随机扰动下双星的演化
Evolution of Binaries Under Stochastic Perturbations
AI总结：
研究随机扰动下开普勒双星的演化，通过福克-普朗克框架，针对绝热潮汐、白噪声潮汐及脉冲相遇三种情况给出轨道要素系数等，扩展了相关处理方法，还展示了方程在多天体物理场景的应用，提供了数学框架和实用工具包。
AI中文摘要：
我们开发了一个通用的福克-普朗克框架，用于描述受随机扰动的开普勒双星的动力学演化。该形式体系提供了一种算法方法，可根据扰动统计获得任何一组轨道变量的福克-普朗克漂移和扩散系数。我们将该方法应用于三种物理上不同的情况：绝热潮汐扰动、白噪声潮汐扰动以及与任意密度分布的第三体的脉冲相遇。在每种情况下，我们给出了所有六个轨道要素的明确漂移和扩散系数，推导了相关的演化时间尺度，并获得了解析稳态分布函数。我们的结果扩展了先前的处理方法，包括双星方向的演化、保留潮汐相关器的完整张量结构、处理非点状扰动体以及解决脉冲相遇的精确几何问题。后者的修正导致稳态偏心率分布略低于热分布。我们还展示了这些方程如何直接应用于几种天体物理场景，包括受暗物质次晕、超轻暗物质和星际介质扰动的双星。这项工作为随机双星演化提供了一个完整的数学框架和实用工具包，提供了可直接应用于双星群体数据的易于评估方程。
英文摘要：
We develop a general Fokker-Planck framework describing the dynamical evolution of Keplerian binaries subjected to stochastic perturbations. The formalism provides an algorithmic way to obtain the Fokker-Planck drift and diffusion coefficients of any set of orbital variables given the statistics of the perturbations. We apply the method to three physically distinct regimes: adiabatic tidal perturbations, white-noise tidal perturbations, and impulsive encounters with a third body of arbitrary density profile. In each regime we provide explicit drift and diffusion coefficients for all six orbital elements, derive the associated evolution timescale, and obtain analytic steady-state distribution functions. Our results extend previous treatments by including the evolution of the binary's orientation, retaining the complete tensor structure of tidal correlators, treating non-pointlike perturbers, and resolving the exact geometry of impulsive encounters. The latter correction leads to a steady-state eccentricity distribution that is slightly sub-thermal. We also show how these equations can be applied directly in several astrophysical scenarios, including binaries perturbed by dark matter subhaloes, ultralight dark matter, and the interstellar medium. This work delivers both a complete mathematical framework and a practical toolkit for stochastic binary evolution, providing ready-to-evaluate equations to be applied directly to binary population data.
