2017MNRAS.467..747C

In addition to the transits of a planet in front of its star and the eclipses of the planet by its star, researchers have reported flux variations at the orbital frequency and its harmonics: planetary reflection and/or emission and Doppler beaming of starlight produce one peak per orbit, while ellipsoidal variations of a tidally distorted star and/or planet produce two maxima per orbit. Researchers have also reported significant photometric variability at three times the orbital frequency, as yet unexplained. Reflected phase variations of homogeneous planets only contain power at the orbital frequency and its even harmonics. We show that odd harmonics can, however, be produced by an edge-on planet with a time-variable map, or an inclined planet with a north-south (N-S) asymmetric map. For tidally locked planets with thick atmospheres, either of these scenarios entail weather: planets with zero obliquity experience N-S symmetric stellar forcing. North-south asymmetry would therefore suggest stochastic localized features, i.e. weather. However, we find that previous claims of large-amplitude odd modes in Kepler photometry are artefacts of removing planetary transits rather than modelling them. The only reliable claims of odd harmonics remain HAT-P-7b and Kepler-13Ab, for which the third mode amplitude is 6-8 per cent of the planetary flux. Although time-variable albedo maps could in principle explain these odd harmonics, upper-limits on the infrared variability of other hot Jupiters make this scenario unlikely. We recommend further studying the tidal effects of close-in planets on their host stars, as this remains the only plausible hypothesis.