  We present an improved formula for the anomalous radial velocity of the star
during planetary transits due to the Rossiter-McLaughlin (RM) effect. The
improvement comes from a more realistic description of the stellar absorption
line profiles, taking into account stellar rotation, macroturbulence, thermal
broadening, pressure broadening, and instrumental broadening. Although the
formula is derived for the case in which radial velocities are measured by
cross-correlation, we show through numerical simulations that the formula
accurately describes the cases where the radial velocities are measured with
the iodine absorption-cell technique. The formula relies on prior knowledge of
the parameters describing macroturbulence, instrumental broadening and other
broadening mechanisms, but even 30% errors in those parameters do not
significantly change the results in typical circumstances. We show that the new
analytic formula agrees with previous ones that had been computed on a
case-by-case basis via numerical simulations. Finally, as one application of
the new formula, we reassess the impact of the differential rotation on the RM
velocity anomaly. We show that differential rotation of a rapidly rotating star
may have a significant impact on future RM observations.
