STATISTICAL MECHANICS OF COLLISIONLESS ORBITS. IV. DISTRIBUTION OF ANGULAR MOMENTUM
STATISTICAL MECHANICS OF COLLISIONLESS ORBITS. IV. DISTRIBUTION OF ANGULAR MOMENTUM
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DOI：
10.1088/0004-637x/783/1/13
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发表时间：
2014-01
期刊：
影响因子：
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通讯作者：
L. Williams;J. Hjorth;R. Wojtak
中科院分区：
文献类型：
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作者：
L. Williams;J. Hjorth;R. Wojtak
在以前的工作中已经表明，DARKexp，这是一个理论推导的，最大熵，一个形状参数模型的各向同性无碰撞系统，提供了非常好的适合模拟和观察到的暗物质晕。具体来说，它拟合能量分布N（E）和密度分布，包括中心尖点。在这里，我们扩展DARKexp N（E），以包括球对称系统的角动量分布L2。首先，我们认为，基于理论，半分析和模拟结果，虽然暗物质晕的能量是放松的，但它们的角动量几乎没有放松，这就排除了使用最大熵来唯一地导出N（E，L2）。相反，我们要求当对平方角动量积分N（E，L2）时，得到DARKexp N（E）。从N（E，L2）的一般表达式开始，我们展示了L2中粒子的分布如何与速度分布函数VDF和速度各向异性剖面β（r）的形状相关。然后，我们证明了天体物理学上真实的晕，由VDF形状和β（r）判断，必须有线性或凸分布在L2，为每个单独的能量箱。大多数束缚粒子的能量分布必须接近平坦，并且变得更加倾斜，有利于束缚较少的粒子的径向轨道。这些结果是一致的数值模拟，并代表一个重要的一步推导完整的分布函数的球对称暗物质晕。
It has been shown in previous work that DARKexp, which is a theoretically derived, maximum entropy, one shape parameter model for isotropic collisionless systems, provides very good fits to simulated and observed dark matter halos. Specifically, it fits the energy distribution, N(E), and the density profiles, including the central cusp. Here, we extend DARKexp N(E) to include the distribution in angular momentum, L2, for spherically symmetric systems. First, we argue, based on theoretical, semi-analytical, and simulation results, that while dark matter halos are relaxed in energy, they are not nearly as relaxed in angular momentum, which precludes using maximum entropy to uniquely derive N(E, L2). Instead, we require that when integrating N(E, L2) over squared angular momenta one retrieves the DARKexp N(E). Starting with a general expression for N(E, L2) we show how the distribution of particles in L2 is related to the shape of the velocity distribution function, VDF, and velocity anisotropy profile, β(r). We then demonstrate that astrophysically realistic halos, as judged by the VDF shape and β(r), must have linear or convex distributions in L2, for each separate energy bin. The distribution in energy of the most bound particles must be nearly flat, and become more tilted in favor of radial orbits for less bound particles. These results are consistent with numerical simulations and represent an important step toward deriving the full distribution function for spherically symmetric dark matter halos.