The fundamental definition of ``radial velocity''
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 and astrometric techniques. Already in a classical (nonrelativistic) framework the lineofsight 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 the time coordinate. Relativistic velocity effects and spectroscopic measurements made inside gravitational fields add further complications, causing wavelength shifts to depend, e.g., on the transverse velocity of the object and the gravitational potential at the source. Aiming at definitions that are unambiguous at accuracy levels of 1 m s^{1}, we analyse different concepts of radial velocity and their interrelations. At this accuracy level, a strict separation must be made between the purely geometric concepts on one hand, and the spectroscopic measurement on the other. Among the geometric concepts we define kinematic radial velocity, which corresponds most closely to the ``textbook definition'' of radial velocity as the lineofsight component of space velocity; and astrometric radial velocity, which can be derived from astrometric observations. Consistent with these definitions, we propose strict definitions also of the complementary kinematic and astrometric quantities, namely transverse velocity and proper motion. The kinematic and astrometric radial velocities depend on the chosen spacetime metric, and are accurately related by simple coordinate transformations. On the other hand, the observational quantity that should result from accurate spectroscopic measurements is the barycentric radialvelocity measure. This is independent of the metric, and to first order equals the lineofsight velocity. However, it is not a physical velocity, and cannot be accurately transformed to a kinematic or astrometric radial velocity without additional assumptions and data in modelling the process of light emission from the source, the transmission of the signal through space, and its recording by the observer. For historic and practical reasons, the spectroscopic radialvelocity measure is expressed in velocity units as cz_{B}, where c is the speed of light and z_{B} is the observed relative wavelength shift reduced to the solarsystem barycentre, at an epoch equal to the barycentric time of light arrival. The barycentric radialvelocity measure and the astrometric radial velocity are defined by recent resolutions adopted by the International Astronomical Union (IAU), the motives and consequences of which are explained in this paper.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 April 2003
 DOI:
 10.1051/00046361:20030181
 arXiv:
 arXiv:astroph/0302522
 Bibcode:
 2003A&A...401.1185L
 Keywords:

 techniques: radial velocities;
 techniques: spectroscopic;
 astrometry;
 reference systems;
 stars: kinematics;
 methods: data analysis;
 Astrophysics
 EPrint:
 19 pages, 1 figure. Accepted for publication in Astronomy &