Determination of Three-dimensional Spin-orbit Angle with Joint Analysis of Asteroseismology, Transit Lightcurve, and the Rossiter-McLaughlin Effect: Cases of HAT-P-7 and Kepler-25
Determination of Three-dimensional Spin-orbit Angle with Joint Analysis of Asteroseismology, Transit Lightcurve, and the Rossiter-McLaughlin Effect: Cases of HAT-P-7 and Kepler-25
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DOI：
10.1093/pasj/psu069
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发表时间：
2014-07
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影响因子：
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通讯作者：
O. Benomar;K. Masuda;H. Shibahashi;Y. Suto
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文献类型：
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作者：
O. Benomar;K. Masuda;H. Shibahashi;Y. Suto
我们开发了一种详细的方法来确定恒星自旋和行星轨道轴矢量之间的三维角度，$\psi$，用于过境行星系统。确定$\psi$需要独立估计恒星自转轴和行星轨道轴相对于视线（$i_\star$和$i_{\rm orb}$）的倾角，以及自转轴在天空平面上的投影（$\lambda$）。这些主要分别来自星震学、凌日光曲线和Rossiter-McLaughlin效应。对这三个数据集进行详细的联合分析，除了$\psi$之外，还可以准确和精确地确定表征行星系统的众多参数。我们展示了对HAT-P-7和Kepler-25这两个特定系统进行联合分析的能力。HAT-P-7b是第一颗被怀疑是逆行（或极地）行星的系外行星，因为它的显著偏差$\lambda \approx 180^\circ$。我们的联合分析显示$i_\star \approx {30D}$和$\psi \approx 120^\circ$，表明行星轨道更接近极地而不是逆行。开普勒-25是为数不多的测量到$\lambda$的多行行星系统之一，拥有两颗短周期凌日行星和一颗外部非凌日行星。较大的凌日行星开普勒-25c的预计自旋轨道角已被测量为$\lambda \approx 0^\circ$，这意味着该系统是对齐良好的。然而，借助星震学的严格约束，我们得到了$i_\star={65.4}^{+{10.6}}_{-{6.4}}$和$\psi={26.9}^{+{7.0}}_{-{9.2}}$，从而发现系统实际上是轻度失调的。
We develop a detailed methodology of determining three-dimensionally the angle between the stellar spin and the planetary orbit axis vectors, $\psi$, for transiting planetary systems. The determination of $\psi$ requires the independent estimates of the inclination angles of the stellar spin axis and of the planetary orbital axis with respect to the line-of-sight, $i_\star$ and $i_{\rm orb}$, and the projection of the spin--orbit angle onto the plane of the sky, $\lambda$. These are mainly derived from asteroseismology, transit lightcurve and the Rossiter-McLaughlin effect, respectively. The detailed joint analysis of those three datasets enables an accurate and precise determination of the numerous parameters characterizing the planetary system, in addition to $\psi$. We demonstrate the power of the joint analysis for the two specific systems, HAT-P-7 and Kepler-25. HAT-P-7b is the first exoplanet suspected to be a retrograde (or polar) planet because of the significant misalignment $\lambda \approx 180^\circ$. Our joint analysis indicates $i_\star \approx {30D}$ and $\psi \approx 120^\circ$, suggesting that the planetary orbit is closer to polar rather than retrograde. Kepler-25 is one of the few multi-transiting planetary systems with measured $\lambda$, and hosts two short-period transiting planets and one outer non-transiting planet. The projected spin--orbit angle of the larger transiting planet, Kepler-25c, has been measured to be $\lambda \approx 0^\circ$, implying that the system is well-aligned. With the help of the tight constraint from asteroseismology, however, we obtain $i_\star={65.4}^{+{10.6}}_{-{6.4}}$ and $\psi={26.9}^{+{7.0}}_{-{9.2}}$, and thus find that the system is actually mildly misaligned.