Analytic Description of the Rossiter-McLaughlin Effect for Transiting Exoplanets: Cross-Correlation Method and Comparison with Simulated Data

TL;DR

This paper derives an improved analytical formula for the Rossiter-McLaughlin effect in transiting exoplanets, accounting for stellar line broadening, and validates it with simulated data, enhancing the understanding of stellar rotation influence.

Contribution

It introduces a new analytical expression for the Rossiter-McLaughlin effect that includes stellar linewidth effects, improving accuracy over previous models.

Findings

New formula matches mock data better than previous models.

Accounts for stellar line broadening effects.

Explains dependence of velocity anomaly on stellar rotation.

Abstract

We obtain analytical expressions for the velocity anomaly due to the Rossiter- McLaughlin effect, for the case when the anomalous radial velocity is obtained by cross-correlation with a stellar template spectrum. In the limit of vanishing width of the stellar absorption lines, our result reduces to the formula derived by Ohta et al. (2005), which is based on the first moment of distorted stellar lines. Our new formula contains a term dependent on the stellar linewidth, which becomes important when rotational line broadening is appreciable. We generate mock transit spectra for four existing exoplanetary systems (HD17156, TrES-2, TrES- 4, and HD209458) following the procedure of Winn et al. (2005), and find that the new formula is in better agreement with the velocity anomaly extracted from the mock data. Thus, our result provides a more reliable analytical description of the velocity anomaly due to the Rossiter-McLaughlin effect, and explains the previously observed dependence of the velocity anomaly on the stellar rotation velocity.