Comparison of Limb-Darkening Laws from Plane-Parallel and Spherically-Symmetric Model Stellar Atmospheres

Limb-darkening is a fundamental constraint for modeling eclipsing binary and planetary transit light curves. As observations, for example from Kepler, CoRot, and Most, become more precise then a greater understanding of limb-darkening is necessary. However, limb-darkening is typically modeled as simple parameterizations fit to plane-parallel model stellar atmospheres that ignores stellar atmospheric extension. In this work, I compute linear, quadratic and four-parameter limb-darkening laws from grids of plane-parallel and spherically-symmetric model stellar atmospheres in a temperature and gravity range representing stars evolving on the Red Giant branch. The limb-darkening relations for each geometry are compared and are found to fit plane-parallel models much better than the spherically-symmetric models. Assuming that limb-darkening from spherically-symmetry model atmospheres are more physically representative of actual stellar limb-darkening than plane-parallel models, then these limb-darkening laws will not fit the limb of a stellar disk leading to errors in a light curve fit. This error will increase with a star's atmospheric extension.