Modeling dark matter halos with self-interacting fermions: A polytropic approach

Abstract

In this work we study the possibility of modeling the dark matter content in galaxies as a core-halo model consisting of self-gravitating, self-interacting fermions by means of an effective polytropic equation of state. For the core of the halo, the dark matter fermions are degenerate, while for the halo we have considered two possibilities: the fermions have thermalized as a perfect fluid, or they will follow a standard cold dark matter Navarro-Frenk-White profile. The core density profile is obtained by solving the Tolman-Oppenheimer-Volkoff equations, and their properties are determined by the fermion mass, the central density and the interaction strength. The mass of the fermion and the strength of the fermion self-interaction is fixed by doing a $\chi^2$ analysis to fit that fit the rotational curves of Low Surface Brightness galaxies. It was found that the fermion mass should be in the range $155.10~\rm{eV}< m_{f} < 313.26~\rm{eV}$ and the interparticle strength in the range $1465.31 < y <6002.04$ at $68$ C.L. in order to reproduce the rotational curves adequately, in the case when the halo is modeled as a thermalized ideal gas. Similar values are obtained if the halo is modeled following a Navarro-Frenk-White case, namely $42.31 ~\rm{eV} < m_{f} <49.23 ~\rm{eV}$ and $71.43< y < 132.65$. Once fixed the values of the mass of the fermion $m_f$ and the interaction strength $y$, we tested the core-halo model with data from the Milky Way, local dwarf spheroidal galaxies and the SPARC database. We have found good agreement between the data and the core-halo models, varying only one free parameter: the central density. Thus a single fermion can fit hundreds of galaxies. Nevertheless, the dark matter halo surface density relation or the halo total mass and radius depend strongly on the model for the halo.