8 Conclusions

At the accuracy level ($\la$100 m s^-1) permitted by modern spectrometers such as ELODIE it is necessary to review standard procedures for radial-velocity determination in order to produce results that have a clear physical meaning and are reproducible in an absolute sense. For instance, ambiguities of the classical radial-velocity concept have led to the IAU recommendation that accurate spectroscopic measurements should be given as "barycentric radial-velocity measures''. Moreover, these measures refer to spectral features that also need to be clearly specified.

Based on observations obtained with the ELODIE spectrometer, we describe and apply a digital cross-correlation method specifically designed to meet the requirements for accurate radial-velocity measures. In particular:

1.

The absolute wavelength scale of the observations is defined by the Solar Flux Atlas (Kurucz et al. 1984) and transferred to the stellar spectra via observations of the Moon (for long-term stability) and Th-Ar calibration spectra (for short-term stability).

2.

A synthetic template is used for cross-correlation with the stellar spectra. For the present results the template consists of 1340 Fe I lines placed at their laboratory wavelengths and having a Gaussian shape with ${\it FWHM}=5$ km s^-1. Together with the instrumental profile this defines the spectral features from which the line shifts are determined.

3.

Normalisation of the extracted one-dimensional spectrum reduces the arbitrary weighting of different spectral regions (depending on stellar effective temperature and instrument characteristics) normally affecting cross-correlation techniques.

4.

Observed line shifts are transformed to barycentric radial-velocity measures in accordance with a recent IAU resolution, using JPL ephemerides and formulae from Lindegren & Dravins (2002).

Results for the Sun and 42 stars are given in Tables 1 and 2. The median random (internal) standard error for the stellar radial-velocity measures is 27 m s^-1, while the external error is estimated at $\pm 120$ m s^-1. The main contributor to the external error is the uncertainty in the wavelength scale of the Solar Flux Atlas.

Acknowledgements

We thank the staff at Observatoire de Haute Provence and the ELODIE team for their enthusiastic help before, during, and after the observing runs, especially Alain Vin (Haute-Provence) and Didier Queloz (Geneva). Principal Investigator for the ELODIE observing programme Astrometric versus spectroscopic radial velocities is Prof. D. Dravins at Lund Observatory, who kindly made the data available for this analysis and provided numerous advice and practical help. We gratefully acknowledge financial support from the Royal Physiographic Society in Lund, the Swedish Natural Science Research Council and the Swedish National Space Board.