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Kepler has detected numerous exoplanet transits by precise measurements ofstellar light in a single visible-wavelength band. In addition to detection,the precise photometry provides phase curves of exoplanets, which can be usedto study the dynamic processes on these planets. However, the interpretation ofthese observations can be complicated by the fact that visible-wavelength phasecurves can represent both thermal emission and scattering from the planets.Here we present a semi-analytical model framework that can be applied to studyKepler and future visible-wavelength phase curve observations of exoplanets.The model efficiently computes reflection and thermal emission components forboth rocky and gaseous planets, considering both homogeneous and inhomogeneoussurfaces or atmospheres. We analyze the phase curves of the gaseous planetKepler-7 b and the rocky planet Kepler-10 b using the model. In general, wefind that a hot exoplanet's visible-wavelength phase curve having a significantphase offset can usually be explained by two classes of solutions: one classrequires a thermal hot spot shifted to one side of the substellar point, andthe other class requires reflective clouds concentrated on the same side of thesubstellar point. The two solutions would require very different Bond albedosto fit the same phase curve; atmospheric circulation models or eclipseobservations at longer wavelengths can effectively rule out one class ofsolutions, and thus pinpoint the albedo of the planet, allowing decompositionof the reflection and the thermal emission components in the phase curve.Particularly for Kepler-7 b, reflective clouds located on the west side of thesubstellar point can best explain its phase curve. We further derive that thereflectivity of the clear part of the atmosphere should be less than 7% andthat of the cloudy part should be greater than 80% (abridged)

A Semi-Analytical Model of Visible-Wavelength Phase Curves of Exoplanets and Applications to Kepler-7 b and Kepler-10 b