2 What is the "true'' radial velocity?

Following the general introduction of efficient CCD detectors in astronomy, digital cross-correlation has become a standard technique for determination of stellar radial velocities. In this method the recorded stellar spectrum, after suitable calibration and normalisation, is correlated with a digital mask, or template, and the maximum of the cross-correlation function (CCF) gives the differential velocity of the stellar spectrum with respect to the template. The template could either be based on a real stellar spectrum (e.g. Latham & Stefanik 1992; Baranne et al. 1996; Gunn et al. 1996) or a synthetic spectrum (e.g. Morse et al. 1991; Nordström et al. 1994; Verschueren et al. 1999). Largely driven by the search for exoplanets, the technique has been refined to provide precisions reaching $\sim$10 m s^-1or better for bright solar-type stars (Baranne 1999; Skuljan et al. 2000). Although much attention has also been given to the accuracy of such measurements, i.e. their proximity to "true'' values (Griffin 1999), the present practical limitation to "absolute'' radial velocities seems to be in the 100-200 m s^-1 range (Stefanik et al. 1999; Skuljan et al. 2000).

Accuracy implies absence of (significant) systematic errors. In the present context, the most important sources of systematic errors are either instrumental, e.g. flexure and slit illumination effects, or related to properties of the (observed) stellar spectrum itself, i.e. what is often referred to as "template mismatch'' effects. With the development of highly stable spectrometers it is not unreasonable to assume that instrumental effects can be eliminated to a high degree, and therefore should not be the limiting factor in a well-designed instrument operated under controlled conditions. Systematic errors from template mismatch are an entirely different matter: they seem to be inevitable unless the object and template spectra are almost identical, i.e. resulting from the same source, or at least the same stellar type, and recorded with the same instrument. For instance, it is generally recognised that the use of a single template for different spectral types is likely to cause a sliding and largely unknown zero-point error along the main sequence, with additional systematics caused by differences in stellar rotation, gravity and chemical composition (Smith et al. 1987; Dravins & Nordlund 1990; Verschueren et al. 1999; Griffin et al. 2000).

Systematic errors and the problems of template mismatch are however also connected with an even more fundamental issue, namely what we mean by the "true'' radial velocity (Lindegren & Dravins 2002). Usually, there is an implicit assumption that the quantity to determine is the actual line-of-sight component of the space motion of the star, or more precisely of its centre of mass. However, it is well known from solar studies that convection in the photosphere causes a net Doppler shift of moderately strong absorption lines by some -0.4 km s^-1 in integrated sunlight (Dravins et al. 1981; Allende Prieto & García López 1998b; Dravins 1999; Asplund et al. 2000). The analysis of line bisectors in stellar spectra (Gray 1982; Dravins 1987; Nadeau & Maillard 1988; Gray & Nagel 1989; Allende Prieto et al. 1995; Allende Prieto et al. 2002) indicates that similar or even stronger blueshifts can be expected for other spectral types. Hydrodynamic 3D simulations by Dravins & Nordlund (1990) suggest that the convective shift could be $\simeq$-1.0 km s^-1 for F stars to $\simeq$-0.2 km s^-1 for K dwarfs. Taking into consideration that the gravitational redshift is expected to be fairly constant $\simeq$0.6 km s^-1 for a wide range of spectral types on the main sequence, the resulting total shift would be in the range from -0.4 km s^-1 for F stars to +0.4 km s^-1 for K dwarfs, with the Sun at around +0.2 km s^-1.

While the effects of template mismatch can to some extent be studied by means of synthetic spectra (e.g. Nordström et al. 1994; Verschueren et al. 1999), standard model atmospheres are not yet sufficiently sophisticated, for spectral types significantly different from the Sun, to accurately compute the subtle effects of line shifts and asymmetries caused by photospheric convection (Dravins & Nordlund 1990). On the contrary, empirical determinations of such shifts might be a powerful diagnostic for the study of dynamical phenomena in stellar atmospheres (Dravins 1999). This requires that the true velocity can be established by other means, which was previously possible only for the Sun. Recent advances in space techniques have however made it possible to determine astrometric radial velocities for some stars (Dravins et al. 1997), and future space astrometry missions could provide accurate non-spectroscopic space velocities for a wide variety of stellar types based on purely geometrical measurements (Dravins et al. 1999b).

Given the many problems related to the definition of an accurate spectroscopic velocity zero point, as well as the possibility to determine stellar radial motions by non-spectroscopic means, it has become necessary to make a strict distinction between the two concepts. On one hand, we have the astrometric radial velocity, which by definition refers to the centre-of-mass motion of the star. On the other, we have a spectroscopically determined quantity, which may be expressed in velocity units although it includes non-kinematic effects such as gravitational redshift, as well as local kinematic effects of the stellar atmosphere. The distinction has led to the definition of the (barycentric) radial-velocity measure discussed below.