On the global density slope-anisotropy inequality

TL;DR

This paper explores the global validity of the density slope-anisotropy inequality in spherical systems, providing new analytical cases and numerical evidence supporting its potential universality.

Contribution

The authors extend the known validity of the global density slope-anisotropy inequality with new analytical examples and numerical support, suggesting it may be a universal property.

Findings

The inequality holds in additional analytical cases.

Numerical evidence supports the inequality's universal validity.

No counter-examples have been found to disprove the conjecture.

Abstract

Starting from the central density slope-anisotropy theorem of An and Evans (2006), recent investigations have shown that the involved density slope-anisotropy inequality holds not only at the center, but at all radii (i.e. globally) in a very large class of spherical systems with positive phase-space distribution function. Here we present some additional analytical cases that further extend the validity of the global density slope-anisotropy inequality. These new results, several numerical evidences, and the absence of known counter-examples, lead us to conjecture that the global density slope-anisotropy inequality could actually be a universal property of spherical systems with positive distribution function.