CLASSICAL ROTATIONAL BROADENING OF SPECTRAL-LINES

In this paper we investigate the extent to which the classical approach to stellar rotation can yield reliable estimates of the projected stellar rotational velocity. We compare the classical picture of stellar rotation developed by Carroll, Struve, Unsold, and others with ab initio models of rotating stellar atmospheres having known characteristics. We estimate the extent to which the differences between the simple model and the more physically motivated model can be attributed to various assumptions of the simple model. In addition to the simplest model envisioned by early investigators, we consider the use of an empirically determined ''sharp-line profile'' in conjunction with the classical model, and the extent to which this improves the results. Particular attention is paid to the effects of limb darkening both in the line and in the continuum. To accomplish this comparison between these two classes of models, we employ two traditional methods of analysis for rotationally broadened line profiles, the relation of the half-width of the line, and the zeros of the Fourier transform of the line as measures of the projected rotational velocity of the star. This analysis is carried out both for the early assumption that the local stellar line profile can be represented by a strong, arbitrarily sharp line and for the more common case where the local line profile can be approximated by a flux profile appropriate for a similar star that shows no rotation. We find that stars exhibiting rapid rotation are poorly described by the classical model in any form. What is somewhat surprising is that even early-type stars showing moderate rotation may suffer significant departures from the classical model. Inappropriate treatment of the limb darkening seems to be a central reason for the breakdown of the classical model at modest speeds. Applications of the classical model as a probe of the more sophisticated aspects of the atmospheric velocity field, such as differential rotation, zonal wind flow, and turbulence, are discussed. As expected because of the departure of the projected rotational speed of the classical model from that of more complete models, the use of the classical treatment for more subtle aspects of the stellar velocity field is problematic at best.