离散自引力微温圆盘中的长期扩散I：紧缠绕极限下的解析解
Secular diffusion in discrete self-gravitating tepid discs I : analytic solution in the tightly wound limit
摘要：
用非齐次Balescu-Lenard方程描述了由有限粒子组成的无限薄的微温孤立星系盘的长期演化。假设只有紧密缠绕的瞬态螺旋存在于光盘中，WKB近似提供了一个简单和易于处理的正交相应的漂移和扩散系数。它提供了深入的物理过程中的长期扩散的自引力离散盘的工作，并在行动空间中的分布函数的初始变化的定量预测。当应用到一个孤立的固定的自引力Mestel光盘的长期演变，这种形式主义最初预测的重要性，在光盘的内部区域的共转共振导致一个制度，涉及径向迁移和加热。它预测，特别是形成一个“脊状”的功能，在行动空间，在协议与模拟，但高估的时间尺度，其外观。摆动放大可能会解决这种差异。在天体物理学中，非齐次Balescu-Lenard方程及其WKB极限也可以描述星系盘中巨分子云的长期扩散、原行星盘中星子的长期迁移和分离，甚至银河系中心恒星种群的长期演化。
英文摘要：
The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is described using the inhomogeneous Balescu-Lenard equation. Assuming that only tightly wound transient spirals are present in the disc, a WKB approximation provides a simple and tractable quadrature for the corresponding drift and diffusion coefficients. It provides insight into the physical processes at work during the secular diffusion of a self-gravitating discrete disc and makes quantitative predictions on the initial variations of the distribution function in action space. When applied to the secular evolution of an isolated stationary self-gravitating Mestel disc, this formalism predicts initially the importance of the corotation resonance in the inner regions of the disc leading to a regime involving radial migration and heating. It predicts in particular the formation of a "ridge like" feature in action space, in agreement with simulations, but over-estimates the timescale involved in its appearance. Swing amplification is likely to resolve this discrepancy. In astrophysics, the inhomogeneous Balescu-Lenard equation and its WKB limit may also describe the secular diffusion of giant molecular clouds in galactic discs, the secular migration and segregation of planetesimals in proto-planetary discs, or even the long-term evolution of population of stars within the Galactic center.
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