Limb darkening laws for two exoplanet host stars derived from 3D stellar model atmospheres

Abstract

We compare limb darkening laws derived from 3D hydrodynamical model atmospheres and 1D hydrostatic MARCS models for the host stars of the two transiting exoplanet systems HD 209458 and HD 189733. The surface brightness distribution of the stellar disks is calculated using 3D LTE spectrum formation and opacity sampling. We test our predictions using least-squares fits of model light curves to primary eclipses that were observed with the Hubble Space Telescope (HST). The limb darkening law derived from the 3D model of HD 209458 between 2900 A and 5700 A produces significantly better fits to the HST data, removing systematic residuals that were previously observed for model light curves based on 1D predictions. This difference arises mainly from the shallower mean temperature structure of the 3D model, which is a consequence of the explicit simulation of surface granulation. In the case of HD 189733, the model atmospheres produce practically equivalent limb darkening curves between 2900 A and 5700 A, partly due to obstruction by spectral lines, and the data are not sufficient to distinguish between the light curves. We also analyze HST observations between 5350 A and 10500 A for this star; the 3D model leads to a better fit compared to 1D predictions. The significant improvement of fit quality for the HD 209458 system demonstrates the higher degree of realism of 3D models and the importance of surface granulation for the formation of the atmospheric radiation field of late-type stars. This result agrees well with recent investigations of limb darkening in the solar continuum and other observational tests. The case of HD 189733 is no contradiction as the model light curves are less sensitive to the temperature stratification of the atmosphere and the observed data in the 2900 A - 5700 A region are not sufficient to distinguish more clearly between 3D and 1D limb darkening.