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$\sigma$ lower limit found by Viel et al. from a recent
analysis of the Lyman-$\alpha$ 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.
