  A transiting extrasolar planet sequentially blocks off the light coming from
the 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 line
profiles of the stellar spectrum, leading to an apparent anomaly of the radial
velocity curves, known as the Rossiter - McLaughlin effect. Here, we derive
approximate but accurate analytic formulae for the anomaly of radial velocity
curves taking account of the stellar limb darkening. The formulae are
particularly useful in extracting information of the projected angle between
the planetary orbit axis and the stellar spin axis, \lambda, and the projected
stellar spin velocity, V sin I_s. We create mock samples for the radial curves
for the transiting extrasolar system HD209458, and demonstrate that constraints
on the spin parameters (V sin I_s, \lambda) may be significantly improved by
combining our analytic template formulae and the precision velocity curves from
high-resolution spectroscopic observations with 8-10 m class telescopes. Thus
future observational exploration of transiting systems using the Rossiter -
McLaughlin effect is one of the most important probes to better understanding
of the origin of extrasolar planetary systems, especially the origin of their
angular momentum.
