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

TL;DR

This paper presents an analytic method to analyze the Rossiter-McLaughlin effect, accounting for stellar differential rotation, enabling the determination of stellar inclination and full spin-orbit angle from transit data.

Contribution

It introduces a fully analytic formula for the RM effect that incorporates stellar differential rotation, improving the estimation of stellar inclination and spin-orbit alignment.

Findings

Differential rotation causes RM velocity modulations of several m/s.

The method allows estimation of stellar inclination $i_\star$ from RM data.

Full spin-orbit angle $\psi$ can be derived using the new approach.

Abstract

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