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Inaccurate limb-darkening models can be a significant source of error in theanalysis of the light curves for transiting exoplanet and eclipsing binary starsystems, particularly for high-precision light curves at optical wavelengths.The power-2 limb-darkening law, $I_\lambda(\mu) = 1 -c\left(1-\mu^{\alpha}\right)$, has recently been proposed as a good compromisebetween complexity and precision in the treatment of limb-darkening. I haveused synthetic spectra based on the 3D stellar atmosphere models from theStagger-grid to compute the limb-darkening for several passbands (UBVRI,CHEOPS, TESS, Kepler, etc.). The parameters of the power-2 limb-darkening lawsare optimized using a least-squares fit to a simulated light curve computeddirectly from the tabulated $I_\lambda(\mu)$ values. I use the transformedparameters $h_1 = 1-c\left(1-2^{-\alpha}\right)$ and $h_2 = c2^{-\alpha}$ todirectly compare these optimized limb-darkening parameters to the limbdarkening 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 muchless strongly correlated than the PPDs for $c$ and $\alpha$. The agreementbetween the computed and observed values of ($h_1$, $h_2$) is generally verygood but there are significant differences between the observed and computedvalues for Kepler-17, the only star in the sample that shows significantvariability between the eclipses due to magnetic activity (star spots). Thetabulation of $h_1$ and $h_2$ provided here can be used to accurately model thelight curves of transiting exoplanets. I also provide estimates of the priorsthat should be applied to transformed parameters $h_1$ and $h_2$ based on myanalysis of the Kepler light curves of 16 stars with transiting exoplanets.

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