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

Abstract

An analytical approach was suggested for an examination of the density profile of a dust-like matter at the center of a galaxy. For this purpose, a distribution function of particles over all possible trajectories was considered and the relation between the behavior of the density profile and an asymptotic at zero of a distribution function of particles over a module of angular momentum was established. We restrict ourselves to the consideration of the static and spherically symmetric on average particle distribution but still assume that a single particle movement could violate spherical symmetry. It was shown that if a formation of density profile occurs in the previously formed spherically symmetric gravitational potential as a background then angular momentum module distribution has linear asymptotic at zero and core-distribution takes place. Such formation could happen for a regular dust-like matter density profile if the potential well has already been created by dark matter. On the other hand, if the regular matter density profile is forming simultaneously with the gravitational potential then a significant deviation from spherical symmetry may arise. Such a setup is close to the one usually used in numerical simulations. In that case, supporting arguments could be provided for the existence of a constant value contribution in the mentioned asymptotic which results in cusp-distribution origin.