牛顿引力中的混沌四体问题I：全同点粒子
The chaotic four-body problem in Newtonian gravity I: Identical point-particles
摘要：
本文研究了牛顿引力场中的混沌四体问题。假设点粒子和总碰撞能量$\le$ 0，问题有三种可能的结果。我们将每个结果描述为能量空间中的一系列离散变换，使用Leigh \& Geller（2012;见附录）首次提出的图表。此外，我们开发了一种计算这些结果发生的概率的形式主义，表示使用每单位能量的逃逸配置的密度，并基于Monaghan描述最初开发的三体问题。我们比较这种分析形式主义的结果从一系列的二进制二进制遇到相同的点粒子，模拟使用\texttt{FEWBODY}代码。我们的三个相遇结果中的每一个都会为逃逸的恒星产生一个独特的速度分布。因此，这些分布可以潜在地用于约束的起源动态形成的人口，通过预测和观察到的速度分布之间的直接比较。最后，我们表明，遇到形成稳定的三重，模拟的单星逃逸速度分布是相同的三体问题。这也是其他两个遭遇结果的情况，但仅在低维里比。这表明，在稠密星团中，通过单联星和联星-联星相遇处理的单联星和联星，相对于基本的麦克斯韦分布（假设弛豫时间足够长），应该有一个独特的速度分布，这可以通过分析计算出来。
英文摘要：
In this paper, we study the chaotic four-body problem in Newtonian gravity. Assuming point particles and total encounter energies $\le$ 0, the problem has three possible outcomes. We describe each outcome as a series of discrete transformations in energy space, using the diagrams first presented in Leigh \& Geller (2012; see the Appendix). Furthermore, we develop a formalism for calculating probabilities for these outcomes to occur, expressed using the density of escape configurations per unit energy, and based on the Monaghan description originally developed for the three-body problem. We compare this analytic formalism to results from a series of binary-binary encounters with identical point particles, simulated using the \texttt{FEWBODY} code. Each of our three encounter outcomes produces a unique velocity distribution for the escaping star(s). Thus, these distributions can potentially be used to constrain the origins of dynamically-formed populations, via a direct comparison between the predicted and observed velocity distributions. Finally, we show that, for encounters that form stable triples, the simulated single star escape velocity distributions are the same as for the three-body problem. This is also the case for the other two encounter outcomes, but only at low virial ratios. This suggests that single and binary stars processed via single-binary and binary-binary encounters in dense star clusters should have a unique velocity distribution relative to the underlying Maxwellian distribution (provided the relaxation time is sufficiently long), which can be calculated analytically.
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