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

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.

LaTeX, 13 pages. In this version, the study of possible deviations from spherical symmetry was added, the present version corresponds to the published one

References in corpus (5)

• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• The cusp-core problem in gas-poor dwarf spheroidal galaxies
• Modifications of gravity via differential transformations of field variables
• An analytical approach to the dwarf galaxies cusp problem
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Cited by in corpus (3)

• Dark matter as a gravitational effect in the embedding theory approach
• Possible types of dark matter condensation in embedding gravity
• Gravity as embedding theory and the distribution of matter in galaxies