Paper detail

Limb darkening in spherical stellar atmospheres

(Abridged) Context. Stellar limb darkening, I(μ = cosθ), is an important constraint for microlensing, eclipsing binary, planetary transit, and interferometric observations, but is generally treated as a parameterized curve, such as a linear-plus-square-root law. Many analyses assume limb-darkening coefficients computed from model stellar atmospheres. However, previous studies, using I(μ) from plane- parallel models, have found that fits to the flux-normalized curves pass through a fixed point, a common μ location on the stellar disk, for all values of T eff, log g and wavelength. Aims. We study this fixed μ-point to determine if it is a property of the model stellar atmospheres or a property of the limb-darkening laws. Furthermore, we use this limb-darkening law as a tool to probe properties of stellar atmospheres for comparison to limb- darkening observations. Methods. Intensities computed with plane-parallel and spherically-symmetric Atlas models (characterized by the three fundamental parameters L\star, M\star and R\star) are used to reexamine the existence of the fixed μ-point for the parametrized curves. Results. We find that the intensities from our spherical models do not have a fixed point, although the curves do have a minimum spread at a μ-value similar to the parametrized curves. We also find that the parametrized curves have two fixed points, μ1 and μ2, although μ2 is so close to the edge of the disk that it is missed using plane-parallel atmospheres. We also find that the spherically- symmetric models appear to agree better with published microlensing observations relative to plane-parallel models.