1 Introduction

The aim of this project is to define a scheme for determining radial velocities (RVs) of hot (O-B-A) stars to within specified accuracy (systematic errors) and precision (random errors). In this series of papers we investigate the origins of systematic errors from different angles, and discuss methodologies to minimize them. Specific problems relating to random errors in RVs for early-type stars have already been discussed by Verschueren & David (1999).

It has become routine practice to measure RVs by cross-correlating the spectrum of a programme object against a reasonably similar physical template or mask, whose own velocity is either known absolutely or is determined relative to a fiducial spectrum. The incorporation of this principle into machinery gave birth to the Cambridge "radial-velocity spectrometer'' (Griffin 1967) and to an assortment of " CORAVEL''-type instruments which followed it (e.g. Griffin & Gunn 1974; Baranne et al. 1979; Fletcher et al. 1982). In a further refinement, the physical template in such an instrument is replaced with a digital one (e.g. Latham & Stefanik 1992; Baranne et al. 1996). Most of the current effort in that activity is going into velocity determinations of stars of solar types and cooler, which are particularly suitable for such equipment. However, there are pressing astrophysical needs for rapid and plentiful accurate velocities for hotter stars too, as discussed by Verschueren (1991). Improved proficiency with numerical masks has encouraged pilot studies of cross-correlation characteristics for early-type stars. Morse et al. (1991), for instance, investigated whether the systematic errors caused by object-template mismatch in both spectral type and rotational velocity could be held under 1 kms^-1 for narrow-lined stars and under 2 kms^-1 for rapid rotators if appropriate low-frequency filtering were applied. Increasing pressure to achieve a routine working accuracy better than 1 kms^-1 for early-type stars has spurred attempts to improve on the level achieved by Morse et al., both by variations of their technique and by closer investigation of details.

The first paper in this series (Verschueren et al. 1999; hereinafter called Paper I) investigates, via numerical experiments, the factors which affect the level of accuracy that is nominally attainable for radial-velocity measurements of A-type stars by cross-correlation. Differences ("spectrum mismatch'') between object and template can cause systematic errors, and are particularly prevalent in early-type stars where Nature provides rather few lines and many striking differences in spectral features between stars of nominally similar $T_{\rm eff}$ and logg. The present paper is a continuation of those experiments, but sets out from a somewhat different angle and is therefore parallel to, rather than an extension of, Paper I.

Spectrum mismatch errors are liable to occur whenever blending lines in an object and a template spectrum differ in relative strength. The asymmetry affects systematically the shape of the cross-correlation function ( CCF), thereby introducing corresponding errors into the location of its maximum (i.e. the measured RV). Each of the many variable characteristics in a stellar atmosphere - temperature, luminosity and metallicity are rather obvious ones - is therefore capable in principle of contributing a systematic error to a measured RV.

In late-type stars the richness and family likeness of lines available for RV measurement far outweigh the instances of serious differences or deleterious blends, but in early-type spectra that ratio falls well below a critical value. The changeover occurs near the late-A/early-F border, depending on rotational velocity and spectral peculiarity: a late Am star can be measured for RV with a K-type mask in a CORAVEL instrument; the orbit of the double-Am binary HD 177390/1 (Griffin 1988), for instance, was based on measurements from 4 different CORAVEL-type instruments all employing a physical K-type mask derived from the spectrum of Arcturus. For early types in general, the shortage of conforming features requires balancing the need to include as many lines as possible against the need to avoid lines which would contribute systematic errors greater than the expected random errors.

In view of the relatively frequent and often highly bizarre spectroscopic peculiarities to which stars in the temperature range $\sim15\,000-7\,000$ K (types B-F) seem particularly prone, it is necessary to examine the errors contributed by different spectral regions, and to define suitable spectral windows to eliminate specific features or regions where necessary. In Paper I we generated a grid of noise-free synthetic spectra corresponding to late B- early F dwarfs and sub-dwarfs and cross-correlated pairs, allowing $T_{\rm eff}$ and logg to vary within specified limits for selections of $v_{\rm rot}$ between 0 and 300 kms^-1. By thus maintaining tight control over the production of differential asymmetries from those causes, we were able to establish the basic levels of RV errors from spectrum mismatch.

Real spectra, however, are complicated by additional problems which standard model stellar atmospheres do not address, so the experiments with synthetic spectra contributed a very necessary but not a sufficient set of results. In the present paper (Paper II) we investigate a similar sub-set of stellar types and luminosities but proceed from observed stellar spectra, with a view to examining the influences of individual idiosyncrasies. The compass of this study is therefore broader than that of Paper I, though its borders are less stringently defined. Inevitably, because real spectra are not noise-free, this study is also slightly less decisive. When spectral lines are blurred by rotation, or when they are naturally weak, the contrast of the CCF is reduced and the noise proportionally increased. In this paper we have largely circumvented the first of those problems by selecting stars with sharp-lined spectra ($\le$ 30 kms^-1 projected rotation).

We first discuss the problems from the perspective of an observational approach (Sect. 2), and describe the methods and techniques we adopt to meet the technical challenges which they present (Sect. 3). In Sect. 4 we describe cross-correlations of pairs of spectra through a variety of wavelength intervals, justify the techniques we adopt, and examine the associated errors. In Sect. 5 we assess the trends we find, and offer in Sect. 6 some practical suggestions for the continuation of studies on the design of a programme of radial-velocity measurements.