Milky Way mass constraints from the Galactic satellite gap
  We use the distribution of maximum circular velocities, $V_{max}$, of
satellites in the Milky Way (MW) to constrain the virial mass, $M_{200}$, of
the Galactic halo under an assumed prior of a $\Lambda$CDM universe. This is
done by analysing the subhalo populations of a large sample of halos found in
the Millennium II cosmological simulation. The observation that the MW has at
most three subhalos with $V_{max}\ge30 km/s$ requires a halo mass
$M_{200}\le1.4\times10^{12} M_\odot$, while the existence of the Magellanic
Clouds (assumed to have $V_{max}\ge60 km/s$) requires
$M_{200}\ge1.0\times10^{12} M_\odot$. The first of these conditions is
necessary to avoid the "too-big-to-fail" problem highlighted by Boylan-Kolchin
et al., while the second stems from the observation that massive satellites
like the Magellanic Clouds are rare. When combining both requirements, we find
that the MW halo mass must lie in the range $0.25 \le M_{200}/(10^{12} M_\odot)
\le 1.4$ at $90\%$ confidence. The gap in the abundance of Galactic satellites
between $30 km/s\le V_{max} \le 60 km/s$ places our galaxy in the tail of the
expected satellite distribution.
