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Gaia astrometry for stars with too few observations. A Bayesian approach

Michalik, Daniel LU ; Lindegren, Lennart LU ; Hobbs, David LU and Butkevich, Alexey G. (2015) In Astronomy & Astrophysics 583.
Abstract
Context. The astrometric solution for Gaia aims to determine at least five parameters for each star, representing its position, parallax, and proper motion, together with appropriate estimates of their uncertainties and correlations. This requires at least five distinct observations per star. In the early data reductions the number of observations may be insufficient for a five-parameter solution, and even after the full mission many stars will remain under-observed, including faint stars at the detection limit and transient objects. In such cases it is reasonable to determine only the two position parameters. The formal uncertainties of such a two-parameter solution would however grossly underestimate the actual errors in position, due to... (More)
Context. The astrometric solution for Gaia aims to determine at least five parameters for each star, representing its position, parallax, and proper motion, together with appropriate estimates of their uncertainties and correlations. This requires at least five distinct observations per star. In the early data reductions the number of observations may be insufficient for a five-parameter solution, and even after the full mission many stars will remain under-observed, including faint stars at the detection limit and transient objects. In such cases it is reasonable to determine only the two position parameters. The formal uncertainties of such a two-parameter solution would however grossly underestimate the actual errors in position, due to the neglected parallax and proper motion. Aims. We aim to develop a recipe to calculate sensible formal uncertainties that can be used in all cases of under-observed stars. Methods. Prior information about the typical ranges of stellar parallaxes and proper motions is incorporated in the astrometric solution by means of Bayes' rule. Numerical simulations based on the Gaia Universe Model Snapshot (GUMS) are used to investigate how the prior influences the actual errors and formal uncertainties when different amounts of Gaia observations are available. We develop a criterion for the optimum choice of priors, apply it to a wide range of cases, and derive a global approximation of the optimum prior as a function of magnitude and galactic coordinates. Results. The feasibility of the Bayesian approach is demonstrated through global astrometric solutions of simulated Gaia observations. With an appropriate prior it is possible to derive sensible positions with realistic error estimates for any number of available observations. Even though this recipe works also for well-observed stars it should not be used where a good five-parameter astrometric solution can be obtained without a prior. Parallaxes and proper motions from a solution using priors are always biased and should not be used. (Less)
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author
organization
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type
Contribution to journal
publication status
published
subject
keywords
astrometry, methods: data analysis, methods: numerical, parallaxes, proper motions, space vehicles: instruments
in
Astronomy & Astrophysics
volume
583
publisher
EDP Sciences
external identifiers
  • wos:000365072200132
  • scopus:84946555278
ISSN
0004-6361
DOI
10.1051/0004-6361/201526936
language
English
LU publication?
yes
id
012c0496-a92e-4dac-9a36-6651afbf608a (old id 8539618)
date added to LUP
2016-01-20 12:48:05
date last changed
2017-06-11 03:57:47
@article{012c0496-a92e-4dac-9a36-6651afbf608a,
  abstract     = {Context. The astrometric solution for Gaia aims to determine at least five parameters for each star, representing its position, parallax, and proper motion, together with appropriate estimates of their uncertainties and correlations. This requires at least five distinct observations per star. In the early data reductions the number of observations may be insufficient for a five-parameter solution, and even after the full mission many stars will remain under-observed, including faint stars at the detection limit and transient objects. In such cases it is reasonable to determine only the two position parameters. The formal uncertainties of such a two-parameter solution would however grossly underestimate the actual errors in position, due to the neglected parallax and proper motion. Aims. We aim to develop a recipe to calculate sensible formal uncertainties that can be used in all cases of under-observed stars. Methods. Prior information about the typical ranges of stellar parallaxes and proper motions is incorporated in the astrometric solution by means of Bayes' rule. Numerical simulations based on the Gaia Universe Model Snapshot (GUMS) are used to investigate how the prior influences the actual errors and formal uncertainties when different amounts of Gaia observations are available. We develop a criterion for the optimum choice of priors, apply it to a wide range of cases, and derive a global approximation of the optimum prior as a function of magnitude and galactic coordinates. Results. The feasibility of the Bayesian approach is demonstrated through global astrometric solutions of simulated Gaia observations. With an appropriate prior it is possible to derive sensible positions with realistic error estimates for any number of available observations. Even though this recipe works also for well-observed stars it should not be used where a good five-parameter astrometric solution can be obtained without a prior. Parallaxes and proper motions from a solution using priors are always biased and should not be used.},
  articleno    = {A68},
  author       = {Michalik, Daniel and Lindegren, Lennart and Hobbs, David and Butkevich, Alexey G.},
  issn         = {0004-6361},
  keyword      = {astrometry,methods: data analysis,methods: numerical,parallaxes,proper motions,space vehicles: instruments},
  language     = {eng},
  publisher    = {EDP Sciences},
  series       = {Astronomy & Astrophysics},
  title        = {Gaia astrometry for stars with too few observations. A Bayesian approach},
  url          = {http://dx.doi.org/10.1051/0004-6361/201526936},
  volume       = {583},
  year         = {2015},
}