Contents

Contributors

Acronyms

Preface

Part I Astrometry in the twenty-first century

1 Opportunities and challenges for astrometry in the twenty-first century

Introduction

1.1 Some history

1.2 The Hipparcos mission

1.2.1 Provision of an accurate reference frame

1.2.2 Constraints on stellar evolutionary models

1.2.3 Galactic structure and dynamics

1.2.4 Other applications

1.3 Other recent advances

1.4 The future

1.4.1 Gaia

1.4.2 SIM

References

2 Astrometric satellites

Introduction

2.1 Advantages of making astrometric observations from space

2.2 The Hubble Space Telescope (HST)

2.3 The Hipparcos mission

2.4 Global astrometry using scanning satellites

2.5 Step-stare observation mode

2.6 The Gaia mission

2.7 Interferometry

2.8 Future prospects

References

3 Ground-based opportunities for astrometry

Introduction

3.1 Radio astrometry

3.2 Optical astrometry

3.2.1 Differential astrometry

3.2.2 Wide-field astrometry

3.2.3 Photometric surveys for astrometric research

3.2.4 Studies in Galactic structure (see also Chapter 22)

3.2.5 Using star clusters as laboratories for stellar evolution (see also Chapter 25)

3.2.6 Measuring the masses of black holes and stars

3.2.7 Solar System astrometry

3.2.8 Teaching of astronomy

References

Part II Foundations of astrometry and celestial mechanics

4 Vectors in astrometry: an introduction

Introduction

4.1 What are vectors?

4.1.1 Vectors and matrices

4.1.2 Unit vectors

4.1.3 Some important formulae

4.2 Coordinate systems and triads

4.3 Spherical coordinates

4.3.1 From spherical coordinates to vector

4.3.2 From vector to spherical coordinates

4.3.3 The normal triad

4.3.4 The proper-motion vector

4.4 Rotations

4.5 Example: conversion between equatorial and galactic coordinates

References

5 Relativistic foundations of astrometry and celestial mechanics

Introduction

5.1 Newtonian modeling of astrometric observations

5.2 Why general relativity?

5.3 General schema of relativistic reduction of astronomical observations

5.4 Relativistic reference systems

5.4.1 Barycentric Celestial Reference System

5.4.2 Geocentric Celestial Reference System

5.4.3 Other versions of the GCRS

5.4.4 Rigidly rotating relativistic reference systems

5.5 Motion of observers and observed objects

5.6 Modeling of light propagation

5.7 Computation of observables

5.7.1 Proper time

5.7.2 Proper direction

5.8 Relativistic model for positional observations

5.9 Celestial reference frame

5.10 Beyond the standard relativistic model

5.11 Astrometry as a laboratory for gravitational physics

References

6 Celestial mechanics of the N-body problem

Introduction

6.1 Equations of motion and integrals of the N-body problem in Newtonian physics

6.2 The three-body problem

6.3 The two-body problem and the Keplerian elements

6.4 Perturbation theory and osculating elements

6.5 The N-body problem in the relativistic framework

6.6 Beyond the N-body problem: oblateness of the central body and non-gravitational effects

6.7 Modern ephemerides of the Solar System

6.8 Can an observer determine its own velocity from positional observations?

References

7 Celestial coordinate systems and positions

Introduction

7.1 Definitions

7.1.1 Coordinates of a celestial object

7.1.2 Reference systems and their realization

7.1.3 Essential reference systems and frames for astrometry

7.1.4 Timescales for astrometry

7.2 The transformation from ICRS to observed positions

7.2.1 Requirements

7.2.2 The Earth orientation parameters

7.2.3 Transformation from ICRS to observed place

7.2.4 Description of the different effects and models to be used

7.3 Astronomical coordinates

7.4 UT1, UTC and their relation to TAI

7.4.1 Definitions

7.4.2 Relations

7.5 Practical relationships and measurements

References

8 Fundamental algorithms for celestial coordinate systems and positions

Introduction

8.1 Useful references

8.2 Notes on the transformation steps

8.3 Computational efficiency

8.4 External inputs

References

Part III Observing through the atmosphere

9 The Earth's atmosphere: refraction, turbulence, delays, and limitations to astrometric precision

Introduction

9.1 Refraction through a plane-parallel atmosphere

9.2 Refraction in right ascension and declination

9.3 Turbulence in the atmosphere

9.4 Atmospheric limitations on astrometric precision and accuracy

9.4.1 Total motion of a star

9.4.2 Observations in the isoplanatic region (adaptive optics and speckle interferometry)

9.4.3 Observations in the isokinetic region (CCD observations)

9.5 Optical interferometry

9.6 Radio astrometry

9.7 Summary

References

10 Astrometry with ground-based diffraction-limited imaging

Introduction

10.1 Speckle imaging

10.1.1 Method

10.1.2 Examples of astrometric speckle-imaging results

10.2 Adaptive optics

10.2.1 Method

10.2.2 Examples of astrometric results

10.3 The future

References

11 Optical interferometry

Introduction

11.1 Preliminaries and definitions

11.2 Principles of optical interferometry

11.2.1 The visibility

11.2.2 Temporal coherence

11.2.3 Spatial coherence

11.2.4 Quasi-monochromatic approximation

11.3 Visibility and mutual coherence function

11.3.1 Amplitude interferometry

11.3.2 Intensity interferometry

11.4 Fizeau and Michelson interferometry

11.4.1 Fizeau configuration

11.4.2 Michelson configuration

11.5 Small objects - imaging

11.5.1 Coverage of the (u,v)-plane

11.6 Widely separated objects - astrometry

11.6.1 Atmospheric turbulence

11.7 Beating atmospheric turbulence

11.7.1 Fringe tracking

11.7.2 Closure phase

11.8 Optical interferometers and observatories

References

12 Radio astrometry

Introduction

12.1 Fundamentals of radio astrometry

12.1.1 The basic radio interferometer

12.1.2 The visibility function and Fourier relationships

12.1.3 Resolution and (u, v) coverage

12.1.4 The correlator output

12.1.5 Telescope-based imperfections, closure and self-calibration

12.1.6 The astrometric phase equation

12.2 Macro-astrometry

12.2.1 The group delay

12.2.2 Use of simultaneous dual frequencies

12.2.3 Observing schedules

12.2.4 Session astrometric solutions

12.2.5 Global astrometric solutions and the ICRF2

12.2.6 Radio-source calibrators over the sky

12.3 Micro-astrometry

12.3.1 Phase-referencing technique

12.3.2 Temporal and angular coherence

12.3.3 Phase-referencing equation

12.3.4 Improved phase-referencing images and positions

12.3.5 Astrometric examples using phase referencing

12.3.6 Spacecraft navigation

12.3.7 Position precision and ICRF source stability

References

Part IV From detected photons to the celestial sphere

13 Geometrical optics and astrometry

Introduction

13.1 Paraxial optics

13.1.1 Sign conventions

13.1.2 Paraxial equations for refraction

13.1.3 Paraxial equations for reflection

13.1.4 Two-surface refracting elements

13.1.5 Two-mirror telescopes

13.1.6 Object space to image space revisited

13.2 Aberrations

13.2.1 Conic sections

13.2.2 Aberration example

13.2.3 Off-axis aberrations

13.2.4 Telescopes and aberrations

13.2.5 Misalignments and aberrations

13.3 Concluding comments

References

14 CCD imaging detectors

Introduction

14.1 What is a charge-coupled device?

14.2 CCD characterization parameters

14.2.1 Quantum efficiency

14.2.2 Readout noise

14.2.3 Dark current

14.2.4 Linearity of response

14.2.5 Gain

14.2.6 Charge-transfer efficiency (charge diffusion)

14.3 Types of CCD exposures

14.3.1 Bias frame, pedestal or zero exposure

14.3.2 Flat-field exposure

14.3.3 Dark frame

14.3.4 Object frame

14.4 Components of the CCD signal

14.4.1 Signal-to-noise ratio (SNR)

14.5 Photometry and astrometry with CCDs

14.5.1 Magnitude and color systems

14.5.2 Measuring the flux

14.5.3 Image centers

14.5.4 Sky background

14.5.5 Sampling and pixel size

14.6 Summary

References

15 Using CCDs in the time-delay integration mode

Introduction

15.1 The drift-scan method

15.2 Field distortions in drift scanning

15.3 Object detection and astrometry

15.4 The Palomar Quest camera

References

16 Statistical astrometry

Introduction

16.1 Effects complicating the interpretation of astrometric data

16.2 Know your catalog

16.3 Dealing with correlated errors

16.4 Astrophysical parameter estimation through inversion

16.4.1 Statistical biases in simplistic luminosity calibration

16.4.2 Minimizing bias with alternative approaches

16.5 Forward modeling of the data

16.5.1 Bayesian luminosity calibration

16.5.2 Other examples of astrometric data modeling

16.6 Recommendations

References

17 Analyzing poorly sampled images: HST imaging astrometry

Introduction

17.1 The need for a good PSF

17.2 The PSF

17.3 The effective PSF

17.4 An accurate PSF model

17.5 The ultimate limitations caused by undersampling

17.6 Distortion

17.7 Applications

References

18 Image deconvolution

Introduction

18.1 Theory of deconvolution

18.1.1 The imaging equation

18.1.2 Noise sources

18.1.3 Dealing with aberrated PSFs

18.1.4 Algorithms

18.1.5 The Richardson-Lucy algorithm

18.2 Correcting for atmospheric degradation

18.3 Potential gains in precision and limiting magnitude

18.3.1 Gain in limiting magnitude

18.3.2 Gain in limiting resolution and blended images

18.3.3 Gain in astrometric precision

18.3.4 Absence of bias

18.4 CPU cost

18.5 Summary

References

19 From measures to celestial coordinates

Introduction

19.1 Telescope and detector alignment

19.2 Transforming from the detector plane to the celestial sphere

19.3 Transforming between two tangential coordinate systems

19.4 Correcting the (x, y) measures for various errors and systematic effects

19.4.1 Detector and measuring machine errors

19.4.2 Instrumental errors

19.4.3 Spherical corrections

19.5 Transforming the (x, y) measures to the tangential coordinate system

19.5.1 Image centering

19.5.2 Transformation models

19.5.3 Reference stars

19.6 Mosaics of CCDs

19.7 Differential astrometry

19.8 Summary

References

20 Astrometric catalogs: concept, history, and necessity

Introduction

20.1 History of astrometric catalogs

20.2 Visual catalogs

20.3 Photographic catalogs

20.4 Hipparcos and the modern catalogs

20.5 Space-based astrometric surveys

20.6 The Virtual Observatory

20.7 Radio astrometry

References

21 Trigonometric parallaxes

Introduction

21.1 The mathematical foundation of parallax

21.2 Differential versus global astrometry

21.3 Differential parallaxes with HST

21.3.1 Reference stars

21.3.2 Modeling

21.4 The utility of parallaxes

21.4.1 From parallaxes to absolute magnitudes

21.4.2 The Leavitt law for Galactic Cepheids

21.5 The future of parallax determinations

References

Part V Applications of astrometry to topics in astrophysics

22 Galactic structure astrometry

Introduction

22.1 Going Galactic: equatorial vs. Galactic coordinates

22.2 Galactic rest frame vs. Galactocentric velocities

22.3 Grand-scale Galactic motions

22.4 Kinematics in the solar neighborhood

22.5 The solar Galactocentric distance and the LSR speed

22.6 From radial velocities to proper motions, and back - Part I: systemic motions

22.7 From radial velocities to proper motions, and back - Part II: perspective effects

22.8 Nearby galaxies: Local Group motions

22.9 Concluding remarks

References

23 Binary and multiple stars

Introduction

23.1 A brief review of the dynamical problem

23.2 Computing the apparent orbit

23.3 Observational techniques

23.3.1 Speckle interferometry

23.3.2 Adaptive optics

23.3.3 Long baseline optical interferometry

23.3.4 Space-based astrometry

23.4 Relating the orbit to astrophysics

References

24 Binaries: HST, Hipparcos, and Gaia

Introduction

24.1 The HST, Hipparcos, and Gaia

24.1.1 Hipparcos binaries

24.2 HST missions

24.3 Gaia missions

24.4 Conclusion

References

25 Star clusters

Introduction

25.1 Cluster membership

25.2 Absolute proper motions and Galactic orbits

25.3 Internal velocity dispersion

25.4 Virial theorem and kinematic distance

References

26 Solar System astrometry

Introduction

26.1 The purposes of Solar System astrometry

26.1.1 Solar System mapping

26.1.2 Solar System dynamics

26.1.3 Reference frame

26.1.4 Asteroid masses

26.1.5 Planetary physics

26.2 Motion of Solar System objects

26.2.1 The apparent motion

26.2.2 The planetary phase

26.3 Observational techniques

26.3.1 Photographic plates

26.3.2 CCD astrometry

26.3.3 Stellar occultations

26.3.4 Mutual events

References

27 Exoplanets

Introduction

27.1 Emerging properties of planetary systems

27.2 The future of direct and indirect detection techniques

27.3 The potential of microarcsecond astrometry

27.3.1 Observable model

27.3.2 Planet formation and migration models

27.3.3 Multiple-planet systems

27.3.4 Direct detections of giant exoplanets

27.3.5 The hunt for other Earths

References

28 Astrometric measurement and cosmology

Introduction

28.1 Cosmological parameters

28.2 How astrometric measurements can help constrain cosmological parameters

References

Index