. Torus construction, by contrast, has to be tuned to the dominant orbit families. Moreover, Schwarzschild's method deals properly with families of resonant orbits whereas torus construction sweeps these under the rug for possible subsequent examination by perturbation theory. Schwarzschild's method has several weaknesses, however. One is that it is cumbersome numerically because phase-space points have to be stored at many points along each orbit, with the result that an "orbit library" of 10000 orbits will occupy of order 1 Gb on disk. Moreover, the resolution in space and velocity of the final model is determined by the number of orbits and the temporal frequency at which each is sampled. In the torus method, by contrast, each torus is represented by a relatively small number of expansion coefficients from which phase-space points can be evaluated dynamically as the model is compared to the data. There is no limit to how densely a given torus is sampled, and once a reasonable torus library is to hand, additional tori can be quickly constructed without reference to the Hamiltonian by interpolation on the expansion coefficients for nearby tori in the library. Finally, in its classical form Schwarzschild's method gives no insight into which orbits are "close" to each other in phase space. This has two consequences. One is that there is no way of requiring the weights of neighbouring orbits to be nearly equal, as seems physically reasonable. The other is that one cannot determine the density of a component at a given point in phase space, which makes it impossible to compare the phase-space structure of models built with different orbit libraries, even if the potentials are identical. In fact, communication of a model requires transmission of both the ~1 Gb of the orbit library and a

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complete set of orbit weights (~100 Kb per component). By contrast, a model constructed by the torus method can be communicated by tabulating the four or five parameters in the DF of each component. Hafner et al. [19] show how Schwarzschild's method may be upgraded to the point at which it returns the DF at the location of each orbit. Moreover following Zhao [20], one can assign "effective integrals" to each orbit which enable one to say, in an approximate way, which orbits are close to one another, and thus impose continuity of the DF. Moreover, one could insist that the weights were those implied by an analytic function of the effective integrals that depends on a small number of parameters, in the same way that the torus method assumes the DF to be a parameterized function of the actions. Used in this mode, Schwarzschild's method could be equal to the task of modelling the GAIA data set. 4.2

N-Body Models

Fux [21] has made a significant contribution to our understanding of the dynamics of the inner Galaxy simply by observing a suitable TV-body model. Could this approach make a significant contribution to our understanding of the GAIA dataset? If we were to set up an TV-body model simply by using the coordinates returned by GAIA as initial conditions, we would run up against the problems with observational selection that were described above. A better way of choosing initial conditions would be to start by fitting to the GAIA data to DFs of the form f a (r, r) = pa(r)pa(r), where pa is an analytic fit to the density distribution of component a and pa is an analytic probability density that approximately describes the distribution of velocities within this component. For judiciously chosen pa and pa the initial conditions might soon settle to a steady-state that resembled the Galaxy. Setting up an TV-body model in this way would be by no means trivial, however, because choosing the functions pa(r) is likely to be a delicate business. The technique devised by Syer & Tremaine [22], in which the masses of particles are dynamically adjusted, may be able to make up for short-comings in the choice of the pa. All of these particle-based schemes - Schwarzschild's technique, and TV-body modelling with or without the refinements of Syer & Tremaine - will suffer from the drawback that, for feasible numbers of masses in the model, errors in the model's observables, such as velocity distributions near the Sun, will far exceed those in the data. Consequently, none of these schemes is likely to do justice to the precision of the GAIA data. 5

Conclusion

GAIA poses an enormous challenge to the theorist because it is essential that its vast data set be modelled as a whole and in a single sweep. The modelling must include not only the dynamics of the contemporary Galaxy, but many aspects of its history as well, most particularly the star-formation history of its various components.

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In view of the scale of this enterprise, it is fortunate that the data will not arrive for more than a decade. In that period Moore's law for the growth of computer power will ensure that the necessary computational resources will be available. If we start now, there is a reasonable chance that appropriate computational schemes will also be on hand for modelling the Galaxy in the requisite depth and breadth. Developing these schemes will be astronomically rewarding in the short term also, since there is an abundance of ground-based data to model that poses the same conceptual problems in heightened form. The richness of the GAIA database will ultimately allow us to study the Galaxy in exquisite detail, and to learn about the various chance events that have cumulatively shaped it. Extracting this detail from the database will require subtlety, however, and it is likely that the best strategy for mining the database will be one in which models of systematically increasing sophistication are successively fitted to the data. The first models would assume that the Galaxy has a globally integrable potential and is in a strictly steady state. Discrepancies between the data and the best-fitting model of this type might indicate that certain resonances are not to be ignored. At the next level a model that included these resonances but was still in a strictly steady-state would be fitted to the data. Discrepancies between model and data might now point to non-steady phenomena such as spiral structure. Perturbation theory would then be used to model these effects, and discrepancies again sought. Proceeding in this manner one can imagine constructing a very detailed model that reflected many of the chance events that have fashioned the Galaxy, as well as ongoing evolution driven by the bar, spiral structure and the Sagittarius dwarf galaxy. The torus programme has a number of features that suit it very well to this programme of work. Most importantly, it allows one to start with an extremely simple model that can be described by only a handful of parameters, and to upgrade this model through a systematic sequence of well defined stages. At each stage, the model fitted to the data at the preceding stage provides a clear basis from which to advance to a more elaborate model. Another important advantage of the torus programme is the facility to beat discreteness noise down to any predefined value in a straightforward way. A number of published papers demonstrate the basic principles of the torus programme for the case of two-dimensional potentials, which effectively includes all three-dimensional axisymmetric potentials. The generalization of these principles to general, nearly integrable, three-dimensional potentials is straightforward though computationally costly. Important tasks that must be accomplished before the torus programme can be applied to the GAIA database include exploring its application to chaotic orbits and, through perturbation theory, to non-steady systems. References [1] Dehnen, W., 1999, ApJ, 524, L35 [2] Binney, J. & May, A., 1986, MNRAS, 218, 743

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[3] Jiang, I.-G. & Binney, J., 1999, MNRAS, 303 L7 [4] Dehnen, W., 1998, AJ, 115, 2384 [5] Helmi, A., White, S.D.M., de Zeeuw, P.T. & Zhao, H.-S., 1999, Nature, 402, 53 [6] Ibata, R., Irwin, M., Lewis, G.F. & Stolte, A., 2000, ApJ, 547, L133 [7] Dehnen, W. &; Binney, J., 1996, in Formation of the Galactic Halo... Inside and Out, ASP Conf. Ser. 92, Heather Morrison and Ata Sarajedini (eds.), 393 [8] Binney, J. & Tremaine, S., 1987, Galactic Dynamics (Princeton University Press) [9] McGill, C. & Binney, J., 1990, MNRAS, 244, 634 [10] Binney, J. & Kumar, S., 1993, MNRAS, 261, 584 [11] Kaasalainen, M. & Binney, J., 1994, MNRAS, 268, 1033 [12] Kaasalainen, M. & Binney, J., 1994, Phys. Rev. Lett., 73, 2377 [13] Kaasalainen, M., 1995, MNRAS, 275, 162 [14] Kaasalainen, M., 1994, Oxford University D.Phil. Thesis [15] Binney, J., 1994 , in Galactic and solar system optical astrometry, L. Morrison (ed.) (Cambridge University Press), 141 [16] May, A. & Binney, J., 1986, MNRAS, 221, 857 [17] Schwarzschild, M., 1979, ApJ, 232, 236 [18] Schwarzschild, M., 1982, ApJ, 263, 599 [19] Hafner, R., Evans, N.W., Dehnen, W. & Binney, J., 2000, MNRAS, 314, 433 [20] Zhao, H.-S., 1996, MNRAS, 283, 149

[21] Fux, R., 1999, A&A, 345 787 [22] Syer, D. & Tremaine, S., 1996, MNRAS, 282, 223

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

ASTROMETRIC MICROLENSING WITH THE GAIA SATELLITE V. Belokurov1 and N.W. Evans1,

2

Abstract. The capabilities of the GAIA satellite for the detection of microlensing events are analyzed. The all-sky averaged photometric optical depth is ~7.0 x 10–8 and there are ~4000 photometric microlensing events during the five year mission lifetime. The all-sky averaged astrometric microlensing optical depth is ~5 x 10–5 and ~50 000 sources will have a significant variation of the centroid shift, together with a closest approach, during the mission lifetime. We show that GAIA is the first instrument with the capability to measure the mass locally in very faint objects like black holes and very cool white and brown dwarfs.

1

Introduction

A small fraction of the objects monitored by GAIA will show signs of microlensing. GAIA can detect microlensing by measuring the photometric amplification of a source star when a lens and a source are aligned. This is the approach followed by the large ground-based microlensing surveys like MACHO, EROS, OGLE and POINT-AGAPE [1-4]. GAIA is inefficient at discovering photometric microlensing events, as the sampling of individual objects is relatively sparse (about two or three times a month on average) and the all-sky averaged photometric microlensing optical depth is low. However, there is a more powerful strategy available to GAIA. Generally, a microlensed source has two images, unresolvable by GAIA. But, the centroid of the two images makes a small excursion around the trajectory of the source as a result of varying magnification and image positions during lensing. The excursion of the centroid during microlensing is of the order of a fraction of a milliarcsec (mas) and is often measurable by GAIA. Astrometric microlensing is the name given to this shift in the image centroid [5-9]. 1 Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK e-mail: [email protected] 2 e-mail: [email protected]

© EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002024

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Fig. 1. Left panel: astrometric shift of the microlensing event as seen by a barycentric (dotted line) and a terrestrial observer (solid line). The lens is a nearby disk star just 150 pc away, while the source is also a disk star but 1.5 kpc away. Right panel: simulated data incorporating typical sampling and astrometric errors for GAIA. Also shown for comparison are the theoretical trajectories of the source with (grey line) and without (dashed line) the event. The insets show the deviations at the beginning and the midpoint of this high signal-to-noise event. (The accuracy$$$aof individual astrometric measurements is 300 $$$as.)

2

Numbers of Events

Figure 1 shows an astrometric microlensing event: the lens is just 150 pc away from the observer, while the source is a disk star 1.5 kpc away. The left-hand panel shows the right ascension and declination recorded by a barycentric and a terrestrial observer (or equivalently a satellite at the L2 Lagrange point, like GAIA). The proper and parallactic motion of the source have been subtracted out. The astrometric deviation is a pure ellipse in a barycentric frame, but is distorted by parallactic effects in a terrestrial frame. The right-hand panel shows the event as seen by GAIA, which records a series of one-dimensional transits of the twodimensional astrometric curve. The simulated data points have been produced by generating random transit angles, and sampling the astrometric curve according to GAIA's scanning law for the ASTRO-1 and ASTRO-2 telescopes. The transits are strongly clustered, as GAIA spins on its axis once every 3 hours and so may scan the same patch of sky four or five times a day. Gaussian astrometry errors with standard deviation $$$a== 300$$$ashave been added to the simulated data points. The two insets show the astrometric deviations at the beginning and at the maximum of the event, from which it is clear that GAIA has the capability to detect that a microlensing event has occurred. Let us calculate the number of astrometric and photometric microlensing events that GAIA will record. The cross-section of an astrometric event is defined as the area in the lens plane for which the centroid shift of the projected source varies by more than 5$$$a.The size of this area is proportional to the transverse velocity and the mission life-time, and inversely proportional to the astrometric accuracy and

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Fig. 2. Upper panel: all-sky map of the source-aver aged astrometric optical depth including the effects of extinction. Meridians of galactic latitude are shown at 60° intervals, parallels of longitude at 30° intervals. Lower panel: all-sky map of the source-aver aged photometric optical depth.

the lens distance [10, 11]. We also impose an additional criterion requiring the closest approach between lens and source to take place during the mission life-time, as this helps identify the event in the GAIA data base. The upper panel of Figure 2 shows contours of astrometric microlensing optical depth. The map uses a standard model for the sources and lenses in the Galaxy, together with an extinction law and a luminosity function (see [11] for more details). It has been produced assuming that the relative source-lens velocity in the lens plane is ~100 kms –1 . Extinction is an important effect for GAIA's microlensing capabilities, as the accuracy of both the astrometry and photometry depends on source magnitude. The all-sky averaged value of the astrometric optical depth is ~5 x 10–5. Here, the averaging is performed by weighting the optical depth with the starcount density. There are ~109 stars brighter than V = 20 in the Galaxy [12]. This means that, during the GAIA mission, there are$$$50000astrometric microlensing events. These events have a variation of the centroid shift greater than 5$$$atogether with a closest approach during the lifetime of the mission. However, it remains to be seen how many of the displacements can be identified by GAIA as microlensing

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Fig. 3. The panels show the recovery of the flat, rising and falling mass functions from the subsamples of high quality astrometric microlensing events generated from simulations.

events, as the signal-to-noise of some events will be too low. The lower panel of Figure 2 shows contours of photometric microlensing optical depth, again including the effects of extinction. The all-sky averaged photometric optical depth is ~7.0 x 10–8, which is more than two orders of magnitude less than the astrometric optical depth. The typical event duration is ~1 month, so that there are a total of ~4000 photometric microlensing events during the GAIA mission. GAIA's sampling is sparse compared to ground-based programs, so some of these of events will be hard to identify with confidence.

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High Quality Events and the Local Mass Function

Our next task is to understand the propagation of errors, so that we can identify how many of the ~50 000 astrometric microlensing events are useful. Most events will not be measured photometrically by GAIA. The quantity that will generally be provided is the source displacement along the scan. This contains information on the microlensing event, but is contaminated with the source parallactic and proper motion as well. (We assume that the GAIA datastream has already been corrected for aberration due to satellite motion and gravitational deflection caused by Solar System objects.) There are a total of 11 parameters to be computed from the data, namely the source proper motion vector, the source parallax, the relative source-lens parallax, the zero-point of the source, the angular Einstein radius, the Einstein radius crossing time, the time of the closest approach, the lens proper motion angle and the lens impact parameter. The mass of the lens can be calculated if the angular Einstein radius $$$E and the relative source-lens parallax $$$S1 are recovered to good accuracy, as

First of all, an event must last an adequate time for the microlensing shift to be distorted by parallactic movement of the lens. Thus, the error in the mass depends on the duration of the astrometric event. Second, the amplitude of the distortion is dictated by the Einstein radius projected onto the observer's plane [13], namely

For close lenses, the Einstein radius projected onto the observer's plane is

where D\ is the lens distance. For a measurable distortion, we require $$$E to be about an astronomical unit or smaller. If it is too large, then the Earth's motion about the Sun has a negligible effect. So, accuracy in the relative parallax is a trade-off between duration and lens distance. It is the close lenses with longer timescales that provide the most propitious circumstances for measuring$$$S1and hence mass from the data. Using a Galaxy model with disk and bulge, we create a sample of 50000 microlensing events as a synthetic GAIA database. For each member of the sample, we compute the error in the mass of the lens $$$M from the errors in the astrometry using the standard methods of covariance analysis [13, 14]. This yields the formula

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Table 1. This gives the percentage of events in the whole sample with an error of less than 50% in the estimate of mass M, or the Einstein crossing time $$$E, or the angular Einstein radius $$$E or the relative parallax $$$s1.

where C is the correlation coefficient between $$$E and$$$s1.The cross-term is important because errors in$$$Eand$$$S1are strongly correlated for most of the events. We define the high quality events as those for which the error in the mass is less than 50%; there are ~4000 such events in the synthetic database. The median source distance is about 500 pc for the high quality events; the median lens distances are still smaller. So, the high quality astrometric microlensing events recorded by GAIA are overwhelmingly dominated by the very local stars. Table 1 shows the percentage of events for which lens mass M, Einstein crossing time$$$E,angular Einstein radius$$$Eand relative parallax $$$S1 can each be recovered to within 50%. We see that roughly 40% of all the events will have good estimates for tE and $$$E from the GAIA astrometry alone. Current ground-based programs like MACHO and EROS attempt to recover the characteristic masses of lenses from estimates of tE alone for samples of a few tens to hundreds of events. By contrast, GAIA will provide a much larger dataset of ~20000 microlensing events with good estimates of both tE and $$$E. The typical locations and velocities of the sources and lenses can be inferred for the ensemble using statistical techniques based on Galactic models (much as MACHO and EROS do at present). From the high quality sample, we investigate whether the local mass function (MF) can be recovered. We use the three different MFs as spanning a range of reasonable possibilities. Above 0.5 M$$$, the MF is always derived from the ReidHawley luminosity function [15]. Below 0.5 M$$$, there are three possibilities. It may be flat ( f ( M )$$$M – 1 ), rising ( f ( M )$$$M –1.44 ) or falling (f(M)$$$M 0.05 ). For each of the three MFs, we generate samples of 50000 astrometric microlensing events using Monte Carlo simulations. We extract the high quality events and compute the mass uncertainty using the covariance analysis. (In practice, the high quality events would be selected on the basis of the goodness of their x2 fits.) We build up the MF as a histogram. The three cases are shown in Figure 3 with the solid line representing the underlying MF. The simulated datapoints with error bars show the MFs reconstructed from the high quality events. Note that the error bars are very small at masses greater than 1 M$$$, but appear large as an artifact of the choice of logarithmic axes. It is evident that GAIA can easily distinguish between the flat, rising and falling MFs. The MFs are reproduced accurately above ~0.3 M$$$. Below this value, the reconstructed MFs fall below the true curves, as a consequence of the bias against smaller Einstein radii. However, this does not

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compromise GAIA's ability to discriminate between the three possibilities. In practice, of course, simulations can be used to re-calibrate the derived MFs at low masses and correct for the bias. We have also carried out simulations with MFs containing spikes of compact objects, such as populations of ~0.5M$$$white dwarfs. They lie in the mass regime to which GAIA's astrometric microlensing signal is most sensitive. Such spikes stand out very clearly in the reconstructed MFs [11]. 4

Conclusions

One of the major scientific contributions of GAIA that can make is the determination of the mass function in the solar neighbourhood. Of course, direct mass measurements are presently possible just for binary stars with well-determined orbits. Microlensing is the only technique which can measure the masses of individual stars. GAIA is the first instrument with the ability to survey the astrometric microlensing signal provided by nearby lenses. We have used Monte Carlo simulations to show that GAIA can reconstruct the mass function in the solar neighbourhood from the sample of its highest quality events. This works particularly well for masses exceeding ~0.3 M$$$. Below 0.3 M$$$, the reconstructed mass function tends to underestimate the numbers of objects, as the highest quality events are biased towards larger angular Einstein radii. If there are local populations of low mass black holes, or very cool halo and disk white dwarfs or very old brown dwarfs, then they will have easily eluded detection with available technology. However, the astrometric microlensing signal seen by GAIA will be sensitive to local populations of even the dimmest of these stars and the darkest of these objects. GAIA is the first instrument that has the potential to map out and survey our darkest neighbours. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]

Alcock, C., et al., 1997, ApJ, 486, 697 Aubourg, E., et al., 1995, A&A, 301, 1 Auriere, M., et al., 2001, ApJ, 553, L137 Udalski D., Szymanski, M., Kaluzny, J., et al, 1994, ApJ, 426, L69 H0g, E., Novikov, I.D., Polnarev, A.G., 1995, A&A, 294, 287 Walker, M.A., 1995, ApJ, 453, 37 Miralda-Escude, J., 1996, ApJ, 470, L113 Paczyriski, B., 1996, Acta Astron., 46, 291 Boden, A.F., Shao, M., van Buren, D., 1998, ApJ, 502, 538 Dominik, M., Sahu, K.C., 2000, ApJ, 534, 213 Belokurov, V., Evans, N.W., 2001, MNRAS, submitted Mihalas, D., Binney J., 1981, Galactic Astronomy (Freeman: San Francisco) Gould, A., Salim, S., 1999, ApJ, 524, 794 Boutreux, T., Gould, A., 1996, ApJ, 462, 705 Reid, IN., Hawley, S., 2000, New Light on Dark Stars (Springer Verlag: New York), Chaps. 7, 8

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

STAR FORMATION: ON GOING AND PAST G. Bertelli1, 2 Abstract. GAIA will be of paramount importance to understand the Galactic structure. Here we focus on the determination of the star formation history (SFH) of the Galactic disk and bulge. We discuss whether GAIA will be able to isolate a sample of stars with the same characteristics of Hipparcos data (completeness over a certain critical magnitude and high precision in the distance) which will cast light on the SFH of the whole disk. We analyze the expected results in two directions, namely the BW and the Galactic pole. Finally we discuss the contribution of GAIA to the study of the SFH of the bulge.

1

Introduction

Determining the past history of star formation from the Color-Magnitude Diagram (CMD) of composite stellar populations is one of the main targets of modern astrophysics. For nearby galaxies, in which individual stars are resolved and CMDs are derived, the problem is easier to be tackled as all stars are placed nearly at the same distance. However in our own Galaxy the problem is by far more complicated because there are differences in the distances of the stars and only CMDs containing stars of inhomogeneous age, chemical composition and distance are available. With the advent of the Hipparcos mission, for the first time it was possible to derive the CMD, in absolute magnitudes, of field stars in the solar vicinity [1] and from this CMD to study the past history of the solar neighborhood. The GAIA mission will extend significantly the performances of Hipparcos permitting the determination of the star formation histories of the disk, bulge and halo of the Milky Way.

1 Consiglio Nazionale delle Ricerche, CNR, Roma, Italy e-mail: [email protected] 2 Dipartimento di Astronomia, Universita di Padova and Osservatorio Astronomico di Padova, Italy

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GAIA: A European Space Project The Methods Used in the Study of the SFH

There are two main approaches to the study of the star formation histories through the analysis of the Color-Magnitude Diagrams: - first approach: direct comparison of an observed stellar population with synthetic populations created from evolutionary tracks. This comparison is generally done by the utilization of a statistical estimator from which it is possible to discriminate the model better representing the observations. In this context different techniques have been adopted: i) The star formation rate of the models changes parametrically and the comparison with the observed CMD is made through a number of indicators sensitive to the distribution of stellar ages and metallicities. These indicators are defined conveniently each time and can be ratios between number of stars in different regions of the HR diagram, edges of populous zones, x2 statistics in particular zones [2-4]; ii) The first step is the creation of a grid of synthetic CMDs. Each model uses a constant star formation and is specified by the interval of age, metallicity, initial mass function (IMF). The SFH will be determined by the best linear combination of the theoretical models which match the observed data [5, 6]; iii) They express a function which represents the conditional probability density of observing the ensemble of data points given the ensemble of model points (known as the Likelihood). The ratio of the Likelihoods for two different models will correctly reflect the ratio of probabilities with which the models are a match to the data [7]. — second approach: direct determination of the star formation history by solving maximum likelihood problems through variational calculations. i) The method consists in obtaining by a direct approach the best star formation rate (SFR) compatible with the stellar evolutionary models and the observations, in contrast with the statistical methods which require the construction of synthetic colour-magnitude diagrams for each possible star formation rate considered. This is because it is possible to transform the problem from one searching for a function which maximizes a product of integrals to one of solving an integro-differential equation. This methodology has been applied to a C-M diagram of a volume-limited sample of the solar neighborhood complete to My $$$ 3.15. The result concerns the last 3 Gyr and shows a certain level of constant star formation superimposed on a strong, quasi-periodic component having a period close to 0.5 Gyr [8, 9]. 3

The SFH of the Solar Vicinity from the Hipparcos Data

Recently Bertelli & Nasi [2] determine the SFH of the solar vicinity from Hipparcos data. The adopted method can be included in the cases labeled as "first approach"

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in the previous section and will be appropriate as well as for the GAIA data. With respect to the results of Hernandez et al. [9], where the involved time interval covers only the last 3 Gyr of the SFH, Bertelli & Nasi [2] considered the total lifetime of the disk (10 Gyr). The star sample is selected from the Hipparcos catalogue and contains all stars more luminous than My = 4.5, inside a sphere of radius r = 50 pc. Two analytical SFR functions are considered: — the const-const model: it is a combination of two constant SFR with a discontinuity at a time Tb ranging between the initial time (10 Gyr ago) and the final time (0.1 Gyr ago). The parameter Ib, defined at time Tb, is the ratio of the SFR after and before the discontinuity. — the var-var model: it corresponds to an increasing rate during the first time interval and then to a variable slope (decreasing, constant or increasing). The MS and the evolved star region (red region) are divided in a convenient number of zones. A x2 statistic is applied separately to the MS and to the red region. The values of the parameters Tb and Ib which minimize at the same timeX$$$MSand$$$ X$$$red identify the best solution. The main results are: • All the solutions point in favour of an increasing star formation rate (in a broad sense) from the beginning up to the present time (with an IMF Salpeter slope); • All the cases in which good solutions for the MS region are found, have the correspondingx$$$redvalues too high and the ratio between the He-burning and MS stars of the models is always of a factor 1.5-2.0 larger than the observed values. This fact could be due to the approximations in the treatment of the convective overshoot which render the theoretical models partly inadequate. 4

The Disk Towards the Galactic Center

An important question is whether the stellar population in the solar vicinity is representative of the whole Galactic disk. To answer to this question, we use the HRD-GST (HRD-Galactic Software Telescope) of Ng et al. [10] and Bertelli et al. [11]. HRD-GST is a package suitably designed to study the structure of the Galaxy. It requires: i) one or more stellar populations, ii) a model for the Galactic distribution of the density, iii) the reddening along the line of sight. Then the HRD-GST shoots the stars of the given stellar population in a cone along the line of sight, accordingly to the Galactic density law and the reddening. The simulated CMD obtained in this way can be compared with the corresponding Galactic field. We analyze a field in the direction towards BW8, inside the Baade's Window [2]. In the field BW8 the contribution from the Galactic disk is given by an almost vertical blue plume which appears as an extension of the turn off of the bulge towards brighter magnitudes. In the simulation of the same field using the SFR

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inferred from the Hipparcos CMD, we note that the blue plume of the disk is much bluer than the observed one, suggesting that the SFR holding for the solar vicinity cannot be extended to the whole disk [12]. The immediate conclusion is that the population of the solar vicinity (within 50 pc) as seen by Hipparcos is not representative of the whole Galactic disk. If Hipparcos data cannot be used to infer the past history of star formation in the Galactic disk, would it be possible to get a significant sample of stars confined in a definite volume, covering in distance and position a large portion of the Galaxy and possessing the same degree of accuracy as that obtained by Hipparcos? This ideal sample of stars should satisfy the following requirements: 1) It must be complete up to My =4.5 mag, as with Hipparcos, so that all evolved stars will be included. This means that all stars more luminous than My — 4.5 mag must also satisfy the condition: mv < m V,lim , where mv,lim is the limiting magnitude considered. 2) It must possess accurate parallaxes with $$$/ $$$ 0.1. 3) It must be statistically significant. We define inside the solid angle of 1 degree completely subtending the Baade Window (BW) a volume (a truncated cone) whose height is 400 pc having a variable distance d from the vertex located at the Sun. This distance d acts as the coordinate along the line of sight. With the aid of HRD-GST and the Galactic model, we simulate the disk population falling into the volume as a function of d. Considering for GAIA two limiting magnitudes T l i m — 17 and Vlim — 19 and adopting its estimated parallax precision $$$ (in$$$as)as a function of spectral type (or colour), reddening Ay and magnitude (according to Table 8.4 of [13]), we compute the following quantities: $$$4.5: the number of stars inside the volume at the distance d, more luminous than Mv = 4.5 mag. $$$lim: the number of stars more luminous than My = 4.5 mag and at the same time more luminous than the limiting magnitude V lim . $$$p: the number of stars more luminous than My = 4.5 mag and at the same time with $$$/ $$$ 0.1. The above star counts are shown in the left panel of Figure 1 for Vlim = 17 mag. The dotted line represents$$$4.5.The shape of this curve is governed by the interplay between the volume increasing with d2 and the density of disk stars, which beyond a certain distance starts decreasing, thus generating the peak in the distribution. The solid line represents the ratio $$$lim/$$$4.5. It is evident that at the distance where this ratio starts decreasing below 1.0, more and more stars satisfying the condition My $$$ 4.5 mag are lost because of the limiting magnitude; the distance dlim is the maximum distance at which the condition (1) above is verified. The long-dashed curve is the ratio$$$/$$$4.5.The distanced$$$at which $$$/$$$4.5 falls below 1.0 corresponds to the situation in which no longer all stars more luminous than My = 4.5 mag have also $$$/ $$$ 0.1.

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Fig. 1. The solid line represents the ratio niim/ru.s- The long-dashed curve is the ratio $$$/$$$4.5. The dotted line represents $$$4.5. Left panel: case Vlim = 17. Right panel: case Vlim = 19.

The minimum value between dlim and d$$$ fixes the distance up to which conditions (1) and (2) are verified, i.e. completeness of the sample down to Mv — 4.5 mag and parallaxes with the precision $$$ 0.1. In the case Vlim = 17 mag, we get dlim = 2 while d$$$ = 2.5. This means that conditions (1) and (2) are simultaneously satisfied up to 2 kpc distance. There is also a minimum distance of 1.5 kpc set by condition (3), because at closer distance the number of sampled stars get too small. Interestingly enough, passing from Vlim = 17 mag to Vlim = 19 mag (right panel of Fig. 1) does not improve the situation. In this case dlim = 4–4.5 kpc, however, these larger distances cannot be reached because of the constraint imposed by d$$$ which is independent of Vlim and remains fixed at the valued$$$= 2.5 kpc. 5

At Different Heights Over the Galactic Plane

The GAIA performances offer the unique opportunity of disentangling the two populations (thin and thick disk) which constitute the Galactic disk and deriving for each one the SFH at different heights over the Galactic plane. With the help of the HRD-GST we compute the CMD of a thin and thick disk population inside a square parallelepiped, centered on the sun, normal to the Galactic plane, having a side of 50 pc. In order to simulate the thin disk a synthetic stellar population is adopted having a SFR as that obtained by Hipparcos data, ages in the interval 1-10 Gyr, a Salpeter IMF slope, and stellar metallicity ranging from 0.008 to 0.03. In the case of the thick disk the synthetic stellar population has the following characteristics: ages in the range 12-8 Gyr, SFR exponentially decreasing by

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Fig. 2. Left panel: synthetic thin disk population at different distances from the Galactic plane (details are in the text). Right panel: thick disk population (see text). a factor 2.7 from 12 to 8 Gyr, Salpeter IMF slope and metallicity going from 0.004 to 0.008. In Figures 2 (left and right panel) the stars of the synthetic thin and thick disk respectively are shown and selected at different distances from the Galactic plane up to a maximum distance of 1 kpc. The part of the CMD which is maximally sensitive to the star formation history is represented by the evolved stars brighter than the main-sequence turnoff. As it appears from the figure, the evolved stars of both the disk components closer than 1 kpc are brighter than 15–16 mag. This fact is very important because it means that up to that distance GAIA data of the evolved stars are of high quality. Since for these bright objects the radial velocities can be measured, the two disk components can be separated kinematically and chemically. As a consequence the SFH as a function of the distance from the Galactic plane can be obtained for both of them. 6

The SFH of the Galactic Bulge from GAIA

In Bertelli et al. [2] the SFH of the bulge from HST data of the Baade Window is studied. The HRD has been divided in strips of colour in order to derive the distribution of the stars as a function of the magnitude inside every strip. The solution is obtained by the minimization of a function which is the sum of the x2 in every stripe. The best solution is characterized by an age range from $$$ = 12 Gyr to tf = 9 Gyr. an exponentially declining star formation rate of the form e$$$Twith$$$= 0.1, a metal enrichment law linearly varying with time and having 0.01$$$z$$$0.03, an IMF parameter x = 1.35 (Salpeter slope: x = 2.35). However we know that this result is weakened by the uncertainties related to the hypotheses on which this result stands. In fact the modeling of the bulge requires the following

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assumptions: i) the modeling of the disk population which lays in front and inside the bulge. This imply a precise knowledge of the interstellar absorption along the line of sight up to the bulge. The uncertainty on the value of the reddening at the distance of the bulge is of the order of ±0.15 mag. Additionally the spatial distribution of the disk stellar population is an input parameter quite uncertain. Unfortunately, from simulations with reasonable input parameters it appear that the disk population in front of the bulge presents something like a turn off point at F555 = 20 which overlaps that of the bulge. ii) the modeling of the density distribution of the stars inside the bulge. Adopting different models of the density distribution, differences of the order of$$$V== 0.3 at the magnitude of the turn off of the bulge are obtained [14]. iii) the distribution of the chemical abundance of the stars as a function of the age (the metal enrichment law). What could be the contribution of GAIA on the above topics? - From photometry and spectroscopy of the bright disk stars (which appear as a blue plume in the CMD of the bulge), GAIA will provide the absorption along the line of sight in the direction of bulge. Additionally disk stars and eventual young bulge objects can be disentangled on the basis of kinematic information and distance; - Information on the age, metallicity and SFR of the stellar population belonging to the disk along the line of sight towards the BW can be obtained as discussed in the previous Section 4; - The information given by GAIA about distances and proper motions of red luminous stars in different directions inside the bulge will provide further constraints on the mass distribution of the bulge itself. To distinguish between different spatial distributions distance determinations more precise than 10% are required. This imply that suitable targets are stars brighter than V = 16. 7

Conclusions

The high performances of GAIA will greatly improve our understanding of the Galaxy. This paper focus on the determination of the SFH. The main conclusions are: 1) At low Galactic latitudes GAIA will be able to measure a significant sample of stars having the same degree of accuracy as Hipparcos data up to a distance of 2-2.5 kpc. 2) GAIA will allow to disentangle the two populations (thin and thick disk) which constitute the Galactic disk. For each of them the SFH at different heights over the Galactic plane up to a distance of 1 kpc can be derived. 3) GAIA is going to contribute significantly to the determination of the SFH of the bulge giving information about metallicity range, reddening, and mass distribution.

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References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

Perryman M.A.C., et al., 1995, A&A, 304, 69 Bertelli G., Nasi E., 2001, AJ, 121, 1013 Bertelli G., Mateo M., Chiosi C., Bressan A., 1992, ApJ, 388, 400 Gallart C., Aparicio A., Bertelli G., Chiosi C., 1996, AJ, 112, 1950 Aparicio A., Gallart C., Bertelli G., 1997, AJ, 114, 680 Dolphin A., 1997, New Astron., 2, 397 Tolstoy E., Saha A., 1996, ApJ, 462, 672 Hernandez X., Valls-Gabaud D., Gilmore G., 1999, MNRAS, 304, 705 Hernandez X., Valls-Gabaud D., Gilmore G., 2000, MNRAS, 316, 605 Ng Y.K., Bertelli G., Bressan A., Chiosi C., Lub J., 1995, A&A, 295, 655 Bertelli G., Bressan A., Chiosi C., Ng Y.K., Ortolani S., 1995, A&A, 301, 381 Bertelli G., Bressan A., Chiosi C., Vallenari A., 1999, Baltic Astron., 8, 271 ESA 2000, GAIA: Composition, Formation and Evolution of the Galaxy, Technical Report ESA-SCI(2000)4 (scientific case on-line at http://astro.estec.esa.nl/GAIA) [14] Vallenari A., Bertelli G., Bressan A., Chiosi C., 1999, Baltic Astron., 8, 159 [15] Bertelli G., Vallenari A., Ng Y.K., 2001, in preparation

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

MAPPING THE GALACTIC HALO TODAY AND IN THE FUTURE A. Helmi1

Abstract. Presently data from several ongoing surveys, and in particular from the Spaghetti Project Survey have allowed us to map substructure in the halo associated to multiple passages of the Sagittarius dwarf. Future astrometric missions such as GAIA will be able to recover truly ancient accretion, thus providing us with the formation history of the Milky Way.

1

Introduction

The hierarchical paradigm of the formation of structure in the Universe predicts that the Galactic halo should have been predominantly assembled from mergers and accretion of smaller systems. Evidence of the past mergers that lead to the formation of our Galaxy should be identifiable as fossil remains in the Galactic halo as coherent substructure in space, velocity, or both. In the outer halo, the expected signatures will generally be traceable as distinct tidal tails which remain coherent in space due to the longer mixing timescales. On the contrary, the inner halo is expected to be composed of many hundred of spatially diffuse streams, whose most distinct feature are their extremely small internal velocity dispersions. The observational evidence in favour of the hierarchical formation of our Galaxy has been mounting over the past few years. Examples of coherent groups are becoming more common, especially in the outer Galaxy. One of the most dramatic is the Sagittarius dwarf. Recently, the Sloan Digital Sky Survey (SDSS) commissioning data showed overdensities of blue horizontal-branch (HB) and RR Lyrae-type stars (Ivezic, Z. et al. [1]), covering 35 degrees on the sky and located about 50 kpc from the Sun, and 60 degrees from the center of the Sgr dwarf. Comparison with models of the disruption of the Sgr galaxy strongly suggests that this structure is tidally stripped material from the Sgr dwarf.

Max-Planck-Institut fur Astrophysik, Garching, Germany © EAS, EDP Sciences 2002 DOT: 10.1051/eas:2002026

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Fig. 1. Distance vs. radial velocity for the Sgr dwarf stellar models [4]. The model points come from the ranges 300° < l < 10°, and have been divided into latitude bins. Also plotted in the top panels are the giants with measured radial velocity. The gray diamonds mark the two most distant giants at 80 kpc, the filled circles mark the four giants near 50 kpc, the gray triangles mark stars matching the model near 20 kpc. and the open and gray circles mark stars that do not match the model within their error box.

2

The Spaghetti Survey and the Sagittarius Dwarf

As part of the Spaghetti Project Survey (SPS; [2.3]), we have serendipitously identified 21 giants associated with the SDSS overdensity and have measured their radial velocities and distances. We use the modified Washington photometric system to identify candidate red giants, which we then observe spectroscopically to confirm the photometric classification and metallicity and to obtain a radial velocity. In Figure 1, we plot the locations of all giants with measured radial velocities. For comparison we plot the same quantities for the particles in the Helmi & White [4] stellar model that fall within our selected region of the sky. The excellent agreement with model predictions, as shown in Figure 1 leads us to conclude that the structure at 50 kpc is, indeed, tidal debris from the Sgr dwarf. Furthermore, we have identified additional structures at different distances (20 kpc and 80 kpc) that may be multiple wraps of the Sgr dwarf tidal stream. Finally, we note that the mean metallicity of the six stars that we claim to be part of the Sgr stream is about [Fe/H] ~ —1.5, 0.5 dex lower than the mean for field stars in the main body of the Sgr galaxy, suggestive of a metallicity gradient in the progenitor of Sgr.

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The Future

Surveys like the SDSS and the SPS will help us gain much insight into the formation of the Galactic halo in the near future. These studies are most sensitive to structures which have remained coherent in space over a Hubble time, and will thus generally be located in the outer Galaxy. The hierarchical paradigm would predict that a system like the Milky Way forms from the mergers of only a few objects of comparable mass coming together at high redshift. Thus most of the action probably took place in the very inner 10 kpc of the Galaxy. To recover its formation history we thus need to focus on this region of the Galaxy. Here we will need to know 6 phase-space coordinates with extremely high accuracy for very large samples of stars. GAIA unique capabilities will give us this information, and probably much more. I would like to thank the members of the Spaghetti Project Survey, with whom much of the work presented here has been done: Robbie Dohm-Palmer, Heather Morrison, Mario Mateo, Ed Olszewski, Paul Harding, Ken Freeman, and John Norris.

References [1] [2] [3] [4]

Ivezic, Z., et al., 2000, AJ, 120, 963 Morrison, H.L., Mateo, M., Olszewski, E.W., et al.. 2000, AJ, 119, 2254 Dohm-Palmer, R.C., et al., 2001, ApJ, 555, L37 Helmi, A.. White, S.D.M., 2001, MNRAS, 323, 529

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

PREPARING FOR THE GAIA MISSION: ASTROPHYSICAL PARAMETER DETERMINATION A.G.A. Brown1,

2

Abstract. The exquisite astrornetric data to be delivered by GAIA can only be successfully exploited if complemented by accurate astrophysical information on all observed objects. In this contribution I will discuss the preparations that are necessary for obtaining this information. The emphasis will be on the task of optimising the GAIA photometric system and the development of photometric data analysis algorithms. 1

Introduction

The science goals of the GAIA mission are very broad, including the understanding of the formation and history of the Galaxy, stellar astrophysics, the Local Group, fundamental physics, the Solar system, and studies of specific objects such as quasars and supernovae. All these science goals require not only accurate astrometric and radial velocity information but also accurate astrophysical information about the objects under study. For example, the interpretation of the dynamics and structure of the Galaxy in terms of its formation and history cannot be achieved by a mapping, from astrornetry and radial velocities, of Galactic phase space alone. To unravel the details of the formation history of the Galaxy it is essential to obtain accurate astrophysical information for all stars. As described in Section 2.3.1 of the GAIA Study Report [1], the distribution function of stellar abundances must be determined to ~0.2 dex and effective temperatures must be determined to ~200 K. A separate determination of the abundance of Fe and$$$-elementsat the same accuracy level is essential for mapping the Galactic chemical evolution. These same accuracies will allow a separation of the different stellar populations (i.e., thin/thick disk. halo). The astrophysical information has to be obtained from the broad and intermediate band photometry, supplemented by the data contained in the radial velocity 1

Leiden Observatory. P.O. Box 9513. 2300 RA Leiden, The Netherlands European Southern Observatory, Karl-Schwarzschildstrafie 2, 85748 Garching bei Mimchen, Germany 2

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spectra. The challenge is to design a photometric system, as well as a means of analysing the corresponding data, that is capable of meeting all of the science goals as laid out in the GAIA Study Report [1]. In the following sections a number of important tasks that have to be carried out in this context before the mission will be discussed. Section 2 contains a discussion on how to proceed with finalising the design of the photometric system, an important aspect there is the need for large stellar spectral libraries, containing both observed and synthetic spectra. Section 3 is about the development of methods for analysing the large amounts of photometric data to be obtained by GAIA. This task will also influence the finalisation of the photometric system. An important issue, discussed in Section 4. is that of the determination of interstellar extinction. No meaningful interpretation of the astrophysical information can be obtained without an accurate knowledge of the extinction towards each star. Finally, Sections 5 and 6 contain discussions of the photometric data reduction and the possibilities of obtaining spectra from the ground for stars that are too faint for the radial velocity instrument. 2

Finalising the Photometric System

Several photometric systems have been proposed for GAIA, the design of all of them based on the knowledge of the spectral energy distribution of stars one is interested in. The task now is to converge on the design of a single photometric filter system for GAIA. The broad band photometric system is primarily intended for the chromaticity calibration for GAIA astrometry and its niters should only be optimised with that aim in mind. Hence, I will concentrate here on the optimisation of the medium band photometric system. The filter recommendations will be based on single stars across the Hertzsprung-Russell diagram and then it should be evaluated how the filter system performs in the case of binaries, asteroids, galaxies, quasars etc. It is very important to keep in mind that the photometric system should be capable of addressing the full science case described in the study report [1]. For the design and optimisation of the photometric system one needs access to a stellar spectral library covering a large range in Teff, metallicity [M/H], aelement enhancements, logg and age. For the design and study of the filters themselves one needs spectra with resolution higher than 3000, covering the range 300-900 nm (the range over which the GAIA CCDs will be sensitive), which should be flux calibrated. For the calibrations of the filter system in terms of astrophysical parameters higher resolution spectra covering the same range are required (R > 17000). but these need not be flux calibrated. A quick survey of available spectral libraries reveals that only the effective temperature and surface gravity are well covered. The metallicities of the libraries of observed spectra are heavily biased towards Solar and almost no variation in a-elernent enhancements is present. Hence additional spectrophotometric observations are required.

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The present schedule calls for convergence of the photometric systems within 6-12 months from mid 2001. Collecting the necessary spectrophotometric observations on this time scale will not be possible. This means that the filter convergence process should be based on the presently available spectral libraries. However, studies of the photometric system will continue to 2005 so we should plan observations aimed at filling the gaps in the spectral libraries. This requires a number of steps, the first of which is a more detailed investigation of the available spectral libraries to more clearly identify their deficiencies. Secondly a set of objects should be defined which are to be commonly used by everyone involved in the finalisation of the photometric system. Finally, a list of targets to be observed should be defined. This set will largely overlap with the set of objects on which the filter system is to be tested. The targets to be observed should include metal-poor stars, peculiar stars (such as WR, Be, Ap and carbon stars), young/active stars (such as T-Tau), open clusters with a range of extinctions, globular clusters over a range in [M/H], and bulge fields for further studies into the effects of varying extinction. For variations in a-element enhancements one can carry out observations in the globular cluster 47 Tuc for example, while the cu Cen cluster allows studies of the effects of CNO anomalies. Once the photometric filters have been agreed upon the ones that are within the atmospheric transmission bands may be tested from the ground. Reasons to carry out ground-based tests are: the enormous variety of objects and real sky, the presence of varying ratios of elements in stellar atmospheres and the CNO problem, as well as being confronted with all kinds of spectral peculiarities not covered in the spectral library. Furthermore it offers the possibility of testing data reduction procedures and evaluating the expected precision of the filter system and finally, scientific results can already be obtained. However, it may be that using the spectral library only is sufficient for finalising the filter system. 3

Analysis of the Photometric Data

The analysis of the photometric data consists of the classification of objects followed by the determination of the relevant astrophysical parameters for each class. All this will be based on the spectral energy distribution contained in the combined photometric and spectroscopic data obtained with GAIA. Given the unprecedented amount of objects to be observed by GAIA one is forced to consider automated methods of classification and parameter extraction. In principle one could automate the familiar methods of colour-colour and colourmagnitude diagram analysis. However this is a wasteful way to use the available photometric information. There is no reason to rely on specific colour indices for classification and parameter extraction. All the information is present in the fluxes and the known colour index analyses have the disadvantage that they have been optimised for specific parts of the astrophysical parameter space. The GAIA data will provide multi-colour photometry as well as spectroscopic and parallax information for all types of objects all over the sky. The only way

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to successfully exploit such data is to use multidimensional analysis methods. Much work has recently been done on automated stellar classification techniques for large surveys and an overview is provided by Bailer-Jones [2]. Well known examples of these techniques are principal component analysis, neural networks, minimum distance methods and Gaussian probabilistic models. A separate task within the overall preparation for the GAIA mission has been identified which is to address the problem of identification, classification and physical parameterisation of objects observed by GAIA. This will necessarily include the task of the identification of objects as stars, galaxies, quasars, asteroids etc. After the identification process follows the astrophysical parameterisation of these objects. The (multi-dimensional) classification method will be tested using the proposed photometric system and an extensive library of both observed and synthetic spectra. The aim is to develop and optimise a classification algorithm and to test the photometric system itself. The results can then be fed back into the finalisation of the design of the photometric system. Finally, it is important to keep in mind that the photometric data analysis should not be seen in isolation from the astrometric and radial velocity data. Parallaxes can constrain an object's luminosity, while its kinematic properties, derived from proper motions and radial velocities, can help identify the population to which the object belongs. The radial velocity spectra contain additional astrophysical information. Hence an integrated approach to the data analysis will be essential. 4

Determination of Interstellar Extinction

The accurate determination of the interstellar extinction for each observed object is crucial to the success of the GAIA mission. A wrong estimate of Av and E(B — V) will lead to erroneous absolute magnitudes and colours which will in turn have a negative impact on the determination of effective temperatures, abundances, ages etc. For example, for stars with relative parallax errors less than 1 per cent the error in Ay will dominate the error in the derived value for Mv. Traditionally one determines the colour excess E(B — V) = (B — V) — (B — V)0 from photometric observations and then the value of total extinction in the Vband. Av, follows from the ratio R == A v / E ( B — V). The dependence of the extinction on wavelength is usually given in terms of colour excess relative to E(B – V): E($$$ – V)/E(B - V) vs.1/$$$,the so-called extinction curve. This curve reflects the chemical composition, crystalline structure and other properties of interstellar dust particles. The value of R depends on the form of the extinction curve and is difficult to determine reliably. See the paper by Krelowski & Papaj [3] for a more extensive discussion of these issues. Unfortunately there is no single extinction curve valid throughout the Galaxy. The extinction curve along the line of sight towards any star depends on the properties of the interstellar clouds located along that line of sight. For nearby stars there may be only one such cloud and then the extinction curve (and value of

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R) can vary greatly from one star to the other. This is illustrated in Figure 10 of Krelowski & Papaj [3], where one can see the large variations in E($$$—V)/E(B — V) for stars at distances less than ~4 kpc. Beyond that distance these ratios converge and one may then speak of an average Galactic extinction curve. However this should not be used for nearby objects. Because of a lack of standard stars with zero extinction it is very difficult to determine extinction curves for individual stars, which one would ideally like to have. Various methods exist for determining extinction curves for aggregates of stars [3] but these rely on using stars of very similar spectral type and luminosity class and the assumption of a homogeneous medium causing the extinction. Hence, these methods work only for stellar aggregates in sufficiently small regions on the sky. For the GAIA case other methods of determining the extinction will have to be developed. One approach might be the creation of a 3D extinction model for the entire Galaxy, containing free parameters that will be determined from the GAIA data. The question is then what kind of model to use. Another more "local" approach was proposed by J. Knude (this volume). He suggests the selection of stars with similar parallaxes in small regions on the sky and then determining the values of E($$$ — V) and A\ from main sequence fitting. In that way one can build an extinction map for the whole sky as a function of distance. It remains to be investigated what sizes of sky fields to use and how well the method works in practice. By the time GAIA is launched there will be information available on the interstellar extinction from surveys such as DENIS, 2MASS and SDSS. Because they map dust throughout the Galaxy, constraints on the extinction can be obtained from missions such as IRAS, COBE. MAP, Planck etc. It remains to be investigated how to incorporate these data. 5

Photometric Data Reduction and the Sampling Strategy

Prior to any analysis of the photometry from GAIA, the raw data coming from the satellite have to be reduced to a vector of fluxes for each object at each occasion that it transits the GAIA focal plane. All the data collected by the GAIA satellite will be sent down in the form of "patches", which correspond to small regions of the sky centered on each detected star (point source). The patches containing the multi-colour photometric information will comprise a set of "samples" (most of these sets being one-dimensional), which in turn consist of a number of CCD pixels binned together electronically before readout. Sometimes additional numerical binning is applied before transmission of the data to the ground. Details are in Section 3.3 of the GAIA Study Report [1] and in the contribution by E. H0g in this volume. Hence there will be no images to which classical photometric data analysis methods (for example, aperture or PSF photometry) can be applied. However, accounting for faint background sources and tackling the cases of binaries and galaxies does require 2D information around each observed GAIA target. Reconstructing these 2D images from the GAIA data will be very

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complicated. GAIA will provide for each target a huge amount of information. Each Astro instrument gives the sky mapper detection outputs, including the confirmation field patches, 17 AF and 4 BBP patches, while the Spectro instrument will provide the sky mapper outputs, the radial velocity spectra and 11 MPB patches (as detailed in Fig. 3.7 of the study report [1]). The patches have different sampling, signal to noise ratios, and one or two-dimensional resolution which will make 2D image reconstruction very complex. In particular the information coming from the Astro instrument is of much higher resolution than that coming from the Spectro instrument. This means that the sky looks very different for both instruments, which creates problems when trying to match sources detected in the two instruments. A central task will thus be the development of (photometric) data reduction algorithms that are capable of handling complex data like this. This should take place in parallel with an optimisation of the sampling scheme. Because of the complexities involved the only practical way to develop these algorithms is to perform detailed simulations of the focal plane of GAIA, which provide as output the raw data from which the photometric information has to be extracted. These simulations should include an accurate sky simulation (base on HST images for example), detailed instrument characteristics (CCD, PSF, noise etc.), an implementation of the detection/confirmation and selection algorithms as well as the tracking of the sources across the focal plane [4]. Data reduction algorithms can then be tested on the output of these simulations and proposed changes in the sampling scheme can then easily be implemented in an iterative scheme aimed at optimising both the algorithms and the sampling. An effort to build such a simulator is now underway at the Institute of Astronomy in Cambridge and is described in a report by Babusiaux et al. [4]. One possible data reduction algorithm is suggested in Section 9.4.2 of the study report which is based on a linear least squares approach. This proposal was worked out in more detail by me in the form of a mathematical formulation of the least squares problem [5]. In order to do this one has to use a set of rather restrictive assumptions, an important one being the knowledge of positions of stars around each target to a limit (V = 23) above the GAIA survey limit of V = 20. Other assumptions include: a constant PSF over the focal plane, perfectly linear CCDs with no pixel response function complexities, and no parallactic or proper motions for the sources. Many of these assumptions can be relaxed but non-linear behaviour of the CCDs cannot easily be taken into account in such a model. However, in relation to directly taking, e.g., an iterative approach to the photometric data analysis (where one can take non-linearities into account), the least squares approach has the advantage that it is easy to implement and provides a means of quickly gaining insight into a number of important issues concerning the photometric data analysis. The results can be used to guide the efforts aimed at the construction of the actual data reduction algorithms. The algorithms presented in [5] rely on information about the positions of stars fainter than the GAIA survey limit. Out to which distance on the sky around a particular star is positional information on other sources necessary, and to what

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magnitude limit? How accurately do we need to know these positions and what is the effect of the parallactic and proper motion of the background stars? This will help determine how the sky should be partitioned for the overall data analysis task. Assuming the full astrometric catalogue for the GAIA targets is available as well as knowledge on the background sources; what photometric accuracies can ultimately be achieved (as a function of the number density of stars on the sky and the magnitude limit out to which stellar positions are known)? A closely related issue that needs to be studied is how the positions and magnitudes of the background stars can be derived from the patches observed in the wide G-band in ASMS, AF17 and SSM. This involves the reconstruction of an image of the piece of sky around each target star covered by these patches. This is not trivial in the case of purely one-dimensional patches. The answers combined with those to the questions above will provide additional constraints on the optimal sampling scheme. 6

Spectra for Faint Stars

The final issue I will address here is that of spectra for faint V > 18 stars. Currently it is not foreseen that the radial velocity instrument will provide spectra for these stars. However, many very interesting targets, such as Local Group Dwarf galaxies, the Magellanic Clouds, faint Bulge stars etc., are to be found in this magnitude range. The science capabilities of GAIA will be greatly enhanced if full phasespace coverage (so including radial velocities) is available for stars beyond V = 18. For instance, this will provide much larger samples for 3D kinematic studies of Local Group Galaxies and make a great deal easier the angular momentum based selection of stars in the tidal tails of satellite galaxies on orbits with large apocentres (see also the contribution by A. Helmi in this volume). Finally, an important reason to obtain spectra for the faint stars is that they can be used to constrain the photometric data analysis. Obtaining these spectra from the ground certainly is a major task and should be restricted to a subset of the most important sources at V > 18. These spectra will not only be of benefit to the GAIA mission but will be more generally useful too. Existing spectroscopic instrumentation can be used to obtain spectra for faint field stars. For targets where one wants to obtain many spectra over a limited field of view the prospects are good because of large multi-object spectrographs coming on line at various observatories around the world (such as FLAMES and VIMOS at the European Southern Observatory). Furthermore, plans are being developed for multi-object spectrographs that can obtain data for even larger numbers of stars at a time. Some of these plans were discussed recently at a meeting organised by ESO [6]. One of the proposals (see contribution by Pasquini & Kissler-Patig in [6]) is to build instruments capable of carrying out massive spectroscopic surveys analogous to the photometric surveys carried out by, for example, the MACHO project. The science case includes the dynamics and metallicity of Magellanic Clouds, the Bulge,

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the Local Group and nearby galaxies. This presents an overlap with the GAIA science case. It will be useful to establish contacts between the GAIA community and those interested in carrying out these spectroscopic surveys. From the GAIA side part of the science case for such an instrument can be contributed as well as lists of priority targets to be observed in order to complement the data from GAIA. References [1] ESA 2000, GAIA: Composition, Formation and Evolution of the Galaxy, Technical Report ESA-SCI(2000)4 (scientific case on-line at http://astro.estec.esa.nl/GAIA) [2] Bailer-Jones, C.A.L., 2001, in Automated Data Analysis in Astronomy, R. Gupta, H.P. Singh, C.A.L. Bailer-Jones (eds.) (Narosa Publishing House. New Dehli), in press [3] Krelowski, J., Papaj, J., 1993, PASP, 105, 1209 [4] Babusiaux, C., Arenou, F., Gilmore, G.. 2001, The GAIA Instrument and Basic Image Simulator, report GAIA-CB-01 [5] Brown, A.G.A., 2001, Photometric Data Analysis for GAIA: Mathematical Formulation, report GAIA-AB-01 [6] Bergeron, J., Monnet. G., 2001, Proceedings of the ESO Workshop Scientific Drivers for ESO Future VLT/VLTI Instrumentation (Springer-Verlag), in press

Outside our Galaxy

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

GAIA AND THE STELLAR POPULATIONS IN THE MAGELLANIC CLOUDS M. Spite1 Abstract. GAIA will measure with precision, position, velocity, and colours of tens of thousands of stars in the Magellanic Clouds and thus, will provide an important contribution to our knowledge of these two close dwarf irregular galaxies. We will consider here the impact of GAIA on the determination of the distance modulus of the LMC and the SMC, on our understanding of the global dynamics of the Magellanic system and of its star formation history. The existence of a stellar pressure-supported halo around the Magellanic Clouds can be also tested from the velocities measurements of the old stars. Moreover we show that the first generation of stars in the Magellanic Clouds could be detected from the GAIA spectra, if it could be possible to obtain spectra of stars as faint as, at least, V = 17.5. A resolution of R = 5000 would be sufficient for this detection.

1

Introduction

The Large and the Small Magellanic Clouds are two irregular galaxies located at a distance of only 50 and 60 kiloparsecs ($$$ 20 and 17 $$$as) to the Galactic Center. They offer the unique opportunity of studying dwarf irregular galaxies and also the consequences of interaction between galaxies since structure and kinematics of the Magellanic Clouds may have been strongly affected by mutual interactions, and interactions with our Galaxy. Much new data have been recently collected, and have lead to many controversial discussions. The total LMC mass is about 2 x 1010M$$$. It is generally regarded as a thin flat disk with a tilt to the plane of the sky of about 45°. The extension in depth of the LMC is around 8 kpc. The SMC mass is only 3 x109M$$$The SMC disk has a larger inclination than the LMC disk, it is estimated to about 60°, its extension in depth is probably more than 15 kpc, its structure is complex and the SMC could be a disrupted galaxy. 1

GEPI, Observatoire de Paris-Meudon, 92195 Meudon, France © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002028

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More details about the structure of the Magellanic Clouds and their main characteristics can be found in [1]. Different populations coexist in the Magellanic Clouds: an old population of low mass stars and a young population. Among the young Population, many bright massive stars still exist and high resolution spectra of these stars have been obtained with 4 m class telescopes. Thus the chemical composition of the young stars in the Magellanic Clouds is rather well known. It has been shown that the metallicity of these young stars (and of the interstellar gas) in the LMC is two times lower than the metallicity of the young stars (and the interstellar gas) in our Galaxy. This factor is about 4 in the SMC. On the other hand, it has been shown from deep photometry that the age of the oldest globular clusters is the same in the Milky Way, the LMC and the SMC [2, 3]. Thus the star formation began at the same time in the three galaxies. As a consequence since the present metallicity is lower in the Magellanic Clouds than in our Galaxy, the enrichment has been less efficient in the Magellanic Clouds and thus the star formation has been different. During the past 25 years the dominating questions in Magellanic Clouds research concerned their distance, their structure, their kinematics and their chemical composition with the aim of understanding their evolution. GAIA will be able to measure with precision the position, the velocity and the colours of tens of thousands of stars in the Magellanic Clouds and thus it will bring an important contribution to our knowledge of these close galaxies. We will consider here the impact of GAIA on a) the determination of distance modulus of the LMC and SMC; b) our understanding of the global dynamics of the Magellanic system; c) of the star formation history; d) the existence of a stellar halo; e) the detection of the "first" Magellanic Stars. 2

Distances Moduli of the Magellanic Clouds

Up to now it has not been possible to measure directly with precision the parallax of individual stars in the Magellanic Clouds. Generally speaking, in order to estimate the distance of the Clouds the absolute magnitude of a given type of stars is first measured in our Galaxy and then it is assumed that the corresponding stars in the Magellanic Clouds, have the same properties than in our Galaxy and thus the same absolute magnitude (e.g. [4]). Let us note that the interesting parameter is in fact the distance between the Galactic center and the center of the LMC or the SMC. But since the extension in depth of the Clouds is not negligible, if a small number of stars is used or if the distribution of stars is not uniform, the measurement has to be corrected taking into account the distance of stars to the center of LMC or SMC.

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The distance modulus of the LMC is now generally estimated to 18.6, and the distance modulus of the SMC to 18.9 (cf. [1,4,5] and references therein). With GAIA, and for the first time, it will become possible to measure directly the distance of a large sample of stars in the LMC and the SMC. In the LMC there are many young stars brighter than V — 12 (B stars, F and K supergiants, Cepheids); the error on the distance of these stars is expected to be about 10 kpc. This precision is not sufficient to determine the relative position of individual stars inside the Clouds since it is of the order of the depth. But since there are a large number of these stars, the LMC and SMC center positions will be determined with an unsurpassed precision. Moreover it will become possible to compare the relation period luminosity of the Cepheids in the LMC and in our Galaxy. It will become possible also to determine the relative position of the young clusters and to study LMC and SMC fine structure (extension in depth in different directions, position of the bar relative to the disk, fragmentation of the SMC, etc.).

3

Global Dynamic of the Magellanic System

A close encounter of two galaxies leads to star formation. Following Byrd & Howard [6], a global burst of star formation takes place when M2 > M1/100 where M1 and A^2 are the masses of the galaxies in interaction. As a consequence a description of the global dynamics of the Magellanic system (interactions between the LMC and SMC and our Galaxy) is needed before star formation and chemical evolution can be fully understood in these three galaxies. The two MCs are connected by a common HI envelope. The strongest part of the envelope forms a bridge with embedded stars. Beyond is a long tail of metal-poor gas "the Magellanic Stream". It is generally assumed that the SMC and LMC have been bound to each other for a long time, and that the Clouds have also be bound to our Galaxy for at least the last 7 Gyr; there are several models of the Magellanic system (cf. in particular [7-11]). All the Magellanic System models assume that: the LMC and SMC in their orbital motion lead the Stream which has been presumably tidally striped on a previous approach of the Clouds to the Galaxy. Because the Stream nearly forms a great circle in the sky whose plane is perpendicular to the Galactic plane, the Clouds would have orbits running over the Galactic poles. It is alsc supposed that the Clouds are near their perigalacticon. These models are able to guess the tracks of (for example) the LMC relative to our Galaxy during the past 14 Gyr [9]. Let us note however that these orbits are, for the moment, very uncertain and depend strongly on the models parameters. But all the current models agree to predict that the proper motion of the LMC H cos 8 is between 1.5 and 2 mas yr~ x with a position angle 9 = 90°.

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These predictions were in good agreement with a) the determination of Jones et al. (1994) [12] who measured the position of 251 giant stars on plates centered on NGC 2257 and covering an epoch span of 14 Gyr, and b) the measurements of Kroupa fe Bastian (1997) [13] who determined LMC center proper motion using the Hipparcos data for 36 stars in the LMC. But recently Anguita et al. (2000) [14], measuring LMC proper motion relative to three background QSOs on 125 CCD frames obtained between 1989 and 1997 found [icosd — 3.4 ± 0.2mas yr"1 with B = 30° This result is not compatible with the generally adopted models of the Magellanic system. Let us note that Majewski suggested that the disagreement between the measurements of Anguita and the previous ones could be due to the fact that the stars measured in the LMC were too red compared to the blue QSOs but following Anguita a correction has been done (cf. the discussion in [15]). The LMC and SMC center proper motions will be precisely measured with GAIA and we will know whether the presently adopted models of the Magellanic system are or not compatible with the measurements. Anyhow, following Kroupa et al. (1994) [16] for a significant improvement of our understanding of the Magellanic System, both LMC and SMC proper motions are needed with an accuracy better than about 0.1 mas yr"1, a precision which is expected to be achieved with GAIA. 4

Star Formation History in the Magellanic Clouds

The history of the star formation in the Magellanic Clouds probably differs greatly from that in our Galaxy and is still poorly known... For a long time, it was assumed that the cluster formation was proportional to the star formation. Ages (and also metallicities) of the clusters are known [17,18]; the ages of old clusters have been in particular dramatically improved with deep high resolution photometry [2], and HST photometry [3]. As a consequence, an histogram "Number of the clusters" versus Age can be drawn. In the SMC the rate of cluster formation is rather uniform with time, but in the LMC there are two groups of clusters: one born about 15 Gyr ago and the other one spanning over the past 3 Gyr (Fig. la). There are practically no clusters between 5 and 12 Gyr. This lack of clusters correspond to a lack in metallicity: there are no clusters in the range —1.8 < [Fe/H] < —1.1 dex (Fig. Ib). However it has been shown that the field RR Lyrae stars, in the LMC which are very old stars have a mean metallicity of about —1.3 dex (cf. for example [19]) a metallicity which falls in the metallicity gap of the clusters (Fig. Ib). Moreover Van den Bergh (1998) [20] remarks that between 5 and 12 Gyr the metallicity has increased by a factor of about 4. This is difficult to explain if no new stars have been formed... Thus, it is now admitted that cluster formation in the LMC does not reflect star formation. Then the history of the star formation in the Magellanic Clouds has to be discussed through analysis of Colour magnitude diagrams (CMD) and luminosity functions: for a given (constant) IMF, the CMD can be computed

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Fig. 1. a) Number of clusters versus age in the LMC arid b) metallicity of the LMC clusters versus age.

for different Star Formation Rates assuming that the stellar evolutionary tracks are known [21,22]. From the large scale photometry and spectroscopy of GAIA in the LMC and SMC, it will become possible to obtain direct measurement of the metallicity distribution in many regions of the Magellanic Clouds and then to build a much better representation of the star formation in the different regions of the Clouds.

5

Is There a Pressure Supported Halo Around the Magellanic Clouds?

With GAIA it will be possible to recover the 6 dimensional "phase space" coordinates (position and velocity of each star) with an unsurpassed precision. At the present time the precision of the annual proper motion in the LMC, is about 3 mas yr"1 or 700 km s"1. With GAIA for the stars brighter than V = 20 the precision will become better than 0.150 mas yr-1 or 35km s"1. and even 0.030 mas yr"1 or 7km s^1 for all the stars brighter than 17. As a consequence, GAIA will bring an extreme improvement in our knowledge of the internal motions in the Magellanic Systems in particular for the old stars (which are all fainter than V = 16) and it will become possible to check the existence of a pressure supported halo of old stars (similar to the Galactic one) around the Magellanic Clouds. The existence or the absence of a halo is an important parameter to understand the formation of the Magellanic Clouds. It has been shown that if there is a halo around the Magellanic Clouds, then the velocity dispersion of the objects belonging to this halo must be about 50 km s ~ { . The old LMC clusters have a velocity dispersion of only 23km s"1 and thus they can be distributed in a thick disk. The velocity dispersion of the old metal-poor stars (RR Lyrae, old metal-poor K giants) measured with GAIA will be a test of the existence of a spherical halo around the Magellanic Clouds.

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GAIA: A European Space Project Will GAIA Be Able to Detect the "First Magellanic Stars"?

Our Galaxy and Magellanic Clouds were born about 15 Gyr ago. All the stars formed at that time with a mass M.< 0.8 A^Q are still living, they are now G, K, M dwarfs or giants. They are expected to have a chemical composition very close to the products of the Big-Bang (H, He, no metals). It is very important to have a good sample of very low metallicity stars. Many topics may be explored with them. These topics have been reviewed [23]. I will retain: i) the nature of the metallicity function (how low can we go?), ii) the relative abundances of heavy metal species in the first generation of stars (test of masses of the first supernovae). iii) the efficiency of mixing processes... A way to detect these stars is to search for cool stars with no (or at least very weak) calcium lines. This work has been undertaken in our Galaxy by Beers et al. since 1985 [24]. They detected 5000 metal-poor stars up to 15th magnitude, none without metals, but 100 with a metallicity lower than [Fe/H] = —3 (1/1000 of the solar metallicity).

Fig. 2. Computation of one of the lines of the Ca II triplet at 8542 A with one hundred, one thousand and ten thousand times less calcium than in the SUN. The model adopted for this computation (Teff = 4200 K logg = 1.2) is typical of a cool metal-poor giant.

GAIA will measure the infrared calcium triplet, these lines remain visible even at a very low metallicity (Fig. 2) and they could be an excellent tool to detect more extremely metal poor stars in our Galaxy. To extend this work toward the Magellanic Clouds, since all the old stars in the Magellanic Clouds are fainter than V — 16, it would be extremely important that the spectrograph of GAIA be able to observe faint stars, at least all the stars brighter than V = 17.5. A high resolution is not necessary, R = 5000 would be sufficient to select these stars. Later the most metal poor stars could be analysed from high resolution spectra, for example with UVES on the VLT. Then, for the first time, we would be able to compare properties of the first generation of stars in our Galaxy and in external galaxies like the LMC and the SMC.

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References [1] Westerlund, B., 1997, The Magellanic Clouds, Cambridge Astr. Ser., 29 (Cambridge University Press) [2] Brocato, E., Castellani, V., Ferraro, F.R., Piersimoni, A.M., Testa, V., 1996, MNRAS, 282, 614 [3] Olsen, K.A.G., Hodge, P.W., Mateo, M., et al, 1998, MNRAS, 300: 665 [4] Groenewegen, M.A.T., Oudmaijer, R.D., 2000, A&A, 356, 849; 1998, A&A, 335, L81 [5] Feast, M., 1999, in New Views of the Magellanic Clouds, IAU Symp., 190, Y.H. Chu, N. Suntzeff, J.E. Hesser and D.A. Bolender (eds.) (San Francisco ASP), 542 [6] Byrd, G., Howard, S., 1992, AJ, 103, 1089 [7] Gardiner, L.T., Sawa, T., Fujimoto, M., 1994, MNRAS, 266, 567 [8] Lin, D.N.C., Lynden-Bell, D., 1982, MNRAS, 198, 707 [9] Lin, D.N.C., Jones, B.F., Klenmola, A., 1995, ApJ, 439, 652 [10] Murai, T., Fujimoto, M., 1980, PASPJ, 32, 581 [11] Shuter, W.L., 1992, ApJ, 386, 101 [12] Jones, B.F., Klemola, A.R., Lin, D.N.C, 1994, AJ, 107, 1333 [13] Kroupa, P., Bastian, U., 1997, in B. Battrick, M.A.C. Ferryman and P.L. Bernacca (eds.), HIPPARCOS '97, Presentation of the Hipparcos and Tycho catalogues and first astrophysical results of the Hipparcos space astrometry mission, ESA SP-402, Noordwijk, 615 [14] Anguita, C., Loyola, P., Pedreros, M.H., 2000, AJ, 120, 845 [15] Anguita, C, 1999, in New Views of the Magellanic Clouds, IAU Symp., 190, Y.H. Chu, N. Suntzeff, J.E. Hesser and D.A. Bolender (eds.) (San Francisco ASP), 475 [16] Kroupa, P., Roser, S., Bastian, U., 1994, MNRAS, 266, 412 [17] Geisler, D., Bica, E., Dottori, H., Claria, J.J., Piatti, A.E., Santos, J.F.C. Jr., 1997. AJ, 114, 1920 [18] Sarajedini, A., 1998, AJ, 116, 738 [19] Hill, V., Beaulieu, J.-P., 1997, in Variable stars and the astrophysical returns of the microlensing surveys, R. Ferlet, J.-P. Maillard &: B. Raban (eds.) (Editions Frontieres). 267 [20] van den Bergh, S., 1998, ApJ, 507, L39 [21] Geha, M.C., Holtzman, J.A., Mould, J.R., et al, 1998, AJ, 115, 1045 [22] Olsen, K.A.G., 1999, AJ, 117, 2244 [23] Beers, T.C., 1999, Astrophys. Space Sci., 265, 105 [24] Beers, T.C., Preston, G.W., Shectman, S.A., 1985, AJ, 90, 2089

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

M 31, M 33 AND THE MILKY WAY: SIMILARITIES AND DIFFERENCES R.F.G. Wyse1 Abstract. The large galaxies in the Local Group, as all disk galaxies, have diverse stellar populations. A better understanding of these differences, and a physical understanding of the causes, requires more detailed study of the older populations. This presents a significant challenge to GAIA but the scientific returns are also significant.

1

Introduction

Study of the resolved stellar populations of galaxies in the Local Group offers great scientific returns in our understanding of how galaxies form and evolve. The Local Group member galaxies (cf. [1]) include the three disk galaxies M 31, M 33 and the Milky Way, and numerous dwarf companions, both gas-rich and gas poor. What causes their similarities and also their diversity? There are two main aspects to galaxy formation and evolution, namely the history of mass assembly and re-arrangement and the history of star formation. The old stellar populations play a particular role in deciphering these histories, since old stars usually retain a memory of certain aspects of their early life, such as the surface chemical abundances, and often orbital angular momentum and orbital energy. The important questions concerning the mass assembly, apart from its rate, both past and present-day, include: what was the nature of the mass? - since collisionless dark matter, collisionless stars and collisional gas behave differently; what was the density distribution of any and all components? - since physical processes such as tidal stripping depend on relative densities, and dynamical friction timescale depends on mass ratios; what are the specific angular momenta and orbits? - since the coupling efficiencies of various processes depend on these. The important questions concerning star formation history include: what was the rate of star formation and how did/does it vary as function of spatial location?; 1

The Johns Hopkins University, Department of Physics and Astronomy, Baltimore, MD 21218, USA © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002029

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what was and is the stellar Initial Mass Function? - the visibility of galaxies at high redshift, their contributions to background light in different passbands, their chemical enrichment, stellar feedback, the supernova rate, gas consumption rate etc. depend on the IMF; what was/is the mode of star formation? - what fraction formed in super star clusters?; and of course - what is the connection to the history of mass assembly of the various components. Spiral galaxies are clearly diverse in their properties, for example in bulge-todisk ratio, but theories should be able to produce the galaxy population in the Local Group rather naturally, without appeal to special conditions. Thus the Local Group members are "typical" galaxies in their properties and for theory, but they are atypical for observation. From their resolved stellar populations we can obtain age distributions, chemical elemental abundance distributions, kinematics - all as a function of spatial location. The tracers that can be used include stars of a range of evolutionary stage and mass, planetary nebulae, star clusters, and gas through HII regions, 21cm emission and CO emission. The stellar properties in satellite companion galaxies provide important complementary constraints, for example, limiting the possible contribution of disrupted satellites to larger systems (cf. [2]). We have learned much about the Milky Way Galaxy from its resolved stellar populations, but we still have only an incomplete picture, and it is clear that GAIA will play a major role in furthering our understanding. Study of M 31 and M 33 with existing ground-based telescopes and with the Hubble Space Telescope has been limited, but as I will describe below, has provided clear evidence of differences in some aspects of their stellar populations and also of similarities. While detailed space motions and distances have a unique role to play in understanding how the Local Group disk galaxies decompose into different stellar components such as bulge/halo/disk/thick disk, much can be inferred from mean kinematic quantities, such as the net azimuthal streaming motion of a population. To illustrate, Figure 1 shows the specific angular momentum distributions for these components of the Milky Way. The similarity between the angular momentum curves for the bulge and stellar halo can be explained by a model in which the proto-bulge gas is ejected from star forming regions in the early halo [3], while the similarity between the curves for the thick and thin disks is expected in a model where the thick disk is a remnant of the early stages of disk formation (see below). It is clear that ejecta from the halo did not "pre-enrich" the disk. Old stars are important for deciphering both the mass assembly and star formation histories, and this poses a significant challenge for GAIA capabilities, since at a distance modulus of ~24.5, the tip of the Red Giant Branch (T-RGB) in M 31 is at / ~ 20.5 [4], and there is no good evidence for an intermediate-age population in the bulge of M 31 that would contribute Asymptotic Giant Branch (AGB) stars brighter than the tip [5]. However, significant scientific returns would be achievable with mean kinematics of red giants in M 31, M 33 and their satellites, as I describe below. I hope to convey the exciting science that could be possible were GAIA to push through its nominal limit of G = 20 (/ ~ 20), to reach below the T-RGB. Of course, for those galaxies with (intermediate-age) stars brighter than the old T-RGB, the nominal GAIA limit will still provide significant results.

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Fig. 1. Estimated angular momentum distributions for the stellar components of the Milky Way. The curves correspond to, from the left, the central bulge, the stellar halo, the thick disk and the thin disk. This figure is taken from Wyse & Gilmore [3]. I will first describe some of the advances we have made so far through study of the stellar populations of the Milky Way. I will then discuss what is known of the stellar populations of the remaining large members of the Local Group, and raise some open questions, including ones that may be addressed with GAIA. 2

The Thick Disk and Constraints on Mass Assembly of the Milky Way Galaxy

The effects of mergers between galaxies are to fatten disks, by putting orbital energy of the galaxies into their internal degrees of freedom, and to build up bulges and haloes, through a combination of heating and angular momentum and mass re-arrangement resulting from gravitational torques and bar formation, and assimilation of stars removed from their parent galaxy by tidal effects. The amplitudes of these effects are dependent on the (many) parameters of the interaction, such as mass ratio of the merging systems, gas content, orbital inclination and angular momentum (both the sense and the magnitude). The age distributions, kinematics and metallicities of the different stellar components of a galaxy - and of different tracers, such as young stars, old stars, or globular clusters - are very important in deciphering a complex situation, in which some properties can be approximately conserved (such as angular momentum of a stellar orbit or stellar metallicity) and some are not (such as the velocity dispersions of the disk stellar population). A merger between a stellar disk and a stellar satellite of around 10-20% by mass results in a fattening of the disk (as opposed to the destruction of the disk that happens for mass ratios that are more equal), and the thinness of disks can be used to constrain their merging history (cf. [6]) and cosmological parameters [7].

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Indeed recent TV-body simulations [8,9] have produced fattened disks that have spatial distributions and kinematics rather similar to the thick disk of the Milky Way Galaxy (see [10] for a recent review). This is particularly interesting for the mass assembly history, since the thick disk, at least at the solar circle, is exclusively old, as illustrated in Figure 2. We know that the thin disk has been forming stars fairly continuously over the last ~12 Gyr [15], with the consequence that if a significant merger had occurred more recently, younger stars would also be in a thicker disk. However, these younger stars are not observed in the thick disk (cf. [16-19]). Thus the last significant merger of the Milky Way occurred ~12 Gyr ago, when the globular clusters like 47 Tuc were formed. Of course, if the thick disk is not the product of a "minor" merger, but e.g. formed by slow settling of the proto-disk to the disk plane [20] then the merging history is even more quiescent!

Fig. 2. Scatter plot of iron abundance vs. B — V colour for thick disk F/G stars, selected in situ in the South Galactic Pole at 1-2 kpc above the Galactic Plane (stars), together with the 14 Gyr turnoff colours (crosses) from van den Berg & Bell [11] (Y = 0.2) and 15 Gyr turnoff colours (asterisks) from van den Berg [12] (Y = 0.25). The open circle represents the turnoff colour (de-reddened) and metallicity of 47 Tuc (Hesser et al. [13]). The vast majority of thick disk stars lie to the red of these turnoff points, indicating that few, if any, stars in this population are younger than this globular cluster. This figure is based in Figure 6 of Gilmore et al. [14].

Further, the thick disk contributes >10% of stars in the solar neighbourhood, and falls off perpendicular to the plane with a scale-height 3-4 times that of the thin disk. Thus a significant fraction, some ~30%, of disk stars at the solar Galactocentric distance, 2-3 scale-lengths from the centre, formed at lookback times of ~12 Gyr, or at redshifts ~2. This is not easily understood in the context of

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hierarchical-clustering models of structure formation, such as the cold-dark-matter scenario. In these models, the angular momentum transport that accompanies the merging process to form galaxies [21,22] leads to disks that are too small, and one must appeal to "feedback" processes to delay disk formation, to redshifts < unity [23,24]. This is perhaps another way of saying that the merging history of the Milky Way appears to be unusual in these models. But is the Milky Way unusual? What of the other large galaxies in the Local Group? There are clearly some large, relaxed-looking disk galaxies at redshifts of unity [25] - can we identify their counterparts and descendants locally? First, we need to establish the properties of the thick disk in the Milky Way far from the solar Galactocentric radius; GAIA will play a key role in this, providing accurate distances, metallicities, proper motions and radial velocities for tracer stars (main sequence turn-off stars, red giants, Horizontal Branch etc.) at distances as far as <20 kpc. 3

The Thick Disk, Bulge or Halo of M 31

The globular clusters in the Milky Way have a bimodal metallicity distribution, with peaks at [Fe/H] ~ —1.5 dex and ~—0.6 dex [26], and around one-third being in the metal-rich population. The clusters in these two peaks are further distinguished by kinematics and spatial distribution. The metal-poor population consists of the classic halo globular clusters, which are old and on orbits of low angular momentum. The metallicity and kinematics characteristic of the metalrich globular clusters (of which 47 Tuc is a member) are very similar to those of the thick disk, and these clusters are usually ascribed to this population [26,27], though their concentration towards the centre of the Galaxy has led to their association with the bulge [28,29]. If indeed the last significant merger event experienced by the Milky Way formed the thick disk, one might expect there to be globular clusters associated with it, by analogy with the young "globular clusters" (super star clusters) identified in merging systems [30]. Further, this merger could have initiated bulge formation, consistent with the similar characteristic ages of thick disk and bulge. The globular clusters of M 31 also have a bimodal metallicity distribution [31], with peaks at metallicities remarkably similar to those of the Milky Way system, and again most clusters being in the metal-poor population. Furthermore these two populations appear to be similarly distinct in their kinematics and spatial distributions, as are the two Milky Way globular cluster populations. The globular cluster systems of the Milky Way and M 31 appear to be analogues of each other. Associating the more metal-rich globulars, with peak [Fe/H] ~ —0.6, with the thick disk, as in the Milky Way, would lead to the expectation of a field thick disk with similar mean metallicity. The field stellar population of M 31 has been studied through colour-magnitude diagrams (both ground-based and from the Hubble Space Telescope) of its evolved stars and spectroscopy of bright red giant branch stars. All studies [4,32-36], following the pioneering work of Mould & Kristian [37], find that the dominant

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field population probed down the minor axis has a mean metallicity2 of around ~—0.6 dex, from projected distances of ~5 kpc out to ~20 kpc (the "bulge" minor-axis effective radius is ~1.5 kpc [38], significantly larger than that of the Milky way). The metallicity distribution is asymmetric, and can be fit by the superposition of two populations, metal-poor and metal-rich, with peaks similar to the globular clusters, at ~—1.5 dex and ^—0.6 dex. The bulk of the stars, even out at 20 kpc, is in the metal-rich population. Thus unlike the case for the globular clusters, the field stars of the "halo" in M 31 are predominantly metal-rich. It should be remembered that these field stars are members of Baade's "Population II" [39,40], raising the issues of which stars in the Milky Way should have been identified as "Pop II" - perhaps [41] the members of the Milky Way thick disk, whose mean metallicity is comparable to that of the dominant population in M 31's "halo". Indeed, perhaps the "halo" in M 31, which is rather flattened with an axial ratio of ~0.6, is actually a thick disk (cf. [41]). This could have been formed during a significant merger - as discussed more fully in Ibata's contribution, wide-area star counts of the evolved population in the "halo" of M 31 have revealed a large overdensity most easily explained as a remnant star stream from tidal interactions, albeit of the same high mean metallicity. Mean kinematics, as could be possible with GAIA, would provide further signatures of "streams". The red giant luminosity function, in fields at projected distances from the centre of ~1 kpc to ~20 kpc [4,42], is consistent with no young, luminous AGB stars, providing a weak limit on the age distribution of the bulge/halo/thick disk of M 31, as older than a few Gyr. The red giant luminosity functions are in fact very similar to that of the evolved stars in the Milky Way bulge (measured in Baade's window, 4° from the centre), for which we know from deep photometry below the turnoff that the population is old [43]. Optical imaging of fields at projected distances from the centre of ~1 kpc also show no evidence for stars brighter than the tip of the RGB (after taking careful account of blending; [5,44]). The presence of RR Lyrae stars in the bulge/halo of M 31 [45] argues for an old component, age >10 Gyr. Horizontal branch morphology can provide clues, though is not yet available; ground-based data thus far have prohibitively large errors by the V > 25 level of the HB. HST studies of M 31 up to now have been primarily globular cluster fields, mostly in fields with too much disk contamination to study the field halo/bulge. Even more intriguing is the fact that colour-magnitude diagrams for fields in lines-of-sight that should be predominantly outer disk have a RGB morphology very similar to that of "halo"-dominated fields [46], with an additional metalrich component that may be "thick disk" [47] or simply the thin disk. There is apparently a significant old component in these outer disk fields, with important implications for the onset of disk formation [46], as indicated above.

2 Most of these metallicities are based on the colour of the red giant branch and are subject to calibration uncertainties including the elemental abundance mix.

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Or is the disk so warped that one cannot calculate reliably its contribution in a given line-of-sight, based on simple surface brightness profiles? Thus the CMDs of M 31 offer fascinating clues to the past history of our nearest large galaxy, but kinematics and metallicities are required to untangle the different populations projected into the same line-of-sight. Radial velocities of the bright giants are possible with 10-m class telescopes [34]. Multi-band wide-field mapping of the field population below the tip of the RGB i.e. I > 20.5 is feasible with existing ground-based telescopes; GAIA could provide the information necessary for their interpretation through measurements of mean/systematic motions of populations defined by, for example, colour or position (as a reminder, at the distance of M 31, ~750 kpc, expected individual proper motions are less than ^100 /xarcsec/yr, somewhat less than the expected accuracy of GAIA measurements for stars with G = 20). The surface brightness at the effective radius of the "halo" of M 31 is HB ~ 22 mag/sq arcsec [38], and determining the limiting background stellar surface brightness at which GAIA will achieve its full accuracy is obviously important. Out at 20 kpc along the minor axis, where the bulge field is still metal-rich, the surface brightness is only fj,y ~ 30 mag/sq arcsec [48]. Even old, metal-rich stellar populations can contain small numbers of stars brighter than the T-RGB, as evidenced by the handful of Long Period Variables in the globular cluster 47 Tuc [49]. These are plausibly in the Thermally-Pulsing (TP) phase of the AGB [50] and their increased luminosity relative to metal-poor stellar populations may be related to mass loss at the Helium shell flash that marks the onset of the TP-AGB. Further, non-variable bright AGB stars are expected as the descendents of any "Blue Stragglers" that may have formed, either in the field itself or perhaps in globular clusters that were later disrupted. Identification of these rare stars, possible through the full coverage across the face of the galaxy with GAIA, would be exciting. 4

M 33 - halo/bulge and clusters

The early work of Mould & Kristian [37] established that the field stars of M 33 some ^7 kpc projected distance from the centre of that galaxy, along the minor axis and thus expected to have little contribution from the disk, have a mean metallicity of only ~ — 2 dex, with a small spread. There is a kinematic "halo" as traced by the globular clusters [51]. Analysis of the CMDs resulting from deep imaging with the Hubble Space telescope [52] has shown that some of these "halo" clusters have a red horizontal branch despite low metallicity (~—1.5 dex), perhaps indicating a younger age (~7 Gyr), with others probably as old as the classical Galactic halo globular clusters. The field surrounding the globular clusters studied with HST are disk-dominated and show a complex star formation history [52]. Luminous star clusters have been identified across the face of M 33 from HST images [53,54], with ages (inferred from integrated colours) ranging from <107 yr to the ~1010 yr of classical halo globular clusters. Derived masses are in the range of 102M0 to 106M0 and correlate with age, but there are apparently clusters of masses greater than ~104 M© with ages of only a few hundred million years [54].

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There are some similarities to the populous intermediate-age clusters in the Large Magellanic Cloud [55] - is there some aspect of the star formation process in very late-type disk galaxies that favours populous clusters? The luminous stars in these clusters should be easily accessible to GAIA, allowing the association of the parent clusters with disk, thick disk, bulge or halo. Ground-based near-IR (J, K) imaging with adaptive optics on the CFHT, of the central regions of M 33 (inner 18", or ~50 pc) find the fascinating result [56] that there is a strong AGB component, indicative of a burst of star formation 13 Gyr ago, but with metallicity only < — 1 dex, much lower than the metallicity of the inner disk inferred from HII regions, of around the solar value (e.g. [57]). Why is the M 33 inner bulge so different from that of M 31 or of the Milky Way? How far out does the AGB component extend? Kinematics of the AGB population, and a larger-scale survey, are of obvious importance to attempt to understand the connections between disk and "bulge", and the metal-poor "halo". These stars are brighter than the Tip-RGB (by some 2.5 mag in the X-band, less so in the y-band) and should be amenable for study with GAIA. 5

M 32 - an Elliptical Since When?

While not strictly part of my remit, the compact dwarf elliptical galaxy M 32 offers an intriguing target for GAIA. The evolution of this galaxy has clearly been strongly influenced by its proximity to M 31, and indeed a very plausible scenario invokes severe tidal truncation [58] perhaps of a former disk galaxy, to leave the central bulge [59]. There is a ubiquitous bright AGB population in M 32, wellmixed with the underlying older stars [60]. Integral-field spectroscopy of the inner regions suggests that the typical population has around solar metallicity and an age of ~4 Gyr [61]. It has been speculated that the bright AGB stars are the remnant of a merger of some smaller system with M 32 itself [60], or the result of gas inflow, star formation and mixing during the stripping of a disk galaxy [59]. These bright stars are ~3 mag brighter than the TRGB in the /C-band, and again their mean kinematics should be measurable. This information, especially if the lower luminosity (older) stars are also accessible by pushing GAIA to its limits, should allow us to distinguish these two possibilities. The proper motion of the centre-of-mass of M 32, which should be measurable with GAIA, is obviously very important for deciphering the orbit and the past history of the interaction between M 31 and M 32. 6

Summary

Cosmic variance requires that we confront theories of galaxy formation and evolution with the detailed properties of as diverse a sample of galaxies as possible. The Local Group offers the opportunity to study large galaxies with similar large-scale morphologies but different present-day stellar populations. GAIA could provide kinematic, distance and metallicity information to aid the deciphering of the histories of these different galaxies and thus the physics of galaxy evolution.

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I would like to thank the organisers for inviting me to this stimulating school, and for their financial support. I really enjoyed being back at Les Houches.

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LOCAL GROUP DYNAMICS WITH GAIA R. Ibata1

Abstract. The GAIA satellite will bring about a revolution in the understanding of the dynamics of the Local Group. Here I discuss some salient problems that may be solved with the expected GAIA dataset. 1

Introduction

Over much of the Universe we are permitted a restricted view in projection. We see positions and can measure radial velocities, and have therefore only half of the full six-dimensional phase space information of astronomical structures. This of course greatly limits our understanding of their dynamics. After the GAIA mission, the Local Group will be the only group-sized region for which we will have a nearly complete view of the phase space, and the remaining parameter, distance, may still be estimated from photometry. This will allow us to study the internal dynamics of the Local Group members, and thereby the distribution of the dark matter on small scales. We will be able to study the stellar substructure of the outer Halo, and investigate the existence of steams. The space motions of individual galaxies will be obtained, from which we will be able to answer the question of whether they had a common origin, and what the influence of their past interactions has been. 2

Internal Dynamics

Studying the internal dynamics of the nearby satellite galaxies of the Milky Way is a feasible goal for GAIA. With a measurement accuracy equivalent to ~2 km s^1 for individual bright stars in the Sagittarius dwarf and in the LMC, it will be strait-forward to measure the proper motion dispersion due to the intrinsic dispersion of velocities in these objects. Coupled with accurate radial velocities, these measurements will allow us to develop realistic models of their internal structure, with which we may understand the role that self-gravity has in maintaining their structures against the disruptive forces due to the Galactic tides. Observatoire de Strasbourg, 11 rue de 1'Universite, 67000 Strasbourg, France © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002030

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The case of the two dwarf galaxies Draco and Ursa Minor, with their high apparent mass to light ratio (M/L ~ 100) is even more interesting. Several studies have questioned their dark matter content. For instance, Klessen & Kroupa [1] find that completely unbound remnants distributed with their tidal streams along the line of sight may give rise to clumps of stars on the sky that appear similar to the observed dwarf spheroidal galaxies. Their models contain no dark matter, yet they have a high line of sight velocity dispersion, due to the fact that the stars are distributed over a large distance along the line of sight, probing velocities at different positions along the orbit of the disrupted remnant. If this model is correct, the proper motion dispersion should be smaller than the line of sight velocity dispersion, a measurement which is feasible with proper motions accurate to GAIA specifications. Furthermore, of the ensemble of such disrupted galaxies, the majority would not be aligned along the line of sight, and the many other disrupted steams required by this scenario should easily be found from the all-sky catalog. 3

Outer Halo Substructure

Helmi et al. (1999, [2]) have shown that GAIA measurements can easily recover large substructures in the halo of the Milky Way. The disrupted streams from satellite galaxies retain much of their initial kinematic traits and remain easily distinguishable from the background. The kinematics of such streams are extremely useful for measuring the distribution of galactic mass. One can integrate backwards in time from the present positions of the observed stream stars, with the constraint that all particles once had to reside within a bound galaxy. This gives a strong constraint on the galactic potential. Johnston et al. (1999, [3]) have shown that with proper motion measurements on as few as 10 stars, one can determine the potential to about 10% accuracy, and even time-variations of the potential can be recovered [4]. 3.1

Are There Halo Streams

Do any such Halo streams exist? Currently one strong stellar stream is known, coming from the tidal disruption of the Sagittarius dwarf galaxy around the Milky Way. This stream was identified in an all high-latitude-sky survey of carbon stars (luminous red AGB stars). These stars are less than about 7Gyr old and can therefore trace recent accretions into the Milky Way halo of galaxies that contained a young or intermediate age component. The left-hand panels of Figures 1 show the distribution of observed carbon stars; obvious clumps are seen in both position and velocity, which match the expected position and velocity of the orbit of the Sagittarius dwarf around the Milky Way. Since the stellar stream of a disrupted low-mass satellite is expected to follow closely the orbit of the progenitor, it appears quite likely that the stellar stream of the Sagittarius dwarf has been traced by the carbon stars. In [5], we undertook TV-body simulations of the disruption of the Sgr dwarf galaxy with the particular aim of reproducing the observed

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Fig. 1. Aitoff projections of the positions of Halo carbon stars (left-hand panels) and the end-point structure of an TV-body model of the disruption of the Sgr dwarf (righthand panels). The upper panels display colour-coded Heliocentric radial velocities, while the bottom panels show the stellar distances, colour-coded as a function of the observed apparent magnitude [5].

distribution of C-stars. We modelled the Milky Way potential as a series of rigid potentials, and studied in detail the variation of the kinematics and position of the stream as a function of the mass distribution of the Halo. The main result is clearly seen in the data of Figures 1: the carbon stars lie along a great circle on the sky. In a spherical potential, there is no torque on the stream, the stream experiences no precession, and follows a great circle orbit. In a flattened potential, however, the torque due to the flattening precesses any non-polar or non-equatorial structure, and in general a stream can not be aligned on a great circle. On the high-hand panels of Figures 1 we show the result of an TV-body simulation in an oblate Halo that is flattened in density to qm = 0.9. Halo mass distributions flatter than this are inconsistent with the observed distribution of carbon stars. With these data alone, we see that we can begin to place constraints on the distribution of the (dark) mass in the Halo. But we have had to assume certain functional forms for the circular velocity curve of the Galaxy. Proper motions of just a few stream stars would break the degeneracy, and vastly improve our understanding of the Galactic mass distribution in the region of the Halo where the Sagittarius stream resides, that is, between ~12 kpc and ~60 kpc.

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Fig. 2. Surface density of red giant branch (RGB) stars over the outer south-eastern halo of M 31. An over-density of stars is clearly seen as a stream extending out of that galaxy close to its minor axis [6]. The Milky Way is not the only galaxy with faint stellar streams. In a recent survey [6], we have recently discovered evidence that M 31 also has a similar stream (Fig. 2), probably due to the ongoing tidal destruction of the two companions M 32 and NGC 205. The brighter members of this stream have / ~ 20.5, at the limit of the foreseen GAIA catalog. If such stars can be observed with GAIA, they will provide an invaluable probe of the mass distribution in the outer regions of M 31, for much the same reasons as detailed above for the Sagittarius stream. The only two halos of large spiral galaxies that have been surveyed to a depth equivalent to a surface brightness limit of XV ^ 31 mag/arcsec2 are those of the Milky Way and Andromeda, and a single giant stellar stream has been found in both these systems. The existence of the Sgr and And streams suggests that giant stellar streams are common features of galaxy halos. It would appear that only a few streams are the dominant stellar population of the outer halo, and that halo stars cannot possibly trace the dark halo. 3.2

A Clumpy Dark Halo?

A generic prediction of Cold Dark Matter models of the formation of structure in the Universe is the existence of copious amounts of substructure in galaxy halos (in fact, there is a hierarchy of structure down to the smallest scales probed by these simulations). The halo of a large galaxy like the Milky Way should contain

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many hundred substructures. Furthermore, these substructures are predicted to be strongly centrally-condensed which renders them effectively indestructible to tidal forces. We have performed numerical simulations [7] to investigate the evolution of a 106 M0 globular cluster in the Galactic potential. The globular cluster is modelled as a King model, with parameters similar (but slightly more extended) than the Galactic globular cluster Omega-Centauri. In Figures 3 we show the end-point result of the integration of the initially spherical self-gravitating model in a smooth Galactic potential. The Galactic tidal forces have induced the formation of a tidal tail, which at the end of the simulation (10 Gyr) stretches in a band across the sky. The width of the band is very narrow - comparable to the initial tidal diameter of the King model. The bottom panel shows the effect of the presence of a population of 500 dense halo substructures, of mass down to 106 MQ. Even though the total mass in the substructures is only 1 % of the total mass of the Halo, the cumulative effect of many close encounters with these dense substructures heats the tidal tail, which now has become substantially wider than in the smooth simulation. We have performed such simulations for a wide range of globular cluster initial conditions, drawing them from a halo distribution function. A similar effect to that shown in Figures 3 is seen in all these simulations. This consequence of cold dark matter substructure can be verified with GAIA - a massive globular cluster would leave some 1000 giant-branch stars spread over the Halo, all sharing the same orbit. With proper motions velocities, and positions it will be straightforward to identify such streams. Given the current disruption rate of globular clusters, several hundred such objects are expected to have initially inhabited the Galaxy - so we can expect to find many such streams. GAIA data should therefore allow us to investigate the existence of cold dark matter halo substructure down to masses comparable of that of the globular clusters themselves (~105M0). 4

Space Motions of Galaxies

The proper motions of galaxies can be used to probe the global potential they reside in. This will clearly be undertaken with the mean proper motions of the Galactic satellites determined from GAIA. By combining GAIA with NGST, however, this sort of analysis is even possible for Andromeda satellites. The systematic centroiding error with HST is 0.002 pixels [8] and a factor of 3 better precision can be expected from NGST. Suppose several NGST images of some Andromeda stellar population are taken over the course of the GAIA mission. On their own such a dataset would not provide particularly accurate proper motion information, since it will be limited by the number of compact background sources (at best, one could point in the field of a single quasar). However, the NGST frames can be tied into the GAIA reference frame. With this setup, it will be possible to measure accurate proper motions to many magnitudes below the GAIA detection limit, and thereby obtain proper motion measurements of individual stars in the M 31 neighbourhood accurate to ~40km s~1.

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Fig. 3. Aitoff projections of the distribution of stream stars from TV-body simulations of a disrupting globular cluster in a smooth halo (left-hand panels) and a halo containing NFW substructure (right-hand panels).

Another interesting problem that it will be possible to investigate is whether the Galactic satellites have a common origin? A striking feature of the Galactic satellite system is its non-uniform distribution on the sky; indeed these objects appear to be distributed along a few preferred planes [9]. This would suggest that families of satellites exist with a common origin - presumably from the tidal disruption of some ancient progenitor. Accurate proper motion information is necessary to investigate this possibility. 5

Dynamical Evolution of the Local Group

What role does the interaction of dwarf galaxies with their large neighbours play in galaxy evolution? In the Milky Way there are two large on-going interactions: that of the LMC-SMC binary with the Milky Way and the interaction of the Sagittarius dwarf galaxy with the Milky Way. Both of these interactions strongly affect the stellar composition of the dwarf galaxies, but the dwarf galaxies in turn also affect the Milky Way. by corrugating the Milky Way, and warping its disk. We have studied the case of the Sgr dwarf, which collides with the outer disk of the Milky Way every ~1 Gyr, and have found that these repeated collisions may induce starformation and strongly perturb the outer regions of the Galaxy [10]. A similar

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interaction may currently be ongoing in M 31 with the accretion of M 32, NGC 205 and the Andromeda Stream [6]. LMC - SMC - Milky Way: [11,12]. To quantify this issue, the system needs to be modelled accurately, and the missing information are high quality proper motion measurements, which will become available with the GAIA mission. 6 Conclusions The GAIA proper motion database will dramatically improve our understanding of the dynamics of the Local Group. The internal dynamics of the dwarf spheroidal and dwarf irregular satellites of the Milky Way will allow us to ascertain their dark matter content and study their tidal deformation. Proper motions of tidal stream stars, together with distance estimates from photometry will allow us to measure the mass distribution of the dark halo, and its evolution. By finding the long stellar streams from (possibly defunct) globular clusters will we also be able to discover whether the dark matter substructure predicted by cold dark matter theories is present. From the mean motions of the Local Group galaxies, we will be able to study the role of galaxy interactions in their evolution, determine how often and how drastic galaxy collisions between the small mass systems or between the small and high mass galaxies are, and reveal what the past history and future dynamical fate of the Local Group is. References [1] Klessen, R., Kroupa, P., 1998, ApJ, 498, 143 [2] Helmi, A., Zhao, H., de Zeeuw, T., 1999, in ASP Conf. Ser. 165, The Third Stromlo Symposium: The Galactic Halo, 125 [3] Johnston, K., Zhao, H., Spergel, D., Hernquist. L., 1999. ApJ, 512. L109 [4] Zhao, H., Johnston, K., Hernquist, L., Spergel. D.. 1999, A&A, 348, L49 [5] Ibata, R., Lewis, G.P., Irwin, M., Totten. E.. Quinn, T., 2001a, ApJ, 551, 294 [6] Ibata, R., Irwin, M., Lewis, G.F., Ferguson, A., Tanvir. N.. 2001b, Nature, 412, 49 [7] Ibata, R., Lewis, G., Irwin, M., 2001, in preparation [8] Anderson, J., King, L, 2000, PASP, 112, 1360 [9] Lynden-Bell, D., Lynden-Bell, R., 1995, MNRAS, 275, 429 [10] Ibata, R., Razoumov, A., 1998, A&A, 336, 130 [11] Murai, T., Fujimoto, M., 1980, PASJ, 32; 581 [12] Putman, M., et al., 1998, Nature, 394, 752

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

GAIA GALAXY SURVEY: A MULTI-COLOUR GALAXY SURVEY WITH GAIA M. Vaccari

Abstract. The performance expected from a galaxy survey to be carried out with GAIA, the GAIA Galaxy Survey, is outlined. From a statistical model of galaxy number density, size and surface brightness distribution, and from detailed numerical simulations based on real images, it is conservatively estimated that GAIA would be able to detect and observe about 3 million galaxies brighter than V — 17 and to provide multi-colour and multi-epoch broad-band photometry of these with an end-of-mission angular resolution of ~0.35 arcsec and a photometric accuracy of ~0.2 mag/arcsec2 at nv = 20 mag/arcsec2. The substantial scientific case for performing such a survey and the additional efforts required in terms of mission preparation, operations and telemetry are also discussed.

1

Introduction

Since the very beginning of the feasibility studies, the GAIA mission design was driven by the need of determining the position and the brightness of huge numbers of stars with the uttermost accuracy. During the Concept and Technology Study completed in July 2000 (see [1] and [2]), however, it clearly emerged that such a star-driven mission could also provide, several socalled by-products which would substantially enrich its already impressive scientific yield. In particular, it was realized that the scientific case for GAIA imaging of high-surface brightness sky regions such as the central regions of nearby galaxies was dramatic. The issues connected with this opportunity have been addressed in a certain detail in a number of studies (see [3-6]), and such observations were included in the mission baseline design as described in [2] under the name of GAIA Galaxy Survey. In this paper the current ideas on the implementation of such a survey and on the expected performance are presented. 1 Dipartimento di Astronomia and CISAS "Giuseppe Colombo", Universita di Padova, Vicolo dell'Osservatorio 2, 35122 Padova, Italy e-mail: [email protected]

© EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002031

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In Section 2, the overall strategy for galaxy detection and observation with GAIA is outlined. In Sections 3 and 4 the detection and observation, respectively, are discussed in greater detail and results of dedicated studies are presented. In Section 5 the substantial scientific case for performing such a survey is briefly sketched, and in Section 6 the additional efforts required in terms of mission preparation, operations and telemetry are discussed. Only the measurement of relatively large enhancements of the surface brightness with respect to the sky background is discussed here, although it is believed that the rather similar issue of the observation of Galactic Nebulae could be addressed along the same lines. The measurement of the surface brightness of the sky background, instead, calls for a substantially different approach, as described in [7]. 2

Galaxy Detection and Observation with GAIA

During its scientific operations, the GAIA satellite will continuously spin about its symmetry axis, and the charges contained in the CCD pixels will correspondingly be shifted along-scan to integrate the image for a longer exposure time, a technique known as Time-Delay Integration (TDI). In order to limit the CCDs' reading frequency and the corresponding readnoise and telemetry rate, a dedicated CCD readout process was devised, consisting in detecting objects as they enter the field of view, determining their position, magnitude and signal-to-noise ratio, and, if the latter exceeds a certain limit, collecting data from regions around such stars only. While this approach was the subject of detailed studies as far as point-like objects were concerned, leading to the definition of the Astro telescopes' focal plane and the CCD binning strategy described e.g. in [8], the process of galaxy detection and observation called for a rather different approach in order to identify and measure faint surface brightness variations. As first suggested in [9], galaxies could be detected in the Astro Sky Mapper (ASM) as an average surface brightness significantly in excess over the local sky background and observed in different colours in the Broad Band Photometer (BBP). This observing strategy preventing from optimally observing stars whenever a galaxy is being observed (which is however less than 1% percent of the time), it could be implemented in one of the two Astros only. In order to follow this general idea, one had to optimize: • the size of the areas over which the average surface brightness and the local sky background values are computed. It is presently envisaged to determine the former through trimmed median filtering of ASM 1 samples of 2 x 2 pixels and the latter over a few degrees of scan with the same algorithm. However, the exact method used to determine the local sky background is not of interest for our purposes, since the readnoise is by far the dominant noise source; • the value for the detection area and S/N limit so that useful data are transmitted to the ground without being swamped in less interesting data from

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the Milky Way or the zodiacal light. The larger the detection area, the fainter the detection limit can be for objects of constant surface brightness, if the error on the sky background is negligible. On the other hand, the detection area should be small enough that a large number of small objects would not be missed; • the sampling scheme for galaxy observations, so as to establish a trade-off between angular resolution, readnoise and telemetry. As with stars, a larger sample size yields a smaller error on the (average) surface brightness, lower readnoise and telemetry rate but also a lower angular resolution. This aspect is critical for the observations of galaxies, since their potentially very large angular extension will require in some cases the full readout of CCDs. In the context of the studies carried out to demonstrate the feasibility of the GAIA Galaxy Survey (summarized in [6]), these questions have been given satisfactory (if subject to further improvements) answers. 3

Detection Via Statistical Formulae

As for the detection, a statistical model of galaxy number density, size and surface brightness distribution was developed in order to characterize the "typical" galaxy (see [3]). While this model obviously cannot do justice to the well-known strong individuality displayed by many galaxies, it is believed to yield sufficiently reliable results when, as in our case, only statistical properties, i.e. properties averaged over large samples, are of interest. On the basis of such a model, adopting current estimates of GAIA sensitivity and noise, and adapting the statistical formulae for the estimation of the S/N obtained in the observation of point-like objects presented in [10] to the case of extended objects, one can estimate whether a given galaxy could be significantly detected above the sky background. It is thus concluded that a typical galaxy of I = 17 would be detected about 60% of the times (i.e. 50 times on average during a 5-year mission) with a S/N > 4 using an area of 2 x 2 arcsec2 for the detection, as shown in Figure 1. According to our afore-mentioned statistical model, there are about 3 million galaxies brighter than this limit away from the Galactic plane (i.e. with |b| > 15, where galaxy detection shouldn't be hampered by the high density of stars). It can thus be conservatively concluded that GAIA would be able to reliably detect at least 3 million galaxies, in agreement within a factor of two with the more optimistic estimation obtained in [5] following a different approach. Bright galaxies such as those appearing in [11] would thus typically be detected down to cfaet — 400 Mpc or 2;det ~ 0.1. 4

Galaxy Observation Via Numerical Simulations

In order to assess the angular resolution and the photometric accuracy obtainable from GAIA galaxy observations, complete simulation software based on HST

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Fig. 1. Galaxy detection: a galaxy is detected as an average surface brightness significantly in excess with respect to the sky background over areas of 2 x 2 arcsec2. Data from these areas (solid lines) and from the surrounding regions (dashed line) should then be readout from the CCDs and transmitted to the ground. WFPC2 images and generating representative all-mission sets of GAIA observations of the same field was developed. Among other things, this has also allowed to determine the optimal sample size and to test different stacking techniques. The Astro PSF resulting from different smearing effects was modelled using the tools provided in [12], whereas the expected CCD readnoise was calculated using the formulae given in [13] and conservatively assuming full CCD readout in all cases. The results of the simulations are shown in Figure 2, where the original HST WFPC2 900 s image is compared with GAIA BBP flux map obtained from stacking of 50 observations of 0.9 s each, i.e. with an effective exposure time of 45s, and a sample size of 6 x 4 pixels, chosen as the best trade-off between the needs of angular resolution and photometric accuracy. Notwithstanding the great difference in exposure time, most details are still clearly visible in GAIA flux map, and the median photometric accuracy is of ~0.2 mag/arcsec2 at a median surface brightness of ^v — 20 mag/arcsec2, interestingly very similar to the predictions based on statistical formulae taking into account photon noise and readnoise. The angular resolution achievable in GAIA BBP flux maps can instead be evaluated in Figure 3, where two bright HII regions with a separation of less than 0.5 arcsec are clearly resolved in GAIA flux map as well. More accurate estimates of the angular resolution based on model PSFs give an angular resolution as low as 0.35 arcsec, comparable to superb ground-based observing sites in the rare moments of excellent seeing. Galaxy observations could therefore be profitably carried out in Astro 2, where a sample size of 6 x 4 pixels is not in conflict with the baseline sample size of 6 x 8 pixels adopted for the observation of stars.

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Fig. 2. HST Images and GAIA Flux Maps: HST WFPC2 900 s image of the M100 Spiral Galaxy and GAIA BBP simulated flux map obtained from 50 observations, thus with a total effective exposure time of 45s. The side of both images is 16 arcmin.

Fig. 3. Angular Resolution of GAIA Flux Maps: a small portion near the center of the same HST WFPC2 image and GAIA BBP flux map shown in Figure 2, showing two HII regions with a separation of about 0.5 arcsec. 5

Scientific Case

The scientific case for a wide-angle high-resolution photometric (and possibly astrometric, even though the latter issue has not been studied in detail as yet) survey of bright galaxies is enormous. The high reliability catalogues extending down to low Galactic latitudes and high spatial resolution imaging of all sufficiently high

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surface brightness galaxies provided by GAIA will make up a remarkably vast, homogeneous and well-defined database that will have a tremendous impact at two levels: for statistical analysis of the photometric structure of the central regions of tens of thousands of well-resolved galaxies, and for the study of the large scale structure of the Local Universe from the spatial distribution of all detected galaxies. Detailed analysis of the inner luminosity profiles of a large sample of galaxies will define the true incidence of core structures and complex morphologies. Inner color gradients will map recent star formation and dust lanes, and central luminosity cusps may indicate massive black holes. Multi-colour and multi-epoch information will allow the identification of variable sources for dedicated follow-up by other telescopes. More in general, in conjunction with the proposed high-resolution survey for the detection of stars fainter than the nominal detection limit and the low-resolution survey of the sky background surface brightness, GAIA promises to yield the first uniform measurements of brightness gradients of the "real sky" at all spatial scales. 6

Mission Preparation, Operations and Telemetry

Several aspects of the picture which was outlined require careful definition. The galaxy detection process must be validated through the development of a dedicated algorithm, suitable for the reliable detection of faint extended objects on a bright complex background. One must then make sure that the Astro CCDs can be operated so that they can switch to the galaxy observation mode, possibly reading the full CCD, whenever a galaxy is detected. The opportunity of galaxy observations in the AF17 and in the SSM, where the much higher sensitivity and spectral resolution, respectively, would result in a much higher accuracy in surface photometry and astrophysical characterization of the observed galaxies, should be discussed. Finally, but perhaps most importantly, it must be evaluated how the required telemetry (on average 120 kbits/s/band before compression, where most readout samples will carry little signal and thus allow efficient compression) can be accommodated within the overall telemetry budget. 7

Conclusions

The proposed GAIA Galaxy Survey will provide a nearly all-sky, multi-color and multi-epoch astrometric and photometric galaxy survey. In the framework of the present mission design, the feasibility, scientific case and optimization of such a survey were discussed. From both statistical considerations and numerical simulations it appears that galaxies could be reliably detected in the ASM 1 within square areas of 2 x 2 arcsec2 and observed in the Astro 2 BBP with a sample size of 6 x 4 pixels. The first choice should yield the highest number of detected galaxies without too many false detections, whereas the second one would provide the best trade-off between angular resolution, readnoise and telemetry. Under the present assumptions about the instrumental performance of the satellite payload,

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and provided some effort is put into its planning in the near future, the following measurement capabilities are expected from a 5-year mission: • At least 3 million galaxies brighter than / ~ 17 will be detected. • All detected galaxies will be observed with a 0.35 arcsec angular resolution and an all-mission accuracy in surface photometry of 0.2 mag/arcsec2 at 20.0 mag/arcsec2 in the V band. • Multi-color (in the 45 BBP broad bands) and multi-epoch (c±50 epochs) information will be available for all observed objects. White light and mediumband photometry could as well be obtained. These outstanding measurement capabilities will result in a unique dataset providing state-of-the-art information on galaxy spatial distribution and surface photometry over a well-defined sample extending down to low Galactic latitudes, which is in turn expected to yield significant scientific results concerning the large-scale structure of the Local Universe and the multi-color photometric structure of galaxy innermost regions. References [1] Ferryman, M.A.C., et al., 2001, GAIA: Composition, Formation and Evolution of the Galaxy, A&A, 369, 339 [2] ESA 2000, GAIA: Composition, Formation and Evolution of the Galaxy, Concept and Technology Study Report, ESA-SCI(2000)4 [3] Vaccari, M., H0g, E., 1999a, Statistical Model of Galaxies, Technical Report GAIA_CUO_61, HTML version available at http://hal.pd.astro.it/~mattia/research/smog/ [4] Vaccari, M., H0g, E., 1999b, Simulated GAIA Observations of Galaxies, Technical Report GAIA-CUO-69 [5] Lindegren, L., 2000, Detection of faint galaxies with GAIA, Technical Report GAIA_LL_29 [6] Vaccari, M., 2000, GAIA Galaxy Survey, Master Thesis, University of Padova. Available at http://hal.pd.astro.it/~mattia/research/ or upon request writing to [email protected] [7] H0g, E., 2002, EAS Publ. Ser., 2, 321 [8] H0g, E., 2002, EAS Publ. Ser., 2, 27 [9] H0g, E., Fabricius C., Knude J. and Makarov V.V. 1998, GAIA Surveys of Nebulae and Sky Background, Technical Report SAG_CUO_32 [10] H0g, E.. Fabricius C.. Knude J. and Makarov V.V. 1999, Sky Survey and Photometry by the GAIA Satellite, Technical Report SAG_CUO_53 and Baltic Astron., 8, 25 [11] de Vaucouleurs G., de Vaucouleurs A., Corwin H.G., et al., 1991, Third Reference Catalogue of Bright Galaxies (Springer) [12] Lindegren, L., 1998, Point Spread Functions for GAIA including aberrations, Technical Report GAIA_LL_25 [13] Vannier, M., 1998, Noise of GAIA Astro Instrument, Technical Report GAIA_MV_04

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

MULTI-COLOUR PHOTOMETRY WITH GAIA OF THE DIFFUSE SKY BACKGROUND E. H0gx and K. Mattila2 Abstract. The report discusses the possible multi-colour photometry of the diffuse sky surface with the Astro and Spectro telescopes of GAIA. The ordinary photometry of faint stars will give good results of the background for at least 500 million spots on the sky. Measurement from about 100 of these spots in a small area could be averaged to obtain a precision of about 0.5 S'lo of GAIA medium-band photometry in each of the 5 million areas. It is concluded that GAIA mediumband photometry is suited to tackle a whole range of astrophysically interesting diffuse sky components. After modelling and subtracting the time-variable Zodiacal Light, GAIA could provide multi-wavelength all sky maps of the low galactic latitude Diffuse Galactic Light and the high latitude Galactic Cirrus Clouds. Possibly also the Extragalactic Background Light could be detected.

1

Introduction

The possible multi-colour photometry of the sky surface with the Astro and Spectro telescopes of GAIA has been discussed in some detail in the technical report [1] of which a summary is given here. This photometry makes use of the data in the patches for stars, thus no extra telemetry is required, only a proper data reduction on the ground, for instance as described in [2,3]. We only discuss the diffuse sky background, not however the locally increased brightness on nebulae or galaxies; GAIA measurement of galaxies has been studied in [4] and [5]. The reference paper on diffuse night sky brightness is [6]. The ordinary photometry of the faintest stars will give gooc results of the background for at least 500 million spots on the sky. The precision per spot for the mission average values is derived. At a typical sky brightness of JJLV = 23.0 mag/arcsec2 at high ecliptic and galactic latitudes (covering most of the sky) 1 2

Copenhagen University Observatory, Juliane Maries Vej 30, 2100 Copenhagen 0, Denmark Observatory, P.O. Box 14, Taehtitorninmaki, University of Helsinki, 00014 Helsinki, Finland © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002032

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a precision of 0.003 mag is obtained in G and about 0.06 mag in all medium width photometric bands for spots of 7 arcsec diameter. We conclude that GAIA medium-band photometry is suited to tackle a whole range of astrophysically interesting diffuse sky components. The required accuracy and low level of straylight can probably be realised. A main issue to be solved is the separation of the variable zodiacal light component from the two other known components of diffuse galactic light and galactic cirrus. A further yet unknown component, extragalactic background light, might then be detected. The multi-colour capability of the GAIA medium-band photometer is important here. 2

Measurements and Precision

Some characteristics of the various detection chains and the detailed results for the Astro and Spectro telescopes are given in [1]. The sky areas per patch obtained from the Spectro telescope are much larger than from Astro, and the total noise per sample is much smaller. This, together with longer integration times, leads to a much better precision for surface photometry with the Spectro telescope. The Spectro sky mapper measures the sky in the G band and we assume that effectively 30 arcsec2 contribute. The G band employs no filter, the whole CCD response corresponds to a central wavelength of 700 nm and a FWHM = 800 nm. For the medium-band photometer in the Spectro telescope the patch covers an area of 7.0 x 2.0 arcsec2, and the mission average is therefore obtained over a circle with diameter 7 arcsec, centred on a star. We assume that effectively 10 arcsec2 are available for the surface photometry in each band. The precision per spot on the sky given in Table 1 is calculated from the following formulae. Let b be the counts per sample from the sky during the integration time, and r be the total noise from the reading of a basic sample. The standard error of the sample is then

with b calculated as

where S is the count rate per sample, A is the sky area of the patch, t is the integration time per sample, and n^ is the number of samples per patch containing background. The standard error per sample of the mean value for the mission is

where np is the number of patches collected during the mission. Usually one patch per scan of the star is collected, but sometimes (for P and u) 2 or 3 patches are collected in the medium-band photometer.

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Table 1. The diffuse surface brightness measurements with the Spectro telescope. The wide G band measured in the Spectro sky mapper, and the medium width P band centred at 380 nm (FWHM = 26 nm). p,v is the surface brightness, a the standard error of the average of 100 scans with GAIA. The left and right half of the table give the same information in different units: in mag/arcsec2 at left and in unit of 6*10 at right.

Hv 21.0 22.0 23.0 24.0

<JG crp [mag/arcsec2]

0.001 0.002 0.003 0.006

0.013 0.027 0.062 0.149

/4 [Sw]

515 205 82 32

°'G [Sio]

a'P [Sw}

0.5 0.4 0.2 0.2

6.2 5.1 4.7 4.5

The signal-to-noise value is then

and the standard error in magnitudes is

The surface brightness fiy may also be expressed in units of 5io as

where the unit is defined as 1 SIQ = 27.8 mag/arcsec2 or 1 star of my = 10 mag per square degree. The corresponding standard error is

These errors, multiplied with a margin factor 1.2, arc given in Table 1, where the diffuse sky has been assumed to have a solar type spectrum. There are about 100 scans per star per band during the 5 year mission time which has been taken into account in the standard errors. The standard error per scan is therefore about 10 times the values in the table. This must be taken into account when a variable sky background is encountered, especially in the zodiacal light. The tables in [1] show that at a typical surface brightness of fj,V = 23.0 mag/arcsec2 a precision of 0.003 mag is obtained in G and about 0.06 mag in all medium width photometric bands for spots of 7 arcsec diameter. Inside each spot a resolution about 0.5 arcsec will be obtained, with correspondingly lower photometric precision.

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Table 2. The components of diffuse sky background in the optical as seen from above the Earth's atmosphere.

Zodiacal Light (ZL) 30-100 SIQ Diffuse Galactic Light (DGL) i.e. scattered light from interstellar dust near the plane 30-50 5"io Galactic Cirrus i.e. scattered light plus fluorescence emission (ERE) from interstellar dust at high latitudes 1-20 5io Line emission (H Q ) from typical ionised high latitude galactic gas 0.2-2 rayleigh = 0.5-5 xlO~ 7 erg/s cm2 sterad Extragalactic Background Light (EBL) (not yet detected) 0.5-2 SIQ

3

Scientific Interest

The considerations in [1,7] are followed here. With our current knowledge of the diffuse sky background in the optical as seen from above the Earth's atmosphere, there are four main components, listed in Table 2. For three of them an estimated range of values at 380 nm is given in units of SIQ. A possible fifth component (EBL) has not yet been detected. Zodiacal Light: there are probably no major open scientific issues about the ZL itself which would make an extensive multifilter optical photometry justified. But this may be a bit pessimistic in the sense that the multifilter aspect provided by GAIA would still be unique and would provide an accurate measure of the colour variation of the ZL over the sky. However, ZL is the main foreground component for the diffuse sky background as seen from above the Earth's atmosphere. Therefore an accurate knowledge of ZL distribution over the sky and its variation with time are needed when studying the other components. Diffuse Galactic Light, I: low galactic latitudes: about 1/3 of the (total) integrated galactic surface brightness at low latitudes is due to scattered light from interstellar dust. It is commonly called the Diffuse Galactic Light (DGL). The DGL has previously been measured over limited regions of the sky, but already in several filters 350-700 nm. GAIA with its complete sky coverage and many filter bands could contribute substantially to this field. The essential scientific result expected is the albedo and a rough shape of the dust scattering function, both for the full range of GAIA wavelength coverage. These results in turn will provide a good handle on restricting the interstellar grain models. Diffuse Galactic Light, II: high latitude cirrus: the Infrared Cirrus as mapped by IRAS over the whole sky has a counterpart in the optical wave band. In the optical the radiation is due to starlight scattered by interstellar dust plus a

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possible contribution by fluorescence (Extended Red Emission, ERE). This Optical Cirrus has so far been measured only in limited areas. Scientifically one would expect very useful results on dust properties and their variations from cloud to cloud when the optical and IR cirrus measurements are compared with each other and with the accurate extinction measurements provided by GAIA for many million lines of sight. Line emission (H a ) from ionised gas: this emission can be accurately measured also from ground. There are several extensive sky surveys both on the northern and the southern hemisphere going on. Therefore GAIA could probably not produce unique observational material here through its Ha filter photometry (the intensity of this emission is taken from [8] and corrects the too large value given in [7]). Extragalactic Background Light: this is a very weak isotropic component of the diffuse sky background. So far there is no measured value for the EBL in the optical domain, only upper limits. One can estimate that the EBL is about 0.5 to 2 SIQ- This component is of great cosmological importance. Because of the (tentative?) detection of the far-IR EBL by COBE/DIRBE there is increased current interest also in the optical EBL. Being above the Earth's atmosphere the main problem for EBL measurement is how to separate it from the two dominating foreground sky components, i.e. the ZL and the Galactic Cirrus. Thanks to its multi-wavelength capacity the GAIA medium-band photometer would be in a good position to perform the separation based on the different SEDs of ZL, Galactic Cirrus, and EBL. However, the GAIA photometric sensitivity may be a problem here. It appears that, in order to enable a separation of the ZL, DGL, Cirrus, and EBL components from each other, the most important medium band niters are 350, 380, and 405 nm. In order to measure the Red Extended Emission (ERE) a filter at about 700 nm would be needed. 4

Conclusions

The preliminary conclusion is that GAIA diffuse sky medium-band photometry can contribute interesting scientific results, if the following requirements can be met: (1) The average of some 100 spots may be formed to obtain an accuracy of 0.5 £10, and (2) the instrumental stray radiation contribution from stars plus diffuse sky components is less than 0.5 to 1 S\Q. These requirements can be met: (1) A group of 100 spots from the instruments can be averaged to obtain an accuracy of 0.5 5io with the medium-band photometer. This requires a careful calibration of GAIA photometry and this accuracy goal should be kept in mind when the photometric processing is designed and developed. (2) The instrumental straylight from stars plus diffuse sky components should be less than 0.5 to 1 S\Q. This is a requirement for the baffling of the telescopes. This is achieved with a conical baffle extending from the focal plane of the Astro telescopes, discussed in Section 3.2.5 in [9] and shown in Figure 4.2/6 in the GAIA

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CTS Study Final Report. The Spectro telescope has no such baffle at present (see Fig. 5.2/1) but it is possible to introduce it. This baffle seems to be required even for the sake of the medium-band photometer and the radial velocity spectrometer. References [1] H0g, E., 2001, Multi-colour photometry of the diffuse sky background with GAIA, GAIA-CUO-082, Technical Report from Copenhagen University Observatory, http: //www. astro. ku. dk/~er ik/gaia/82 [2] H0g, E., 2002, EAS Publ. Set., 2, 27 [3] Brown, A., 2001, Photometric Data Analysis for GAIA: Mathematical Formulation, 6 pp., GAIA-AB-001, http://www.astro.ku.dk/~erik/gaia/AB/ Technical Report from Leiden Observatory, and 2002, EAS Publ. Ser., 2, 277 [4] Vaccari, M., H0g, E., 1999, Simulated GAIA observations of galaxies, GAIA-CUO-069, Technical Report from Copenhagen University Observatory, http: //www. astro. ku. dk/~erik/gaia/69 [5] Vaccari, M., GAIA Galaxy Survey, Universita degli studi di Padova, Tesi di Laurea in Fisica, Anno Accademico 1999-2000, 313 [6] Leinert, Ch., et al, 1998, A&AS, 127, 1 [7] H0g, E., Fabricius, F., Knude, J., 2001, Report on GAIA Photometry Workshop, Copenhagen 21/22 March 2001, GAIA-CUO-086, Technical Report from Copenhagen University Observatory [8] Reynolds, R.J., 1990, in IAU Symp. 139, The galactic and extragalactic background radiation, S. Bowyer and Ch. Leinert (eds.), 157 [9] ESA 2000, GAIA: Composition, Formation and Evolution of the Galaxy, Technical Report ESA-SCI(2000)4 (scientific case on-line at http://astro.estec.esa.nl/GAIA)

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

OBSERVATIONS OF QSOS AND REFERENCE FRAME WITH GAIA F. Mignard1 Abstract. The astrometric mission GAIA will provide a flux limited census of quasi stellar objects to V = 20 mag. This paper addresses the main physical and observational properties of the quasars, the existing surveys and the relevant statistical distributions of the compilation catalogue of Veron-Cetty & Veron. Then I consider the detection and recognition with GAIA which should be based on the multicolour photometry complemented by hints on the parallaxes and proper motions. In the last section I discuss the possibility to materialize directly in the optical the quasi-inertial frame to the sub-ptas accuracy. It is shown that that with a clean sample of less than 10 000 quasars the residual spin of the GAIA reference frame can be determined to 0.5/^as yr"1.

1

Introduction

The GAIA astrometry mission will allow to determine accurate positions, proper motions, parallaxes and brightness of point sources up to the 20th magnitude using several instruments and by carrying out astrometric, photometric and spectroscopic measurements [1,2]. Among the numerous categories of stellar sources that GAIA will survey, the elusive and still poorly understood quasars hold a particular place because of the cosmological significance and the controversies in which they were entangled since their discovery. Galactic in nature, stellar in manifestation, they appear faint and rare, scattered in a myriad of stars and impossible to recognize just from their stellar images. There are many good reasons for studying quasars as they provide key information on the history of the Universe, when it was much younger than its present age. Knowledge of the spatial distribution of the quasars and of the dependence of their luminosity function with time impacts on numerous astrophysical and cosmological problems [3] and the physics of the quasars is a very active area of astronomical research. 1

OCA/CERGA, avenue Copernic, 06130 Grasse, France © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002033

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GAIA will contribute significantly to the knowledge of quasars in providing for the first time an all sky flux limited survey to V = 20, very difficult to carry out from the ground. The multicolour detection should be very efficient to get rid of the traditional contaminants like the white dwarfs. Simultaneously photometric redshift measurements will be feasible without additional effort for most of the detected sources. At the end one may reasonably expect a census of several hundreds thousands quasars at galactic latitudes |6| > 25° — 30°. Multi-images formed by lensing of intervening galaxies could be detected at separation as small as ~0.2 arcsec, a significant improvement to the resolution of current ground based investigations with nice inferences in the distribution of distant galaxies. Finally the extensive zero-proper motion survey will provide a direct realization of the quasi-inertial celestial reference frame with a residual rotation less than 0.5 /^as per year and a space density hundred times larger than that achieved by the radio version of the ICRF. 2

Overall Properties of QSOs

Quasars (I use QSO and quasar interchangeably) were first identified by Matthews &: Sandage in 1960 from sources of intense radio energy and few years later Maarten Schmidt discovered that these sources were the most distant ever seen in the Universe. He recognized from spectra taken in the visible with the Palomar 200-inch telescope the broad, strong emission lines as Balmer lines redshifted by 15%, yielding a brightness hundred times larger than the most luminous galaxies, provided that the redshift could be related to a distance by the Hubble law. M. Schmidt coined the term Quasi-Stellar Radio Source, a name that was soon shortened to quasar. Soon afterwards, astronomers found several other quasars, some substantially more luminous and distant than 3C 273. Observations of an occultation of the radio source 3C 273 by the moon made by Cyril Hazard and colleagues showed that the position of the radio source was coincident with a 12th magnitude stellar object. It is now known that the vast majority of quasars are in fact radio quiet. For the following it is useful to remind the main properties of the QSO's: • QSO's are the most luminous steady objects in the Universe at any wavelength at which they have been observed radiating ~10n — 1014 L0, that is to say 1 to 10000 times the luminosity of the Milky Way; • Variability in all wavelengths (0.2-0.5 mag) over timescale of days to months are usual, meaning that the size of the emitting core is of the order of few times the size of the Solar System to a maximum of 0.1 pc. This was quickly perceived as a major problem as it was hard to contrive a physical mechanism allowing a region as small as the Solar System able to emit hundreds of times as much energy as the entire Galaxy; • QSO's exhibit very large redshifts (0 < z < 5) and are seen at very large distance and far back in the past, with the widely accepted assumption today that the redshift is of cosmological nature;

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• The spectral energy distribution (SED) is markedly different from that of the stars with large UV fluxes. In addition there are strong and broad emission lines (E.W. « 50 A, Lya, SI IV, OIV, CIV). Figure I shows a typical example of the SED with a redshift z — 2.4 driving the Lya line into the visible region of the spectrum; • Today the most generally accepted explanation for the tremendous energy output and the small size of the quasars is that they are powered by the release of gravitational energy from material falling into a massive black hole (108M0). If one Sun mass is swallowed every year with a 10% energy conversion from gravitational energy into radiation and particle emission, one gets for the luminosity 0.1M0c2/l yr = 1039 W = 1046erg s"1 ~ 1013L0. Direct evidence for the presence of very large and compact masses within the galactic nuclei has come from dynamical studies of gas orbiting in the vicinity of the nuclei by radio, optical or X-ray techniques.

Fig. 1. Typical spectral distribution for a QSO. Note that the high redshifted light brings the Lya line from the UV to the visible (courtesy of the 2dF Survey).

3

Current Surveys and Catalogues

The first catalogue of quasars was published in 1971 and contained 202 objects [4]. Since then the number of identified quasars has steadily increased and several local, or global surveys are under way or in project. No overall survey of QSO's has been carried out so far because of the huge observing resources required, independently of the intrinsic difficulties in identifying quasars in regions crowded by faint stars. However local surveys to a given limiting flux have been attempted in order to investigate the optical luminosity function and its change with the redshift or to provide complete samples in a range of redshifts and magnitudes.

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New efforts are under way like the 2dF QSO Redshift Survey which released recently a catalogue comprising over 10000 QSO's found over an area of nearly 300 deg2 brighter than bj = 20.85 and with z < 3 [5]. The program aims to measure redshifts for ^25000 optically selected sources, with a final release by the end of 2002. This is the most ambitious local survey close to completion. Recently US and Japanese astronomers embarked over the most ambitious effort yet in galactic survey with the on-going Sloan Digital Sky Survey, to be completed by 2006. The Sky Survey is designed to systematically map one-quarter of the entire sky around the north galactic cap to produce a detailed distribution and absolute brightness of more than 100 million celestial objects. The Sky Survey will also detect and record the distances to 100000 colour-selected quasars. The key to SDSS's success in quasar identification is the five colour photometry allowing astronomers to distinguish quasars from more common faint stars. This will be also the main tool that GAIA scientists will use for their own quasar spotting. To

Fig. 2. Distribution of the QSO's in the Veron-Cetty Catalogue. Quasars in blue, AGN's in red and BL Lac in green. date the most extensive compilation of data is that performed by Veron-Cetty & Veron [6] who recently published the 10th edition of their catalogue, containing nearly 30000 entries. Quasars are defined as starlike objects, with broad emission lines and brighter than absolute magnitude MB = — 23. In their compilation they number 23760. Fainter sources are primarily classified as AGNs (5751 entries) and the remainder are BL Lac objects (608) The sky distribution is very heterogeneous, as shown in Figure 2. About half of the sky around the ecliptic plane is not covered due to the interstellar absorption and to the difficulty to select quasars in region overpopulated by stars. Local concentrations result from surveys in small areas. The distribution to be seen by GAIA should exhibit the same overall structure with virtually no QSO's at galactic latitude \b < 30 degrees, but with a much more uniform distribution outside this zone. Relevant photometric distributions are displayed in Figures 3, 4.

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So far no clustering has been found in the spatial distribution of quasars and it is thought that the actual distribution is isotropic. The expected number of QSO's deduced from a combination of regional surveys yields to a cumulative surface density of about 1 QSO per square degree at B < 18 and 20 at B < 20 [3]. Therefore over half of the sky GAIA should detect 20000 objects brighter than 18th mag and up to 400000 at the limiting magnitude and twice that number if the sensitivity limit is pushed up to B = 21, that is to say between 4 and 8 more objects than expected from the Sloan survey after completion.

Fig. 3. Histogram of the distribution of the QSO's in the Veron-Cetty Catalogue as a function of the apparent B magnitude (left) and the absolute magnitude MB (right). The distinction at MB = —23 between the so-called AGN's and the quasars is conventional. The steep drop in number at B w 21 comes from the flux limited survey included in the Catalogue.

Fig. 4. Distribution of the redshifts in Veron-Cetty Catalogue. The difficulty at identifying quasars from white dwarfs beyond z = 2.2 is clearly visible in this diagram and should not be taken as a clue of the actual population.

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4

Photometric Detection

As said before, the major problem in any QSO survey is the recognition among many pointlike sources of the rare quasars. There are several indicators that will help make the decision, like the absence of parallax, the negligible proper motion (in an inertial frame), the short term variability and, before all, the spectral signature summarized by a set of colour indices. Given the astrometric capabilities of GAIA I would suggest that the parallaxes and proper motions should be taken as good indicators only to exclude an object from a preliminary sifting: no quasar will have a significant parallax or a large proper motion (but where to set the threshold to avoid errors of the second kind?), but some stars will have a negligible parallax or proper motion. In addition with the astrometric accuracy of GAIA there are important science issues in trying to detect quasars with non-zero proper motion. So these tests should only be used as confirmation tool, when the photometric testing has concluded positively that a particular source is likely to be a QSO. In principle this step provides a big list of QSO candidates and follow-up spectroscopy is required for a flawless identification and redshift measurement. This is the classical way of organizing QSO surveys on the ground but given the huge number of sources detectable with GAIA one should design a recognition procedure which comes close to providing a list including ~100% of the objects of interest and virtually no contaminant. This seems possible thanks to the photometry planned with GAIA on a rich variety of wavebands. Claeskens and collaborators [7] have crossed a synthetic SED with the different photometric systems proposed for GAIA. They show conclusively that the combination of the broad band and medium band filters permits a photometric identification of quasars from virtually any type of stars, provided the bands overlap, that they are broad enough to cover the Lya line and have a good spectral coverage. Using only the broad band colours makes quite difficult to distinguish QSO's with z < 2 from the white dwarfs, a traditional contaminant in colourselected quasars. On the other hand an ambiguity remains with main sequence stars for 2.5 < z < 3.5. But this can be resolved with the medium band colours thanks to a better sensitivity to the Lya line. The photometric redshift (~ redshift seen in the continuum) can be retrieved as well, even if the actual spectral index differs significantly from that of the template used for the analysis. 5

Testing

As I have mentioned earlier in each range of magnitude the field stars outnumber the QSO's making the recognition of the latter difficult. Any recognition criterion, is more alike an hypothesis testing and prone to two different kinds of errors. • A QSO may be categorized as a star, that is to say be unrecognized by the test. As a result, if the test is not sensitive enough, the survey will be incomplete and many QSO will be left out;

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Table 1. Probability of wrongly labelling a star or a QSO with the recognition tests. The object is a: QSO

star

QSO

l-a

&

star

a

1-/3

Found as:

• On the opposite a star may be mistaken for a QSO and flagged as such. In this case the sample of would be QSO's will be contaminated by genuine stars. Since the stars are much more frequent than the QSO's, even if this occurrence has a low probability, this may end up with a large number of contaminants in the selected sample. Quantitatively this is easily modelled by introducing the frequency / of QSO's among the celestial sources detectable by GAIA. Let a be the probability that a QSO gets unrecognized among the stars and {3 the probability that a common star is declared to be a QSO. This is summarized in Table 1. Application of the elementary laws of probability yields the probability that a source being found as a QSO is in fact a QSO (right) or a star (wrong decision):

Therefore, as expected, if /
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6 6.1

The Inertial Frame Presentation

Reference frames in astronomy are defined by the position of objects on the celestial sphere, usually specified by their direction combined with a minimum set of constants or conventional values for the origins. The role of high quality reference frames in astronomy has been recognized early by both theoreticians and practitioners, and most of the classical astronomy until the emergence of physical astronomy was concerned with the realization of good reference frames. Astrometric data, positional or kinematical, rely on observations referred to a frame, either local or global. The choice of the reference frame may be driven by instrumental consideration or be built from deeper theoretical grounds, as is currently done with the definition of the ICRS which bore a fatal blow to the long astronomical tradition of materializing the inertial frame from observations attached in various ways to the apparent motion of the Sun. The main novelty in the ICRS lies in the adoption of a kinematical system which assumes that the visible Universe does not rotate, so that the most distant sources have no individual motion relative to each other. As a whole these sources define and materialize a non-rotating reference system. The extragalactic reference frame is assumed to approximate an inertial frame, defined within the context of General Relativity, through Mach's Principle. The ICRF was formally adopted as the primary materialization of the International Celestial Reference System as of 1st January 1998. It is basically a fundamental catalogue (i.e. a reference catalogue of positions directly inferred from absolute observations) of carefully observed radiosources [8]. The whole Catalogue comprises 608 compact radiosources, of which only 212 constitute the defining sources, corresponding to the best observed subset with an internal positional accuracy in the range of 0.2-0.5 mas. Aside this primary system, an optical counterpart was also adopted by the IAU in 1997, from the HIPPARCOS Catalogue and its content was refined in a resolution adopted by the IAU in August 2000. The global nature of the HIPPARCOS observations produced a very well defined freely rotating sphere materialized by the positions and proper motions of the stars. Eventually it was linked to the extragalactic frame through a set of radio stars common to the two frames, with a residual rotation estimated to 0.25 mas yr-1 [9]. A mission like GAIA will permit a realization of the ICRS more accurate by two or three orders of magnitude from direct observations of the defining sources brighter than magnitude 20 and also by adding in the visible thousands of QSO's recognized from ordinary stars or white dwarfs with the broad- and narrow-band photometry. The sky coverage will be fairly uniform outside a zone of ±25 degrees centered on the galactic plane. As GAIA will survey the quasars down to an apparent magnitude of 20, there will be plenty of material (about 500000 from current estimates based on local surveys) to select a small sample, maybe less than 10000 very clean sources, to construct the primary reference frame in the visible.

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Orientation and Spin

The frame orientation will be obtained from a comparison with the ICRF sources, so that there will be no discontinuity within the uncertainty of the current version. With ~200 sources usable for the comparison, one should be able to maintain the continuity with an uncertainty less than 50 //as. The spin vector will be constrained by imposing that the selected sample of ~10000 extragalactic sources exhibits no overall rotation. The testing of this feature will be crucial to detect any departure to this essential assumption for the reference frame but also for our knowledge of the quasars. An iterative process would yield the final selection of primary sources and pinpoint the sources with detected transverse motion, a result of major cosmological significance. One assumes that the intermediate astrometric sphere is rotating relative to the extragalactic sources with the spin vector ujx: uy, uoz and that the extragalactic sources have no peculiar transverse motion. In this case the observed components of the proper motion is only due to the global spin motion and to random errors. The observation equations for the components of the spin are then given by,

where the left hand side contains the proper motion components. A refined model should include any systematic motion of the Solar System with respect to the distant matter that could give rise to a reflected motion of the quasars for an observer at the barycenter-of the Solar System. • COBE confirmed beyond all doubt the dipolar anisotropy of the CMB (its existence was established in 1976 using an instrument on board an U2 spy plane) yielding a motion of the Solar System at a velocity of 370 km s~l with respect to the CMB (this is in fact a systematic motion of the local group). Assuming that quasars are comoving with the CMB this should translate into a dipolar proper motion of the quasars similar to the one found by W. Herschel from the motion of the Sun toward the apex. A rapid calculation shows that the maximum proper motion at 90° of the velocity is 0.07 //as yr"1 for a source at 1 Gpc. A redshift z = 0.1 is similar to a distance of 0.4 Gpc with ho — 0.75, therefore the reflected displacement of the Solar System will be too small to be detected from the quasars proper motions; • From the same motion arises a constant aberration of ~250 arcsec of the quasars between the comoving frame and the frame attached to the barycentre of the Solar System. From the principle of relativity we know that this cannot be detected, as long as the speed is uniform; • Any variation of the speed of the Solar System with respect to the distant matter could be detected from the resulting change in the aberration, that is to say as a spurious proper motion of the distant sources. This does not violate the principle of relativity because we are not detecting a uniform

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GAIA: A European Space Project motion of one frame with respect to another, but an accelerated motion between two frames. The classical annual aberration is evidenced in the sky because of the yearly change of the direction of the motion of the Earth about the Sun, even though the speed is constant (neglecting the orbital eccentricity). Were the motion of the Earth uniform in speed and direction, aberration would have never been detected but introduced on a theoretical basis. There is no evidence today that the COBE dipolar motion is not constant over short timescales (were it not constant this would be in fact a major breakthrough in galactic physics or cosmology). However such an effect is foreseen from the galactocentric motion of the Solar System. The effect is more easily grasped if we consider the observation of a very distant source by an observer standing at the barycenter of the Solar System and taking regularly the position during a period of 250 million years, the Great year, as Bradley did on the annual motion in 1726-27 with a Dra. The observer will not fail to notice the elliptical path of 150 arcsec described by the star, that he will soon dubbed galactic aberration ellipse. GAIA will sample this ellipse over five years, so that only a very small arc will be described, not very different from its tangent, so that it will manifest itself as an additional proper motion. The two tips of the line are the direction of the velocity vector of the Sun around the galactic center at the beginning and at the end of the time interval. Therefore the direction of the line is that of the acceleration. The mathematics are simple: the change of the unit vector of a star due to stellar aberration is 6u — v/c. By Differentiating one has for the proper motion vector, Assuming an uniform circular motion with radius R and speed V one has for the induced proper motion from the variable aberration,

where one has computed the velocity change along the radius vector. With R ~ 8.5 kpc and V ~ 250 km s"1 one gets /j, ~ 5 /uas yr-1. This is a non negligible quantity for the quasars, with a well defined pattern: the quasars will be the dual of a rotation field around the direction pointing toward the galactic center, that is to say a vector field with a source at the anti-center, a maximum proper motion of ~5 /^as yr"1 at 90° from the direction of the galactic center and a sink toward the galactic center with no displacement at all. This effect in not considered in the following but it can be shown that in the sense of least squares the residual spin vector and the galactocentric acceleration are orthogonal, and then not correlated. Allowing or disregarding the

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Fig. 5. Left: determination of the precision of the spin rate of the inertial frame determined with GAIA from the observation of the quasars. The precision is given when only sources brighter than B are selected and galactic coordinates have been used. The random instability has been taken equal to 20/uasyr~ 1 . The sample is based on the Veron-Cetty catalogue and its size increases with the limiting magnitude. Though there are many more faint objects than bright ones, the frame is primarily determined with the brightest sources, because of the better astrometric precision. Right: cumulative number of objects in the solution brighter than B.

acceleration in the condition equations has not effect on the spin components. For GAIA one should have to decide whether it is better to try determine the acceleration vector or to model it from our knowledge of the galactic motion. Results for the determination of the acceleration components can be found in the Study Report [1] and indicate that the components of the acceleration are determined with a relative precision of 10% quite comparable to the current knowledge of the galactic rotation.

6.3

Results of a Simulation

By collecting all equations (6.1, 6.2) over the extragalactic sources it is possible to determine the u^ with a least squares solutions, with the equations weighted according to the magnitude and the source jitter. The sample constructed on the Veron-Cetty Catalogue and on the expected astrometric accuracy of GAIA yields an outstanding non-rotating frame at the level of 0.5 /^as yr~ x , provided the source random instability is less than 20 /ias. Variation of this accuracy with the limiting magnitude is shown in Figure 5. The difference between ujx,u)y and ijjz is due to the peculiar space distribution of the sources (Fig. 2) and the use of galactic coordinates to carry out the computations. It appears that using only the brightest quasars (~-B < 18) is perfectly sufficient to reach an almost perfect solution, that is to say with only ~6000 sources. Obviously for larger random instability the marginal contribution of sources fainter than B KI 18 increases.

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The random instability of the source puts a very serious limitation in the ultimate precision of the inertial frame. Extragalactic radiosources display structure on spatial scales from hundreds to one mas [10], with a variety of shape. The variability at radio wavelengths is also correlated to structure change due to relativistic jets. The effect of source structure on position has been studied in radio and found as large as tens of mas yielding apparent motion in right ascension. Values of 10 to 30 //as yr"1 have been reported. Virtually nothing is known in the visible regarding the ~ mas structure and its time change. However the photometric variability in the optical bands might be an indication that photocentric random motions should not be excluded, in addition to the random microlensing. If relativistic jets seen in radio originated from synchrotron radiation of accelerated charges particles, the same mechanism should be seen in the optical band. Selection of a clean sample will be a difficult, but stringent requirement for the primary realization of the inertial frame. Dirty sources should not be simply dumped in the wastebasket but carefully scrutinized individually or collectively for jet motion (only for nearby AGN's) or structured transverse displacements. 6.4

Primary Versus Secondary Inertial Frame

Although the determination of the residual spin bears some resemblance with the HIPPARCOS link to the ICRS, it is much different in spirit. With HIPPARCOS a handful of radio stars observed both with VLBI (and tied to the ICRF) and with HIPPARCOS were used to adjust the HIPPARCOS Catalogue to the ICRF. With this procedure the primary realization of the ICRS remains the ICRF with its 212 denning source, whose quality will not degrade with time. The Hipparcos frame is a secondary solution, losing progressively its initial quality because of the approximated knowledge of the proper motions. The reference frame to be materialized with the observations of QSO's by GAIA will be much more fundamental and will bring back the primary realization in the visible wavebands. It will not be a link to the ICRS but an outright realization based on the theoretical physical concepts underlying the ICRS: the Universe as a whole does not rotate and the most distant sources do not display transverse motion. Equations (6.1, 6.2) are misleading, in that sense they do not ascertain the components of the spin of a link, but the components of a global spin to be applied to the free rotating GAIA sphere. Unlike the HIPPARCOS link, no a priori information on the ICRF sources will be used in this process (this remark applies only to the rotation, not for the origin which is purely conventional with no strong physical meaning). GAIA will do precisely in the visible what Ma et al. [8] have done with the ICRF in radio. References [1] ESA, GAIA, 2000, Composition, formation and evolution of the Galaxy, ESA-SCI(2000)4 [2] Ferryman, M.A.C., et al., 2001, A&A, 369, 339 [3] Hartwick, F.D.A, Schade, D., 1990, ARA&A, 28, 437

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[4] De Veny, J.B., Osborn, W.H., Janes, K., 1971, PASP, 83, 611 [5] Groom, S.M., et al., 2001, MNRAS, 322, L29 [6] Veron-Cetty, M.P., Veron, P., 2001, A&A, 374, 92 [7] Claeskens, J.F., Royer, P. Surdej, J., 2001, QSO colors in the proposed GAIA photometric systems, GAIA internal note, 1 [8] Ma, C., et al., 1998, AJ, 116, 516

[9] Kovalevsky, J., et al., 1997, A&A, 323, 620 [10] Johnston, K.J., de Vegt, C., 1999, ARA&A, 37, 97

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The Solar System Revisited

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

THE IMPACT OF GAIA IN OUR KNOWLEDGE OF ASTEROIDS V. Zappala1 and A. Cellino1

Abstract. GAIA will likely be a real milestone for asteroid science. Its unprecedented astrometric accuracy can be exploited to compute orbits better than those obtained by using the whole set of available astrometric observations carried out from ground during the last 100 years. GAIA will make it possible to measure asteroid masses through the measurement of the tiny displacements caused by asteroid mutual encounters. This will be a major breakthrough for physical studies of minor planets. Moreover, sizes will be also directly measured for a big sample of more than 1000 objects. From masses and sizes, estimates of the average densities will be also obtained. The spectrophotometric capability of GAIA will be used for purposes of taxonomic classification, with important implications for surface mineralogical characterization. Finally, GAIA will be an ideal platform to detect near-Earth asteroids having orbits interior to that of the Earth.

1

Introduction: Asteroids as Bodies of Astrophysical Interest

It has long been recognized that the population of small bodies mostly located in the main asteroid belt between Mars and Jupiter, are the left-overs from an unsuccessful process of planetary accretion, followed by extensive mass depletion in that region of the Solar System [1, 2]. As such, asteroids are supposed to have experienced a generally modest degree of thermal metamorphism since the early epochs of planetary accretion [3]. For this reason, asteroids should provide important information about the population of planetesimals originally formed in that region of the Solar System. At the same time, due to the non-negligible radial extent of the main belt, asteroid reflectance properties are important to study the gradient of mineralogical composition of the early planetesimals as a function of heliocentric distance [4]. The most important process affecting the subsequent evolution of asteroids has been the occurrence of mutual collisions. Current size and spin rate distributions 1

Osservatorio Astronomico di Torino, 10025 Pino Torinese, Italy © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002034

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of the asteroid population are thought to be the final result of a long collisional evolution [5]. On the other hand, the outcomes of a catastrophic collision among asteroid-sized bodies are determined by a very complicated physics, that we have not yet fully understood. For this reason, improving the data about the most important physical properties of the population as a whole (primarily the size distribution) is an important requisite to validate current models of catastrophic disruption processes and to assess the real inventory of the asteroid main belt at small sizes [6,7]. For the above reasons, it is very important for any study of the origin and evolution of the minor bodies and, more in general, of the whole Solar System to deeply investigate the main physical properties of the asteroids, and their distribution in the main belt and in the Trojan clouds. 2

Physical Properties

Some key-problems concerning the physical properties of asteroids are presently open, and can hardly be solved using currently available ground-based observational facilities. In particular: 1. We do not know asteroid masses and densities, but in a very few cases. We do not even know sizes for the majority of the known objects; 2. Taxonomic classes, which are directly related to surface mineralogical composition are known only for a limited and biased sample. In particular, we do not know whether the presently known distribution of taxonomic classes is representative of the whole population, or it is intrinsically size-dependent. The above deficiencies are due to the fact that asteroids are mostly faint, point-like objects when seen from Earth. They have very small masses which can hardly be derived from measurements of the effects of mutual gravitational perturbations on their orbital motion [8]. Apart from a very limited number of measurements of these effects, another method that has been recently applied is the mass measurement from Kepler's Third Law for the few cases of binary asteroid systems recently found by means (mostly) of Adaptive Optics techniques (asteroids 45, 90, 243, 762). GAIA is expected to drastically modify the current situation, by providing a wealth of new data, including masses, directly measured sizes, shapes, and spectrophotometric data to be used for taxonomic classification purposes. All this can produce a real revolution in our current understanding of the asteroid population. 2.1

Masses

Apart from the few above-mentioned cases of binary objects, the possibility of determining asteroid masses lies on the capability of measuring the tiny gravitational perturbations that asteroids experience in case of a mutual close approaches. In

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particular, close approaches can be useful when at least one sizeable object is involved, since otherwise the mutual perturbations can be intrinsically too weak for any reasonable hope of mass determination. Due to the difficulties in measuring very small effects on asteroid motions, currently only about 10 masses determined in this way are known, mostly with quite a poor accuracy. The extremely high astrometric precision achievable by GAIA will enable a large number of asteroid masses to be determined with a good accuracy. This must be considered as a major breakthrough of the mission from the point of view of asteroid studies. The number of mutual close encounters between asteroids over the years 2004 2015 has been estimated. For each event, the minimum distance and relative velocity have been computed. The predicted deflection has been computed whenever the minimal distance is lower than 0.25 AU, and/or the encounter velocity is smaller than 2 kms- 1 . It is assumed that a close encounter is effective from the point of view of mass determination when the computed deflection is greater than 10 mas. In a first step, a set of 174 perturbing asteroids, having diameters larger than 120 km, has been taken into account. As a set of possible targets (deflected bodies) all the known objects larger than 50 km (729 asteroids) were chosen. The results of the computations are that 136/174 perturbing asteroids are involved in 849 effective encounters. The parameters considered in this analysis were conservative, since the expected S/N ratio were larger than 100. Accordingly, we expect that GAIA should be able to provide mass determinations for more than 100 asteroids during the mission lifetime. 2.2

Densities and Sizes

Average density can be determined when both mass and size (and shape) of a given object are known. So far, direct measurements of the apparent angular diameters of asteroids have not been possible but in a very few cases, since most asteroids are simply too small. Alternative techniques based on stellar occultations have not provided but a few reliable measurements, due to the intrinsic difficulties in predicting and observing these events. With a resolving power around 20 mas for extended sources, GAIA should be able to directly measure a number of asteroid diameters ranging from 1300 to 1900, depending on the adopted configuration option. In addition to main belt objects, also a considerable number of Jupiter Trojans (60 90 objects) will be measured. These observations will constitute not only the first, huge catalog of asteroid sizes directly measured, but they also will allow us to calibrate what is at present the major data base on asteroid sizes, namely the IRAS Minor Planet Survey (IMPS). The IMPS catalog of asteroid sizes and albedos lists size and albedo data for about 2000 objects. It is based on the results of the thermal infrared sky survey performed by the IRAS satellite. This technique (radiometry) requires the application of a thermal model, needed to predict the distribution of temperature on the asteroid surface. In turn, thermal models include several poorly constrained parameters [9]. As a consequence, it is very likely that a significant fraction of the objects in the IMPS data-set of sizes and albedos have values affected by considerable uncertainties.

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The GAIA direct measurements of asteroid sizes will play a key-role in terms of calibration of the IMPS results, since the overlap between the IMPS and GAIA size catalogs should be of the order of 1000-1300 objects. GAIA observations will include a large fraction of the IMPS objects that were observed close to the IRAS magnitude limit (V > 15 — 16 mag) where the radiometric results tend to degrade. The knowledge of asteroid sizes is crucial, since the overall size distribution of the asteroid population is essential in order to understand the general process of collisional evolution of the belt. This is thought to be the main evolutive mechanism which has affected asteroids since the early epoch of their formation, and the present size distribution should be a direct consequence of the past collisional history of the whole population [5]. An important point to be noticed is that during the GAIA mission lifetime each asteroid will be observed several times in different geometrical configurations (aspect and phase angles, and rotational phase). Due to the predictable shape irregularities, this will lead to derive different values of angular diameters, depending on the apparent area as seen from the satellite. This will permit to derive also shape estimates. The knowledge of shape, mainly for large asteroids, is important for testing the hypothesis of the existence of triaxial equilibrium bodies as a consequence of fragment reaccumulation after collisional break-up [10]. The GAIA observations should also permit to identify new binary objects, since the deformation of the signal due binarity should be measurable for objects of sufficient brightness. This is important both for the possible existence of quasi-contact binaries with a mass ratio of the order of one (equilibrium double ellipsoids), and for quite separated systems (post break-up binaries). Coupled with independent mass determinations, size determinations will provide reliable values of mean density. This is a crucial parameter, being related to the bulk mineralogic composition, and to the overall physical structure of the bodies. In particular, if asteroids are, at least in some size range, assemblages of different blocks hold together by self gravitation (piles of rubble) a significant fraction of their volume should consist of empty interstices, leading to fairly small density values. Another major point is the relationship, if any, between density and taxonomic class. In particular, it is not clear whether the differences among the known taxonomic classes, which are usually interpreted in terms of differences in mineralogical compositions, correspond also to differences in mean density. This would be the case, if taxonomy really deals with differences in overall composition and if the internal structures, in particular the presence of empty interstices, is not the most important factor in determining density. Of course, if a well defined relationship between density and taxonomy can be evidenced, this would allow us to make reliable density estimates for objects of a known taxonomic characterization. Moreover, density determinations for objects belonging to different taxonomic classes would allow us to perform a quantitative comparison with densities of meteorites. This would lead to strengthen or rule out some commonly accepted ideas about the genetic relationship between different classes of meteorites and

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their supposed asteroid sources (a typical example is the debated relationship between S-type asteroids and ordinary chondrites). 2.3

Albedos and Taxonomy

Direct measurements of sizes, coupled with simultaneous measurements of the apparent magnitude at visible wavelengths, will also lead to the determination of surface albedo for 1000-1300 objects. Albedo is another crucial parameter, being directly related to the mineralogical composition and texture of the surface layers. It is known that asteroid albedos range mostly between 0.03 and 0.5, and their distribution exhibits a well defined trend: higher albedos objects are more common in the inner part of the main belt, while lower albedo tend to be located in the outer regions [11]. This trend continues also beyond the limits of the main belt, and low albedos are exhibited also by Trojans and Edgeworth-Kuiper belt objects. In this respect, GAIA albedo measurements will be of the highest importance, and will lead also to a new calibration of the IMPS albedos for approximately 1000 objects. Albedo is also a useful complement to spectrophotometric data from the point of view of the definition of different taxonomic classes (see below). In particular, albedo is needed to discriminate among different taxonomic types (E, M, P) that cannot be distinguished on the basis of spectrophotometric data alone in the range between 0.5 and 1 /^m. The GAIA-measured colour indexes will be used for taxonomic classification purposes. In particular, an accurate taxonomy should be obtained for the whole set of observed asteroids, expected to be of the order of 15000-25000 objects (considering only the known population and depending on the adopted instrument configuration). The above number will even increase when considering also the new objects discovered for the first time by the GAIA detectors. The importance of having at our disposal a so large number of taxonomic classifications should be clearly stressed. The sample will extend down to objects of small sizes, and will allow us to analyze the distribution of taxonomic classes as a function of size. There are at present several open questions concerning this issue, which are related to the origin of ordinary chondrites, the processes of thermal differentiation, and the effects of surface weathering due to solar wind, cosmic rays and microimpacts. Taxonomic classes have clear counterparts in different classes of known meteorites. Therefore, studying asteroid taxonomy means also to understand the source of meteorites as well as of near-Earth Objects (asteroids having orbits which can approach, or even cross, the orbits of the terrestrial planets). 3

Orbits

The outstanding astrometric capabilities of GAIA will be fully exploited, both directly for what concerns asteroid orbit determinations, and through the derivation

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of a dense astrometric catalog of stars, which will be important for many purposes in future studies. As for direct orbit determinations of known asteroids, preliminary simulations have been performed, in which the covariance matrix of the orbital elements of more than 6000 asteroids were computed using both the whole set of astrometric observations collected from ground-based telescopes since 1895 through 1995, as well as a set of simulated observations carried out by GAIA, computed by considering a 5-year lifetime of the mission, and instrument performances corresponding to the different possible configurations presently under discussion. Another set of simulated ground-based observations covering the period 1996-2015 (the latter year being assumed to be the nominal end of the GAIA mission) were also performed, according to the expected results of present activity and planned observational programs. The results are striking, and show that for the known asteroids the predicted ephemeris errors based on the GAIA observations alone 100 years after the end of the mission are a factor larger than 30, better than the predicted ephemeris errors corresponding to the whole set of past and future ground-based observations. In other words, this means that after the collection of the GAIA data, we could forget without any problem all the results of more than one century of ground-based asteroid astrometry. This impressive result is a consequence of the wonderful astrometric accuracy of the GAIA observations, coupled with the fact that each asteroid should be observed several hundreds of times on the average over the mission lifetime. GAIA observations will also play indirectly an important role through the production of a very dense catalog of stellar positions, measured with accuracies of the order of 10 uas, or better. This will be an unvaluable tool for many fields of research. These include, and are not limited to, orbit determination of faint outer solar system objects; observational verification of relativistic effects in the solar system; detection of non-gravitational, thermal and/or magnetic, effects; dynamics of faint planetary satellites. Another very important application of the new stellar astrometric catalog, coupled with the above-mentioned improvements in asteroid orbit determinations, will be the capability of predicting stellar occultations with sufficient accuracies for developing efficient observing programs, which should produce additional measurements of asteroid sizes. It is important to note that, in addition to known asteroids, GAIA is expected to discover a very large number, of the order of 105 or 106 (depending on the uncertainties on the extrapolations of the known population) new objects. This fact represents a challenge in terms of accurate orbit determination. In particular, in principle, it should be possible to derive precise orbits for all the newly discovered objects, since each of them will be necessarily observed several times during the mission lifetime. This is another very exciting subject, which is presently being quantitatively analyzed. As a final remark, GAIA will detect also a very high number of NEOs. This will lead to a much refined orbit computation for known objects. Moreover, there is here another exciting challenge, related to the possibility of deriving orbits for newly discovered objects. It should be stressed that the advantage of using

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space-based instruments is particularly evident for some particular classes of NEOs, like Atens and IEO (Interior-to-Earth Asteroids [12]), which spend all or most of the time at heliocentric distances smaller than 1 AU, and are hardly observable from the ground, due to small solar elongations. This is another field of research in which GAIA can produce a real major breakthrough. Most of the preliminary assessment of the potential capabilities of GAIA for asteroid orbital and physical determination purposes described in this paper has been made with the essential contribution of Mario Carpino and Daniel Hestroffer.

References [1] Wetherill, G.W., 1989, in Asteroids II, R.P. Binzel, T. Gehrels, M.S. Matthews (eds.) (Univ. of Arizona Press, Tucson), 661 [2] Wetherill, G.W., 1992, Icarus, 100, 307 [3] Scott, E.R.D., et al., 1989, in Asteroids II, R.P. Binzel, T. Gehrels, M.S. Matthews (eds.) (Univ. of Arizona Press, Tucson), 701 [4] Cellino, A., 2000, Space Sci. Rev., 92, 397 [5] Davis, D.R., et ai, 1989, in Asteroids II, R.P. Binzel, T. Gehrels, M.S. Matthews (eds.) (Univ. of Arizona Press, Tucson), 805 [6] Cellino, A., Zappal, V.a, Farinella, P., 1991, MNRAS, 253, 561 [7] Zappal, V.a, Cellino, A., 1996, Completing the Inventory of the Solar System, T.W. Rettig, J.M. Hahn (eds.), ASP Conf. Ser., 107, 29 [8] Hoffmann, M., 1989, in Asteroids II, R.P. Binzel, T. Gehrels, M.S. Matthews (eds.) (Univ. of Arizona Press, Tucson), 228 [9] Lebofsky, L.A., Spencer, J.R., 1989, in Asteroids II, R.P. Binzel, T. Gehrels, M.S. Matthews (eds.) (Univ. of Arizona Press, Tucson), 128 [10] Farinella, P. , Paolicchi, P., Zappala, V., 1982, Icarus, 52, 409 [11] Gradie, J.C., Chapman, C.R., Tedesco, E.F., 1989, in Asteroids II, R.P. Binzel, T. Gehrels, M.S. Matthews (eds.) (Univ. of Arizona Press, Tucson), 316 [12] Michel, P., Zappala, V., Cellino, A., Tanga, P., 2000, Icarus, 143, 421

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

OTHER OBJECTS IN THE SOLAR SYSTEM: TROJANS, CENTAURS AND TRANS-NEPTUNIANS M.A. Barucci1, J. Romon1, A. Doressoundiram1, C. de Bergh1 and M. Fulchignoni1

Abstract. Trojans, Centaurs and Trans-Neptunian objects are small dark objects orbiting in the outer Solar System. These objects, still very poorly known, can be considered as fossils of our Solar System, and, as such, they can still contain information about some primordial processes which governed the evolution of the early Solar System. In the next decade, GAIA with its large sky surveys, can allow the discovery of many new objects belonging to these outer solar system populations. In addition, it will provide very precise orbits and visible broad-band colours for many of them.

1

Introduction

Many small primitive bodies are orbiting in the outer Solar System: Trojans, Centaurs and Trans-Neptunians. Trans-Neptunian objects (TNOs) constitute the newly discovered population of objects orbiting the Sun beyond Neptune, while Centaurs are located between Jupiter and Neptune. Objects belonging to these two populations represent the planetesimals which constituted our planetary system. They contain the most pristine material that originates from about 4.6 billion years ago and that can still be observed today. Many authors, before the first discovery of a TNO (1992 QB1, [1]) had hypothesized the existence of a vast population of small bodies beyond Neptune. In the middle of the last century, Edgeworth [2,3] and Kuiper [4], speculated that the Solar System could be surrounded by a disk of material left over from the formation of the planets, and many others, on the basis of numerical simulations [5-7] had shown the possible existence of a belt or a disk just beyond Neptune. On the basis of the surface mass density of the Solar System known up to Neptune, the extrapolation of the surface mass density with a power law provides a mass of 1 Observatoire de Paris, Meudon, France e-mail: [email protected]

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about 25 A/Earth for the Solar System between 30 and 50 AU. During planetary formation, when the four giant planets accreted most of their mass, the remaining population of icy planetesimals was scattered by gravitational effects to wider orbits (inward and outward). Dynamical effects and intensive collisions could have depleted the population beyond Neptune, but the number of remaining objects must still be very large. Trojan asteroids are recognized as members of the population of objects that are coorbital with Jupiter. The first Trojan asteroid was discovered at the beginning of the last century and .this discovery was a spectacular confirmation of the theoretical work of J.L. Lagrange which proved that regions of stable libration exist around the triangular equilibrium points (the so-called three-body problem). Many other objects were discovered later on near the Jupiter libration points. Five coorbital asteroids have been discovered on the Lagrangian points of Mars, thus expanding the definition of a Trojan asteroid beyond those that are companions to Jupiter, but the other planets may have similar companions that have not yet been found [8]. Our knowledge of these populations is still very limited. The study of the outer Solar System objects, which represent the oldest and least processed planetary materials, will give very valuable information on the origin and evolution of our Solar System. GAIA will allow us to discover many more objects belonging to these populations. In addition, it will provide accurate orbits as well as good photometry for the brightest objects. 2 2.1

The Outer Solar System Populations Trans-Neptunian Objects

Following the continuously updated list from the Minor Planet Center [9], about 500 Trans-Neptunian objects have been discovered so far by ground-based surveys. This number represents only a small sample of a much larger population of icy planetesimals which orbit at the outer edge of the Solar System. The TNOs possess a non-uniform distribution of orbital elements. They can be divided into three main dynamical classes. There are the Resonant objects which have orbits with large eccentricities and inclinations. About 12% of the known TNOs are trapped in the 3:2 mean-motion resonance with Neptune, in the inner part of the Belt, at about 39.5 AU (semi-major orbital axis). These objects are also known as Plutinos for their dynamical similarity with Pluto. A few other objects are trapped in other resonances like the 3:4, 3:5 and 1:2 resonances. Beyond 42 AU, there are the Classical objects with quasi-circular orbits and small eccentricities which represent about two-thirds of the known population. Then, there are the Scattered objects, which have very large semi-major axes and very eccentric orbits. More than 50 bodies have been discovered that belong to this group. They have perihelia close to that of Neptune and their aphelia can exceed 1000 AU. They might constitute the largest fraction of the total TNO population. The dynamical and observational differences between TNOs indicate a complex dynamical history

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and the important role of the collisions. These objects are expected to be the best preserved relics of the protoplanetary disk. As they have been formed at very low temperature (~40-50 K), different types of ices could have been retained over the formation of the Solar System. Collisions and irradiation have probably reworked their surfaces, especially in the inner part of the belt, and extensive cratering can be expected to characterize their surfaces [10]. On the basis of sky surveys made from the ground, it is possible to compute the Cumulative Luminosity Function (CLF) of this population. The CLF (Fig. 1) is the number of objects per unit area of sky brighter than a given magnitude, measured as a function of the magnitude. The CLF is a very important quantity because it reflects both the size distribution and the radial distance distribution of the objects. The CLF is described by the power law:

where S(mn) is the number of objects per square degree brighter than red magnitude mpi, and a and m0 are constants. The least square fit of the CLF shown in Figure 1 corresponds to a = 0.63 ± 0.06 and m0 = 23.23 ± 0.10. Given the size distribution, it is possible to calculate the total mass. On the basis of the last results obtained by Trujillo et al. (2001) [11], the population of TNOs larger than 100 km in diameter is of the order of 4 x 104 in the classical belt (scattered objects excluded). The corresponding total mass of bodies with diameters between 100 km and 2000km has been estimated to be about 0.03 Msarth [11], assuming for the objects a geometric albedo of 0.04 and a bulk density of 1000 kgm- 3 . The extrapolation to small sizes gives a total number of TNOs larger than 1 km in diameter of the order of several billions, while the extrapolation to large size objects seems to indicate the existence of Pluto-size objects not yet discovered. The physical and chemical properties of the TNOs are still poorly known due to their faintness. Spectroscopic data in the visible and the near-infrared are available for only few of them. The spectra range from neutral to very red. Few TNOs have been observed in the near-infrared, but although the spectra have generally a low S/N, they show a wide diversity. There exist, for instance, flat featureless spectra similar to that of dirty water ice, spectra with features that may be due to hydrocarbon ices with a general red behavior suggesting the presence of more complex hydrocarbons, or spectra revealing an inhomogeneous surface covered by small amounts of water ice mixed with other components. This spectral diversity is confirmed by photometric observations of a larger sample. TNO colours exhibit a wide diversity, with a quasi-continuum variation ranging from neutral to very red [12-14]. The colour diversity may originate from a different composition, but it would be very difficult to explain different primordial compositions for objects which formed probably in the same low temperature zone. The observed differences could be due instead to different evolutions. Collisions could have reworked the surface of the objects, and the fresh, excavated unexposed material coming from the interior would have a composition different from that of the exposed surface material. The colour variation of TNOs may be a consequence of differences in the collisional history combined with various degrees of space weathering due to the

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Fig. 1. The Cumulative Luminosity Function (CLF) (Fig. 7 of Trujillo et al. 2001 [11]) represents the number of TNOs deg- 2 (near the ecliptic) brighter than a given apparent red magnitude. The line represents the fit of only Trujillo et al. data (filled circles), yielding a — 0.63 ± 0.06. Other points correspond to previous works (see paper [11] for the abbreviations).

different ages of the exposed surface layers. Measurements of photometric colours for a much wider sample will help us in classifying and understanding the evolution of these objects. 2.2

Centaurs

Centaurs are a dynamical family of objects on unstable orbits with perihelia and semi-major axes between the orbits of Jupiter and Neptune. Their planet-crossing orbits imply a short dynamical lifetime (106-107 yr) compared to the age of the Solar System [15,16]. The origin of the Centaurs is uncertain, but long term orbital integrations indicate that they could have been ejected from the Trans-Neptunian Belt by planetary perturbations or mutual collisions [17]. Levison & Duncan [18] suggested that these objects could be the source of short-period comets, and, later on, Levison et al. [19], on the basis of their numerical model, predicted that some Centaurs could have originated in the Oort cloud. Centaurs seem to constitute

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a boundary between different Solar System populations and their study is very important for understanding the dynamical evolution of the outer Solar System. Although these objects are interesting in their own right, they are also interesting because of their possible origin from the Kuiper Belt. Indeed, as Centaurs are currently much closer to the Sun than TNOs, they are in general brighter than the brightest TNOs and therefore can be more easily studied. To date, about 25 such objects have been discovered. They have very eccentric orbits, with perihelia between 6.9 and 20 AU and aphelia between 9 and 46 AU Although no formal definition exists, Centaurs have been identified as asteroids at the time of their discovery, even though 2060 Chiron was subsequently shown to have cometary activity. Besides Chiron, none of the other Centaurs detected so far show cometary activity, but others coming near the Sun could exhibit some activity. The knowledge on these objects is still very limited. The Centaurs seem to have also a wide diversity of surface characteristics [20] with surface colours ranging from neutral to very red. Ices have been been identified on the surface of some of them: water ice on 10199 Chariklo, 5145 Pholus and 2060 Chiron, methanol ice or other light hydrocarbon ices on 5145 Pholus. Jewitt et al. [21], on the basis of the number of detections in their ecliptic survey, suggested a population of about 2600 Centaurs with diameters greater than 75 km. From the rate of detections by the Spacewatch automated search program, Jedicke & Herron [22] estimated an upper limit of 2000 Centaurs in the absolute magnitude range 4 < H < 10.5. This implies that, although the population is transient, the Centaurs can be as numerous as the main-belt asteroids over the same size range. Using a wide-field sky survey, Sheppard et al. [23] estimate that the Centaur population of objects with radius >1km is about 107 (assuming an albedo of 0.04). They predict about 100 Centaurs larger than 50km in radius, of which only a few have been found. The current total mass of the Centaur population is estimated to be about 10-4 MEarth- From their large survey aimed at searching for the brightest Trans-Neptunians and Centaurs, Larsen et al. [24] found a lower density distribution compared to the Jedicke and Herron survey, but still within the error bars. 2.3

Jovian Trojans

Jovian Trojans exist in two swarms, each consisting of a number of objects that librate about the L4 (respectively L5) Lagrangian point in Jupiter' s orbit. These Lagrangian points are at sixty degrees of heliocentric longitude ahead and behind the planet. Jupiter Trojans possess sufficient dynamical stability to survive over the age of the Solar System [25]. The origin of these objects is still unknown, although it is most likely that they have accreted around the orbit of Jupiter, but the population seems to have undergone a significant collisional evolution. The mean collision velocity in the Trojan clouds is indeed about S k m s - 1 , which is similar to that in the Main Belt [26]. This occurs because the lower Keplerian velocities at the heliocentric distance of the Trojan clouds are compensated by the higher average inclinations of the Trojans. The hypothesis of a considerable

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collisional evolution in the Trojan population is furthermore compatible with the discovery of dynamical families among the Trojans [27]. There are, up to now, 633 asteroids known in the £4 group and 386 in the L$ group, and these asteroids have very low albedos. From a wide-field observational survey carried out at Mauna Kea, Hawaii, Jewitt et al. [28] estimate that the population of the L4 group is of the order of 1.6 x 105 (objects with radii > 1 km), with a combined mass of ~10-4 MEarth assuming a bulk density of 2000kgm- 3 . Only few of the known Trojan asteroids have an assigned taxonomical class, and almost all of them seem to belong to the P or D asteroid compositional types [29]. They show in general neutral-red spectra, and no clear evidence of any feature has been revealed. Their spectra are very similar to the spectra of the nuclei of shortperiod comets and also to some of the spectra of Centaurs and TNOs investigated to date. 3

Conclusions: What Can Be Done with Gaia?

Very little is known about these very interesting outer solar system objects populations. Jovian Trojan asteroids seem to possess the necessary dynamical stability for survival over the age of the Solar System and they surely formed in a region of the solar nebula rich in frozen volatiles. The Centaurs are located on unstable orbits with short dynamical lifetimes. Centaurs appear to have spectral and colour characteristics very similar to those of TNOs, thus supporting the hypothesis that Centaurs originated in the Kuiper belt. However, Centaurs seem to lack colours intermediate between those of the most neutral and those of the reddest TNOs, but many more photometric data are necessary to confirm and to interpret this trend. For the moment, we can hypothesize that only those with the reddest colours can resist solar heating of the surface and keep their reddish crust, while the others (the neutral ones) will easily sublimate their most volatile materials. Outward migration of the planets during their formation, and large-scale impacts may have modified the surface compositions of the objects in the outer Solar System. The Jovian Trojans also show colours and spectral characteristics similar to those of some TNOs (the neutral/red group), Centaurs and short-period cometary nuclei. In conclusion, the study of these low albedo objects, which have been formed at larger heliocentric distance and have been less thermally processed than the main belt asteroids, can provide important information on some processes which governed the evolution of the early Solar System. With Gaia, very good photometric measurements for Jovian Trojans, Centaurs and the brightest Trans-Neptunian objects can be made. Gaia can give many important contributions on new discoveries, on orbit determinations, on the detection of binary objects and, with accurate photometric measurements for a large sample of objects, taxonomies for Trojans, Centaurs and TNOs can be better defined. Starting with the next decade, Gaia will provide an all sky inventory of Solar System objects down to V magnitude ~20-21 and, in special cases, to magnitude 22. New discoveries are important for studying the mass distribution of the outer

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Solar System populations in order to better understand their origin and evolution. Furthermore, other Pluto-size objects can still be discovered. In addition, on the basis of numerical integrations [8], it is estimated that many objects can exist close to the Lagrangian points of Venus and Earth at heliocentric ecliptic longitudes of 60° and 300°. The detection of these objects from the Earth is practically impossible. Due to the huge areas of the sky that need to be explored and the peculiar geometry, only Gaia can allow these discoveries. Also, the search on the Lagrangian points of Mars is incomplete. Several hundreds of Mars Trojans with radii greater than O.lkm could exist, with many of them detectable by Gaia. Based on our current knowledge of the Cumulative Luminosity Function of Trans-Neptunians and Centaurs, we estimate that about 400 TNOs can be detected at the V magnitude limit of 20, 1400 objects at V < 21 and about 4000 for V < 22; while for the Centaurs we have an estimate of 40 objects at V < 20, 120 objects at V < 21 and 600 for V < 22 magnitude. However, the present surveys are generally limited to the ecliptic plane, and the mean observed orbital inclination of about 15° for TNOs used in the above estimates should be considered only as a lower limit due to the observational bias. In fact, objects with high orbital inclinations spend a large fraction of each orbit far from the ecliptic. Our estimates of the number of detectable TNOs may therefore be pessimistic. Only a large survey done by Gaia could give a spatially complete distribution of these objects down to the limiting magnitude. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]

Jewitt, D., Luu, J., 1993, AJ, 362, 730 Edgeworth, K.E., 1943, J. British Astron. Soc., 53, 151 Edgeworth, K.E., 1949, MNRAS, 109, 600 Kuiper, G.P., 1950, in Astrophysics, J.A. Hynek (ed.) (New York, McGraw-Hill), 375 Duncan, M.J., Quinn, T., Tremaine, S., 1988, ApJ, 328, L69 Fernandez, J.A., 1980, MNRAS, 192, 481 Quinn, T., Tremaine, S., Duncan, M.J., 1990, ApJ, 355, 667 Evans, J.M., Tabachnik, S.A., 2001 Marsden, B., http://cfa-www.harvard.edu/iau/lists/TNOs.html Durda, D.D., Stern, S.A., 2000, Icarus, 145, 220 Mon. Not. Astron. Soc., in press Trujillo, C.A., Jewitt, D.C., Luu, J.X., 2001, AJ, 122, 457 Barucci, M.A., Romon, J., Doressoundiram, A., Tholen, D.J., 2000, AJ, 120, 496 Barucci, M.A., Fulchignoni, M., Birlan, M., Doressoundiram, A., Romon, J., Boehnhardt, H., 2001, AfeA, 371, 1150 Doressoundiram, A., Barucci, M.A., Romon, J., Veillet, C., 2001, Icarus, in press Asher, D.J., Steel, D.I., 1993, MNRAS, 263, 179 Hahn, G., Bailey, M.E., 1990, Nature, 348, 132 Duncan, M.J., Levinson, H.F., Budd, S.M., 1995, AJ, 110, 3073 Levison, H.F., Duncan, M., 1997, Icarus, 127, 12 Levison, H.F., Dones, L., Duncan, M., 2001, AJ, 121, 2253 Barucci, M.A., Lazzarin, M., Tozzi, G.P., 1999, AJ, 117, 1929 Jewitt, D., Luu, J.X., Cheng, J., 1996, AJ, 112, 1225

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[22] Jedicke, R.J., Herron, J.D., 1997, Icarus, 127, 494 [23] Sheppard, S.S., Jewitt, D.C., Trujillo, C.A., Brown, M.J.I., Ashley, M.C.B., 2000, AJ, 120, 2687 [24] Larsen, J.A., et al., 2001, AJ, 121, 562 [25] Marzari, F., Sholl, H., 1998, Icarus, 339, 278 [26] Marzari, F., Sholl, H., Farinella, P., 1996, Icarus, 119, 192 [27] Milani, A., 1994. in Asteroids Comets Meteors 1993, Proc. IAU Symp., 160, 159 [28] Jewitt, D., Trujillo, C.A., Luu, J., 2000, AJ, 120, 1140 [29] Barucci, M.A., Capria, M.T., Coradini, A., Fulchignoni, M., 1987, Icarus, 72, 304

GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

PREPARING GAIA FOR THE SOLAR SYSTEM D. Hestroffer1

Abstract. The GAIA satellite will observe a large number of solar system objects, mainly asteroids, and although most of them shall be already known in the next decade, it will possibly discover new ones. The major scientific outcomes of this mission for the science of the Solar System is the survey of the inner-Earth orbits region, the determination of asteroids' physical parameters (masses, sizes, taxonomy...) for a large number of objects, detection of binary asteroids, accurate orbits determination, and tests of general relativity. Here we discuss the preparative work that should be done before launch regarding the scientific case, the software or instruments requirements, the catalogues output, and complementary ground-based observations.

1

Introduction

The GAIA mission will have a major impact on the science of the Solar System going from the inner part to the trans-neptunian region. Ideally no special treatment should be applied for the observations of solar system objects, i.e. they will be considered as stars in the raw data acquisition. However these objects have non-negligible or even large motions in the sky (specially for near-Earth objects), can be resolved or saturate the CCD. The full sky coverage of the scanning law, the relatively faint limiting magnitude, the possibility to observe at small solar elongations, the (modest) imaging resolution, and the high precision astrometric and photometric data that will be acquired during the 5 years of the mission are all together of high importance for the science of solar system objects. We shall first give an evaluation of what objects can be observed and what measure can be obtained (photometry, astrometry, radial velocity). Next we shall discuss what science can be achieved with the available data for asteroids' physical parameters and dynamics determination, reference frames determination, and for fundamental physics. Finally one should also consider the output catalogues: completeness and detection efficiency, what data should be published, is there a need of complementary (ground- or space-based) observations, etc. 1

IMC/Paris Observatory, France © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002036

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GAIA: A European Space Project The Scientific Case Orbits and Physical Parameters

GAIA will provide very accurate, basically uni-dimensional, directions of a huge number of asteroids and they should hence enable tremendous ephemerides improvement [1]. Nevertheless the situation may be less favorable for a fraction of the observed asteroids: newly detected objects and less observed ones. One should hence extend the analysis and study in more scrutiny those particular cases. It should be stressed that the efforts made nowadays by ground-based asteroids surveys (e.g. NEAT, LONEOS, LINEAR) will provide an almost complete catalogue of objects brighter than V < 19.5 and very likely V < 21.5 [2], so that most of the asteroids detected by GAIA will be already known with more or less accurate orbits. In a similar way the ESA mission Bepi-Colombo includes a NEA experiment that should discover asteroids inside the Earth orbit [3]. In fact discovering a new object is by itself of limited value; one will also foreseen for an orbit determination in order not to loose it on a next apparition. This is usually done by an appropriate follow-up which is in contradiction with a regular scanning law. The GAIA observations alone (including the measures of the velocity) may enable the recovery of newly discovered objects and provide sufficiently accurate orbits for this purpose, but this has to be carefully assessed (see Sect. 3.3). The photometry gathered in the various filters should also provide information on the asteroids taxonomy. Further analysis should determine which taxonomic classes can be derived and with what confidence limits, and the best suited photometric system. For instance one may test the efficiency of the G-mode method [4] regarding the photometric precision available as a function of the magnitude and the need of complementary data. The efficiency of the GAIA instrument for detecting (by direct imaging or via an astrometric signature) binary asteroids or satellites of asteroids and characterize their orbits should be analyzed. The mass and density are essential parameters that are in general barely known for asteroids. Presently less than a dozen of asteroids have mass estimates (with precisions that can reach 50%) and accurate density determinations are available for about the same number of bodies. GAIA should provide a huge step in this field with mass estimates for hundreds of objects. Asteroids masses can be determined from the effect of a close encounter on the astrometry of a perturbed body even if the astrometric measures are uni-dimensional and cover a small time-span as was the case for Hipparcos [5]. Further simulations should provide the actual number of deflectors that will be involved in asteroid-asteroid close encounters and more important, the precision of the mass determination (depending also on the actual astrometric precision and distribution of the observations of the perturbed asteroid). 2.2

Fundamental Physics

Asteroids astrometry can provide tests of general relativity, the most common one being derived from the perihelion precession. For this topic the preferred targets

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are asteroids with small semi-major axis and large eccentricities, but past tentative did not yield competitive results [6] mainly because of the limited precision of the measures. Among the 100000 asteroids cataloged today, about 300 show a perihelion precession larger than 20 mas s-l and about 10 would have a precession of the order of that of Mercury. The asteroids population is an interesting one because it provides a test at different distances from the Sun and is less sensitive to the not well known solar quadrupole2 [7]. The actual number of target asteroids, their observations distribution (including the scanning law and the detection efficiency) and their related astrometric precision should be analyzed in more details to better estimate how accurately the /3 parameter of the PPN3 can be determined. Such a study could also be extended to the analysis of planetary satellites with relatively large eccentricities. It has also be shown that observations of trojans and objects in a 2:1 mean-motion resonance may provide Nordvedt's TJ parameter and a test of the equivalence principle [9,10]. The GAIA observations even if very accurate may however cover a too small time-span to be valuable, but this topic should be addressed in more details. The linking of quasi-inertial reference frames can be made through the observations of QSOs and asteroids. Not all available objects may be retained for such a link; one will prefer those asteroids with very accurate orbits where e.g. photocentre displacement or mutual perturbations can be neglected or modeled with enough accuracy. Apart from the geodetic precession, there should be no rotation between these two reference frames. A significant rotation could be the trace of a vortex in the Universe and violate Mach's principle. The precision with which one can actually test this principle with the GAIA observations has to be estimated more carefully. It is stressed that for these topics not only the Earth orbit but also the asteroids' center-of-mass orbits must be accurate and free of any systematic errors. 2.3

Other Objects

GAIA will mainly observe main-belt asteroids (about 0.5-1 xlO 6 objects) but it will also observe or discover Atens, lEOs, trojans of Venus or of the Earth. In the outer region it will observe Chiron, Pluto-Charon and other bright KBOs or Centaurs [11]. Also other solar system objects brighter than magnitude V < 20 will cross the fields of view of the different GAIA instruments. The scientific value and the specificities of observations of comets and planetary satellites has not been addressed yet. Major planets may saturate the CCDs; for Uranus, Neptune accurate positions will be obtained over a short time span. It is stressed that the orbits of the inner planets are better defined than those of the external ones which are not frequently observed. Many planetary satellites will be observed 2 One should however keep in mind that a) the range in semi-major axis will remain relatively limited and b) that in the next decade, the solar quadrupole can be known with good accuracy by other means. 3 The 7 parameter is determined with enough accuracy within the GAIA mission [8].

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by GAIA and the observations will be different in some aspects to those of the asteroids. The proximity to the faint satellite of the parent planet or its rings has to be taken into account for the detection and measurements efficiency. Also the velocity distribution is different to that of asteroids. Orbits improvement has to be analyzed considering for instance the particular distribution in time of the GAIA observations. 3 3.1

Software and Instruments Requirements Instruments

For completeness I add some requirements even if their implementation on GAIA is impossible (x) or highly un-probable (o): x extend the photometry in the near-IR toward 1.1 um to better separate some taxonomic classes; x spectral range around 0.5-0.6 um for the spectra acquisition; x modify the scanning law with a smaller (<55 deg) angle to the Sun for a better detection efficiency of inner-Earth orbiting objects (Atens, trojans of Venus, etc.). o special tracking along the AMF of moving objects Via an adapted CCD reading. The astrometry of rapidly moving objects is not ensured in the Astro main field by a CCD reading phased to the motion of a star, this will decrease the number of observations and the precision on the astrometry (which may already be poor because of the blurring by the TDI mode); o increase the mission duration to better model or detect secular effects; o go to fainter magnitude V < 22 for the Spectro instrument, see [12] for position (detection) and also photometry (physical parameters). This is of special importance for the NEO and even more for the Centaur and KBO population which will be only marginally surveyed by GAIA. 3.2 Simulations The data acquisition and reduction pipe-line has to be written and tested for all instruments (Spectro and Astro). This includes the modelling of the PSF (taking into account the target's velocity, size and shape, and its location in the focal plane), the detection and identification algorithm, the orbit restitution from a short arc and the analysis of the catalogues completion. Once a moving object is detected from the Astro or Spectro instrument one should first check if it is an already known one. This can be done on ground by ephemerides calculation via an up-dated catalogue. The efficiency and robustness of such a minor planet checker has to be tested. If it appears that the object is a newly discovered one, one should ensure first to be able to recover it on the successive transits in the various FOVs and next to derive an approximate orbit in order to recover it on the next observation epoch. The knowledge of the velocity (tangential and eventually radial) and the use of the Spectro instrument with an additional sky mapper (SSM2) can be helpful for such a procedure. If such an identification procedure or orbit

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determination cannot be achieved by GAIA observations alone, one would require ground-based observations on the following night to avoid loosing the object. 3.3

Ground-Based Observations

Ground-based observations (or more generally complementary observations including DIVA, FAME, DENIS, etc.) can be needed for newly discovered objects (time complement) or to provide additional data (e.g. in the IR or near IR domain). If the recovery4 process cannot be ensured from GAIA observations alone, an alert procedure and a follow-up by other pointing telescopes would be helpful or necessary. It should be noted however that the problem of asteroids identification is already encountered in ground-based observations too when one tries to link observations over two short arcs obtained at two different epochs [13]. The necessity and cost of having dedicated telescopes (in both hemispheres), their efficiency in observing at small solar elongations, their size and automation must all be addressed. Note that the Japanese BSGC observatory is designed for such a purpose [14]. In any case, if the orbit determination and dedicated follow-up are not possible within the GAIA mission, an alert procedure should be implemented. For instance the NEO Coordination System of the Spaceguard Foundation provides to the interested community a list of observing priority [15]. 4

Catalogue Outputs

Stellar data (astrometric, photometric and spectrographic) can be corrupted by an asteroid close approach, this has to be properly identified and flagged at the quick-look level. Regarding the solar system, a few points have to be analyzed to know what/how data should be published. GAIA basically provides the gaiacentric uni-dimensional direction of the body's photocentre and magnitude in various filters. For practical reasons one would prefer to publish astrometric positions (i.e. the direction of the object as seen from the center of the Earth), but in order to derive this direction the planet's distance has to be known with a precision of about 30km [16]. In a few cases the ephemerides may not be accurate enough to allow such a construction and one would need to publish the gaiacentric position as well as the satellite orbitography (possibly with a geocentric position with lower accuracy) . Since the ephemeris improvement shall be undertaken during the reduction procedure one may think of publishing also the derived osculating elements. Such ephemeris improvement will have to take into account the perturbations of the more massive asteroids and the photocentre offset. The latter depends on the target size, shape and light diffusion on its surface, and is generally non predictable. It may be derived during the ephemeris improvement for the largest bodies [17], but for medium sized asteroids the situation is more troublesome. In a similar way other catalogues could be published: taxonomy, masses, etc. 4

To identify an object as a previously observed one, or in other words to ensure that 2 short arcs observations correspond to the same object.

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Glossary - Aten: objects evolving on orbit crossing that of the Earth (semimajor axis a < 1 AU and aphelion distance Q > 0.983 AU) and spending most of their time inside the Earth's orbit. These could represent 20% of the Earthcrossing population. - Centaur: object with an orbit between Saturn and Neptune, thought to be a dynamical transient from the Kuiper-belt to the inner region with eventually some cometary activity. - quadrature: position of a planet corresponding to a solar elongation of 90 degrees. - solar elongation: difference between the geocentric longitudes of the Sun and the planet. It is sometimes given as the angle between the Sun and the planet as seen from the Earth. - AMF: astrometric main field. - IEO: inner-Earth object. Objects with an orbit inside that of the Earth that could represent 50% of the Atens population. - KBO: Kuiper-belt object (or TNO). Object with a trans-neptunian orbit. - MBA: main-belt asteroid. - NEA or NEO: near Earth asteroid or near Earth object. - TNO: trans-neptunian object (or KBO).

References [1] ESA 2000, GAIA: Composition, Formation and Evolution of the Galaxy, Technical Report ESA-SCI(2000)4, (scientific case on-line at http://astro.estec.esa.nl/GAIA) [2] Elst, E.W., 2001, P&SS, 49, 781 [3] Bepi-Colombo, System and technology study report, 2000, An interdisciplinary cornerstone mission to the planet Mercury, ESA-SCI(2000)1 [4] Fulchignoni, M., et al., 2000, Icarus, 146, 204 [5] Bange, J.F., 1998, A&A, 340, L1 [6] Sitarski, G., 1992, AJ, 104, 1226 [7] Will, C.M., 1993, Theory and experiment in gravitational physics (Cambridge University Press) [8] Mignard, F., 2002, EAS Publ. Ser., 2 [9] Orellana, R.B., Vucetich, H., 1998, A&A, 200, 248 [10] Plastino, A.R., Vucetich, H., 1992, A&A, 262, 321 [11] Barucci, A., 2002, EAS Publ. Ser., 2, 351 [12] H0g, E., 2002, EAS Publ. Ser., 2 [13] Milani, A., et al., 2000, Icarus, 144, 39 [14] Isobe, S., 2000, Ap&SS, 273, 121 [15] Boattini, A., et al., 1999, DPS, 31, 2807 [16] Mignard, F., Ephemeris requirements for GAIA, SAG_FM_004 [17] Hestroffer, D., 1998, A&A, 336, 776

Posters

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

FURTHER PROCESSING OF THE HIPPARCOS VARIABILITY INDUCED MOVERS S. Detournay 1,2 and D. Pourbaix 2,3 1

Introduction

A small number of objects in the Hipparcos Catalogue Double and Multiple Systems Annex are unresolved binaries in which one of the component is variable. As a result, the photocentre shows a specific motion on the sky. These objects are classified as "Variability Induced Movers" (VIM) [1]. The motion of the photocentre can be modelled, with the assumptions that a reliable model is available for the chromaticity correction and that the pulsations are radial. However, the usefulness of the VIM model when the binarity is very unlikely (R type carbon stars) can also lead to question the reliability of the chromaticity correction (e.g. assumption of a constant V — /, . . . ) . Besides the five astrometric parameters ( p 1 , . . . ,p5) used to model the apparent motion of the center of mass, the VIM model requires two additional parameters (Da*, DS] to specify the position of the photocenter. These seven parameters are the unique minimizer of the least-square problem %2 = IE^V~1'E [2] where

2

Reprocessing the Intermediate Astrometric Data of the 288 Hipparcos VIM

The processing of the Hipparcos Intermediate Astrometric Data (IAD) used here is similar to the one previously applied to the R type carbon stars [3] with the VIM model instead of the single-star one. Unlike the original reduction, we evaluate whether the improvement of the VIM-solution over the single-star solution is significant by performing a F-test. It gives us the significance level a at which the 1 2 3

Universite de Liege, Belgium Universite Libre de Bruxelles, Belgium Postdoctoral Research, F.N.R.S., Belgium © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002037

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hypothesis that the two models are equivalent is accepted. Beside this, the quality of the fit can be characterized by the goodness-of-fit parameter F2

Assuming that %2 follows a chi-square distribution with v degrees of freedom, F2 should follow a N(0,l) distribution [4] even if values above 3 can sometimes represent rather good solutions for non-single stars models [2]. We accept the VIM

Fig. 1. a) w versus WHIP for VD < 25 mas. Filled squares and triangles denote stars for which the median magnitude is larger than 12 mag and for which the Hipparcos photometry might have been not reliable. b) The long-dashed curve represents the values of the Hipparcos Catalogue, the solid line corresponds to our treatment, the shortdashed line shows the values for those stars that we considered as VIM and the dotted line represents the F2 value computed from the main parameters for the 163 stars with Fl = 0. model if a < 5%, the remaining stars (157/288) being treated as single stars. Note that for some stars for which the VIM-model showed not to be justified, their large values of F2 indicate that the single-star model is not satisfactory either (solid and short-dashed curves of Fig. Ib). The comparison with the Hipparcos results is not trivial because the Main catalogue indicates that a few astrometric data were sometimes rejected (Fl) whereas the IAD files do not indicate which data where rejected for the VIM solution. Our reprocessed parallaxes are sometimes appreciably different from those found by Hipparcos, the deviation being greater than 50% for 24 of them when WHIP was positive (Fig. la). Further investigations show that these new parallaxes appear to be astrophysically likely [5].

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VIM in the Context of GAIA

With regard to the Hipparcos' results, about 106 stars observed by GAIA will be expected to be VIM and they should consequently be handled carefully. On the one hand, the GAIA large-scale photometric survey will provide the chromaticity correction needed for astrometry, unlike the Hipparcos reduction which assumed a constant V — I. But on the other hand, the high photometric sensitivity will make it possible to resolve the disk of evolved giant stars where flares could produce an additionnal motion of the photocenter (GAIA WG on Variable Stars). Moreover, VIM with a noticeable orbital motion (which we assumed not to be the case in the present work) should be treated using the full model (orbital+VIM) [6]. References [1] Wielen, R., 1996, A&A, 314, 679 [2] ESA, 1997, The Hipparcos and Tycho Catalogues, ESA SP-1200 [3] Knapp, G., Pourbaix, D. & Jorissen, A., 2001, A&A, 371, 222 [4] Kendall, M.G. & Stuart, A., 1978, The Advanced Theory of Statistics (Griffin) [5] Detournay, S. &: Pourbaix, D., 2001, in preparation [6] Soderhjelm, S., 1999, A&A, 341, 121

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

POTENTIALS AND DISTRIBUTION FUNCTIONS TO BE USED FOR DYNAMICAL MODELLING WITH GAIA-LIKE DATA* B. Famaey1 and H. Dejonghe2 1

Introduction

The GAIA mission will offer the wonderful opportunity to establish galactic dynamical models based on the data of a large number of stars. Indeed, complete positional and kinematical data over a large volume in the Galaxy are needed to construct well constrained models: we do not have such data for the moment, but this is precisely what the GAIA satellite will provide. We present here new tools to establish axisymmetric equilibrium models of the Milky Way, based on GAIA-like data. We know that our Galaxy is a barred one and so, the axisymmetric hypothesis is not correct, but axisymmetric models are a prerequisite for perturbation theory (for example the theory of spiral density waves) and thus they are still very useful. The models we wish to establish are pairs (V, F) where V is the gravitational potential generated by the whole mass distribution including the dark matter, and F is the distribution function in phase space for late-type tracer stars in the galactic disk. For an equilibrium model (stationary potential and stationary distribution function solution of the collisionless Boltzmann equation), we know that the distribution function in phase space depends only on the integrals of the motion. During the last decade, many studies (e.g. [1]) have shown that the distribution function of tracer stars in the Milky Way has to depend on three isolating integrals of the motion, especially if information on the vertical motion of the stars is present as it will be with GAIA. In order to have an analytic third integral, in addition to the binding energy and the vertical component of the angular momentum, we use Stackel potentials [2]. * We would like to thank A. Jorissen and K. Van Caelenberg for their precious help. 1 Institut d'Astronomie et d'Astrophysique, Universite Libre de Bruxelles, Belgium; Ph.D. student F.R.I.A. e-mail: [email protected] 2 Sterrenkundig Observatorium, Universiteit Gent, Belgium © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002038

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Fig. 1. Left: the mass density in the plane. Right for a fixed value of the axis ratio of the thin disk and of the halo, the figure displays all the values of the axis ratio of the thick disk and of the contributions of the disks to the total mass that are consistent with Hipparcos observables. 2

The Potentials

In this contribution, we continue the work of Batsleer & Dejonghe [3], who presented a set of simple axisymmetric Stackel potentials with two mass components (halo and disk) and a flat rotation curve. The existence of a thick disk as a separate stellar component is now well documented (e.g. [4]): so we have generalized the Batsleer's potentials by adding a thick disk to them. Our new Stackel potentials are described by five parameters. They turn out to have an effective bulge because the mass density grows faster than an exponential near the center in the plane. The other motivation to continue Batsleer's work is that, in recent years, Hipparcos data have enabled an accurate determination of some fundamental galactic parameters in the solar neighbourhood: the mass density pQ [5,6] and the Oort constants A and B [7]. We have looked for the Stackel parameters that are consistent with the above observables: as can be seen in Figure 1, many different combinations of the parameters are found to be consistent with those observables. 3

The Modified Fricke Components and the Modeling

In the future we will test the ability of these potentials to be combined with a distribution function, in order to reproduce kinematical data like those that will be provided by GAIA. This distribution function will be expressed as a linear combination of basis functions depending on a few parameters. We have defined new component distribution functions (modified Fricke components) with 9 parameters, that depend on three integrals of the motion and that can represent realistic stellar disks when a judicious linear combination of them is chosen in a realistic galactic potential. These components have a finite extent in the z-direction and have realistic scale lengths. More details can be found in [8]. To construct our model, the method will be iterative: we will choose a potential, find a linear combination of modified Fricke components that fits the data by

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using the quadratic programming technique described in [9], and then modify the potential in the light of the quality of that fit. This will provide some new constraints on the mass distribution in the Galaxy and some information on the dynamical state of the different late-type stars (since the Galaxy is a system with a long memory, this could provide information on the history of the Milky Way). References [1] [2] [3] [4] [5] [6] [7] [8] [9]

Durand, S., Dejonghe, H., Acker, A., 1996, A&A, 310, 97 de Zeeuw, T., 1985, MNRAS, 216, 273 Batsleer, P., Dejonghe, H., 1994, A&A, 287, 43 Ohja, D., Bienayme, O., Robin, A., Mohan, V., 1994, A&A, 290, 771 Creze, M., Chereul, E., Bienayme, O., Pichon, C., 1998, A&A, 329, 920 Holmberg, J., Flynn, C., 2000, MNRAS, 313, 209 Feast, M., Whitelock, P., 1997, MNRAS, 291, 683 Famaey, B., Van Caelenberg, K., Dejonghe, H., 2001, MNRAS, in preparation Dejonghe, H., 1989, ApJ, 343, 113

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

ON THE KINEMATIC DECONVOLUTION OF THE LOCAL LUMINOSITY FUNCTION

A. Siebert1, C. Pichon1, O. Bienayme1 and E. Thiebaut2 Abstract. A method for inverting the equation of stellar statistic including proper motions is tested. The supplementary constraint required by dynamical consistency is used in order to break the degeneracy. The inversion gives access to both the kinematics and the luminosity function of each population. Its application to data such as the Tycho catalog (and in the near future GAIA) will lead - provided the vertical potential, and/or the asymmetric drift or WQ are known to a non-parametric determination of the local neighbourhood luminosity function without any reference to stellar evolution tracks. It should also yield the proportion of stars for each kinematic component and a kinematic diagnostic to split the thin disk from the thick disk or the halo.

1

Introduction

This work focus on the inversion of the stellar statistic equation [1]. We show that it is possible to break the degeneracy of this equation and to recover the luminosity function of the underlying stellar populations if we use the additional constraint given by kinematics [2]. Using this additional constraint the equation writes

where dTV is the number of star in a bin of the observable space, [Lo,0] is the luminosity function in the absolute luminosity, kinematic index space and /,g(r, u) the distribution function indexed kinematically (see Sect. 2). This equation can be inverted using a non parametric regularised method [3] and gives access to a kinematicaly indexed luminosity function. The kinematic index allows us to recover the luminosity function associated to a given population. 1

Observatoire de Strasbourg, 11 rue de 1'Universite, 67000 Strasbourg, France CRAL, Observatoire de Lyon, 9 avenue Charles Andre, 69561 Saint-Genis-Laval Cedex, France 2

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376

Fig. 1. Left: reconstructed luminosity function in the [Lo,/3] plane for a fictitious HR diagram together with the reconstruction error (in %) for two values of B — V in the red part of the HR diagram and at an intermediate colour, showing to the turnoff point of the oldest population. Right: reconstruction error as a function of the signal to noise ratio in the simulated star counts catalog. 2

Epicyclic Model

A distribution function accounting for density and velocity distributions can be written

where H is the Heaviside function, Lz the angular momentum, 0 the angular velocity, K the epicyclic frequency, pD the density, Rc the radius of the circular orbit of angular momentum Lz, CTR (resp. az] the radial (resp. vertical) velocity dispersion and /3 the kinematic index. Here po,£l,K,aR,crz and Ec are known functions of momentum Lz. The energies, Ez and ER are function of the potential given by

3

Results

The inversion procedure has been tested on a fictitious HR-diagram corresponding to the superposition of two populations with distinct turnoff points and velocity dispersions (i.e. age and kinematic index /?). Figure 1 (left panel) shows the reconstructed HR diagram in the [.Z/o,/#] plane together with the reconstruction

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error (in %) for two sections of B — V for a S/N of 103. Those two sections correspond to the colour for the turnoff of the oldest population (upper panel) and to the red part of the assumed HR diagram where giant branch and main sequence are well separated for both populations (lower panel). It should be noticed that no artifact is produced by the method when positivity is imposed on the reconstructed luminosity function. The right panel of Figure 1 shows how the reconstruction quality is influenced by the S/N ratio of the star count catalog. If the S/N ratio is large enough (i.e. large number of stars in the catalog) the reconstruction error becomes very small (less than 1%) but becomes important (roughly 10%) if the S/N ratio is less than 100. References [1] von Seeliger, 1898, Abh. K. Bayer Akad. Wiss Ser. II Kl, 19, 564 [2] Pichon, C., Siebert, A., Bienayme, O., 2001, submitted to MNRAS [3] Wahba, G., Wendelberger, J., 1979, Monthly Weath. Rev., 108, 1122

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

GALACTIC STRUCTURE AND EVOLUTION FROM STELLAR DYNAMICS A. Digby1, J. Cooke1, N. Hambly1, I.N. Reid2 and R. Cannon3 1

Introduction

A better understanding of solar neighbourhood stellar kinematics can significantly further our knowledge of the structure and evolution of the Galaxy. Using large stellar samples with parallaxes and proper motions from SuperCOSMOS scans of Schmidt plates in three fields, we are probing the Galactic structure in three directions. Identifying halo subdwarfs by proper motion selection we can obtain the faint halo luminosity function, and look for kinematic effects such as star streams and velocity gradients. 2

Data and Methods

The plate data consist of a large and unique series of about 70 plates per field with a magnitude limit of V ~ 18.5, taken specifically for the determination of proper motions and parallaxes. The three fields are approximately orthogonal so as to maximise the kinematic and structural information obtainable, and to probe both above and below the Galactic plane. SuperCOSMOS scans return parameters for each image on the plates (position, size, shape, orientation etc.), and these are then analysed using astrometric reduction software developed by Murray [1]. The result is a sample of around 20000 stars per field, each with measured proper motions and parallaxes, and, combined with CCD photometry, calibrated apparent magnitudes. The proper motions and magnitudes can be employed to separate the sample into the Galactic halo and disc components through the method of reduced proper motion (RPM). Defined as Hv = 5 + V + 5 log n = Mv + 5 log VT - 3.378, a plot of RPM against colour separates stars of different populations through their different luminosities and velocity distributions (Fig. 1). 1 2 3

Institute for Astronomy, University of Edinburgh, Blackford Hill, Edinburgh EH9 3HJ, UK STScI, 3700 San Martin Drive, Baltimore, MD 21218, USA AAO, P.O. Box 296, Epping, NSW 2121, Australia © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002040

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380

Fig. 1. Provisional Reduced Proper Motion Diagram (RPMD) for SA94 stars with p, > 0.05"yr-1. The dotted line separates probable halo stars (left) from disc stars (right - thin and thick disc lines indicated). Elimination of remaining systematic errors will significantly improve the population separation.

3

Results

The selection by reduced proper motion allows us to detect large numbers of halo subdwarfs around 200 per field. With all three fields combined this will allow a good estimation of the faint halo luminosity function which is at present only poorly determined [2]. Three widely separated lines of sight also enable us to look for stellar streams in the halo. The extent of these kinematic signatures of initial "fragments" and subsequently absorbed satellites is currently uncertain (see e.g. [3] & references therein). Although our relatively bright magnitude limit does not permit us to probe to great distances, the global halo kinematics can be reconstructed from local halo stars since their orbits extend well into the outer parts of the Galaxy [4]. Any detections of streams can be followed up over a greater area of coverage (most of the southern sky) by using proper motions from the SuperCOSMOS Sky Surveys [5]. We will also be able to investigate other kinematic effects in the disc and halo, such as the possibility of velocity gradients [3].

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4

Current and Future Work

A preliminary 4-plate analysis of one field has derived disc and halo luminosity functions [6]. A 45-plate reduction of the same field is close to completion, and initial results suggest a good population separation in the RPMD (Fig. 1). This will be much improved upon by further removal of systematic positional errors, and new CCD photometry recently obtained for the remaining two fields will provide a better magnitude calibration. With potential subdwarf samples for the three fields, spectroscopic follow-up can be obtained to confirm the stellar type and yield radial velocities; multiobject spectrographs such as 6dF will be ideal for such observations. With threedimensional velocity information any systematic trends in kinematics can be more readily and accurately identified. GAIA will of course be able to measure stellar positions and kinematics to a far greater accuracy over the whole sky. However, until sufficient numbers of long-term CCD observations can be obtained, high-precision scans of photographic material remain one of the best methods for measuring proper motions and parallaxes in order to provide greater insight into the uncertain and complex structure and kinematics of the Galaxy. References [1] Murray, C.A., et al., 1986, MNRAS, 223, 629 [2] Binney, J., 1999, MNRAS, 307, L27 [3] Chiba, M., Beers, T.C., 2000, AJ, 119, 2843 [4] May, A., Binney, J., 1986, MNRAS, 221, 857 [5] Hambly, N.C., et al., 2001, MNRAS, in print (www-wfau.roe.ac.uk/sss) [6] Cooke, J.A., Reid I.N., 2000, MNRAS, 318,

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GAIA: A European Space Project O. Bienayme and C. Turon (eds) EAS Publication Series, Vol. 2, 2002

STELLAR POPULATIONS IN THE LARGE MAGELLANIC CLOUD: THE IMPACT FROM GAIA A. Kucinskas1,2, A. Bridzius3 and V. Vansevicius3 Although GAIA will survey primarily stellar populations of the Milky Way, a large number of extragalactic objects will be accessible as well, including stellar populations of the Magellanic Clouds. It is therefore important to know what and how can GAIA contribute in this context too. In this work we attempt to assess the expected scientific output from the photometric studies of stellar populations in the globular clusters of the Large Magellanic Cloud. Photometric observations of individual stars in the globular clusters were simulated using the numerical GAIA machine developed by the Vilnius GAIA group [1]. Simulated photometric observations were used further to derive basic astrophysical parameters (T e ff, log g, [Fe/H] and EB-V] with the 4-D stellar classification engine [2]. Finally, population ages were derived using isochrone fitting, with the isochrones of the Padova group [3]. We find that accurate effective temperatures of individual stars can be obtained down to V1 ~ 18 (broad-band magnitude V of the ASTRO-1 telescope [4] in GAIA 3G photometric system [5]) for the populations of any metallicity within the studied metallicity range ([Fe/H] = — 0 . 4 . . . — 1.7). Precise metallicities, however, can only be obtained for the brightest cluster stars (V1 < 17.5). However, since the number of such objects usually amounts up to several tens in case of each cluster, this may indeed provide a good estimate of the cluster metallicity (for more details see [6]). Our tests show that age estimates obtained employing V1 vs. Teff diagrams are generally more precise than those obtained from observed CMDs (e.g., V1 vs. (V1 — I1), etc.). This is especially noticeable for young star clusters, where in most cases isochrone fits to the observed CMDs would fail to provide a cluster age estimate (Fig. la). Alternatively, V1 vs. Teff diagrams can effectively trace the main sequence turn-off (MSTO) point of the young clusters (<0.5 Gyr; Fig. Ib), and thus can provide reliable age estimates for a large number of star clusters in the LMC. Age derivation using isochrone fitting becomes increasingly more problematic with increasing cluster age. In case of LMC clusters older than ~l-2 Gyr, the 1 2 3

Institute of Theoretical Physics and Astronomy, Gostauto 12, Vilnius 2600, Lithuania Astronomical Observatory, Vilnius University, Ciurlionio 9, Vilnius 2009, Lithuania Institute of Physics, Gostauto 12, Vilnius 2600, Lithuania © EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002041

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MSTO point can not be reached with GAIA, and thus the age derivations should rely entirely on the isochrone fitting to the RGB and AGB. In such case, however, isochrone fits to both V1 vs. Teff diagrams and observed CMDs practically fail to provide cluster ages for clusters older than ~8 Gyr (for details see [6]).

Fig. 1. (a) Simulated CMD of a cluster with Z = 0.008 and age of 0.125 Gyr. Isochrone ages are indicated (all for Z = 0.008); (b) Simulated Vi versus Teff (derived using 4-D stellar classification engine) of a cluster with Z = 0.008 and age of 0.125 Gyr. Isochrone ages are indicated (all for Z = 0.008). The work was partly supported by a Grant NBOO-NO30 by the Nordic Council of Ministers and by a Grant T-535 by the Lithuanian State Science and Studies Foundation. We also thank the organizers for the financial support helping to attend the conference. References

[i] Deveikis, V., Vansevicius, V., 2001, Ap&SS, submitted Bridzius, A., Vansevicius, V., 2001, Ap&SS, submitted Girardi, L., Bressan, A., Bertelli, G., Chiosi, C., 2000, A&AS, 141, 371 [4] GAIA: Composition, Formation and Evolution of the Galaxy, 2000, ESA-SCI(2000)4, Concept and Technology Study Report [5] Straizys, V., H0g, E., Vansevicius, V., 2000, GAIA-CUO-078, Technical Report from Copenhagen University Observatory [6] Kucinskas, A., Bridzius, A., Vansevicius, V., 2001, Ap&SS, submitted [2]

[3]

Conclusion

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FROM HIPPARCOS TO GAIA, AND BEYOND C. Turon1 1

From Hipparcos to GAIA, and Beyond

High accuracy global astrometry is a clue to many topics in astrophysics as it provides the only model independent determination of distances and transverse kinematics. Hipparcos opened this new field with such a success that it is now followed by several other missions. The most ambitious of these is certainly GAIA, included in the ESA's Science Programme as one of the next two "cornerstones". With Hipparcos, in addition to a precise description of the solar neighbourhood, accurate kinematics of bright stars as far as the Magellanic Clouds have been obtained. Absolute parameters have been derived for all types of stars in the central zone of the HR diagram, and also for the closest stars outside. An impressive harvest of results is following, mainly in the domains of stellar physics (absolute luminosities, ages, evolution, comparison with stellar models, brown dwarf desert, transit of an extra solar planet, etc.); galactic physics (3Dstructure and detailed kinematics of the Hyades; distances, ages and kinematics of Pleiades and of other nearby clusters and associations; disk kinematical evolution, local mass density and dark matter distribution; local structure of the ISM; halo formation; etc.); distance and age scales (longer distances, smaller Hubble constant, older globular clusters, etc.); masses and orbits of minor planets; materialisation of the ICRS; 7 parameter; etc. As a result, about 2500 papers have been published since 1997, i.e. about one publication per day: spectacular advances in our understanding of the physics of stars and of the closest part of our Galaxy, in the determination of distances and ages in the Universe, and... many questions opened by this new knowledge! The GAIA mission [1-4] has been approved in continuation of this success, to take full benefit of the expertise gained from the Hipparcos mission and extend high accuracy astrometric observations to a huge number of objects up to the edges of the Galaxy and into the galaxies of the Local Group. During this week, we had a comprehensive series of presentations detailing the expected performance of GAIA and the impressive potentialities of the mission. The basic data which

1 DASGAL/UMR CNRS 8633, Observatoire de Paris, France e-mail: [email protected]

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will be obtained are the following: • micro-arcsecond astrometry associated with radial velocity determination, leading to high accuracy on the 6 parameters of the phase space (position, distance and spatial velocity); • photometric information covering a large spectral range with 15 bands from ~280 to ~1000 nm, required to obtain the astrophysical complementary information for each object; • a billion of objects observed in a survey mode, i.e. a high discovery potential obtained by a systematic investigation and measurement of all observable stars, solar system and extragalactic objects; • the detection of some 30000 extra-solar planets and of 107 to 108 resolved binaries. This unprecedented collection of observations will allow that precise information is obtained on the totality of the HR diagram (including evolved stars, stars in rapid evolutionary stages, very massive stars, nearby very faint stars, etc.), on all observable stars throughout our Galaxy and tens of thousands of bright stars in nearby galaxies, on the different belts of minor bodies in the solar system (105 to 106 new objects observed), on some 500000 quasars, on 106 to 107 distant galaxies, and on ~105 super novae in very distant galaxies, etc. Hipparcos observed many stars in the solar neighbourhood, but only a few stars in the spiral arms, very few stars in the thick disk and the halo, no stars in the bulge or bar, and no (intrinsically) very bright or very faint stars. GAIA will be able to observe all visible stars in the thin and thick disks, and in the halo, many stars in globular clusters, many stars in the bulge, and 104 to 107 bright stars in the galaxies of the Local Group (106 to 107 in each of the Magellanic Clouds, more than 104 in M 31 or M 33). For comparison, the number and characteristics of stars for which distances accurate to better than 10% have been or will be obtained by the different astrometric missions are given in Table 1. A more detailed comparison is given in [5]. Moreover, GAIA is the only mission simultaneously providing radial velocity observations and a complete astrophysical diagnostic in complement to extremely accurate distance and kinematical measurements [6-8]. The data reduction is a challenge because of the database size (10 to 100 TB of compressed data), but also because of the intricate relationships between the observed object characteristics, the satellite orbital and attitude parameters, and the instrument calibration [2], [9]. However, even if GAIA is to provide a huge amount of data... we will still have to extrapolate to non observed stars because they are too faint in the visible wavelengths, non observed stars because they stand in the zone of avoidance, non observed stars because they stand in extremely high density areas, non observed radial velocities, non observed astrophysical parameters, non observed minor bodies of the solar system because they are too faint, non observed minor bodies because they are not recognized, etc.

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Table 1. Number and characteristics of stars with relative error of distance better than 10%.

Mission Hipparcos GAIA Diva Fame Sim

2

Number of stars

Vlim

21000 220 millions -100000 -200000 -20 000

12.4 20-21 15 15 20

dlim

220 -25 -500 -2000 -25

pc for V pc for V pc for V pc for V pc for V

< 9 < 12 < 9 < 9 < 20

Florilege

After a presentation of the characteristics of the mission, most of this week was devoted to presentations detailing the applications expected from the GAIA data in diverse fields of astronomy and astrophysics. A few striking sentences are quoted below (by definition, the choices made in a "florilege" are somewhat arbitrary: they reflect instant reactions throughout the school): • Even though it is a side objective of the mission, GAIA is probably the best way to determine 7 in the ten coming years (expected precision between 1(10-6 and 10- 7 ) [10]; • We will have to wait for GAIA (after progresses from the theoretical side, from ground-based spectroscopy, and from space asteroseismology) to really probe stellar interiors and to be able to predict most phases of stellar evolution with confidence [11]; • "If you retain only one thing from my talk: observe with the best possible accuracy very massive stars in galaxies of the Local Group at low Z" (accurate determination of WR luminosities will have far reaching implications for the masses of the pre-supernova progenitors and for stellar nucleosynthesis) [12]; • M V (TO) is the best clock that stellar evolution theory can provide for population II stars and GAIA will provide essential contribution in this respect (direct distances, membership in globular clusters, improvement of reddening determinations, etc.) [13]; • The structure, the space distribution, the velocity distribution, the [M/H] distribution of the bulge, thick disk and inner spheroid are described through AB, GB, RHB giants with Mv > 1.5. These are clues to reconstruct the past stellar formation rate; • GAIA will offer the first check of the universality of period-luminositymetallicity relation for Cepheids [14];

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• GAIA will discover and/or characterize more than 107 astrometric binaries, 106 eclipsing binaries, 106 spectroscopic binaries, 105 orbits of resolved binaries, 10000 stars with masses known to better than 1% all over the H-R diagram [15]; • The numbers of giant planets that could be revealed by GAIA add up to more than 2000 orbits of Giant planets around solar mass stars. The statistical value of such a sample is fundamental for critical testing of theories on planet formation and evolution. Also, one immediately realizes the uniqueness of the GAIA sample of measured planets [16]; • GAIA will provide a clear description of the correlations between age, metallicity and kinematics. These are the key parameters to establish a scenario of galactic evolution. The real challenge: the interpretation [17]; • The exciting thing is that the galactic potential will be determined in great detail, hence the distribution of dark matter finally mapped [18]; • GAIA will better study the central part of M 31 than of our Galaxy; • Stars know the final galactic potential when forming... (i.e. they know the size of the galaxy in which they are being formed); • To be able to disentangle the age-metallicity degeneracy, one needs metallicities for every star; • GAIA will unravel the merging history of our Galaxy: past mergers should be identifiable as fossil remains in the Galactic halo [19]; • With GAIA, it will become possible to measure directly the distance of a large sample of stars in the SMC and the LMC and the metallicity distribution in the different regions of the MCs. The chemical abundance of objects with [Fe/H] < — 3.0 contains clues to the conditions of star formation at the earliest times. Possible in the MCs if GAIA is able to obtain (low resolution) spectra of stars with 16 < V < 18 [20]; • GAIA will bring a revolution in the understanding of the dynamics of the Local Group: internal dynamics, stream motions, dark matter content, tidal deformations, etc. [21]; • Similarities and differences of large disk galaxies in the Local Group and of their numerous dwarf companions: GAIA will easily map AGB and other luminous stars (the challenge is to go down to the tip of the Red Giant Branch) in these galaxies [22]; • QSO survey will be very efficiently performed by the GAIA multicolour photometry complemented by hints on the parallaxes and proper motions [23]; • GAIA can discover 105 —10 6 new objects in the solar system (including nearEarth asteroids), and change our views of the inner and outer Solar System objects [24,25]; • Please, with GAIA, find systems similar to the solar system!

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391

Time Scales of the Missions

The time scales of both missions, Hipparcos and GAIA, are comparable. For Hipparcos, the basic idea date back to ~1965. The mission was proposed to ESA in 1977, included in the scientific programme in 1980, and the satellite launched in August 1989. The scientific data was collected until March 1993, and the final catalogue published in June 1997. For GAIA, the basic idea was given in 1993. The mission was proposed to ESA in 1993, included in the scientific programme in 2000. The launch is possible from 2010. Preparations already started in many domains and numerous preliminary studies have to be performed by the scientific community: scientific studies, simulations (of the instrument, of the data collection, of the data reduction scheme, etc.) in order to be ready to provide industry with clear specifications of the instrument by the end of 2003. 4 4.1

To Be Investigated to Optimise the Instrument Astrometric Capabilities • For which scientific applications would a better accuracy for the brightest stars (better than 4 uas) be required? — absolute luminosities of stellar candles? - absolute luminosities of very massive stars? — better astrometric detection of extra-solar planets? — other? • Which is the best accuracy achievable, as a function of magnitude and colour?

4.2

Photometric Capabilities • Investigate the capabilities of various broad band and intermediate band photometric systems — optimise the observation of faint stars, i.e. optimise photon counts; — optimise the determination of astrophysical parameters (effective temperature, metallicity, other abundances, gravity) for large ranges of spectral types and luminosity classes, i.e. optimise the number, position and profile of the filters. • Investigate the uses of a higher photometric accuracy — optimise the photometric detection of extra-solar planets; — optimise the discovery of variables stars, supernovae, etc. • improve the sensitivity towards near IR — for a better detection of minor bodies in the solar system; - for a better detection of stars in obscured areas, etc.

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4.3

Spectroscopic Capabilities • For which scientific applications would it be useful to reach fainter stars, at the expense of lower resolution spectra? • For which scientific applications would it be useful to better determine astrophysical parameters, using higher resolution spectra? • Further investigate the best way to determine the extinction.

4.4

Spectroscopic Sky Mapper Capabilities • For which scientific applications would it be useful to reach fainter stars with the Spectroscopic sky mapper? • Investigate if the Spectroscopic sky mapper could provide good enough parallaxes for brown dwarfs down to 21 mag (very nearby sources)?

4.5

All Instruments • Investigate various sampling schemes, to optimise the detection and observation of different types of objects (point-sources, double or multiple sources, extended sources, overlapping images) versus downlink rate; • Investigate the complementarities between astrometric, photometric and spectroscopic observations; • Explore connectivity of data (satellite, instrument, sources); • Explore the effect of mission length on the detectability of extra-solar planets, of brown dwarfs in stellar systems, etc.

4.6

But Also... Scientific Preparations

In addition to the several points already mentioned above, many other investigations require developments, modelling, simulations, etc. These will have to be realised in the coming years. A first approach of what has to be prepared was presented by F. Mignard for fundamental physics [10], A. Baglin for stellar physics [11], M.A.C. Ferryman for sub-stellar objects, A.G.A. Brown for galactic physics [28], F. Mignard for the inertial frame [23], and D. Hestroffer for solar system objects [29]. A selection of these points are quoted below: • improve the modelling of white dwarfs [10]; • improve hydrodynamics of stellar interiors [11]; • have a fresh look at deriving stellar parameters and improve calibrations of theoretical versus observed global stellar parameters [11,28]; • investigate if it is valuable to detect brown dwarfs down to 21 mag [26,27]; • what follow-up observations will be required on ground for extra-solar planets detected with GAIA? • investigate new methods to determine extinction and build 3D extinction map [28]; • investigate new methods for dynamical modelling of the Galaxy [18];

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• consider massive ground-based spectroscopy of stellar fields with faint stars [28]; • preselect "clean" QSOs and study their photometric stability [23]; • improve ephemerides of solar systems bodies, in particular phase effect [29]. 5

Message to All Participants

From now to the end of 2003, we have the extraordinary chance of having the possibility to influence the final definition of specific parts of the GAIA instrument (with a solid scientific case), and to bring strong arguments to force a launch in 2010.

Think big! Be creative! But... the design of the instrument must converge! Also think of new methods for handling and exploiting this huge amount of data of unprecedented accuracy and homogeneity: start to think statistically!

Think different! References [1] Ferryman, M.A.C., de Boer, K.S., Gilmore, G., et al., 2001, A&A, 369, 339 [2] Ferryman, M.A.C., 2002, EAS Publ. Ser., 2, 3 [3] Lindegren, L., Ferryman, M.A.C., Bastian, U., et al., 1993, GAIA - Proposal for a Cornerstone Mission concept submitted to ESA in October 1993, Technical Report, Lund [4] Lindegren, L., Ferryman, M.A.C., 1996, A&AS, 116, 579 [5] Mignard, F. & Rceser, S., 2002, EAS Publ. Ser., 2, 69 [6] H0g, E., 2002, EAS Publ. Ser., 2, 27 [7] Munari, U., 2002, EAS Publ. Ser., 2, 39 [8] Katz, D., 2002, EAS Publ. Ser., 2, 63 [9] Torra, J., Luri, X., Figueras, F., Jordi, C. & Masana, E., 2002, EAS Publ. Ser., 2, 55 [10] Mignard, F., 2002, EAS Publ. Ser., 2, 107 [11] Lebreton, Y. & Baglin, A., 2002, EAS Publ. Ser., 2, 131 [12] Maeder, A., 2002, EAS Publ. Ser., 2, 145 [13] Cacciari, C., 2002, EAS Publ. Ser., 2, 163 [14] Luri, X., Figueras, F. & Torra, J., 2002, EAS Publ. Ser., 2, 171 [15] Arenou, F., Halbwachs, J.-L., Mayor, M. & Udry, S., 2002, EAS Publ. Ser., 2, 155 [16] Lattanzi, M., Casertano, S., Sozzetti, A. & Spagna, A. 2002, EAS Publ. Ser., 2, 207 [17] Robin, A.C., 2002, EAS Publ. Ser., 2, 233 [18] Binney, J., 2002, EAS Publ. Ser., 2, 245 [19] Helmi, A., 2002, EAS Publ. Ser., 2, 273 [20] Spite, M., 2002, EAS Publ. Ser., 2, 287 [21] Ibata, R., 2002, EAS Publ. Ser., 2, 305 [22] Wyse, R.F.G., 2002, EAS Publ. Ser., 2, 295 [23] Mignard, F., 2002, EAS Publ. Ser., 2, 327

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[24] Zappala, V. & Cellino, A., 2002, EAS Publ. Ser., 2, 343 [25] Barucci, M.A., Romon, J., Doressoundiram, A., de Bergh, C. & Fulchignoni, M., 2002, EAS Publ. Ser., 2, 351 [26] Haywood, M. & Jordi, C., 2002, EAS Publ. Ser., 2, 199 [27] Baraffe, I., 2002, EAS Publ. Ser., 2, 191 [28] Brown, A.G.A., 2002, EAS Publ. Ser., 2, 277 [29] Hestroffer, D., 2002, EAS Publ. Ser., 2, 359

Index

Arenou F. 155 Baglin A. 131 Baraffe I. 191 Barucci M.A. 351 Belokurov V. 257 Bertelli G. 265 Bienayme O. 375 Binney J. 245 Bridzius A. 67, 383 Brown A.G.A. 277 Cacciari C. 163 Cannon R. 379 Casertano S. 207 Cellino A. 343 Cooke J. 379 de Bergh C. 351 Dejonghe H. 371 Detournay S. 367 Digby A. 379 Doressoimdiram A. 351 Drazdys R. 67 Egret D. 179 Evans N.W. 257 Famaey B. 371 Figueras F. 55, 171 Fulchignoni M. 351

Garcia-Berro E. 123 Gomez A. 63 Halbwachs J.-L. 155 Hambly N. 379 Hay wood M. 199 Helmi A. 273 Hestroffer D. 359 H0g E. 27, 321 Ibata R. 305 Isern J. 123 Jordi C. 55, 199 Katz D. 63 Klioner S.A. 93 Knude J. 225 Kucinskas A. 383 Lattanzi M. 207 Lebreton Y. 131 Luri X. 55, 171 Maeder A. 145 Masana E. 55 Mattila K. 321 Mayor M. 155 Mignard F. 69, 107, 327 Morin D. 63 Munari U. 39

Ferryman M.A.C. 3 Pichon C. 375 Pourbaix D. 367 Reid IN. 379 Robichon N. 215 Robin A.C. 233 Roeser S. 69 Romon J. 351 Salaris M. 123 Siebert A. 375 Sozzetti A. 207 Spagna A. 207 Spite M. 287 Thiebaut E. 375 Torra J. 55, 171 Turon C. 387 Udry S. 155 Vaccari M. 313 Vansevicius V. 67, 383 Viala Y. 63 Wyse R.F.G. 295 Zappala V. 34

Acheve d'imprimer sur les presses de I'lmprimerie BARNEOUD B.P. 44 - 53960 BONCHAMP-LES-LAVAL Depot legal: mars 2002 - N° d'imprimeur :

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