关于整体斜率的普适性--各向异性不等式
On the universality of the global slope -- anisotropy inequality
摘要：
最近，一些有趣的结果已经导致猜测是否中心密度斜率-速度色散各向异性不等式（An & Evans）实际上在所有半径的球形动力系统。我们扩展这些研究提供了一个完整的分析的全球斜率-各向异性不等式的所有球形系统中，增广密度是一个可分离的函数的半径和潜力。我们证明了当中心各向异性为$β_0\leq 1/2$时，这类系统确实满足整体不等式.此外，我们提出了几个系统与$β_0 > 1/2$的不等式不成立，从而证明了全球密度斜率-各向异性不等式是不是一个普遍的性质。这一分析是对一般球形系统的关系的理解的重要一步。
英文摘要：
Recently, some intriguing results have lead to speculations whether the central density slope -- velocity dispersion anisotropy inequality (An & Evans) actually holds at all radii for spherical dynamical systems. We extend these studies by providing a complete analysis of the global slope -- anisotropy inequality for all spherical systems in which the augmented density is a separable function of radius and potential. We prove that these systems indeed satisfy the global inequality if their central anisotropy is $β_0\leq 1/2$. Furthermore, we present several systems with $β_0 > 1/2$ for which the inequality does not hold, thus demonstrating that the global density slope -- anisotropy inequality is not a universal property. This analysis is a significant step towards an understanding of the relation for general spherical systems.
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