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We perform a systematic search for atmospheric variability in short-period gas-giant planets (hot Jupiters) observed by the Kepler mission, by looking for temporal variability of their secondary eclipse depths. This is motivated by a recent detection of a decrease in the dayside brightness of KELT-1 b between TESS Sectors 17 and 57, separated by about 3 years. We fit the Kepler light curves of 53 hot Jupiters and measure their secondary eclipse depths during individual Kepler quarters and 4-quarter windows. We detect the secondary eclipses in individual quarters or four-quarter windows for 17 out of the 53 systems. In those 17 systems we do not detect statistically significant astrophysical variation in the secondary eclipse depths. We show that the data is sensitive to the variability seen for KELT-1 b in TESS data. Therefore, the absence of detected secondary eclipse variability in Kepler data suggests that the atmospheric variability in KELT-1 b is not common. In addition, several of the 53 targets we investigated display variability in their transit depths with a period of 4 quarters (1 year). This instrumental signal is likely present in the light curves of other transiting planets we did not analyze and other variable stars observed by Kepler. Finally, we find that Kepler-488 b has a secondary eclipse depth that is unphysically large for a planet, and thus is likely a misclassified red dwarf.
Li et al. (Sat,) studied this question.