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, Iλ(µ) = 1 − c(1−µα), 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 Iλ(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.
The Ariel 0.6 - 7.8 μm stellar limb-darkening coefficients
