Spin-Orbit Misalignment of Two-Planet-System KOI-89 Via Gravity Darkening

We constrain the true spin-orbit alignment of the KOI-89 system by numerically fitting the two \emph{Kepler} photometric lightcurves produced by transiting planets KOI-89.01 and KOI-89.02. The two planets have periods of 84.69 days and 207.58 days, respectively. We find that the two bodies are low-density giant planets with radii $0.45 \pm 0.03~\mathrm{R_{jup}}$ and $0.43 \pm 0.05~\mathrm{R_{jup}}$ and spin-orbit misalignments $72^{\circ} \pm 3^\circ$ and $73^{\circ+11}_{-5}$, respectively. Via dynamic stability tests we demonstrate the general trend of higher system stability with the two planets close to mutual alignment and estimate their coalignment angle to $20^\circ \pm 20^\circ$ -- i.e. the planets are misaligned with the star but may be aligned with each other. From these results, we limit KOI-89's misalignment mechanisms to star-disk-binary interactions, disk warping via planet-disk interactions, planet-planet scattering, Kozai resonance, or internal gravity waves.