Analytical analysis of the origin of core-cusp matter density distributions in galaxies

TL;DR

This paper develops an analytical framework to understand how different symmetry conditions and angular momentum distributions influence the core or cusp nature of galaxy matter density profiles.

Contribution

It introduces a method linking the central density slope to the angular momentum distribution, considering deviations from spherical symmetry.

Findings

Spherical symmetry favors core-type profiles.

Deviations from symmetry can produce cusp-type profiles.

Symmetry breaking leads to steeper cusps.

Abstract

We propose an analytical method to describe a matter density profile near a galaxy center. The description is based on the study of the distribution function of particles over possible trajectories. We establish a relation between the central slope of density profile and the near-origin behavior of the angular momentum distribution function. We consider both a spherically symmetric (on average) matter distribution as well as deviations from it. If the density profile forms in a background of spherical gravitation potential then a core-type distribution arises. A regular matter may behave in such way if the background potential was formed by the dark matter. In the presence of deviation from spherical symmetry the formation of cusp-type distribution is possible. Moreover, a reduction of spherical symmetry to the axial one leads to a less steep cusp profile. The complete symmetry breaking (which corresponds, in particular, to the common setup of numerical simulations), leads to a steeper cusp profile.