脉冲相遇引起的双星轨道飞行
Levy Flights of Binary Orbits due to Impulsive Encounters
摘要：
本文研究了近圆开普勒轨道与非束缚扰动相互作用的演化。我们计算了偏心率和角动量的变化，从一个单一的遭遇，假设相互作用的时间尺度是短于轨道周期。轨道摄动被纳入玻尔兹曼方程，允许偏心耗散。我们提出了一个解析解的玻尔兹曼方程，描述了作为时间的函数的轨道偏心率和相对倾角的分布。偏心率和倾斜度的二进制不演变根据正常的随机行走，但执行利维飞行。扰动的质量谱的斜率决定了近距离的引力散射是否比远距离的潮汐散射更重要。当近距离散射很重要时，质谱设定偏心率和倾斜度分布函数的斜率。我们使用这个一般的框架来理解几个柯伊伯带系统的偏心率：冥王星，2003 EL 61和厄里斯。我们使用Tholen等人（2007）的模型将冥王星外卫星Nix和Hydra的轨道的非开普勒分量与其他柯伊伯带天体相互作用激发的运动分开。我们的分布与Nix，Hydra以及2003年EL 61和Eris的卫星的观测结果一致。我们将这项工作应用于太阳系外的物体，如围绕恒星的太阳系外行星和毫秒恒星。
英文摘要：
We examine the evolution of an almost circular Keplerian orbit interacting with unbound perturbers. We calculate the change in eccentricity and angular momentum that results from a single encounter, assuming the timescale for the interaction is shorter than the orbital period. The orbital perturbations are incorporated into a Boltzmann equation that allows for eccentricity dissipation. We present an analytic solution to the Boltzmann equation that describes the distribution of orbital eccentricity and relative inclination as a function of time. The eccentricity and inclination of the binary do not evolve according to a normal random walk but perform a Levy flight. The slope of the mass spectrum of perturbers dictates whether close gravitational scatterings are more important than distant tidal ones. When close scatterings are important, the mass spectrum sets the slope of the eccentricity and inclination distribution functions. We use this general framework to understand the eccentricities of several Kuiper belt systems: Pluto, 2003 EL 61, and Eris. We use the model of Tholen et al (2007) to separate the non-Keplerian components of the orbits of Pluto's outer moons Nix and Hydra from the motion excited by interactions with other Kuiper belt objects. Our distribution is consistent with the observations of Nix, Hydra, and the satellites of 2003 EL 61 and Eris. We address applications of this work to objects outside of the solar system, such as extrasolar planets around their stars and millisecond pulsars.
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