High-precision Stellar Limb-darkening in Exoplanetary Transits

Characterization of the atmospheres of transiting exoplanets relies on accurate measurements of the extent of the optically thick area of the planet at multiple wavelengths with a precision $\lesssim 100$ parts per million (ppm). Next-generation instruments onboard the James Webb Space Telescope (JWST) are expected to achieve ~10 ppm precision for several tens of targets. A similar precision can be obtained in modeling only if other astrophysical effects, including the stellar limb-darkening, are properly accounted for. In this paper, we explore the limits on precision due to the mathematical formulas currently adopted to approximate the stellar limb-darkening, and due to the use of limb-darkening coefficients obtained either from stellar-atmosphere models or empirically. We recommend the use of a two-coefficient limb-darkening law, named "power-2," which outperforms other two-coefficient laws adopted in the exoplanet literature in most cases, and particularly for cool stars. Empirical limb-darkening based on two-coefficient formulas can be significantly biased, even if the light-curve residuals are nearly photon-noise limited. We demonstrate an optimal strategy to fitting for the four-coefficient limb-darkening in the visible, using prior information on the exoplanet orbital parameters to break some of the degeneracies that otherwise would prevent the convergence of the fit. Infrared observations taken with the JWST will provide accurate measurements of the exoplanet orbital parameters with unprecedented precision, which can be used as priors to improve the stellar limb-darkening characterization, and therefore the inferred exoplanet parameters, from observations in the visible, such as those taken with Kepler/K2, the JWST, and other past and future instruments.