GAIA: At the Frontiers of Astrometry 9782759803019, 9782759806089

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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: 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 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).

F. Mignard and S. Roeser: Space Astrometry Missions

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

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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.

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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

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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.

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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 ( (^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

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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.

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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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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

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,

1040

[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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[12] [13] [14] [15]

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

[23]

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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 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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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

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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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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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

Niels Bohr Institute for Astronomy, Geophysics and Physics, Juliane Maries Vej 30, 2100 K0benhavn 0, Denmark © EAS, EDP Sciences 2002 DOT: 10.1051/eas:2002021

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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

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

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

© EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002022

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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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[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

[27] Fux, R., 1999, A&A, 345, 787 [28] Weiner, B.J., Sellwood, J.A., 1999, ApJ, 524, 112 [29] Lopez-Corredoira, M., Hammersley, P.L., Garzon, F., et al., 2001, A&A, 373, 139 [30] Lopez-Corredoira, M., Garzon, F., Beckman, J.E., et al., 1999, AJ, 118, 381 [31] Burton, W.B., 1988, Galactic Extragalactic Radio Astron., 295 [32] Burton, W.B., Te Lintel Hekkert, P., 1986, A&AS, 65, 427 [33] Derriere, S., 2001, Ph.D. Thesis, Universite Louis Pasteur, Strasbourg [34] Carney, B.W., Seitzer, P., 1993, AJ, 105, 2127 [35] Derriere, S., Robin, A. C., 2000, in The new era of wide-field astronomy, Conference held at Preston, UK, August 2000, ASP Conf. Ser., in press [36] Drimmel, R., Spergel, D.N., 2001, ApJ, 556, 181 [37] Dehnen, W., 1998, AJ, 115, 2384 [38] Grabelsky, D.A., Cohen, R.S., Bronfman, L., Thaddeus, P., May, J., 1987, ApJ, 315, 122 [39] May, J., Alvarez, H., Bronfman, L., 1997, A&A, 327, 325 [40] Diplas, A., Savage, B.D., 1991, ApJ, 377, 126 [41] Robin, A.C., Haywood, M., Creze, M., Ojha, O.K., Bienayme, O., 1996, A&A, 305, 125 [42] Reyle, C. & Robin, A.C., 2001, A&A, 373, 886 [43] Gilmore, G., Wyse, R.F.G., Jones, B.J., 1995, AJ, 109, 1095 [44] Buser, R., Rong, J., Karaali, S., 1999, A&A, 348, 98 [45] Prochaska, J.X., Naumov, S.O., Carney, B.W., McWilliam, A., Wolfe, A.M., 2000, AJ, 120, 2513 [46] Morrison, H.L., Flynn, C., Freeman, K.C., 1990, AJ, 100, 1191 [47] Norris, J., Bessell, M.S., Pickles, A.J., 1985, ApJS, 58, 463 [48] Quinn, P.J., Hernquist, L., Fullagar, D.P., 1993, ApJ, 403, 74 [49] Ivezic, Zeljko, et al., 2000, AJ, 120, 963 [50] Robin, A.C., Reyle, C., Creze, M., 2000, A&A, 359, 103

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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]

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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

© EAS, EDP Sciences 2002 DOI: 10.1051/eas:2002025

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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.

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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

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 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