2 An observational approach to the problem

A star's $T_{\rm eff}$ and logg are globally summarized in its spectral-type and luminosity classification. Early-type spectra, in particular, also display quite striking differences in a number of other parameters besides $T_{\rm eff}$, logg and $v_{\rm rot}$. Actually there may even be some doubt as to the precise effect of logg upon an early-type absorption spectrum; Jaschek & Gómez (1998) compared the luminosity classes of early-type stars given by highly experienced classifiers on the one hand and the absolute magnitudes derived from Hipparcos parallaxes on the other, and drew the somewhat disconcerting conclusion that the assigned luminosity classes do not necessarily correspond monotonically to absolute magnitude. In view of the extensive individuality of early-type stars, it is possible that what is routinely interpreted as a sequence in logg alone is in reality a convolution of effects that mutually mask or reinforce one another. However, our understanding of the subtle yet (in this context) crucial effects of other astrophysical variants is still largely phenomenological, and so can only be examined in observed spectra. The causes and significance of the chief factors besides $T_{\rm eff}$ and logg are mentioned in turn below.

2.1 Chemical peculiarities

The characteristic and very different traits manifested by stars branded as "chemically peculiar'' (CP) are central to the kinds of mismatch which are by no means uncommon in stellar spectra of this temperature range. The differences in appearance (e.g. in lines of CaII, SiII, CrII, rare-earths) often far outweigh the changes in line strengths due to modifications in $T_{\rm eff}$ or logg. Enhancements of such lines will therefore cause problems for RV measurements whenever they happen to be closely blended with lines of TiII or FeII which are common to the same spectra.

2.2 Rotation

The main deleterious effect caused by stellar rotation is increased blending, leading to a loss of distinction between lines which would give accurate RV measurements and others which are responsible for mismatch shifts between two dissimilar stars. Mismatch errors therefore become increasingly unavoidable (see Paper I). The broader, shallower lines resulting from increased rotation cause a reduced contrast in the CCF, with a concomitant increase in random errors. Another somewhat more subtle effect occasioned by increasing rotation is a reduction in the observable convective line-shift (see Sect. 2.3). Other second-order rotationally-dependent influences can cause changes in the basic shapes of lines. For example, if a rapidly-rotating star is viewed nearly pole-on, its decreased surface equatorial temperature causes the emergent profiles of weak lines to be square or trapezoidal rather than Gaussian (Gulliver et al. 1991), giving rise to somewhat ill-defined line centroids and correspondingly raised uncertainties in the CCF. Since the inclination i of a single star is not known, such effects are likely to be overlooked unless the spectra in question are examined at very high resolution. The loss of distinction of individual lines brought about by rotation also presents a particular problem with the determination of wavelength scales by the "zero-velocity'' method used here (see Sect. 3.5).

2.3 Stellar granulation

Stellar surfaces are patterned by small-scale velocity fields or granulation, in which hot, rising (emitting) pockets of material are interspersed with cooler, sinking (absorbing) ones. Slightly different velocities therefore tend to dominate in different layers of the line-forming region of an atmosphere, giving rise to small, characteristic distortions in line profiles. In the Sun, the bisector of a "typical'' line of intermediate strength and excitation potential is C-shaped and has a maximum blue-shift of about 300 ms^-1(Dravins 1999). If a magnetic field is present, the granules are smaller and cause correspondingly weaker distortions. With increasing rotation the asymmetry decreases, the position of the centroid tending towards the small nett shift (bluewards for solar-type stars) corresponding to the statistical bias of hot, rising elements (Dravins 1985).

Though one can (and, to some extent, has to) generalize about the effects of stellar granulation, its behaviour seems to be fairly individualistic and to depend upon the vigor of a star's surface convection, or upon variations in magnetic field-strength with rotation. On the surface of the Sun the degree of line-asymmetry is reduced in sunspot regions, and similar anti-correlations with changes in magnetic-field strength are expected to occur on other stars too. Such changes have indeed been detected in stellar spectra; Toner & Gray (1998) measured the modulation in a line-bisector in the spectrum of the chromospherically-active G8 dwarf $\xi$ Boo. According to high-resolution observations and line-profile modelling of early A stars by Landstreet (1998), certain trends in the granulation effects in non-magnetic stars are predictable. The magnitude of the distortions depends upon temperature (and possibly upon spectral peculiarity), and increases quite dramatically towards the F class; in individual sharp-lined A2m and A5m stars bisectors can be curved asymmetrically in an anti-C, with a span of about 1 kms^-1. The intrinsic shape of the bisector affects the position of the line centroid, and although the distortions will not themselves be resolved at the resolutions typical of radial-velocity spectrometers their effects will nevertheless impinge upon the RV measurements that depend upon those lines. The presence of these highly individualistic line-profile distortions therefore represents one lower limit to the accuracy of current RV measurements of stars in which surface convection is significant. Studies of line asymmetries in stars are still in their infancy, and as yet there is little general information on changes in the asymmetry patterns. If the velocity pattern causing the line asymmetries is static, it will cause a constant offset from the true value; if it fluctuates periodically, the corresponding changes in centroid position will mimic displacements that could be ascribed to a stellar planet.

2.4 Other causes of anisotropy and inhomogeneity

Many of the physical characteristics of these hot stellar atmospheres - stratification, vertical diffusion of elements, horizontal concentrations of material - can influence the small-scale symmetry, and hence the observed centroid, of an absorption line.
(i) Stratification and diffusion. Vertical stratification of material is suspected in slowly-rotating stars (which seem to be dominated, as a group, by Am and CP classes). Since the formation of a strong feature encompasses a large vertical depth of an atmosphere in which stratification may be pronounced, a line such as the CaII K line is unlikely to be reliable for accurate RV determinations, however tempting it may seem; in Vega, for instance, it even appears slightly asymmetrical in the core. If diffusion has operated within the line-forming region, weak lines of different elements might show small mutual displacements reflecting the different small-scale turbulence representative of different heights, but such shifts have not yet been detected, or even sought, as far as we are aware.

(ii) CP stars show isolated condensations associated with surface spots. Abundance inhomogeneities on quiescent stars will tend to cancel if the characteristic areas of their distributions are small compared to the radius of the star; however, on CP stars the active spots are characteristically large and few, and impart signatures of their longitudinal velocity components (i.e. RV shifts) in their line centroids.

(iii) Gross effects such as stellar winds and mass outflow tend to be most pronounced in the strongest lines (e.g. Balmer lines) whose cores are formed at high levels of the atmosphere where the disturbing events are seated. Those lines are therefore likely to be unreliable for stellar RV measurements, especially in (super)giants, except as a last resort - for instance when other lines are too diffuse, as in cases of rapid rotation - though at the cost of lower accuracy.

2.5 Binary membership

There is no astrophysical reason to exclude from this project a member of a spectroscopic binary. That would impose almost impossibly tight restrictions on the choice of spectra if implemented rigorously; faint companions to even quite bright stars are still being discovered (e.g. HR104, Hill et al. 1993). We do indeed include binary systems in the sample selected for this paper (Table 1). However, the possibility of interference from a secondary spectrum, if it is also of early type, is of course very real, so it is necessary to impose suitable restrictions, e.g. truncating the spectrum at a certain distance below the continuum, in order to avoid or minimize such interference.

2.6 Interstellar absorption

Owing to the presence of sharp IS features within the core of the K line in many early-type stars, the Ca II K line is unsuitable for these studies except where stars are sufficiently nearby that IS contributions are negligible.

2.7 Effects of observational selection

Our sample of sharp-lined late-B and early-A stars that are bright enough for high-dispersion observations can be criticized as observationally biased. It is frequently claimed that Am and CP stars have intrinsically sharp-lined spectra, though the statistics are sensitive to observational selection because proving the validity of the converse, namely that spectra whose lines are seriously washed out through rotation definitely do not show fine abundance peculiarities, is extremely challenging. Not only does the demand for increased S/N rise along with rotational velocity, but the problems of blending (i.e. line blurring) become so acute that they can only be handled by spectrum synthesis, thereby relying on the same basic foreknowledge about the individual star which is ipso facto being sought. Even Sirius and Vega, the two brightest A dwarfs in the northern sky and whose spectra have easily the highest S/N ratios in our sample (see Table 1), are "abnormal''. Sirius is classified as mild Am. Vega - once the universal standard for A-type dwarf spectra - has lines that are almost as narrow as those of Sirius, but is somewhat metal-poor; moreover, at high dispersions its line profiles show clear abnormalities to the extent that we were obliged to reject this "standard'' star as a potential template for the purposes of this paper.

Although the present study is necessarily limited to, and possibly restricted by, the types of spectral peculiarity exhibited by those stars for which suitable observational material was available (see Sect. 3.2), the range is sufficient to support a broad attack on the associated problems.