Dealing With $\delta$-Scuti Variables: Transit Light Curve Analysis of Planets Orbiting Rapidly-Rotating, Seismically Active A/F Stars

We measure the bulk system parameters of the seismically active, rapidly-rotating $\delta$-Scuti KOI-976 and constrain the orbit geometry of its transiting binary companion using a combined approach of asteroseismology and gravity-darkening light curve analysis. KOI-976 is a $1.62\pm0.2~\mathrm{M_\odot}$ star with a measured $v\sin(i)$ of $120\pm2$ km/s and seismically-induced variable signal that varies by $\sim$ 0.6\% of the star's total photometric brightness. We take advantage of the star's oblate shape and seismic activity to perform three measurements of its obliquity angle relative to the plane of the sky. We first apply rotational splitting theory to the star's variable signal observed in short-cadence \emph{Kepler} photometry to constrain KOI-976's obliquity angle, and then subtract off variability from that dataset using the linear algorithm for significance reduction software {\tt LASR}. We perform gravity-darkened fits to \emph{Kepler} variability-subtracted short-cadence photometry and to \emph{Kepler's} phase-folded long-cadence photometry to obtain two more measurements of the star's obliquity. We find that the binary system transits in a grazing configuration with measured obliquity values of $36^\circ\pm17^\circ$, $46^\circ\pm16^\circ$, and $43^\circ\pm20^\circ$ respectively for the three measurements. We perform these analyses as a way to demonstrate overcoming the challenges high-mass stars can present to transit light curve fitting and to prepare for the large number of exoplanets \emph{TESS} will discover orbiting A/F stars.