6 Applications of the results, and concluding comments

Considerations of the noise levels even in ostensibly high S/N spectra lead us to conclude that cross-correlations using observed spectra should involve as many metallic lines as possible. That of course reflects the situation with cool stars and CORAVEL instruments, in which one seeks to increase the precision of the CCF peak by designing a template that samples a great many lines simultaneously. One possible feature in the design of high-accuracy RV measurements of early-type stars is therefore a very wide template spectrum in order to maximize the signal from unblended lines and thus outweigh the systematic errors arising from spectrum mismatch, at least in the case of stars with low vsini.

However, we have also found a strong indication that lines in the neighbourhood of $\lambda$ 4570-4600 Å (see Fig. 13) are sufficiently blend-free for slowly-rotating stars that that region alone can yield RV results with very little contamination from spectrum mismatch. The 5 lines of TiII and FeII between $\lambda \lambda$ 4500 - 4524 Å, with which Fekel (1999) has achieved consistent RV measurements for B and A stars, holds out similar promise. Another route to achieving the goal of rapid, accurate RV measurements for an assortment of early-type stars might therefore be to observe a narrow window around those wavelengths with particularly high S/Nratios. Since the causes of spectrum mismatch are only important if lines are blended, a window that is largely devoid of blends should work satisfactorily for a wide range of spectral types, as the present study has demonstrated, and an accurate foreknowledge of the spectral types or colours of the programme stars should not be necessary.

The only spectrum we felt obliged to eliminate at any stage was that of Vega, the one-time archetypal standard A0V, on account of its slightly abnormal line profiles. It is not inconceivable that part of the problem encountered with the spectrum of Vega was caused by systematic errors in the wavelength scales of the individual spectra brought about by the difficulty of measuring the centroids of non-Gaussian profiles. We must add, however, that although our experience with the spectrum of Vega in this context may appear to have been negative, the message behind those results is in fact strongly positive, and makes a clear case for the use of the highest possible spectral resolution in conducting tests of this nature. It is also a warning of one type of astrophysical limitation to the objectives of this project.

In this paper we have not investigated the effects of spectrum mismatch for spectra that are rotating more than about 25 kms^-1. Our method of determining the wavelength scale "internally'' would require particularly high S/Nobservations if large systematic errors in the wavelength scales of more rapidly rotating stars are to be avoided. Tests on a high-resolution spectrum of the A2m dwarf $\epsilon$ Ser, whose vsini we measured as 35 kms^-1, demonstrated that difficulty: even in the case of this relatively rich spectrum, the scatter in the RV shifts was large enough to obliterate the delicate trend of spectral-type mismatch shifts that we now know to exist from the above studies on very narrow-lined stars. This does not mean however that rotationally-broadened spectra can be handled any better by the conventional methods of determining wavelength scales from arc spectra, whether with a classical or an echelle grating, since the absolute velocity of the star still has to be determined. It merely suggests that high S/N will be of paramount importance for measuring the spectra of rotating stars and that even so it will be very difficult to achieve absolute RV measurements for such stars with a precision and accuracy that approaches what we have been able to demonstrate in this paper.

We have not mentioned the possibility of designing a physical mask to measure the RVs of these hot stars. There is already a wide acceptance that the diverse and relatively impoverished nature typical of hot-star spectra will immediately prove such a method to be impracticable. The flexibility offered by the use of numerical templates is surely essential.

We therefore conclude with twin recommendations for the pursuit of high-accuracy RVs for early-type stars: either a very wide window or a very narrow one, depending upon the available observational material and the immediate goals of the investigation. If the objective is to study conditions of spectrum mismatch among stars of very different rotational broadening (an aspect which this paper did not address), a wide window will probably be the better choice for that purpose in consideration of reducing random errors, and of blocking out the worst regions in cases of rapid rotation (see Paper I). Archived spectra would continue to be prime sources for such a study, ensuring a large amount of already-available observational material that needs no expenditure of observing resources.

If, on the other hand, the goal is to establish a small number of very high-quality spectra to serve as templates for as wide a range of spectral types as possible, a narrow window such as Window 15 is likely to serve best. As in the present study, the wavelength scales of the spectra should be determined in their intrinsic velocity frames. A good-quality CCD plus classical grating should be an ideal combination, and we hope to make such an investigation the topic of another paper in this series. Since it will not be so easy to establish accurate results for highly rotating stars by the use of a narrow window, both approaches need to be developed in parallel in order to achieve the overall goal of measuring accurate RVs for early-type stars.

Acknowledgements

We would like to thank the DAO for permisison to use both its plate archives and its PDS, and we also thank J. Pilkington and B. Argyle for their resilience in operating the Cambridge PDS according to our seemingly fussy instructions. We would like to express our appreciation to colleagues, in particular to H. Hensberge (Brussels), R.F. Griffin (Cambridge) and J.M. Fletcher (DAO), for helpful discussions on, and proffered solutions to, specific problems with which this work confronted us, and to W. Schoening (KPNO) for kindly retrieving the original reference to H & D. In addition, we thank Dr. F.C. Fekel for his painstaking refereeing of the paper. REMG is grateful to R.U.C.A. for the award of a Visiting Professorship during whose tenure much of this research was completed, and to the University of Oxford for visitor privileges there. WV acknowledges substantial financial support from the Fund for Scientific Research-Flanders (Belgium) (F.W.O.) through Research Grant No. 1.5.549.98.