Eccentricity is Not Responsible for Odd Harmonics in HAT-P-7 and Kepler-13A

Abstract

The exquisite photometry of Kepler has revealed reflected light from exoplanets, tidal distortion of host stars and Doppler beaming of a star's 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 system's 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.