On a possibile solution of the core-cusp problem and the fundamental properties of self gravitating quasi-stationary states.

One of the crucial problems for the galaxy formation theory is to explain the cusp-core paradox: while the simulations of the theoretical models give rise to a diverging density profile at a small distance (1 / r) from the center,  observations of galaxy profiles show that these  are constant.

To understand the origin of these profiles it is necessary to understand the fundamental properties of the quasi-equilibrium states of gravitational systems and in particular what kind of dynamical path they followed during their formation.

We have found that, depending on the initial conditions, these stationary states can exhibit a small-scale divergent profile or a flat profile. This difference corresponds to a different dynamical nature underlying their origin.

Coming back to  galaxies, the profiles indicate that the dynamic that gave them origin is a violent type of relaxation. That is, a dynamical process different from the “standard” one of cold dark matter models.

arXiv:2009.11624

15 pages, 24 figures, Accepted for publication in Astronomy and Astrophysics

by Francesco Sylos Labini, Roberto Capuzzo-Dolcetta

Initially far out-of-equilibrium self-gravitating systems form, through a collisionless relaxation dynamics, quasi-stationary states (QSS). These may arise from a bottom-up aggregation of structures or in a top-down frame; their quasi-equilibrium properties are well described by the Jeans equation and are not universal, i.e. they depend on initial conditions. To understand the origin of such dependence, we present results of numerical experiments of initially cold and spherical systems characterized by various choices of the spectrum of initial density fluctuations. The amplitude of such fluctuations determines whether the system relaxes in a top-down or a bottom-up manner. We find that statistical properties of the resulting QSS mainly depend upon the amount of energy exchanged during the formation process. In particular, in the violent top-down collapses the energy exchange is large and the QSS show an inner core with an almost flat density profile and a quasi Maxwell-Boltzmann (isotropic) velocity distribution, while their outer regions display a density profile ρ(r)∝r^(−α) (α>0) with radially elongated orbits. We analytically show that α=4 in agreement with numerical experiments. In the less violent bottom-up dynamics, the energy exchange is much smaller, the orbits are less elongated and 0<α(r)≤4, with a a density profile well fitted by the Navarro-Frenk-White behavior. Such a dynamical evolution is shown by both non-uniform spherical isolated systems and by halos extracted from cosmological simulations. We consider the relation of these results with the core-cusp problem concluding that this is naturally solved if galaxies form through a monolithic collapse.