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On the universality of the global density slope-anisotropy inequality

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Abstract
Recently, some intriguing results have led 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) <= 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 toward an understanding of the relation for general spherical systems.
Keywords
DARK-MATTER HALOS, dark matter, DYNAMICAL MODELS, SPHERICAL STELLAR-SYSTEMS, Galaxy: kinematics and dynamics, methods: analytical

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Chicago
Van Hese, Emmanuel, Maarten Baes, and Herwig Dejonghe. 2011. “On the Universality of the Global Density Slope-anisotropy Inequality.” Astrophysical Journal 726 (2).
APA
Van Hese, E., Baes, M., & Dejonghe, H. (2011). On the universality of the global density slope-anisotropy inequality. ASTROPHYSICAL JOURNAL, 726(2).
Vancouver
1.
Van Hese E, Baes M, Dejonghe H. On the universality of the global density slope-anisotropy inequality. ASTROPHYSICAL JOURNAL. 2011;726(2).
MLA
Van Hese, Emmanuel, Maarten Baes, and Herwig Dejonghe. “On the Universality of the Global Density Slope-anisotropy Inequality.” ASTROPHYSICAL JOURNAL 726.2 (2011): n. pag. Print.
@article{1241059,
  abstract     = {Recently, some intriguing results have led 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) {\textlangle}= 1/2. Furthermore, we present several systems with beta(0) {\textrangle} 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 toward an understanding of the relation for general spherical systems.},
  articleno    = {80},
  author       = {Van Hese, Emmanuel and Baes, Maarten and Dejonghe, Herwig},
  issn         = {0004-637X},
  journal      = {ASTROPHYSICAL JOURNAL},
  language     = {eng},
  number       = {2},
  pages        = {6},
  title        = {On the universality of the global density slope-anisotropy inequality},
  url          = {http://dx.doi.org/10.1088/0004-637X/726/2/80},
  volume       = {726},
  year         = {2011},
}

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