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Constraining the WDM Particle Mass with Milky Way Satellites

Well-motivated particle physics theories predict the existence of particles (such as sterile neutrinos) which acquire non-negligible thermal velocities in the early universe. These particles could behave as warm dark matter (WDM) and generate a small-scale cutoff in the linear density power spectrum which scales approximately inversely with the particle mass. If this mass is of order a keV, the cutoff occurs on the scale of dwarf galaxies. Thus, in WDM models the abundance of small galaxies, such as the satellites that orbit in the halo of the Milky Way, depends on the mass of the warm particle. The abundance also scales with the mass of the host galactic halo. We use the \galform semi-analytic model of galaxy formation to calculate the properties of galaxies in universes in which the dark matter is warm. Using this method, we can compare the predicted satellite luminosity functions to the observed data for the Milky Way dwarf spheroidals, and determine a lower bound on the thermally produced WDM particle mass. This depends strongly on the value of the Milky Way halo mass and, to some extent, on the baryonic physics assumed; we examine both of these dependencies. For our fiducial model we find that for a particle mass of 3.3 keV (the 2$σ$ lower limit found by Viel et al. from a recent analysis of the Lyman-$α$ forest) the Milky Way halo mass is required to be $> 1.4 \times 10^{12}$ \msun. For this same fiducial model, we also find that all WDM particle masses are ruled out (at 95% confidence) if the halo of the Milky Way has a mass smaller than $1.1 \times 10^{12}$ \msun, while if the mass of the Galactic halo is greater than 1.8 $\times 10^{12}$ \msun, only WDM particle masses larger than 2 keV are allowed.