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We use dwarf spheroidal galaxies as a tool to attempt to put precise lowerlimits on the mass of the dark matter particle, assuming it is a sterileneutrino. We begin by making cored dark halo fits to the line of sight velocitydispersions 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-Merrittvelocity anisotropy profiles, but find that no benefit is gained over constantvelocity anisotropy. In contrast to previous attempts, we do not assume anyrelation between the stellar velocity dispersions and the dark matter ones, butinstead we solve directly for the sterile neutrino velocity dispersion at allradii by using the equation of state for a partially degenerate neutrino gas(which ensures hydrostatic equilibrium of the sterile neutrino halo). Thisyields a 1:1 relation between the sterile neutrino density and velocitydispersion, and therefore gives us an accurate estimate of the Tremaine-Gunnlimit at all radii. By varying the sterile neutrino particle mass, we locatethe minimum mass for all six dwarf spheroidals such that the Tremaine-Gunnlimit is not exceeded at any radius (in particular at the centre). We findsizeable differences between the ranges of feasible sterile neutrino particlemass for each dwarf, but interestingly there exists a small range 270-280eVwhich is consistent with all dSphs at the 1-$\sigma$ level.

A lower limit on the dark particle mass from dSphs