A lower limit on the dark particle mass from dSphs

TL;DR

This study uses dwarf spheroidal galaxies to set a lower limit on sterile neutrino dark matter particle mass by modeling their halos and applying the Tremaine-Gunn limit, finding a feasible mass range of 270-280 eV.

Contribution

It introduces a novel method that directly solves for sterile neutrino velocity dispersion using the equation of state, avoiding assumptions about stellar and dark matter velocity relations.

Findings

Feasible sterile neutrino mass range: 270-280 eV.

No benefit from Osipkov-Merritt velocity anisotropy profiles.

Method ensures hydrostatic equilibrium and accurate Tremaine-Gunn limit estimates.

Abstract

We use dwarf spheroidal galaxies as a tool to attempt to put precise lower limits on the mass of the dark matter particle, assuming it is a sterile neutrino. We begin by making cored dark halo fits to the line of sight velocity dispersions as a function of projected radius (taken from Walker et al. 2007) for six of the Milky Way's dwarf spheroidal galaxies. We test Osipkov-Merritt velocity anisotropy profiles, but find that no benefit is gained over constant velocity anisotropy. In contrast to previous attempts, we do not assume any relation between the stellar velocity dispersions and the dark matter ones, but instead we solve directly for the sterile neutrino velocity dispersion at all radii by using the equation of state for a partially degenerate neutrino gas (which ensures hydrostatic equilibrium of the sterile neutrino halo). This yields a 1:1 relation between the sterile neutrino density and velocity dispersion, and therefore gives us an accurate estimate of the Tremaine-Gunn limit at all radii. By varying the sterile neutrino particle mass, we locate the minimum mass for all six dwarf spheroidals such that the Tremaine-Gunn limit is not exceeded at any radius (in particular at the centre). We find sizeable differences between the ranges of feasible sterile neutrino particle mass for each dwarf, but interestingly there exists a small range 270-280eV which is consistent with all dSphs at the 1-$\sigma$ level.