New analytical expressions of the Rossiter-McLaughlin effect adapted to different observation techniques ^⋆

¹ Centro de Astrofísica, Universidade do Porto Rua das Estrelas 4150-762 Porto Portugal
² Astronomie et Systèmes Dynamiques, IMCCE-CNRS UMR 8028, Observatoire de Paris, UPMC, 77 Av. Denfert-Rochereau, 75014 Paris, France
³ Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
e-mail: boue@oddjob.uchicago.edu
⁴ Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal

Received: 31 July 2012
Accepted: 31 October 2012

Abstract

The Rossiter-McLaughlin (hereafter RM) effect is a key tool for measuring the projected spin-orbit angle between stellar spin axes and orbits of transiting planets. However, the measured radial velocity (RV) anomalies produced by this effect are not intrinsic and depend on both instrumental resolution and data reduction routines. Using inappropriate formulas to model the RM effect introduces biases, at least in the projected velocity Vsini_⋆ compared to the spectroscopic value. Currently, only the iodine cell technique has been modeled, which corresponds to observations done by, e.g., the HIRES spectrograph of the Keck telescope. In this paper, we provide a simple expression of the RM effect specially designed to model observations done by the Gaussian fit of a cross-correlation function (CCF) as in the routines performed by the HARPS team. We derived a new analytical formulation of the RV anomaly associated to the iodine cell technique. For both formulas, we modeled the subplanet mean velocity v_p and dispersion β_p accurately taking the rotational broadening on the subplanet profile into account. We compare our formulas adapted to the CCF technique with simulated data generated with the numerical software SOAP-T and find good agreement up to Vsini_⋆ ≲ 20 km s^-1. In contrast, the analytical models simulating the two different observation techniques can disagree by about 10σ in Vsini_⋆ for large spin-orbit misalignments. It is thus important to apply the adapted model when fitting data.