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Description
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_{lambda}_({mu})=1-c(1-{mu}^{alpha}^), has recently been proposed as a good compromise between complexity and precision in the treatment of limb-darkening. My aim is to develop a practical implementation of the power-2 limb-darkening law and to quantify the accuracy of this implementation. 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_{lambda}_({mu}) values. I use the transformed parameters h_1_=1-c(1-2^(-{alpha})^) and h_2_=c2^(-{alpha}^) to directly compare these optimized limb-darkening parameters to the limb darkening measured from Kepler light curves of 16 transiting exoplanet systems. 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 {alpha}. 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). 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 transiting exoplanets.
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