Hot Jupiters are expected to be dark from both observations (albedo upper limits) and theory (alkali metals and/or TiO and VO absorption). However, only a handful of hot Jupiters have been observed with high enough photometric precision at visible wavelengths to investigate these expectations. The NASA Kepler mission provides a means to widen the sample and to assess the extent to which hot Jupiter albedos are low. We present a global analysis of Kepler-7b based on Q0-Q4 data, published radial velocities, and asteroseismology constraints. We measure an occultation depth in the Kepler bandpass of 44+-5 ppm. If directly related to the albedo, this translates to a Kepler geometric albedo of 0.32+-0.03, the most precise value measured so far for an exoplanet. We also characterize the planetary orbital phase lightcurve with an amplitude of 42+-4 ppm. Using atmospheric models, we find it unlikely that the high albedo is due to a dominant thermal component and propose two solutions to explain the observed planetary flux. Firstly, we interpret the Kepler-7b albedo as resulting from an excess reflection over what can be explained solely by Rayleigh scattering, along with a nominal thermal component. This excess reflection might indicate the presence of a cloud or haze layer in the atmosphere, motivating new modeling and observational efforts. Alternatively, the albedo can be explained by Rayleigh scattering alone if Na and K are depleted in the atmosphere by a factor of 10-100 below solar abundances.
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