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

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.

20 pages, 11 figures, accepted for publication in PASJ

References in corpus (9)

• Formation of Hot Planets by a combination of planet scattering, tidal circularization, and Kozai mechanism
• On differential rotation and overshooting in solar-like stars
• Determination of Three-dimensional Spin-orbit Angle with Joint Analysis of Asteroseismology, Transit Lightcurve, and the Rossiter-McLaughlin Effect: Cases of HAT-P-7 and Kepler-25
• A Preponderance of Perpendicular Planets
• The atmosphere of HD 209458b seen with ESPRESSO. No detectable planetary absorptions at high resolution
• Hot Stars With Kepler Planets Have High Obliquities
• The misaligned orbit of the Earth-sized planet Kepler-408b
• Star-disk alignment in the protoplanetary disks: SPH simulation of the collapse of turbulent molecular cloud cores
• Possible Outcomes of Coplanar High-eccentricity Migration: Hot Jupiters, Close-in Super-Earths, and Counter-orbiting Planets