Dwarf spheroidal galaxies as degenerate gas of free fermions

TL;DR

This paper proposes a simple degenerate fermion model for dark matter, fitting dwarf galaxy data well with a fermion mass around 200 eV, and explores its implications for galaxy sizes and early universe production.

Contribution

It introduces a degenerate fermion dark matter model that fits dwarf galaxy data and connects it to inflationary production mechanisms.

Findings

Good fit to dwarf spheroidal galaxy velocity dispersion data

Fermion mass around 200 eV is favored

Larger galaxies correspond to non-degenerate fermion gas regime

Abstract

In this paper we analyze a simple scenario in which Dark Matter (DM) consists of free fermions with mass $m_f$. We assume that on galactic scales these fermions are capable of forming a degenerate Fermi gas, in which stability against gravitational collapse is ensured by the Pauli exclusion principle. The mass density of the resulting configuration is governed by a non-relativistic Lane-Emden equation, thus leading to a universal cored profile that depends only on one free parameter in addition to $m_f$. After reviewing the basic formalism, we test this scenario against experimental data describing the velocity dispersion of the eight classical dwarf spheroidal galaxies of the Milky Way. We find that, despite its extreme simplicity, the model exhibits a good fit to the data and realistic predictions for the size of DM halos providing that $m_f\simeq 200$ eV. Furthermore, we show that in this setup larger galaxies correspond to the non-degenerate limit of the gas. We propose a concrete realization of this model in which DM is produced non-thermally via inflaton decay. We show that imposing the correct relic abundance and the bound on the free-streaming length constrains the inflation model in terms of inflaton mass, its branching ratio into DM and the reheating temperature.