Escape in Hill’s problem

D. Heggie
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引用次数: 6

Abstract

This didactic paper is motivated by the problem of understanding how stars escape from globular star clusters. One formulation of this problem is known, in dynamical astronomy, as Hill's problem. Originally intended as a model for the motion of the moon around the earth with perturbations by the sun, with simple modifications it also serves as a model for the motion of a star in a star cluster with perturbations by the galaxy. The paper includes introductory sections on the derivation of the equations of motion of Hill's problem, their elementary properties, and extensions to deal with non-point masses and non-circular orbits. We then show how the rate of escape may be calculated numerically and estimated theoretically, and discuss how this simple picture is modified if the stars in a cluster are also undergoing two-body relaxation. Finally we introduce some established ideas for obtaining the distribution of escape times.
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逃避希尔的问题
这篇说教性的论文的动机是理解恒星如何从球状星团中逃逸的问题。这个问题的一种表述在动力天文学中被称为希尔问题。最初的目的是作为月球绕地球运动的模型,受到太阳的扰动,经过简单的修改,它也可以作为星团中一颗恒星的运动模型,受到星系的扰动。本文介绍了希尔问题运动方程的推导、基本性质以及对非点状质量和非圆轨道的扩展。然后,我们展示了逃逸速率如何在数值上计算和理论上估计,并讨论了如果星团中的恒星也经历两体弛豫,如何修改这个简单的图像。最后,我们介绍了一些已知的求得逃逸时间分布的思路。
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