2010/10/20 by Emmanuel Van Hese, Maarten Baes, Herwig Dejonghe · 16 citations
Mathematics · Physics and Astronomy · #Advanced Optimization Algorithms Research #Anisotropy #Dispersion relation #Function (biology) #Inequality #Probability density function #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #RADIUS #Universality (dynamical systems) #astro-ph.CO #math-ph #math.MP
paper · pdf · doi:10.1088/0004-637x/726/2/80
published in The Astrophysical Journal 726(2), 80 (IOP Publishing) · 8 pages, 1 figure, accepted for publication in ApJ
arxiv created 2010/10/20 · openalex publication_date 2010/12/17 · arxiv updated 2015/05/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 β 0 ⩽ 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 toward an understanding of the relation for general spherical systems.