Spin-Orbit Misalignment and Precession in the Kepler-13Ab Planetary System

TL;DR

This study models the gravity-darkened transit of Kepler-13Ab to confirm and analyze its spin-orbit precession, revealing a consistent rate of impact parameter change through transit and phase curve data.

Contribution

It provides the first evidence of spin-orbit precession in Kepler-13Ab based solely on secondary eclipse variations, using gravity-darkened transit modeling.

Findings

Confirmed temporal change in impact parameter indicating precession.

Measured a consistent precession rate from transit and phase curve data.

Less than 1% light dilution explains seasonal variation in Kepler data.

Abstract

Gravity darkening induced by rapid stellar rotation provides us with a unique opportunity to characterize the spin-orbit misalignment of a planetary system through analysis of its photometric transit. We use the gravity-darkened transit modeling code simuTrans to reproduce the transit light curve of Kepler-13Ab by separately analyzing phase-folded transits for 12 short-cadence Kepler quarters. We verify the temporal change in impact parameter indicative of spin-orbit precession identified by Szab\'o et al. (2012) and Masuda (2015), reporting a rate of change $db/dt = (-4.1 \pm 0.2) \times 10^{-5}$ day$^{-1}$. We further investigate the effect of light dilution on the fitted impact parameter and find that less than 1% of additional light is sufficient to explain the seasonal variation seen in the Kepler quarter data. We then extend our precession analysis to the phase curve data from which we report a rate of change $db/dt = (-3.2 \pm 1.3) \times 10^{-5}$ day$^{-1}$. This value is consistent with that of the transit data at a lower significance and provides the first evidence of spin-orbit precession based solely on the temporal variation of the secondary eclipse.