J. van Paradijs H. M. Maitzen (Eds.)

Galactic High-Energy Astrophysics High-Accuracy Timing and Positional Astronomy

Lectures Held at the Astrophysics School IV

Organized by the European Astrophysics Doctoral Network (EADN) in Graz, Austria, 19-3 1 August 1991

Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong Barcelona Budapest

Editors

Jan van Paradijs Astronomical Institute “Anton Pannekoek” and Center for High-Energy Astrophysics Kruislaan 403, NL-1098 SJ Amsterdam, The Netherlands

Hans Michael Maitzen Institut fur Astronomie der Universitat Wien Ttirkenschanzstral3e 17, A- 1180 Wien, Austria

ISBN 3-540-56874-3 Springer-Verlag Berlin Heidelberg New York ISBN O-387-56874-3 Springer-Verlag New York Berlin Heidelberg

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0 Springer-Verlag Berlin Heidelberg 1993 Printed in Germany

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PREFACE

The 4th Predoctoral Astrophysics School of the European Astrophysics Doctoral Network (EADN) was held from August 19 - 31, 1991 at Graz-Marialrost with the participation of 7 teachers, and 34 students from 11 European countries. With this School EADN has completed half a decade of European collaboration in the field of academic teaching in astrophysics. After the EADN Schools at Les Houches (France, 1988), Ponte de Lima (Portugal, 1989) and Dublin (Ireland, 1990) Austrian astronomy hosted the fourth School and chose Graz as its venue.

Graz is related to both subjects of the School - Galactic High-Energy Astrophysics, and High Accuracy Timing and Positional Astronomy - through historical and contemporary circumstances. It is known as one of the Kepler cities. In 1994 Graz will celebrate the 400th anniversary of Kepler's arrival there where he started both his teaching and scientific careers. Kepler worked on the most accurate and numerous positional observations available at that time through the efforts of Tycho Brahe; he can be said to have also contributed to the field of High Energy Astronomy by his book on the detection of a STELLA NOVA; which in fact was the last naked-eye supernova discovery (1604) before the recent famous supernova SN 1987A.

We would like to mention here also that the discoverer of cosmic rays - part of the fast topic of the Graz School - was the Nobel Prize winner Viktor F. Hess who conducted his research at the Karl-Franzens University of Graz. Other wen-known scientists, who at some time in their careers worked at this University, include Boltzmann, Schr6dinger (Nobel Prize 1933) and Mach.

Like the other two classical Austrian universities of Vienna and Innsbmck the Karl-Franzens University has an Institute for Astronomy. We would like to express our deep gratitude to this institute, especially to its head Prof. Dr. Hermann Haupt and two of his students, Karin Muglach and Robert Greirnel, for their support during the preparatory phase and the School weeks.

We acknowledge with grateful appreciation financial support for the School from: - SCIENCE, the scientific stimulation programme of the Commission of the European Community; - the Austrian Ministry of Science and Research; - the Government of the Land Steiermark (Styria); - the City of Graz, in addition to a truly delightful reception by its mayor Alfred Stingl and City

Counsellor Helmut Strobl; - the Granholm Foundation (Sweden), and - the Oesterreichiscbe Forschungsgemeinschaft.

Extensive cooperation and help came from the home institute of the Local Organizer, the Vienna Institut f'tir Astronomic (head Prof. Dr. Paul Jackson), and especially from its collaborators Dr. Anneliese Schnell, Dr. Ernst Goebel and Mag. Franz Kerschbaum.

Thanks go also to the staff of the Bildungshaus Mariatrost which provided not only dormitories and meeting rooms, but also a relaxed and friendly atmosphere surrounded by magnificent natural beauty.

Last but not least, we wish to specially thank the Coordinator of EADN, Prof. Dr. Jean Heyvaerts who completed with his participation in the Graz School a period of five years at the helm of EADN.

The 4th EADN School in Graz was pronounced successful by teachers and students alike. It occurred at a very critical point in recent European history, since its beginning coincided with the coup d'etat in the former Soviet Union. Together with the scientific educational values and the charming Graz downtown atmosphere this may have contributed to a very special feeling of togetherness of young European doctoral students in astrophysics during those two weeks in August 1991.

Amsterdam/Vienna, October 1992

J. van Paradijs, H.M. Maitzen

C o n t e n t s

Part I Galactic High-Energy Astrophysics

A. A c h t e r b e r g Particle Acceleration in Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Particle Acceleration: General Principles . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Stochastic and Regular Fermi Accelerat ion . . . . . . . . . . . . . . . . . . 4

2.2 The Spectrum due to Stochastic Fermi Accelerat ion . . . . . . . . . . . 8 2.3 Stochastic Accelerat ion by Plasma Waves and Turbulence . . . . . . 9 2.4 "Fermi Deceleration": Expansion Losses . . . . . . . . . . . . . . . . . . . . 15 2.5 The Energy Balance in Stochastic Fermi Accelerat ion . . . . . . . . . 16

3. Particle Acceleration near Astrophysical Shocks . . . . . . . . . . . . . . . . 17

3.1 A Simple Statistical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Diffusive Shock Accelerat ion of Charged Particles . . . . . . . . . . . . 20 3,3 Cycle Time and Momentum Gain for Particles

in Shock Accelerat ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 The Maximum Energy Attainable in Shock Accelerat ion . . . . . . . 25 3,5 Gyro-Resonant Scattering by Al fv tn Waves . . . . . . . . . . . . . . . . . 26

3.6 Maximum Energy for Specific Loss-Mechanisms . . . . . . . . . . . . . 28 3.7 Astrophysical Sites for Shock Accelerat ion . . . . . . . . . . . . . . . . . . 30

3.8 Observat ional Evidence for Shock Accelerat ion . . . . . . . . . . . . . . 32

3.9 "Realis t ic" Shock Acceleration: Non-Linear Effects . . . . . . . . . . . 34

3.10 Outstanding Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.11 Relativist ic Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.12 Shock-Drif t Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.13 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . , . . . . . . . . . . . . . . . . . 41 Refe rences

E .A. Dorf i

I n t e r s t e l l a r M e d i u m a n d Supe rnova R e m n a n t s . . . . . . . . . . . . . . . . . . . . . 43

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1. Theories of the Interstellar Medium . . . . . . . . . . . . . . . . . . . . . . . . . , 44

1.1 Constituents of the ISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.2 Interstellar Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

1.3 Radiation Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

1.4 Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

VIII

1.5 Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 1.6 Further Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

2. Supe rnova R e m n a n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

2.1 Free Expansion Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

2.2 Sedov-Taylor Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

2.3 Cooling Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

2.4 Final SNR Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

2.5 Particle Acceleration in SNR's . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

2.6 X-Ray Emission from SNR's . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

2.7 Gamma-Ray Emission from SNR's . . . . . . . . . . . . . . . . . . . . . . . . 116

Conclus ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

L. Vlahos High E n e r g y Emiss ion f rom N o r m a l Stars . . . . . . . . . . . . . . . . . . . . . . . . . 129

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 1.1 Energy Flow and Particle Acceleration . . . . . . . . . . . . . . . . . . . . . 130

1.2 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

2. Spon taneous Emiss ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

2.1 Bremsstrahlung Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

2.2 Cyclotron and Synchrotron Emission . . . . . . . . . . . . . . . . . . . . . . . 138

3. Collective P lasma Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

3.1 Plasma Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

3.2 Electron Cyclotron Maser Instability . . . . . . . . . . . . . . . . . . . . . . . 148

4. Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 4.1 Hard X-Ray Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

4.2 Radio Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

5. S u m m a r y a n d Conclus ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

A.R. King Accretion in Close Binar ies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

1.1 Energy Yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

1.2 Radiation Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

1.3 Rotational Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 2. Accreting Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

2.1 The Sizes of Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

2.2 The F~ldington Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

3. Tidal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

4. The Roche Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

5. Roche Lobe Overf low . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 5.1 Occurrence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

5.2 The Degree of Roche Lobe Filling . . . . . . . . . . . . . . . . . . . . . . . . . 168 5.3 Driving Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

IX

6. Stellar Wind Accret ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 6.1 OB Supergiant X-Ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 6.2 Be-Star X-Ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 6.3 Mass and Angular Momentum Capture in Wind Accretion . . . . . 171

7. The Fate o f the Accreted Mat te r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 7.1 Roche Lobe Overflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 7.2 Stellar Wind Accretion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

8. Accret ion Discs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 8.1 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 8.2 Viscous Dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 8.3 The Magnitude of Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

9. Disc S t ruc ture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 9.1 Steady Discs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 9.2 Vertical Disc Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

10. Disc Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 11. Discs in Other Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 12. Shor t .Per iod Binary Evolut ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 13. Secular Evolut ion o f CVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

13.1 The Maximum Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 13.2 The Minimum Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 13.3 The Period Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

14. Shor t .Per iod L M X B Evolut ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Par t I I High Accuracy Timing and Posi t ional A s t r o n o m y

D.C. Backer Pulsars - The New Celestial Clocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 1. Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

1.1 A Brief History of Neulxon Stars . . . . . . . . . . . . . . . . . . . . . . . . . . 193 1.2 Standard Model of Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 1.3 Origin and Evolution of Isolated Neutron Stars . . . . . . . . . . . . . . . 198

2. Rad io As t ronomy Fundamenta l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 2.1 Radiation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 2.2 Radio Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 2.3 Radio Astronomy Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 2.4 Propagation in the IntersteLlar Medium . . . . . . . . . . . . . . . . . . . . . 206 2.5 Search Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 2.6 Pulsar Timing Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

3. Fu r the r Topics on Radio Wave Propagat ion . . . . . . . . . . . . . . . . . . . 213 3.1 Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 3.2 Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 3.3 Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 3.4 Solar Wind and Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 3.5 Relativistic Delay in Solar System Potential . . . . . . . . . . . . . . . . . 215

. Pulsar Timing 4.1 4.2

4.3 4.4

4.5 4.6

Arrival Time Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Space Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Pulsar Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rotat ion Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Astrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5. Binary, Millisecond and Globular Cluster Pu l sa r s . . . . . . . . . . . . . .

5.1 Origin and Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Keplerian Binary Pulsar Timing . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.3 Relativistic Binary Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Globular Cluster Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.5 Planets Around Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6. Pulsar Timing Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1 Time Coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Space Coordinate 6.3 Gravitat ional Wave Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Pulsar Timing Array Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . .

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

216 217 219 221 222 224 226 226

226 230

232 233

234

235 235 237 240 247

250

J. Kovalevsky The Mission H I P P A R C O S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 1. What is Stellar Astrometry? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

1.1 What is Stellar Astrometry? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

1.2 Methods of Astrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 1.3 W h y Stel lar Astrometry? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

1.4 Present Situation and Expectat ions from HIPPARCOS . . . . . . . . . 257

2. Principles and Problems of Stellar Astrometry . . . . . . . . . . . . . . . . . 258 2.1 What Direct ion is of Interest to Astronomy? . . . . . . . . . . . . . . . . . 259 2.2 Astronomical Reference Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

2.3 Appl icat ion to Space Astrometry . . . . . . . . . . . . . . . . . . . . . . . . . . 260 3. The HIPPARCOS Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

3.1 General Principle of HIPPARCOS . . . . . . . . . . . . . . . . . . . . . . . . . 262 3.2 Description of the Satelli te and of Its Payload . . . . . . . . . . . . . . . 263

3.3 Observing Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

3.4 The INPUT Catalogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 4. Reduction of Grid Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

4.1 Light Modulat ion by a Periodic Grid . . . . . . . . . . . . . . . . . . . . . . . 267 4.2 Photon Counts Produced by the Modulat ion . . . . . . . . . . . . . . . . . 268

4.3 Light Modulat ion by a Single Slit . . . . . . . . . . . . . . . . . . . . . . . . . 270 4.4 Precision o f the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

5. Attitude Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 5.1 Satelli te to Sky Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 5.2 Equations for Att i tude Determinat ion . . . . . . . . . . . . . . . . . . . . . . . 274 5.3 Representat ion of the Att i tude . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

5.4 Precision o f Att i tude Determination . . . . . . . . . . . . . . . . . . . . . . . . 277

XI

6. Reduc t ion on a Grea t Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

6.1 The Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

6.2 The Design Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

6.3 Geometric Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

6.4 Attitude Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

6.5 Passive Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 6.6 Accuracy of the Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

7. Computation of Astrometric Parameters . . . . . . . . . . . . . . . . . . . . . . 282

7.1 Sphere Reconstitution . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

7.2 Astrometric Parameter Determination . . . . . . . . . . . . . . . . . . . . . . . 283 8. Double and Multiple Star Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . 284

8.1 First Approximation, Double Stars . . . . . . . . . . . . . . . . . . . . . . . . . 285

8.2 Improvement of the Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

9. I te ra t ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 9.1 Principle of Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

9.2 Setting the Sphere Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

9.3 Double and Multiple Star Inclusion . . . . . . . . . . . . . . . . . . . . . . . . 289

9.4 Expected Final Accuracies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

10. T Y C H O P r o g r a m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 10.1 Preparation of the Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

10.2 Detection of Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

10.3 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

10.4 Astrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

List of participants

Anastasiadis, Anastasios

Aparicio, Jose M.

Aringer, Bernhard

Beeharry, Girish K.

Boncheva, Theodora I.

Boulard, Marie-Helene

Cognard, Ismael

Colomer, Francisco

Cuisinier, Francois

Del Rio, Evileo

Dimitrova, Petya

Egonsson, Jim

Ferreira, Jonathan

Greimel, Robert

Ivanov, Milen

Kerschbaum, Franz

Kunz, Mathias

Kuulkers, Eric

Manning, Rodger

Maravelias, Sergios

Marti-Ribas, Josep

Muglach, Karin

Peracaula, Marta

Pfeiffer, Benoite

Prins, Sacha

Quemerais, Eric

Saphonova, Margaret

Schmitz-Fraisse, Christine

Schultheis, Mathias

Siopis, Christos

Torkelsson, Ulf

Villata, Massimo

Wyn, Graham

Zamanov, Radoslav

Thessaloniki (Greece)

Barcelona (Spain)

Wien (Austria)

Meudon (France)

Shoumen (Bulgaria)

Toulouse (France)

Meudon (France)

G6teborg (Sweden)

Strasbourg (France)

Barcelona (Spain)

Shoumen (Bulgaria)

Lund (Sweden)

Grenoble (France) Graz (Austria)

Sofia (Bulgaria)

Wien (Austria)

Ttibingen (Germany)

Amsterdam (Netherlands)

Birmingham (England)

Athens (Greece)

Barcelona (Spain)

Graz (Austria)

Barcelona (Spain)

Toulouse (France)

Amsterdam (Netherlands)

Verrieres le Buisson (France)

Moscow (Russia)

Toulouse (France)

Wien (Austria)

Ioannina (Greece)

Lund (Sweden)

Torino (Italy)

Leicester (England)

Smoljan (Bulgaria)