Improved Modeling of the Rossiter-McLaughlin Effect for Transiting Exoplanets

TL;DR

This paper introduces an improved analytical formula for modeling the Rossiter-McLaughlin effect in transiting exoplanets, accounting for realistic stellar line profiles and broadening mechanisms, enhancing accuracy in radial velocity measurements.

Contribution

The authors develop a more realistic and accurate analytical formula for the RM effect that incorporates various stellar broadening effects, validated through numerical simulations.

Findings

The new formula accurately describes radial velocities measured by different techniques.

Even with 30% errors in broadening parameters, results remain robust.

Differential rotation significantly impacts RM observations for rapidly rotating stars.

Abstract

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.