Analytic models of the Rossiter-McLaughlin effect for arbitrary eclipser/star size ratios and arbitrary multiline stellar spectra

Abstract

We present an attempt to improve models of the Rossiter-McLaughlin effect by relaxing several restrictive assumptions. We consider the entire multiline stellar spectrum rather than just a single line, use no assumptions about the shape of the lines profiles, and allow arbitrary size ratio for the star and its eclipser. However, we neglect the effect of macro-turbulence and differential rotation. We construct our model as a power series in the stellar rotation velocity, $V\sin i$, giving a closed set of analytic formulae for up to three terms, and assuming quadratic limb-darkening law. We consider three major approaches of determining the Doppler shift: cross-correlation with a predefined template, cross-correlation with an out-of-transit stellar spectrum, and parametric modelling of the spectrum. A numerical testcase revels that our model preserves good accuracy for the rotation velocity of up to the limit of $2-3$ times the average linewidth in the spectrum. We also apply our approach to the Doppler data of HD 189733, for which we obtain an improved model of the Rossiter-McLaughlin effect with two correction terms, and derive a reduced value for $V\sin i$.

Accepted to MNRAS; 23 pages, 5 figures, 2 tables

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Cited by in corpus (6)

• Rossiter--McLaughlin models and their effect on estimates of stellar rotation, illustrated using six WASP systems
• The CARMENES search for exoplanets around M dwarfs. Radial velocities and activity indicators from cross-correlation functions with weighted binary masks
• The GAPS Programme with HARPS-N at TNG. XIII. The orbital obliquity of three close-in massive planets hosted by dwarf K-type stars: WASP-43, HAT-P-20 and Qatar-2
• Homogeneously derived transit timings for 17 exoplanets and reassessed TTV trends for WASP-12 and WASP-4
• PlanetPack3: a radial-velocity and transit analysis tool for exoplanets
• The impact of photospheric brightness field on exoplanetary transit timings and the TTV excess of HD 189733 b