一个简单的无规行走模型解释分层偏心三体系统的破裂过程
A Simple Random-Walk Model Explains the Disruption Process of Hierarchical, Eccentric 3-Body Systems
摘要：
我们研究了具有可比质量的分层三体系统的破裂过程。这种系统具有很长的生存时间，其数量级取决于初始条件。通过与三体数值积分的比较，我们证明了这类系统的演化和破裂可以用外轨道能量的简单随机行走过程来统计描述，其中每近心通道的能量交换（步长）由初始条件计算。在我们的推导的步长，我们使用以前的分析结果抛物面遇到，平均（Kozai-Lidov）振荡的轨道参数，这是更快的能量扩散时标。虽然类似的随机游走模型之前进行了研究，这项工作在两个方面有所不同：（a）这是第一次Kozai-Lidov平均步长是从第一原理推导出来的，并证明在没有拟合参数的情况下再现了数值系综的统计演化，以及（b）它提供了一个特征寿命，而不是回答二元问题（稳定/不稳定），由特定情况下的标准设置。
英文摘要：
We study the disruption process of hierarchical 3-body systems with bodies of comparable mass. Such systems have long survival times that vary by orders of magnitude depending on the initial conditions. By comparing with 3-body numerical integrations, we show that the evolution and disruption of such systems can be statistically described as a simple random-walk process in the outer-orbit's energy, where the energy-exchange per pericenter passage (step-size) is calculated from the initial conditions. In our derivation of the step-size, we use previous analytic results for parabolic encounters, and average over the (Kozai-Lidov) oscillations in orbital parameters, which are faster then the energy diffusion timescale. While similar random-walk models were studied before, this work differs in two manners: (a) this is the first time that the Kozai-Lidov averaged step-size is derived from first principles and demonstrated to reproduce the statistical evolution of numerical ensembles without fitting parameters, and (b) it provides a characteristic life-time, instead of answering the binary question (stable/unstable), set by case-specific criteria.
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