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تسجيل مستخدم جديدOdd Harmonics in Exoplanet Photometry: Weather or Artifact?
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Photometry of short-period planetary systems allows astronomers to monitor exoplanets, their host stars, and their mutual interactions. 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, sometimes much greater than the predictions of tidal theory. The reflected phase variations of a homogeneous planet contains power at even orbital harmonics-important for studies of ellipsoidal variations-but cannot contain odd orbital 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. Either of these scenarios entail weather: short-period planets are expected to have zero obliquity and hence N-S symmetric stellar forcing. North-South asymmetry in a giant planet would therefore suggest stochastic localized features, such as weather. However, we find that previous claims of large-amplitude odd modes in Kepler photometry are artifacts of removing planetary transits rather than modeling them. The only reliable claims of odd harmonics remain HAT-P-7b and Kepler-13Ab, for which the third mode amplitude is 6-8% of the planetary flux. Although time-variable albedo maps could in principle explain these odd harmonics, upper-limits on the infrared variability of hot Jupiters make this hypothesis unlikely. We urge theorists to study the effects of close-in planets on stellar atmospheres, as this remains the only plausible hypothesis.
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The exquisite photometry of Kepler has revealed reflected light from exoplanets, tidal distortion of host stars and Doppler beaming of a stars light due to its motion (Borucki 2016; Demory et al. 2012; Welsh et al. 2010; Bloemen et al. 2012). Esteves
et al. (2013, 2015) and Shporer et al. (2014) reported additional odd harmonics in the light curves of two hot Jupiters: HAT-P-7b and Kepler-13Ab. They measured non-zero power at three times the orbital frequency that persisted while the planet was eclipsed and hence must originate in the star (Esteves et al. 2015). Penoyre & Sandford (2018) showed that orbital eccentricity could result in time-dependent tidal deformation of the star that manifests itself at three times the orbital frequency and suggested this could be the origin of the measured odd modes. In this Research Note, we show that the small orbital eccentricities of HAT-P-7b and Kepler-13Ab cannot generate the odd harmonics observed in these systems. Esteves et al. (2015) hypothesized that the odd modes could be due to tidal distortion of the star if its spin is misaligned with the systems orbital motion, as is the case in both of these systems (Benomar et al. 2014; Herman et al. 2018), but this mechanism has yet to be verified theoretically or numerically.
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