A lower limit on the dark particle mass from dSphs

Here we make the first attempt to put precise lower limits on the mass of the dark matter particle, assuming it is a sterile neutrino. We begin by making the first published cored dark halo fits to the line of sight velocity dispersions as a function of radius (taken from Walker et al. 2007) for six of the Milky Way’s dwarf spheroidal galaxies. We use Osipkov-Merritt velocity anisotropy profiles that are centrally isotropic in all cases and either mildly tangentially or radially anisotropic at the periphery, where the only free parameter is the anisotropy scale radius. 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 the lowest feasible sterile neutrino particle mass is different for each dwarf, but varies only from 320-520eV and is roughly a third the best previous estimate. Finally, we discuss our dark halo fits in the context of two scaling relations.