Spin-Orbit Alignment For 110-Day-Period KOI368.01 From Gravity Darkening

We fit the \emph{Kepler} photometric light curve of the KOI-368 system using an oblate, gravity-darkened stellar model in order to constrain its spin-orbit alignment. We find that the system is relatively well-aligned with a sky-projected spin-orbit alignment of $\lambda=10^{\circ}\pm2^{\circ}$, a stellar obliquity of $\psi=3^{\circ}\pm7^{\circ}$, and a true spin-orbit alignment of $\varphi=11^{\circ}\pm3^{\circ}$. Although our measurement differs significantly from zero, the low value for $\varphi$ is consistent with spin-orbit alignment. We also measure various transit parameters of the KOI-368 system: $R_{\star}=2.28\pm0.02 R_{\odot}$, $R_{p}=1.83\pm0.02R_{jup}$, and $i=89.221^{\circ}\pm0.013^{\circ}$. This work shows that our gravity-darkened model can constrain long-period, well-aligned planets and M-class stars orbiting fast-rotators, allowing for measurement of a new subcategory of transiting bodies.