Spin-Orbit Angles of Kepler-13Ab and HAT-P-7b

Spin-Orbit Angles of Kepler-13Ab and HAT-P-7b from Gravity-Darkened Transit Light Curves

Author:

Masuda

Abstract:

Analysis of the transit light curve deformed by the stellar gravity darkening allows us to photometrically measure both components of the spin-orbit angle ψ, its sky projection λ and inclination of the stellar spin axis i⋆. In this paper, we apply the method to two transiting hot Jupiter systems monitored with the Kepler spacecraft, Kepler-13A and HAT-P-7. For Kepler-13A, we find i⋆=81∘±5∘ and ψ=60∘±2∘ adopting the spectroscopic constraint λ=58.6∘±2.0∘ by Johnson et al. (2014). In our solution, the discrepancy between the above λ and that previously reported by Barnes et al. (2011) is solved by fitting both of the two parameters in the quadratic limb-darkening law. We also report the temporal variation in the orbital inclination of Kepler-13Ab, d|cosiorb|/dt=(−7.0±0.4)×10−6day−1, providing further evidence for the spin-orbit precession in this system. By fitting the precession model to the time series of iorb, λ, and i⋆ obtained with the gravity-darkened model, we constrain the stellar quadrupole moment J2=(6.1±0.3)×10−5 for our new solution, which is several times larger than J2=(1.66±0.08)×10−4 obtained for the previous one. We show that the difference can be observable in the future evolution of λ, thus providing a possibility to test our solution with follow-up observations. The second target, HAT-P-7, is the first F-dwarf star analyzed with the gravity-darkening method. Our analysis points to a nearly pole-on configuration with ψ=101∘±2∘ or 87∘±2∘ and the gravity-darkening exponent β consistent with 0.25. Such an observational constraint on β can be useful for testing the theory of gravity darkening.