High-precision stellar limb-darkening measurements

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 u 2 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.

The center-to-limb variation across the Fraunhofer lines of HD 189733

“…Claret (2004) give both limb-darkening coefficients derived from (onedimensional) PHOENIX and ATLAS model atmospheres, which are similar but not identical. Müller et al (2013) find both sets of coefficients to be consistent with Kepler data. Hayek et al (2012) compare CLV predictions resulting from one-and three-dimensional model atmospheres to transit light curves of HD 189733 and HD 209458.…”

“…In the analysis of transit light curves of extrasolar planets, the CLV has long been acknowledged as a critical factor (e.g., Müller et al 2013). In the modeling, the brightness distribution of the stellar disk is usually parametrized by one of many available so-called limb-darkening laws.…”

Theoretical gravity and limb-darkening coefficients for the MOST satellite photometric system

“…One of the most relevant papers on this subject is by Southworth (2012) who analysed 38 transits of exoplanets, paying special attention to limb-darkening. More recently, Müller et al (2013) also investigated transits of 38 Kepler planetary candidates. On the other hand, Csizmadia et al (2013) studied the effects of the LDC on the accuracy of exoplanets radii.…”

“…In addition to precision, the accuracy of the LDC is also a matter of concern. Müller et al (2013) have looked at this issue, and recommend fixing the LDC to their theoretical values for data with S/N lower than that of the Kepler data used in their study. This is the case for MOST transit photometry for which we also find that the uncertainties in the transit parameters are of the order of a few percent, significantly larger than the ∼1% error they find is introduced in the transit parameters by the differences between measured and theoretical LDC.…”

“…Fortunately, the situation is changing. Gradually, some high quality data are allowing these comparisons: for instance, light curves from double-lined eclipsing binaries (Claret 2008), planetary transits (Southworth 2008;Claret 2009;Sing 2010;Howarth 2011;Claret & Bloemen 2011;Southworth 2012;Csizmadia et al 2013;Müller et al 2013), or microlensing events (Zub et al 2011).…”