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arXiv 2501.02587astro-ph.SRastro-ph.EPastro-ph.GA
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宽双星在理论与 Gaia 数据中的分布:I. 广义 Ambartsumian(1937)方法及偏心率幂律分布族

Distributions of wide binary stars in theory and in Gaia data: I. Generalized Ambartsumian (1937) approach and the family of power-law distributions of eccentricity

Valeri V. Makarov

AI总结:

本文在广义 Ambartsumian 方法下,利用 copula 分布导出轨道偏心率幂律分布族,并结合 17 万 Gaia 双星样本通过蒙特卡洛模拟推断偏心率固有分布。

摘要:

宽距、弱束缚双星的轨道参数空间既受到其仍不甚清楚的形成环境塑造,也受到随后在母星团和场中的动力学演化影响。Gaia 任务天体测量的进展将宽恒星系统的统计研究提升到了前所未有的精度和范围。在该问题的理论方面,本文重新审视了由 Jeans 提出、Ambartsumian 发展的旧方法。研究表明,在一般 copula 分布框架下对双星系统相密度所作的某些简化假设,可以导出一族轨道偏心率边缘分布的解析表示,其中包括具有适应性和灵活性的幂律模型。我们进一步以 Gaia 列出的 170K 双星系统为例,展示了这些模型在相对速度矢量与间距矢量之间实测运动角的正向蒙特卡洛模拟中的应用,从而对轨道偏心率的固有分布进行推断。

英文摘要:

The orbital parameter space of wide, weakly bound binary stars has been shaped by the still poorly known circumstances of their formation, as well as by subsequent dynamical evolution in parent clusters and in the field. The advance of the Gaia mission astrometry takes statistical studies of wide stellar systems to an unprecedented level of precision and scope. On the theoretical side of the problem, the old approach proposed by Jeans and developed by Ambartsumian is revisited here. It is shown how certain simplifying assumptions about the phase density of binary systems in the framework of general copula distributions can lead to a family of analytical representations for the marginal distribution of orbital eccentricity, including accommodating and flexible power-law models. We further demonstrate the application of these models in forward Monte Carlo simulations of the measured motion angles between the relative velocity and separation vectors on the example of 170K listed Gaia binary systems, providing inference in the intrinsic distribution of orbital eccentricity.

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