MEASUREMENT OF THE SPIN-ORBIT MISALIGNMENT OF KOI-13.01 FROM ITS GRAVITY-DARKENED KEPLER TRANSIT LIGHTCURVE

Abstract

We model the asymmetry of the KOI-13.01 transit lightcurve assuming a gravity-darkened rapidly-rotating host star in order to constrain the system's spin-orbit alignment and transit parameters. We find that our model can reproduce the Kepler lightcurve for KOI-13.01 with a sky-projected alignment of λ = 23 • ± 4 • and with the star's north pole tilted away from the observer by 48 • ± 4 • (assuming M * = 2.05 M ⊙ ). With both these determinations, we calculate that the net misalignment between this planet's orbit normal and its star's rotational pole is 56 • ± 4 • . Degeneracies in our geometric interpretation also allow a retrograde spin-orbit angle of 124 • ± 4 • . This is the first spin-orbit measurement to come from gravity darkening, and is one of only a few measurements of the full (not just the sky-projected) spin-orbit misalignment of an extrasolar planet. We also measure accurate transit parameters incorporating stellar oblateness and gravity darkening: R * = 1.756 ± 0.014 R ⊙ , R p = 1.445 ± 0.016 R Jup , and i = 85.9 • ± 0.4 • . The new lower planetary radius falls within the planetary mass regime for plausible interior models for the transiting body. A simple initial calculation shows that KOI-13.01's circular orbit is apparently inconsistent with the Kozai mechanism having driven its spin-orbit misalignment; planet-planet scattering and stellar spin migration remain viable mechanisms. Future Kepler data will improve the precision of the KOI-13.01 transit lightcurve, allowing more precise determination of transit parameters and the opportunity to use the Photometric Rossiter-McLaughlin effect to resolve the prograde/retrograde orbit determination degeneracy.

Revisiting a gravity-darkened and precessing planetary system PTFO 8-8695: A spin–orbit non-synchronous case

“…The stellar gravity-darkening effect provides another methodology to measure φ through the analysis of photometric transit lightuchrves for rapid rotators (Barnes et al 2011, Zhou & Huang 2013, Ahlers et al 2014, Masuda 2015. Advantages of this method are that one can determine three-dimensional (i.e., not projected) spin-orbit angle directly and that the analysis is possible without the spectroscopical data (i.e., all we need is the photometric transit lightcurves).…”

The PLATO 2.0 mission

“…In some cases, high precision photometric measurements allow the determination of the spin-orbit alignment of transiting bodies, providing additional constraints for the theories studying the formation and evolution of planetary and stellar systems (Barnes et al 2011;Shporer et al 2012). …”

High-precision stellar limb-darkening measurements

“…Its light curve has been studied by Barnes et al (2011), who report on an asymmetry in the model residuals which they attribute to gravitational darkening. The same asymmetry is seen in our analysis, resulting in a red noise detection (β ≈ 1.40).…”