5 Discussion and conclusion

The selection of several suitable spectral lines and the evaluation of their reliability as a function of broadening and effective temperature allows the computation of over the whole spectral range of A-type stars and a robust estimate of the associated relative error.

Up to 150  , a statistical analysis indicates that the standard deviation is about 6% of the . It can be seen, in both Figs. 17 and 18, that the dispersion increases beyond 180  approximately, when comparing rotational velocities to previous determination by Abt & Morrell and SCBWP. SCBWP estimate a larger uncertainty for rotational velocities higher than 200  ; nevertheless our precision estimation for a 200  is extrapolated from Fig. 8. Errors may thus be larger, due to the sampling in Fourier space, which is proportional to $(\ensuremath{v\sin i} )^2$.

In addition, determination of continuum level induces a systematic underestimation of that reaches about 5 to 10% depending on the lines and broadening.

Gravity darkening (von Zeipel effect, von Zeipel 1925) is not taken into account in this work. Hardorp & Strittmatter (1968) quantify this effect, showing that could be 15 to 40% too small if gravity darkening is neglected for stars near break-up velocity. Nevertheless, in a recent work (Shan 2000), this effect is revised downwards and found to remain very small as long as angular velocity is not close to critical velocity ( $\omega < 0.8$): it induces an underestimation lower than 1% of the FWHM. In our observed sample, 15 stars (with spectral type from B8V to A1V) have $\ensuremath{v\sin i} >250$  . According to their radii and masses, derived from empirical calibrations (Habets & Heintze 1981), their critical velocities $v_{\rm c}$ are higher than 405  (Zorec, private communication). Only seven stars have a high , so that $\ensuremath{v\sin i} /v_{\rm c}> 0.7$. The fraction of stars rotating near their break-up velocity remains very small, probably lower than 2% of the sample size.

A systematic shift is found between the values from the catalogue of AM (1995). This difference arises from the use of the calibration relation from SCBWP, for which a similar shift is found. The discrepancy observed with standard values given by SCBWP has already been mentioned in the literature. Ramella et al. (1989) point out a similar shift with respect to the from SCBWP. They suppose that the discrepancy could come from the models SCBWP used to compute theoretical FWHM of the Mg II line. Brown & Verschueren (1997) derived for early-type stars. For low (up to $\sim$60 ), their values are systematically higher than those of SCBWP. They attribute this effect to the use of the models from Collins & Sonneborn (1977) by SCBWP; they assert that using the modern models of Collins et al. (1991) to derive from FWHM eliminates the discrepancy. Fekel (private communication) also finds this systematic effect between values from AM (1995), which are directly derived from the SCBWP's calibration, and the he measured using his own calibration (Fekel 1997).

In addition, some stars used as standards turn out to be multiple systems or to have spectral features such that their status as a standard is no longer valid. The presence of these "faulty'' objects in the standard star sample may introduce biases in the scale. There is no doubt that the list of standards established by SCBWP has to be revised.

The above comparisons and remarks lead us to call into question the values of the standard stars from SCBWP.

This paper is a first step, and a second part will complete these data with a northern sample of A-type stars.

Acknowledgements

We are very grateful to Dr M. Ramella for providing us the computer program used to derive the . We also thank the referee, Prof. J. R. de Medeiros, for his several helpful suggestions. Precious advice on statistical analysis was kindly given by Dr F. Arenou and was of great utility. We want to acknowledge Dr F. C. Fekel for his help in comparing $v\sin i$with data from the literature. Finally, we are thankful to B. Tilton for her careful reading of the manuscript. This work made use of the SIMBAD database, operated at CDS, Strasbourg, France.