耗散和非耗散双星-单星碰撞的解析统计近似解
An Analytical, Statistical Approximate Solution for Dissipative and non-Dissipative Binary-Single Stellar Encounters
摘要：
我们提出了一个统计近似解的约束，非层次的三体问题，并将其扩展到硬双星系统和单星之间的遭遇的一般分析。当三颗恒星中的一颗被弹射到无穷远处时，任何这样的相遇都会终止，留下一颗残余双星;双星-单星散射的问题包括找到残余双星轨道参数的概率分布，作为总能量和总角动量的函数。在这里，我们将相遇建模为一系列紧密的，非分层的，三重的方法，穿插着分层的阶段，其中系统由一个内部的双星和一颗围绕它运行的恒星组成-这将整个相遇的演变转变为连续分层阶段之间的随机行走。我们使用的解决方案的约束，非层次的三体问题，找到步行者的过渡概率，我们概括的情况下，潮汐相互作用是重要的。除了潮汐，任何耗散过程都可以纳入随机游走模型，因为它是完全通用的。我们的近似解可以再现过去数值模拟的结果，并可以考虑不同的环境和不同的耗散效应。因此，该模型可以有效地取代直接的少体积分的需要，在任何环境下的双单相遇的研究。此外，它允许简单地包括耗散力，通常不占在完整的N体积分方案。
英文摘要：
We present a statistical approximate solution of the bound, non-hierarchical three-body problem, and extend it to a general analysis of encounters between hard binary systems and single stars. Any such encounter terminates when one of the three stars is ejected to infinity, leaving behind a remnant binary; the problem of binary-single star-scattering consists of finding the probability distribution of the orbital parameters of the remnant binary, as a function of the total energy and the total angular momentum. Here, we model the encounter as a series of close, non-hierarchical, triple approaches, interspersed with hierarchical phases, in which the system consists of an inner binary and a star that orbits it -- this turns the evolution of the entire encounter to a random walk between consecutive hierarchical phases. We use the solution of the bound, non-hierarchical three-body problem to find the walker's transition probabilities, which we generalise to situations in which tidal interactions are important. Besides tides, any dissipative process may be incorporated into the random walk model, as it is completely general. Our approximate solution can reproduce the results of the extensive body of past numerical simulations, and can account for different environments and different dissipative effects. Therefore, this model can effectively replace the need for direct few-body integrations for the study of binary-single encounters in any environment. Furthermore, it allows for a simply inclusion of dissipative forces typically not accounted for in full N-body integration schemes.
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