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

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 h 1 = 1 − c (1 − 2 − α ) and h 2 = c 2 − 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 h 1 and h 2 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 ( h 1 , h 2 ) 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 h 1 and h 2 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 h 1 and h 2 based on my analysis of the Kepler light curves of 16 stars with transiting exoplanets.