引力相遇与星系核的演化。III。异常松弛
Gravitational Encounters and the Evolution of Galactic Nuclei. III. Anomalous Relaxation
摘要：
本文是第三个在一个系列介绍的结果直接数值积分的Fokker-Planck方程的恒星轨道的超大质量黑洞（SBH）在星系的中心。该算法的文件II包括扩散系数，描述了随机（“经典”）和相关（“共振”）松弛的影响。在本文中，文件II的扩散系数已被推广到占的影响，“异常松弛”，在质量上不同的方式，偏心轨道的发展制度的快速相对论性岁差。两个功能形式的异常扩散系数的研究，基于幂律或指数修正的共振扩散系数。定义修改系数的参数首先通过比较Fokker-Planck积分与先前发表的N体积分的结果来约束。稳态解，然后通过福克-普朗克方程的性质类似于银河系核的模型。列入异常松弛导致形成不突出的核心比单独的共振松弛的情况下，由于偏心轨道的扩散时标的延长。恒星的稳态捕获率的SBH被发现总是少，多达一个数量级，比捕获率在共振弛豫单独存在。
英文摘要：
This paper is the third in a series presenting the results of direct numerical integrations of the Fokker-Planck equation for stars orbiting a supermassive black hole (SBH) at the center of a galaxy. The algorithm of Paper II included diffusion coefficients that described the effects of random ("classical") and correlated ("resonant") relaxation. In this paper, the diffusion coefficients of Paper II have been generalized to account for the effects of "anomalous relaxation," the qualitatively different way in which eccentric orbits evolve in the regime of rapid relativistic precession. Two functional forms for the anomalous diffusion coefficients are investigated, based on power-law or exponential modifications of the resonant diffusion coefficients. The parameters defining the modified coefficients are first constrained by comparing the results of Fokker-Planck integrations with previously-published N-body integrations. Steady-state solutions are then obtained via the Fokker-Planck equation for models with properties similar to those of the Milky Way nucleus. Inclusion of anomalous relaxation leads to the formation of less prominent cores than in the case of resonant relaxation alone, due to the lengthening of diffusion timescales for eccentric orbits. Steady-state capture rates of stars by the SBH are found to always be less, by as much as an order of magnitude, than capture rates in the presence of resonant relaxation alone.
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