恒星盘中的自引力、共振和轨道扩散
Self-gravity, resonances and orbital diffusion in stellar discs
摘要：
恒星系统的引力场的波动导致恒星轨道的演变。一旦扩散张量已知，系统的演化可以用轨道平均的Fokker-Planck方程计算。我们提出的形式主义，使一个计算的扩散张量从一个给定的噪声源在引力场时，系统的动态响应的噪声。在冷恒星盘的情况下，我们能够将扩散张量的计算简化为一维积分。我们实现这个公式的锥形Mestel光盘是暴露于散粒噪声，并发现我们能够解释分析的主要特点，这样的光盘的数值模拟。特别是在行动空间中的密度增强的狭窄的脊的形成被恢复。随着圆盘的Toomre $Q$值减小，圆盘变得更加敏感，圆盘内部区域通过林德布拉德内共振的加热状态转变为圆盘中间区域通过共转共振的近圆形轨道的径向迁移状态。这里发展的形式主义提供了一个理想的框架，在其中研究各种恒星盘的长期演化。
英文摘要：
Fluctuations in a stellar system's gravitational field cause the orbits of stars to evolve. The resulting evolution of the system can be computed with the orbit-averaged Fokker-Planck equation once the diffusion tensor is known. We present the formalism that enables one to compute the diffusion tensor from a given source of noise in the gravitational field when the system's dynamical response to that noise is included. In the case of a cool stellar disc we are able to reduce the computation of the diffusion tensor to a one-dimensional integral. We implement this formula for a tapered Mestel disc that is exposed to shot noise and find that we are able to explain analytically the principal features of a numerical simulation of such a disc. In particular the formation of narrow ridges of enhanced density in action space is recovered. As the disc's value of Toomre's $Q$ is reduced and the disc becomes more responsive, there is a transition from a regime of heating in the inner regions of the disc through the inner Lindblad resonance to one of radial migration of near-circular orbits via the corotation resonance in the intermediate regions of the disc. The formalism developed here provides the ideal framework in which to study the long-term evolution of all kinds of stellar discs.
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