A Balescu–Lenard-type kinetic equation for the collisional evolution of stable self-gravitating systems
A Balescu–Lenard-type kinetic equation for the collisional evolution of stable self-gravitating systems
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DOI：
10.1111/j.1365-2966.2010.16899.x
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发表时间：
2010-05
影响因子：
4.8
通讯作者：
J. Heyvaerts
中科院分区：
文献类型：
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作者：
J. Heyvaerts
建立了稳定、束缚、自引力和慢弛豫体系碰撞演化的动力学方程，该方程在组分数量很大时是有效的。它解释了碰撞粒子的集体引力相互作用的详细动力学和自一致修饰，以及系统的非均匀性和不同成分的质量。它描述了碰撞相互作用的群体的耦合演化，例如厚圆盘中的恒星和它们分散的分子云。动力学方程来自BBGKY层次结构，在弱但不消失的二元相关的极限下，这种近似很好地证明了大型恒星系统的合理性。描述了单体分布函数在作用角空间中的演化。集体响应是用密度势函数对的双正交基来计算的。碰撞算符以现有分布函数在任何给定时间允许的集体响应函数表示，并涉及共振运动的粒子。这些方程被证明满足H定理。由于系统的非均匀性，弛豫引起粒子的势和轨道的特殊演化。轨道的变化也导致基势的角傅里叶系数随时间变化。我们导出了描述球对称系统的分布函数、势和基傅立叶系数耦合演化的方程组。在齐次极限下，牺牲了对系统空间结构演化的描述，但保留了集体引力修饰的作用，动力学方程简化为类似于等离子体物理学的Balescu-Lenard方程的形式。
A kinetic equation for the collisional evolution of stable, bound, self-gravitating and slowly relaxing systems is established, which is valid when the number of constituents is very large. It accounts for the detailed dynamics and self-consistent dressing by collective gravitational interaction of the colliding particles, for the system's inhomogeneity and for different constituents' masses. It describes the coupled evolution of collisionally interacting populations, such as stars in a thick disc and the molecular clouds off which they scatter. The kinetic equation derives from the BBGKY hierarchy in the limit of weak, but non-vanishing, binary correlations, an approximation which is well justified for large stellar systems. The evolution of the 1-body distribution function is described in action–angle space. The collective response is calculated using a biorthogonal basis of pairs of density–potential functions. The collision operators are expressed in terms of the collective response function allowed by the existing distribution functions at any given time and involve particles in resonant motion. These equations are shown to satisfy an H theorem. Because of the inhomogeneous character of the system, the relaxation causes the potential as well as the orbits of the particles to secularly evolve. The changing orbits also cause the angle Fourier coefficients of the basis potentials to change with time. We derive the set of equations which describes this coupled evolution of distribution functions, potential and basis Fourier coefficients for spherically symmetric systems. In the homogeneous limit, which sacrifices the description of the evolution of the spatial structure of the system but retains the effect of collective gravitational dressing, the kinetic equation reduces to a form similar to the Balescu–Lenard equation of plasma physics.