Disentangling the stellar inclination of transiting planetary systems: Fully analytic approach to the Rossiter-McLaughlin effect incorporating the stellar differential rotation

The Rossiter-McLaughlin (RM) effect has been widely used to estimate the sky-projected spin-orbit angle, λ, of transiting planetary systems. Most of the previous analysis assumes that the host stars are rigid rotators in which the amplitude of the RM velocity anomaly is proportional to v_⋆ sin i_⋆. When their latitudinal differential rotation is taken into account, one can break the degeneracy, and determine separately the equatorial rotation velocity v_⋆ and the inclination i_⋆ of the host star. We derive a fully analytic approximate formula for the RM effect adopting a parametrized model for the stellar differential rotation. For those stars that exhibit a differential rotation similar to that of the Sun, the corresponding RM velocity modulation amounts to several m s^-1. We conclude that the latitudinal differential rotation offers a method to estimate i_⋆, and thus the full spin-orbit angle ψ, from the RM data analysis alone.