On the universality of the global slope -- anisotropy inequality

Details On the universality of the global slope -- anisotropy inequality On the universality of the global slope -- anisotropy inequality

2010-10-20

arxiv.org/abs/1010.4301v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

8 pages, 1 figure, accepted for publication in ApJ

Scientific paper

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 $\beta_0\leq 1/2$. Furthermore, we present several systems with $\beta_0 > 1/2$ 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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