We present a comprehensive analysis of planetary phase variations, including possible planetary light offsets, using eighteen quarters of data from the Kepler space telescope. Our analysis found fourteen systems with significant detections in each of the phase curve components: planet's phase function, secondary eclipse, Doppler boosting, and ellipsoidal variations. We model the full phase curve simultaneously, including primary and secondary transits, and derive albedos, day- and night-side temperatures and planet masses. Most planets manifest low optical geometric albedos ( 0.25), with the exception of Kepler-10b, Kepler-91b, and KOI-13b. We find that KOI-13b, with a small eccentricity of 0.0006 ± 0.0001, is the only planet for which an eccentric orbit is favored. We detect a third harmonic for HAT-P-7b for the first time, and confirm the third harmonic for KOI-13b reported in Esteves et al.: both could be due to their spin–orbit misalignments. For six planets, we report a planetary brightness peak offset from the substellar point: of those, the hottest two (Kepler-76b and HAT-P-7b) exhibit pre-eclipse shifts or on the evening-side, while the cooler four (Kepler-7b, Kepler-8b, Kepler-12b, and Kepler-41b) peak post-eclipse or on the morning-side. Our findings dramatically increase the number of Kepler planets with detected planetary light offsets, and provide the first evidence in the Kepler data for a correlation between the peak offset direction and the planet's temperature. Such a correlation could arise if thermal emission dominates light from hotter planets that harbor hot spots shifted toward the evening-side, as theoretically predicted, while reflected light dominates cooler planets with clouds on the planet's morning-side.
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