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arXiv 1503.05446astro-ph.EPastro-ph.SR
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从引力变暗的Transit光变曲线计算Kepler-13 Ab和HAT-P-7 b的自旋轨道角

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

Kento Masuda

备注：
15 pages, 8 figures, accepted for publication in ApJ, typo in the abstract fixed
发表信息：
Astrophys.J. 805 (2015) 28
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摘要：

分析的过境光变曲线变形的恒星重力变暗，使我们能够光度测量的两个组成部分的自旋轨道角$ψ$，其天空投影$λ$和倾斜的恒星自旋轴$i_\star$。在本文中，我们将该方法应用到两个凌日热木星系统监测开普勒航天器，开普勒-13A和HAT-P-7。对于开普勒-13 A，我们发现$i_\star=81^\circ\pm5^\circ$和$ψ=60^\circ\pm2^\circ$采用Johnson等人（2014）的光谱约束$λ=58.6^\circ\pm2.0^\circ$。在我们的解决方案中，上述$λ$与Barnes等人（2011）先前报道的$λ$之间的差异通过拟合二次边缘变暗定律中的两个参数来解决。我们还报道了Kepler-13 Ab，$\mathrm{d} |\cos i_{\rm orb}|/\mathrm{d}t=(-7.0\pm0.4)\times10^{-6}\,\mathrm{day}^{-1}$的轨道倾角随时间的变化，为该系统的自旋-轨道进动提供了进一步的证据。通过拟合的岁差模型的时间序列的$i_{\rm orb}$，$λ$，$i_\star$与重力暗化模型，我们约束的恒星四极矩$J_2=(6.1\pm0.3)\times10^{-5}$为我们的新的解决方案，这是几倍小于$J_2=(1.66\pm0.08)\times10^{-4}$获得前一个。我们表明，在$λ$的未来发展中可以观察到的差异，从而提供了一种可能性，以测试我们的解决方案与后续观察。第二个目标，HAT-P-7，是第一个用引力暗化方法分析的F-矮星。我们的分析指出，一个接近极点的配置与$ψ=101^\circ\pm2^\circ$或$87^\circ\pm2^\circ$和重力暗化指数$β$与$0.25$一致。这种对$β$的观测约束对于检验引力变暗理论是有用的。

英文摘要：

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 $i_\star$. 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 $i_\star=81^\circ\pm5^\circ$ and $ψ=60^\circ\pm2^\circ$ adopting the spectroscopic constraint $λ=58.6^\circ\pm2.0^\circ$ 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, $\mathrm{d} |\cos i_{\rm orb}|/\mathrm{d}t=(-7.0\pm0.4)\times10^{-6}\,\mathrm{day}^{-1}$, providing further evidence for the spin-orbit precession in this system. By fitting the precession model to the time series of $i_{\rm orb}$, $λ$, and $i_\star$ obtained with the gravity-darkened model, we constrain the stellar quadrupole moment $J_2=(6.1\pm0.3)\times10^{-5}$ for our new solution, which is several times smaller than $J_2=(1.66\pm0.08)\times10^{-4}$ 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 $ψ=101^\circ\pm2^\circ$ or $87^\circ\pm2^\circ$ 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.

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