2009A&A...506.1335C

There are very few comparisons between theoretical and empirical limb-darkening coefficients (LDCs). To develop this scenario, we analyse the case of the HD 209458 planetary system for which 10 passband measurements of linear and quadratic LDCs are available. The empirical data for HD 209458 were derived from the light curves obtained with the Hubble Space Telescope (HST). Since the corresponding effective wavelengths differ from those usually adopted, we computed monochromatic calculations to gain some insight into the problem. The theoretical LDCs were computed by adopting the least-squares method (LSM) but with a larger numerical resolution (100 µ points instead of 11). The flux conservation method (FCM) was also applied. The plane-parallel stellar atmosphere model ATLAS and the spherically symmetrical PHOENIX model were adopted in the calculations. We found systematic disagreement between the theoretical and empirical LDCs for the linear case. Disagreements are also found when we compared the quadratic LDCs with observations. Even taking into account uncertainties in the metallicity, micro-turbulent velocity, and effective temperature in the calculation of the theoretical LDCs, the corresponding shifted curves cannot match the empirical data. It seems that the current atmosphere models are unable to explain the specific intensity distribution of HD 209458.