挤球形奶牛的奶：论球坐标系中的非球面动力学
Milking the spherical cow: on aspherical dynamics in spherical coordinates
摘要：
星系和包含它们的暗物质晕并不是球对称的，但是球对称对于理想化的计算和观测数据的分析是一个有用的简化近似。这个假设导致了每个粒子的角动量都精确守恒，使得动力学不切实际。但是，这种不准确性在实际分析恒星分布函数、无碰撞弛豫或暗物质核心创造时有多大影响呢？我们提供了一个一般的答案，这个问题的广泛的一类非球面系统，具体来说，我们认为分布函数是“最大限度地稳定”，即不发展时，在一阶外部潜力（产生重子，大规模的潮汐场或下落子结构）应用。我们表明，这种系统的球对称分析引起的错误结论，相空间中的粒子密度是遍历（能量的函数）。利用这一思想，我们能够证明：（a）错误地假设球对称的观测分析是更准确的，通过强加一个强烈的优先选择近各向同性的速度分散体的中心的球体;（b）数值模拟，使用一个理想化的球对称设置可能会产生误导性的结果，应尽量避免;（c）三轴暗物质晕（在无碰撞宇宙学模拟中形成）几乎达到我们的最大稳定极限，但它们的演化在达到极限之前就冻结了。
英文摘要：
Galaxies and the dark matter halos that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealised calculations and analysis of observational data. The assumption leads to an exact conservation of angular momentum for every particle, making the dynamics unrealistic. But how much does that inaccuracy matter in practice for analyses of stellar distribution functions, collisionless relaxation, or dark matter core-creation? We provide a general answer to this question for a wide class of aspherical systems; specifically, we consider distribution functions that are "maximally stable", i.e. that do not evolve at first order when external potentials (which arise from baryons, large scale tidal fields or infalling substructure) are applied. We show that a spherically-symmetric analysis of such systems gives rise to the false conclusion that the density of particles in phase space is ergodic (a function of energy alone). Using this idea we are able to demonstrate that: (a) observational analyses that falsely assume spherical symmetry are made more accurate by imposing a strong prior preference for near-isotropic velocity dispersions in the centre of spheroids; (b) numerical simulations that use an idealised spherically-symmetric setup can yield misleading results and should be avoided where possible; and (c) triaxial dark matter halos (formed in collisionless cosmological simulations) nearly attain our maximally-stable limit, but their evolution freezes out before reaching it.
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