The Determination and Interpretation of the Rotation Parameter v sin i

Abstract

Abstract. In this paper we review the development of the concept of the stellar rotation parameter commonly known as v sin i. We emphasize that the interpretation of the parameter in terms of physical characteristics of the star always depends on comparison with a model that is intended to represent the physical properties of the star. To that end we will trace the development of such models along with the observational means of determining the parameter. Emphasis will be place on the traditional methods involving stellar spectroscopy, but some attention will be place on indirect methods involving direct measurement of the rotation period and recent interferometric determination of stellar oblatness. In addition we will comment on recent techniques involving the simultaneous measurement of many spectral lines and synthetic spectra to improve the accuracy of rotational half-widths.The natural desire for simplicity of such models has often resulted in erroneous values for stellar parameters. This is particularly the case for the most rapidly rotating stars generally of early spectral type, but may also be present in some giants and supergiants where rapid rotation is difficult to detect. Finally, we will comment on the possibilities of improving the quality of both the measurement and interpretation of this important stellar rotation parameter. IntroductionEver since Galileo proclaimed, in the Sidereal Messenger (1610), that some celestial objects both rotated and revolved those who observe the heavens have enquired into the rotation of stars. Thomas Wright (1750) noted that stars were like the sun and vice verse and, by noting that the sun rotated on its axis, he may be credited with being the first to speculate that stars do so as well. But the actual observation of such phenomenon had to wait until stellar spectroscopy improved sufficiently to quantitatively observe the shape of stellar spectra lines. While Otto Struve is generally credited with being the "father of stellar rotation", seminal work by a number of astronomers early in the 20th century laid a broad foundation for the quantitative determination of stellar rotation. Although Shapley & Nicholsen (1919) were the first to formalize the concept of rotational broadening, Carroll (1928Carroll ( , 1933 and Carroll & Ingram (1933) developed the first workable model and applied it to stellar systems. Collins & Truax (1995) Rossiter's (1924) explanation of an anomaly in the radial velocity curve (3 Lyrae as resulting from the axial rotation of the eclipsed star during the eclipse. The systematic covering of the eclipsed disk yields shifts in the center of spectral lines during the eclipse resulting from apparent changes in the mean line-of-sight motion of the rotating eclipsed star. This effect, which is yet to be described for any star by an ab initio model, is still generally known as the Rossiter Effect and is considered to be first direct confirmation that stars do rotate. It was almost immediately confirmed by, Rossiter's doctoral advisor, McLaughlin (1...