Constraints on the Dark Matter Particle Mass from the Number of Milky Way Satellites

Abstract

We have conducted $N$-body simulations of the growth of Milky Way-sized halos in cold and warm dark matter cosmologies. The number of dark matter satellites in our simulated Milky Ways decreases with decreasing mass of the dark matter particle. Assuming that the number of dark matter satellites exceeds or equals the number of observed satellites of the Milky Way, we derive lower limits on the dark matter particle mass. We find with 95% confidence ${m}_{s}g13.3\text{ }\text{ }\mathrm{keV}$ for a sterile neutrino produced by the Dodelson and Widrow mechanism, ${m}_{s}g8.9\text{ }\text{ }\mathrm{keV}$ for the Shi and Fuller mechanism, ${m}_{s}g3.0\text{ }\text{ }\mathrm{keV}$ for the Higgs decay mechanism, and ${m}_{\mathrm{WDM}}g2.3\text{ }\text{ }\mathrm{keV}$ for a thermal dark matter particle. The recent discovery of many new dark matter dominated satellites of the Milky Way in the Sloan Digital Sky Survey allows us to set lower limits comparable to constraints from the complementary methods of Lyman-$\ensuremath{\alpha}$ forest modeling and x-ray observations of the unresolved cosmic x-ray background and of dark matter halos from dwarf galaxy to cluster scales. Future surveys like LSST, DES, PanSTARRS, and SkyMapper have the potential to discover many more satellites and further improve constraints on the dark matter particle mass.