Potassium detection in the clear atmosphere of a hot-Jupiter : FORS2 transmission spectroscopy of WASP-17b⋆

We present exact analytic formulae for the eclipse of a star described by quadratic or nonlinear limb darkening. In the limit that the planet radius is less than a tenth of the stellar radius, we show that the exact lightcurve can be well approximated by assuming the region of the star blocked by the planet has constant surface brightness. We apply these results to the HST observations of HD 209458, showing that the ratio of the planetary to stellar radii is 0.1207+-0.0003. These formulae give a fast and accurate means of computing lightcurves using limb-darkening coefficients from model atmospheres which should aid in the detection, simulation, and parameter fitting of planetary transits.

We report high precision spectrophotometric observations of four planetary transits of HD 209458, in the region of the sodium resonance doublet at 589.3 nm. We find that the photometric dimming during transit in a bandpass centered on the sodium feature is deeper by (2.32 +/- 0.57) x 10^{-4} relative to simultaneous observations of the transit in adjacent bands. We interpret this additional dimming as absorption from sodium in the planetary atmosphere, as recently predicted from several theoretical modeling efforts. Our model for a cloudless planetary atmosphere with a solar abundance of sodium in atomic form predicts more sodium absorption than we observe. There are several possibilities that may account for this reduced amplitude, including reaction of atomic sodium into molecular gases and/or condensates, photoionization of sodium by the stellar flux, a low primordial abundance of sodium, or the presence of clouds high in the atmosphere.