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arXiv 1602.07014astro-ph.EP
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基于CORBITS的多凌日系外行星系统的有效几何概率

Efficient Geometric Probabilities of Multi-Transiting Exoplanetary Systems from CORBITS

Joshua Brakensiek, Darin Ragozzine

摘要:

美国宇航局的开普勒太空望远镜使用凌日法成功发现了数千颗系外行星候选者,其中包括数百颗拥有多颗凌日行星的恒星。为了估计这些有价值的系统的频率,必须考虑到在同一母恒星周围探测到多个凌日系外行星的独特几何概率。为了改善以前的研究,使用数值方法,我们已经构建了一个有效的,半解析算法称为CORBITS,给定一个集合的绕恒星运行的系外行星,计算的概率,任何特定的一组系外行星可以观察到过境。该算法应用初等微分几何的定理来计算球体表面上由圆形曲线限定的面积(参见Ragozzine & Holman 2010)。与蒙特卡罗模拟相比,实现的算法比以前的算法更准确,速度也快了几个数量级。我们使用CORBITS表明,目前的太阳系将只显示最多3个过境行星,但这随着时间的推移,由于动力学演化而变化。我们还使用了CORBITS几何去偏开普勒的多凌日行星候选者的周期比和相互希尔球分布,这导致这些分布向略大的值移动。在附录中,我们提出了额外的半分析方法来确定系外行星共同事件的频率,即,两颗行星相互凌日的几何概率(行星-行星掩星,与凌日环联行星有关)以及当它们凌日恒星时同时发生凌日的概率。在https://github.com/jbrakensiek/CORBITS上可以公开获得CORBITS算法和几个工作示例

英文摘要:

NASA's Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called CORBITS which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets can be observed to transit. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere (see Ragozzine & Holman 2010). The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparisons with Monte Carlo simulations. We use CORBITS to show that the present solar system would only show a maximum of 3 transiting planets, but that this varies over time due to dynamical evolution. We also used CORBITS to geometrically debias the period ratio and mutual Hill sphere distributions of Kepler's multi-transiting planet candidates, which results in shifting these distributions towards slightly larger values. In an Appendix, we present additional semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability that two planets will transit each other (Planet-Planet Occultation, relevant to transiting circumbinary planets) and the probability that this transit occurs simultaneously as they transit their star. The CORBITS algorithms and several worked examples are publicly available at https://github.com/jbrakensiek/CORBITS

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