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The fundamental definition of "radial velocity''

Lindegren, Lennart LU and Dravins, Dainis LU (2003) In Astronomy & Astrophysics 401(3). p.1185-1201
Abstract
Accuracy levels of metres per second require the fundamental concept of``radial velocity'' for stars and other distant objects to be examined,both as a physical velocity, and as measured by spectroscopic andastrometric techniques. Already in a classical (non-relativistic)framework the line-of-sight velocity component is an ambiguous concept,depending on whether, e.g., the time of light emission (at the object)or that of light detection (by the observer) is used for recording thetime coordinate. Relativistic velocity effects and spectroscopicmeasurements made inside gravitational fields add further complications,causing wavelength shifts to depend, e.g., on the transverse velocity ofthe object and the gravitational potential at the source.... (More)
Accuracy levels of metres per second require the fundamental concept of``radial velocity'' for stars and other distant objects to be examined,both as a physical velocity, and as measured by spectroscopic andastrometric techniques. Already in a classical (non-relativistic)framework the line-of-sight velocity component is an ambiguous concept,depending on whether, e.g., the time of light emission (at the object)or that of light detection (by the observer) is used for recording thetime coordinate. Relativistic velocity effects and spectroscopicmeasurements made inside gravitational fields add further complications,causing wavelength shifts to depend, e.g., on the transverse velocity ofthe object and the gravitational potential at the source. Aiming atdefinitions that are unambiguous at accuracy levels of 1 ms<SUP>-1</SUP>, we analyse different concepts of radial velocity andtheir interrelations. At this accuracy level, a strict separation mustbe made between the purely geometric concepts on one hand, and thespectroscopic measurement on the other. Among the geometric concepts wedefine kinematic radial velocity, which corresponds most closely to the``textbook definition'' of radial velocity as the line-of-sightcomponent of space velocity; and astrometric radial velocity, which canbe derived from astrometric observations. Consistent with thesedefinitions, we propose strict definitions also of the complementarykinematic and astrometric quantities, namely transverse velocity andproper motion. The kinematic and astrometric radial velocities depend onthe chosen spacetime metric, and are accurately related by simplecoordinate transformations. On the other hand, the observationalquantity that should result from accurate spectroscopic measurements isthe barycentric radial-velocity measure. This is independent of themetric, and to first order equals the line-of-sight velocity. However,it is not a physical velocity, and cannot be accurately transformed to akinematic or astrometric radial velocity without additional assumptionsand data in modelling the process of light emission from the source, thetransmission of the signal through space, and its recording by theobserver. For historic and practical reasons, the spectroscopicradial-velocity measure is expressed in velocity units ascz<SUB>B</SUB>, where c is the speed of light and z<SUB>B</SUB> is theobserved relative wavelength shift reduced to the solar-systembarycentre, at an epoch equal to the barycentric time of light arrival.The barycentric radial-velocity measure and the astrometric radialvelocity are defined by recent resolutions adopted by the InternationalAstronomical Union (IAU), the motives and consequences of which areexplained in this paper. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
techniques: radial velocities, techniques: spectroscopic, astrometry, reference systems, stars: kinematics, methods: data analysis
in
Astronomy & Astrophysics
volume
401
issue
3
pages
1185 - 1201
publisher
EDP Sciences
external identifiers
  • wos:000181929900038
  • scopus:0037389999
ISSN
0004-6361
DOI
10.1051/0004-6361:20030181
language
English
LU publication?
yes
id
916de449-33ee-415b-9fbd-cc44aeb50d58 (old id 130549)
date added to LUP
2007-07-13 13:52:58
date last changed
2018-01-07 08:39:12
@article{916de449-33ee-415b-9fbd-cc44aeb50d58,
  abstract     = {Accuracy levels of metres per second require the fundamental concept of``radial velocity'' for stars and other distant objects to be examined,both as a physical velocity, and as measured by spectroscopic andastrometric techniques. Already in a classical (non-relativistic)framework the line-of-sight velocity component is an ambiguous concept,depending on whether, e.g., the time of light emission (at the object)or that of light detection (by the observer) is used for recording thetime coordinate. Relativistic velocity effects and spectroscopicmeasurements made inside gravitational fields add further complications,causing wavelength shifts to depend, e.g., on the transverse velocity ofthe object and the gravitational potential at the source. Aiming atdefinitions that are unambiguous at accuracy levels of 1 ms&lt;SUP&gt;-1&lt;/SUP&gt;, we analyse different concepts of radial velocity andtheir interrelations. At this accuracy level, a strict separation mustbe made between the purely geometric concepts on one hand, and thespectroscopic measurement on the other. Among the geometric concepts wedefine kinematic radial velocity, which corresponds most closely to the``textbook definition'' of radial velocity as the line-of-sightcomponent of space velocity; and astrometric radial velocity, which canbe derived from astrometric observations. Consistent with thesedefinitions, we propose strict definitions also of the complementarykinematic and astrometric quantities, namely transverse velocity andproper motion. The kinematic and astrometric radial velocities depend onthe chosen spacetime metric, and are accurately related by simplecoordinate transformations. On the other hand, the observationalquantity that should result from accurate spectroscopic measurements isthe barycentric radial-velocity measure. This is independent of themetric, and to first order equals the line-of-sight velocity. However,it is not a physical velocity, and cannot be accurately transformed to akinematic or astrometric radial velocity without additional assumptionsand data in modelling the process of light emission from the source, thetransmission of the signal through space, and its recording by theobserver. For historic and practical reasons, the spectroscopicradial-velocity measure is expressed in velocity units ascz&lt;SUB&gt;B&lt;/SUB&gt;, where c is the speed of light and z&lt;SUB&gt;B&lt;/SUB&gt; is theobserved relative wavelength shift reduced to the solar-systembarycentre, at an epoch equal to the barycentric time of light arrival.The barycentric radial-velocity measure and the astrometric radialvelocity are defined by recent resolutions adopted by the InternationalAstronomical Union (IAU), the motives and consequences of which areexplained in this paper.},
  author       = {Lindegren, Lennart and Dravins, Dainis},
  issn         = {0004-6361},
  keyword      = {techniques: radial velocities,techniques: spectroscopic,astrometry,reference systems,stars: kinematics,methods: data analysis},
  language     = {eng},
  number       = {3},
  pages        = {1185--1201},
  publisher    = {EDP Sciences},
  series       = {Astronomy & Astrophysics},
  title        = {The fundamental definition of "radial velocity''},
  url          = {http://dx.doi.org/10.1051/0004-6361:20030181},
  volume       = {401},
  year         = {2003},
}