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

We obtain analytical expressions for the velocity anomaly due to the RossiterMcLaughlin 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, TrES4, 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. Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan Research Center for the Early Universe, School of Science, The University of Tokyo, Tokyo 113-0033, Japan Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo, Chiba 277-8582, Japan National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan Global Edge Institute, Tokyo Institute of Technology, 2-21-1 Ookayama, Meguro, Tokyo 152-8550, Japan 7 Department of Astrophysics, The California Institute of Technology, MC 249-17 Pasadena, CA 91125 Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139