| |
 |
| Paper: |
Exactly What Is Stellar 'Radial Velocity'? |
| Volume: |
185, Precise Stellar Radial Velocities, IAU Colloquium 170 |
| Page: |
73 |
| Authors: |
Lindegren, L.; Dravins, D.; Madsen, S. |
| Abstract: |
Accuracy levels of metres per second require the fundamental concept of 'radial velocity' to be examined, in particular due to relativistic velocity effects, and spectroscopic measurements made inside gravitational fields. Naively, 'radial velocity' equals the line-of-sight component of the stellar velocity vector, measured by the Doppler shifts of stellar spectral lines. Although many physical effects in stellar atmospheres contribute to the line shifts, those could in principle be corrected for, leaving the 'true' (centre-of-mass) velocity. However, also this concept becomes ambiguous at accuracy levels around 10-100 m/s. Radial velocity is the change in distance with respect to 'time'. But is this the time of light emission (at the star) or light reception (at the observer)? The former seems natural if radial velocity is considered a 'property' of the star, while the latter is more natural for the observer. The difference is of second order in velocity (v*v/c), exceeding 100 m/s for v > 173 km/s. Similar differences exist between the classical and the relativistic Doppler formulae, and depend on how the transverse Doppler effect is treated. Thus, the determination of the radial velocity component cannot be separated from the determination of the transverse one, requiring knowledge also of the stellar proper motion, and distance. Gravitational redshift caused by the Sun diminishes with distance as 1/r. At the solar surface (r = Ro), it is 636 m/s, diminishing to 3 m/s at the Earth's distance (215 Ro). Thus, in principle, all stars will have such a blueshift component, if measured near the Earth. A general-relativistic treatment introduces additional complications, e.g. that the numerical velocities depend on the chosen metric. Also, variable relativistic delay along the light path would introduce line shifts, e.g. during microlensing events. Among the effects influencing the measurement of accurate line shifts, only local ones can be reliably calculated. These depend on the motion and gravitational potential of the observer relative to the desired reference frame, usually the solar system barycentre. We argue that the barycentric fractional wavelength shift z is therefore the proper observational quantity to be derived from spectroscopic measurements. However, this barycentric shift cannot be uniquely interpreted as a radial motion of the object. If velocity units are desired, this shift can be expressed as cz, analogous to the case in cosmology. |
|
|
|
|
|
