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Rigorous treatment of barycentric stellar motion Perspective and light-time effects in astrometric and radial velocity data

Butkevich, A. G. and Lindegren, Lennart LU (2014) In Astronomy & Astrophysics 570.
Abstract
Context. High-precision astrometric and radial-velocity observations require accurate modelling of stellar motions in order to extrapolate measurements over long time intervals, and to detect deviations from uniform motion caused, for example, by unseen companions. Aims. We aim to explore the simplest possible kinematic model of stellar motions, namely that of uniform rectilinear motion relative to the solar system barycentre, in terms of observable quantities including error propagation. Methods. The apparent path equation for uniform rectilinear motion is solved analytically in a classical (special-relativistic) framework, leading to rigorous expressions that relate the (apparent) astrometric parameters and radial velocity to the (true)... (More)
Context. High-precision astrometric and radial-velocity observations require accurate modelling of stellar motions in order to extrapolate measurements over long time intervals, and to detect deviations from uniform motion caused, for example, by unseen companions. Aims. We aim to explore the simplest possible kinematic model of stellar motions, namely that of uniform rectilinear motion relative to the solar system barycentre, in terms of observable quantities including error propagation. Methods. The apparent path equation for uniform rectilinear motion is solved analytically in a classical (special-relativistic) framework, leading to rigorous expressions that relate the (apparent) astrometric parameters and radial velocity to the (true) kinematic parameters of the star in the barycentric reference system. Results. We present rigorous and explicit formulae for the transformation of stellar positions, parallaxes, proper motions, and radial velocities from one epoch to another, assuming uniform rectilinear motion and taking light-time effects into account. The Jacobian matrix of the transformation is also given, allowing accurate and reversible propagation of errors over arbitrary time intervals. The light-time effects are generally very small, but exceed 0.1 mas or 0.1 m s(-1) over 100 yr for at least 33 stars in the Hipparcos catalogue. For high-velocity stars within a few tens of pc from the Sun, light-time effects are generally more important than the effects of the curvature of their orbits in the Galactic potential. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
methods: data analysis, technique: radial velocity, astrometry, parallaxes, proper motions, reference systems
in
Astronomy & Astrophysics
volume
570
publisher
EDP Sciences
external identifiers
  • wos:000344158500120
  • scopus:84907966246
ISSN
0004-6361
DOI
10.1051/0004-6361/201424483
language
English
LU publication?
yes
id
432486a7-d607-4b06-a1dc-028bc1d46716 (old id 4875696)
date added to LUP
2014-12-30 10:22:50
date last changed
2017-01-01 05:47:28
@article{432486a7-d607-4b06-a1dc-028bc1d46716,
  abstract     = {Context. High-precision astrometric and radial-velocity observations require accurate modelling of stellar motions in order to extrapolate measurements over long time intervals, and to detect deviations from uniform motion caused, for example, by unseen companions. Aims. We aim to explore the simplest possible kinematic model of stellar motions, namely that of uniform rectilinear motion relative to the solar system barycentre, in terms of observable quantities including error propagation. Methods. The apparent path equation for uniform rectilinear motion is solved analytically in a classical (special-relativistic) framework, leading to rigorous expressions that relate the (apparent) astrometric parameters and radial velocity to the (true) kinematic parameters of the star in the barycentric reference system. Results. We present rigorous and explicit formulae for the transformation of stellar positions, parallaxes, proper motions, and radial velocities from one epoch to another, assuming uniform rectilinear motion and taking light-time effects into account. The Jacobian matrix of the transformation is also given, allowing accurate and reversible propagation of errors over arbitrary time intervals. The light-time effects are generally very small, but exceed 0.1 mas or 0.1 m s(-1) over 100 yr for at least 33 stars in the Hipparcos catalogue. For high-velocity stars within a few tens of pc from the Sun, light-time effects are generally more important than the effects of the curvature of their orbits in the Galactic potential.},
  articleno    = {A62},
  author       = {Butkevich, A. G. and Lindegren, Lennart},
  issn         = {0004-6361},
  keyword      = {methods: data analysis,technique: radial velocity,astrometry,parallaxes,proper motions,reference systems},
  language     = {eng},
  publisher    = {EDP Sciences},
  series       = {Astronomy & Astrophysics},
  title        = {Rigorous treatment of barycentric stellar motion Perspective and light-time effects in astrometric and radial velocity data},
  url          = {http://dx.doi.org/10.1051/0004-6361/201424483},
  volume       = {570},
  year         = {2014},
}