The Rossiter‐McLaughlin Effect and Analytic Radial Velocity Curves for Transiting Extrasolar Planetary Systems

A transiting extrasolar planet sequentially blocks off the light coming fromthe different parts of the disk of the host star in a time dependent manner.Due to the spin of the star, this produces an asymmetric distortion in the lineprofiles of the stellar spectrum, leading to an apparent anomaly of the radialvelocity curves, known as the Rossiter - McLaughlin effect. Here, we deriveapproximate but accurate analytic formulae for the anomaly of radial velocitycurves taking account of the stellar limb darkening. The formulae areparticularly useful in extracting information of the projected angle betweenthe planetary orbit axis and the stellar spin axis, \lambda, and the projectedstellar spin velocity, V sin I_s. We create mock samples for the radial curvesfor the transiting extrasolar system HD209458, and demonstrate that constraintson the spin parameters (V sin I_s, \lambda) may be significantly improved bycombining our analytic template formulae and the precision velocity curves fromhigh-resolution spectroscopic observations with 8-10 m class telescopes. Thusfuture observational exploration of transiting systems using the Rossiter -McLaughlin effect is one of the most important probes to better understandingof the origin of extrasolar planetary systems, especially the origin of theirangular momentum.Comment: 39 pages, 16 figures, Accepted to ApJ. To match the published version (ApJ 623, April 10 issue