The Spectroscopic Determination of Stellar Rotation and its Effect on Line Profiles

Abstract

Philosophy in the University of Aberdeen. I. In a previous communication to the Society* I discussed the effects of axial rotation of a star on the observed form of its absorption lines, and formulated the integral equation connecting the observed form of the line with the "true" form. By the true form is meant the form which would be observed by an observer at rest with respect to axes fixed in the star, or, in other words, the form of the line yielded by an element of the disc moving only across the observer's line of sight. The problem existing is twofold. Firstly, to determine the rotational speed of the star, or, more correctly, its equatorial velocity in the line of sight, and secondly, given this quantity, to deduce from the observed line the form of the line emitted by an element of the stellar surface. At the time of my earlier discussion few measurements of the shapes of stellar lines existed. As it was not thought that stellar rotational speeds exceeded some 20-30 km./sec. at the star's equator, I obtained a solution of the equations valid only when the distortion of the line due to rotation is slight, and dealt for the most part with the change in the central intensity of a stellar absorption line. Since then many observations have been made of the profiles f of stellar absorption lines, and in particular the observations of Struve and Elvey have shown J that velocities of the order of ten times the limit formerly supposed to exist are quite likely. Shajn and Struve J showed that in rapidly rotating stars the lines are often of a broad shallow form to which the name "dish-shaped" was very appropriately attached. Elvey showed, by working out numerically from a line of ordinary shape the observed form due to various rotational speeds, that this is the shape to be expected when the speed is high. Strictly speaking, as will be shown below, this shape is characteristic not specifically of high rotational speeds but of great distortion of the original line, though since stellar lines are not usually very narrow a high speed will as a rule be required to produce the effect. Struve and Elvey have made estimates of rotational speeds for a number of stars, by a process of matching the observed form of the line with shapes calculated from an assumed original or true shape at various speeds. It * M.N., 88, 548, 1928. f At the 1932 Meeting of the I.A.U. it was agreed informally, after discussion by the Solar Physics Commission, that the use of the word "contour" to denote the shape of a spectrum line is undesirable, and the word "profile" was recommended as more suitable.