3 Data analysis

3.1 The internal precision

The different error origins are the zero-point for each observing run, the choice of synthetic spectra and a possible peculiarity of the star (shell, binary or multiple), the noise of CCD being negligible. The zero-point error was determined as described in Sect. 2.4. The error on the radial velocity arising from the choice of the synthetic spectrum depends on vsini and $T_{\rm eff}$: it is lower than 0.1kms^-1 for vsini$\leq$25kms^-1, about 1.0kms^-1 for vsini =125kms^-1, and gets 9kms^-1 for vsini=250kms^-1 and $T_{\rm eff}\,=$12500K.

 

Table 2: Error on the radial velocity in kms^-1 arising from the choice of the parameters $T_{\rm eff}$ in K and rotation in kms^-1 in synthetic spectra

This estimation is made by correlation between two adjacent synthetic spectra for every possible combinations and is given in Table2. Another error depends on the shape and symmetry of the peak. Its estimation is computed by $dv_{\rm gp}$ as described in Sect. 2.5 and given in Table7. When the shape of the peak is clearly too asymmetric and irregular, the radial velocity is not given. HIP and HD numbers of these stars are given in Table5. Finally we adopt as estimation of internal error $\sigma_{i0}$:

$${\sigma_{i0}}^{2} = {\sigma_{\rm run}}^{2} + {\sigma_{\rm mask}}^{2} +{dv_{\rm gp}}^{2}$$

$\sigma_{\rm run}$ is the rms of the zero-point of each run, $\sigma_{\rm mask}$, depending on synthetic spectrum, is given in Table2 and $dv_{\rm gp}$ gives an estimation of the asymmetry of the peak. To check the reality of this estimation, the unit-weight error was computed: for each star having several measurements v_i, the mean radial velocity $\overline{v}$ was computed and the distribution of the values $(v_{i} - \overline{v})\,/\,\sigma_{i0}$ has shown that the estimation of $\sigma_{i0}$ was slightly pessimistic. Subsequently, the given internal error $\sigma_{i}$ has been adopted as 0.85$\sigma_{i0}$.

3.2 Comparison with classical method

The radial velocities obtained by correlation were compared with those obtained by the classical method of individual measurements of spectral lines upon a part of the same spectrum. In the classical method in which the internal error estimation is strongly function of the vsini of stars, the number of measured lines decreases quickly with the projected rotational velocity. Comparable internal rms are found for stars with small vsini, the correlation method becoming quickly more accurate for vsini>30kms^-1.

3.3 Comparison with published radial velocities

Our radial velocities were compared to those already published. We have used the homogeneous radial velocities published by Andersen & Nordström (1983) and Nordström & Andersen (1985), quoted AN in Table3, and those published in the WEB (Duflot et al. 1995) and Barbier-Brossat & Figon (1998) catalogues quoted B in Table3. In all cases, variable radial velocities are excluded as well as those whose discrepancy (dv) with our results exceeds 8kms^-1. Moreover, in the WEB and Barbier-Brossat & Figon catalogues, we have eliminated those with less than 3 measurements and an error greater than 2.2kms^-1. 138 common stars remained with AN and 164 with B. Our results are more reliable, probably due to a better resolution, but unfortunately have often only one measurement making an eventual undetectable binary (stars having a published radial velocity have been observed only to obtain vsini). As can be seen in Table3, the average of dv is close to zero showing that our radial velocities are statistically in the same system as the literature. The independence of $\overline{dv}$ from the spectral type has been verified with AN.

 

Table 3: Comparison with published radial velocities