Comparison of the power-2 limb-darkening law from the STAGGER-grid to Kepler light curves of transiting exoplanets^★

Astrophysics Group, Keele University, Keele, Staffordshire, ST5 5BG, UK
e-mail: p.maxted@keele.ac.uk

Received: 2 March 2018
Accepted: 21 April 2018

Abstract

Context. Inaccurate limb-darkening models can be a significant source of error in the analysis of the light curves for transiting exoplanet and eclipsing binary star systems, particularly for high-precision light curves at optical wavelengths. The power-2 limb-darkening law, I_λ(µ) = 1 − c(1−µ^α), has recently been proposed as a good compromise between complexity and precision in the treatment of limb-darkening.

Aims. My aim is to develop a practical implementation of the power-2 limb-darkening law and to quantify the accuracy of this implementation.

Methods. I have used synthetic spectra based on the 3D stellar atmosphere models from the STAGGER-grid to compute the limb-darkening for several passbands (UBVRI, CHEOPS, TESS, Kepler, etc.). The parameters of the power-2 limb-darkening laws are optimized using a least-squares fit to a simulated light curve computed directly from the tabulated I_λ(μ) values. I use the transformed parameters h₁ = 1 − c(1 − 2^−α) and h₂ = c2^−α to directly compare these optimized limb-darkening parameters to the limb darkening measured from Kepler light curves of 16 transiting exoplanet systems.

Results. The posterior probability distributions (PPDs) of the transformed parameters h₁ and h₂ resulting from the light curve analysis are found to be much less strongly correlated than the PPDs for c and α. The agreement between the computed and observed values of (h₁, h₂) is generally very good but there are significant differences between the observed and computed values for Kepler-17, the only star in the sample that shows significant variability between the eclipses due to magnetic activity (star spots).

Conclusions. The tabulation of h₁ and h₂ provided here can be used to accurately model the light curves of transiting exoplanets. I also provide estimates of the priors that should be applied to transformed parameters h₁ and h₂ based on my analysis of the Kepler light curves of 16 stars with transiting exoplanets.