High-precision stellar limb-darkening measurements

A transit study of 38 Kepler planetary candidates^⋆

Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
e-mail: hmueller@hs.uni-hamburg.de

Received: 13 June 2013
Accepted: 25 September 2013

Abstract

Context. Planetary transit light curves are influenced by a variety of fundamental parameters, such as the orbital geometry and the surface brightness distribution of the host star. Stellar limb darkening (LD) is therefore among the key parameters of transit modeling. In many applications, LD is presumed to be known and modeled based on synthetic stellar atmospheres.

Aims. We measure LD in a sample of 38 Kepler planetary candidate host stars covering effective temperatures between 3000 K and 8900 K with a range of surface gravities from 3.8 to 4.7. In our study we compare our measurements to widely used theoretically predicted quadratic limb-darkening coefficients (LDCs) to check their validity.

Methods. We carried out a consistent analysis of a unique stellar sample provided by the Kepler satellite. We performed a Markov chain Monte Carlo (MCMC) modeling of low-noise, short-cadence Kepler transit light curves, which yields reliable error estimates for the LD measurements in spite of the highly correlated parameters encountered in transit modeling.

Results. Our study demonstrates that it is impossible to measure accurate LDCs by transit modeling in systems with high impact parameters (b ≳ 0.8). For the majority of the remaining sample objects, our measurements agree with the theoretical predictions, considering measurement errors and mutual discrepancies between the theoretical predictions. Nonetheless, theory systematically overpredicts our measurements of the quadratic LDC u₂ by about 0.07. Systematic errors of this order for LDCs would lead to an uncertainty on the order of 1% for the derived planetary parameters.

Conclusions. We find that it is adequate to set the commonly used theoretical LDCs as fixed parameters in transit modeling. Furthermore, it is even indispensable to use theoretical LDCs in the case of transiting systems with a high impact parameter, since the host star’s LD cannot be determined from their transit light curves.