Are the most super-massive dark compact objects harbored at the center of dark matter halos?

Abstract

Essay selected for Honorable mention 2014 by the Gravity Research Foundation. We study an isothermal system of semi-degenerate self-gravitating fermions in General Relativity (GR). The most general solutions present mass density profiles with a central degenerate compact core governed by quantum statistics followed by an extended plateau, and ending in a power law behaviour $r^{-2}$. By fixing the fermion mass $m$ in the keV regime, the different solutions depending on the free parameters of the model: the degeneracy and temperature parameters at the center, are systematically constructed along the one-parameter sequences of equilibrium configurations up to the critical point, which is represented by the maximum in a central density ($ρ_0$) Vs. core mass ($M_c$) diagram. We show that for fully degenerate cores, the Oppenheimer-Volkoff (OV) mass limit $M_{c}^{cr}\propto M_{pl}^3/m^2$ is obtained, while instead for low degenerate cores, the critical core mass increases showing the temperature effects in a non linear way. The main result of this work is that when applying this theory to model the distribution of dark matter in big elliptical galaxies from miliparsec distance-scales up to $10^2$ Kpc, we do not find any critical core-halo configuration of self-gravitating fermions, able to explain both the most super-massive dark object at their center together with the DM halo simultaneously.