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

Kento Masuda

doi:10.1088/0004-637X/805/1/28

paper

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

arXiv:1503.05446 · doi:10.1088/0004-637X/805/1/28

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 $i_{⋆} = 8 1^{\circ} \pm 5^{\circ}$ and $ψ = 6 0^{\circ} \pm 2^{\circ}$ adopting the spectroscopic constraint $λ = 58. 6^{\circ} \pm 2. 0^{\circ}$ 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, $d ∣ cos i_{orb} ∣/ d t = (- 7.0 \pm 0.4) \times 1 0^{- 6} day^{- 1}$ , providing further evidence for the spin-orbit precession in this system. By fitting the precession model to the time series of $i_{orb}$ , $λ$ , and $i_{⋆}$ obtained with the gravity-darkened model, we constrain the stellar quadrupole moment $J_{2} = (6.1 \pm 0.3) \times 1 0^{- 5}$ for our new solution, which is several times smaller than $J_{2} = (1.66 \pm 0.08) \times 1 0^{- 4}$ 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 $ψ = 10 1^{\circ} \pm 2^{\circ}$ or $8 7^{\circ} \pm 2^{\circ}$ 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.

arXiv comment15 pages, 8 figures, accepted for publication in ApJ, typo in the abstract fixed

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

Abstract

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