Abstract

Most transit exoplanets (85%) were discovered with the Kepler space telescope. However, the mass, which was measured mainly with the radial velocity method, is known only for ~15% of them. The mass of an exoplanet may be estimated by its radius from the statistical dependences based on the observational data, though no unambiguous interrelation between the mass and the radius of planets exists. Here, we calculate the earlier unknown masses of exoplanets from four statistical mass–radius relationships (Bashi et al., 2017; Chen and Kipping, 2017; Ning et al., 2018, and the averaged dependence derived) and added the results to the distribution of planets with known masses. The mass distributions of transit exoplanets obtained in this way are analyzed with taking into account the observational selection effect inherent in the transit method. The distributions are approximated by the power law ∂N/∂M ~ M^α, where the exponent (α < 0) is determined by the maximum likelihood estimation for the samplings acquired with four mass–radius relationships: α = –2.12 ± 0.03, –2.09 ± 0.03, –1.94 ± 0.03, and –2.27 ± 0.04. Moreover, for one of these distributions, we determine the parameters of the power law, the exponent of which differs on three intervals (with the boundaries at 0.025, 0.28, and 1.34 Jupiter masses): –1.99, –0.62, and –2.88. We also conclude that there is no evidence of the interrelation between the mass of an exoplanet and its average distance to the host star (the structurization within planetary systems), if this distance is smaller than 1 AU; besides, the dependence of the exponent α on the considered mass interval is analyzed. The above estimates appertain to exoplanets detected by the space telescopes: Kepler Space Telescope and Transiting Exoplanet Survey Satellite (TESS) (these exoplanets compose group 1). The masses of the other transit exoplanets, which were detected by ground-based instruments, were known (they compose group 2). For the latter group, the exponent α is estimated at –2.21 ± 0.04. In general, the results of our analysis agree with those of the earlier statistical and theoretic studies. A key idea of the present paper is to apply the model interrelations between the mass and the radius of exoplanets to the analysis of the mass distribution of exoplanets on the basis of the recent data of observations.

中文翻译：

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来自质量-半径关系的凌日系外行星的质量分布：行星系统内的结构化

摘要

大多数凌日系外行星 (85%) 是由开普勒发现的太空望远镜。然而，主要用径向速度法测量的质量只有约 15%。系外行星的质量可以根据基于观测数据的统计依赖关系通过其半径来估计，尽管行星的质量和半径之间不存在明确的相互关系。在这里，我们根据四种统计质量半径关系计算了早期未知的系外行星质量（Bashi 等人，2017 年；Chen 和 Kipping，2017 年；Ning 等人，2018 年，以及得出的平均依赖性）并将结果添加到已知质量的行星分布。以这种方式获得的凌日系外行星的质量分布在考虑凌日方法固有的观测选择效应的情况下进行了分析。分布近似于幂律 ∂N /∂ M ~ M ^α，其中指数 (α < 0) 由通过四个质量半径关系获取的采样的最大似然估计确定：α = –2.12 ± 0.03、–2.09 ± 0.03、–1.94 ± 0.03 和 –2.27 ± 0.04。此外，对于这些分布之一，我们确定幂律的参数，其指数在三个区间（边界为 0.025、0.28 和 1.34 木星质量）不同：–1.99、–0.62 和 –2.88。我们还得出结论，如果该距离小于 1 AU，则没有证据表明系外行星的质量与其到主恒星的平均距离（行星系统内的结构化）之间存在相互关系；此外，还分析了指数 α 对所考虑的质量区间的依赖性。上述估计适用于太空望远镜探测到的系外行星：开普勒太空望远镜和凌日系外行星勘测卫星 (TESS)（这些系外行星构成第 1 组）。由地面仪器探测到的其他凌日系外行星的质量是已知的（它们构成第 2 组）。对于后一组，指数 α 估计为 –2.21 ± 0.04。总的来说，我们的分析结果与早期的统计和理论研究一致。本文的一个关键思想是根据最近的观测数据，将系外行星质量与半径之间的模型相互关系应用于系外行星质量分布的分析。指数 α 估计为 –2.21 ± 0.04。总的来说，我们的分析结果与早期的统计和理论研究一致。本文的一个关键思想是根据最近的观测数据，将系外行星质量与半径之间的模型相互关系应用于系外行星质量分布的分析。指数 α 估计为 –2.21 ± 0.04。总的来说，我们的分析结果与早期的统计和理论研究一致。本文的一个关键思想是根据最近的观测数据，将系外行星质量与半径之间的模型相互关系应用于系外行星质量分布的分析。