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arXiv 1306.4982astro-ph.EP
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用Beta分布参数化系外行星偏心率分布

Parametrizing the exoplanet eccentricity distribution with the Beta distribution

David M. Kipping

摘要:

研究表明,太阳系外行星的轨道偏心率分布可以用Beta分布很好地描述。Beta分布的几个性质使其成为实现这一目的的强大工具。例如,Beta分布可以仅使用两个形状参数(a和b)来再现各种范围的概率密度函数(PDF)。我们认为,这使得它非常适合作为贝叶斯比较人口分析的参数模型。贝塔分布在0到1的区间内也是唯一定义的,这意味着它可以在分析太阳系外行星的观测结果时作为偏心率的适当先验。使用嵌套抽样,我们发现通过径向速度检测到的396颗系外行星的偏心率分布具有高信噪比,可以很好地描述为Beta分布,参数a = 0.867+/-0.044,b = 3.03+/-0.17。贝塔分布被证明是3.7倍更有可能代表潜在的分布的系外行星偏心率比下一个最好的模型:瑞利+指数分布。同样的数据也用于一个例子人口比较利用贝塔分布,我们发现,短周期和长周期的行星是由不同的贝塔分布在11.6西格玛的信心,并显示与潮汐循环的影响一致的签名。

英文摘要:

It is suggested that the distribution of orbital eccentricities for extrasolar planets is well-described by the Beta distribution. Several properties of the Beta distribution make it a powerful tool for this purpose. For example, the Beta distribution can reproduce a diverse range of probability density functions (PDFs) using just two shape parameters (a and b). We argue that this makes it ideal for serving as a parametric model in Bayesian comparative population analysis. The Beta distribution is also uniquely defined over the interval zero to unity, meaning that it can serve as a proper prior for eccentricity when analysing the observations of bound extrasolar planets. Using nested sampling, we find that the distribution of eccentricities for 396 exoplanets detected through radial velocity with high signal-to-noise is well-described by a Beta distribution with parameters a = 0.867+/-0.044 and b = 3.03+/-0.17. The Beta distribution is shown to be 3.7 times more likely to represent the underlying distribution of exoplanet eccentricities than the next best model: a Rayleigh + exponential distribution. The same data are also used in an example population comparison utilizing the Beta distribution, where we find that the short- and long-period planets are described by distinct Beta distributions at a confidence of 11.6 sigma and display a signature consistent with the effects of tidal circularization.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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