KELT-9 b's Asymmetric TESS Transit Caused by Rapid Stellar Rotation and Spin-Orbit Misalignment

KELT-9 b is an ultra hot Jupiter transiting a rapidly rotating, oblate early-A-type star in a polar orbit. We model the effect of rapid stellar rotation on KELT-9 b's transit light curve using photometry from the Transiting Exoplanet Survey Satellite (\tess) to constrain the planet's true spin-orbit angle and to explore how KELT-9 b may be influenced by stellar gravity darkening. We constrain the host star's equatorial radius to be $1.089\pm0.017$ times as large as its polar radius and its local surface brightness to vary by $\sim38$\% between its hot poles and cooler equator. We model the stellar oblateness and surface brightness gradient and find that it causes the transit light curve to lack the usual symmetry around the time of minimum light. We take advantage of the light curve asymmetry to constrain KELT-9 b's true spin orbit angle (${87^\circ}^{+10^\circ}_{-11^\circ}$), agreeing with \citet{gaudi2017giant} that KELT-9 b is in a nearly polar orbit. We also apply a gravity darkening correction to the spectral energy distribution model from \citet{gaudi2017giant} and find that accounting for rapid rotation gives a better fit to available spectroscopy and yields a more reliable estimate for the star's polar effective temperature.