气体介质中圆轨道微扰的动力学摩擦
Dynamical Friction of a Circular-Orbit Perturber in a Gaseous Medium
摘要：
本文用半解析方法研究了均匀气体介质中沿圆轨道运动的微扰子的引力尾流和动力学摩擦。这项工作是Ostriker（1999）的直接扩展，Ostriker研究了直线轨迹的情况。圆形轨道使背景介质中的尾流沿轨道弯曲，形成长长的拖尾。因此，尾流分布是不对称的，在与扰动器的运动相反的方向（方位角）和横向（径向）上产生阻力，尽管后者对轨道衰减的贡献不大。对于亚音速运动，具有弱尾的密度尾流只是Ostriker中密度尾流的弯曲形式，不表现出前后对称性。在相反方向上产生的拖曳力与有限时间线性轨道的对应物非常相似。另一方面，超音速扰流器能够超越自己的尾流，可能是多次，并形成非常明显的尾流。超音速尾部以尾随螺旋方式围绕扰动体，增强了扰动体后部和远前部的扰动密度。给出了阻力随马赫数变化的拟合公式，当Vp t=2 Rp时，其方位角部分与Ostriker公式惊人地吻合，其中Vp和Rp分别是扰动物的速度和轨道半径。
英文摘要：
We investigate the gravitational wake due to, and dynamical friction on, a perturber moving on a circular orbit in a uniform gaseous medium using a semi-analytic method. This work is a straightforward extension of Ostriker (1999) who studied the case of a straight-line trajectory. The circular orbit causes the bending of the wake in the background medium along the orbit, forming a long trailing tail. The wake distribution is thus asymmetric, giving rise to the drag forces in both opposite (azimuthal) and lateral (radial) directions to the motion of the perturber, although the latter does not contribute to orbital decay much. For subsonic motion, the density wake with a weak tail is simply a curved version of that in Ostriker and does not exhibit the front-back symmetry. The resulting drag force in the opposite direction is remarkably similar to the finite-time, linear-trajectory counterpart. On the other hand, a supersonic perturber is able to overtake its own wake, possibly multiple times, and develops a very pronounced tail. The supersonic tail surrounds the perturber in a trailing spiral fashion, enhancing the perturbed density at the back as well as far front of the perturber. We provide the fitting formulae for the drag forces as functions of the Mach number, whose azimuthal part is surprisingly in good agreement with the Ostriker's formula, provided Vp t=2 Rp, where Vp and Rp are the velocity and orbital radius of the perturber, respectively.
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