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We use the distribution of maximum circular velocities, $V_{max}$, ofsatellites in the Milky Way (MW) to constrain the virial mass, $M_{200}$, ofthe Galactic halo under an assumed prior of a $\Lambda$CDM universe. This isdone by analysing the subhalo populations of a large sample of halos found inthe Millennium II cosmological simulation. The observation that the MW has atmost 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 MagellanicClouds (assumed to have $V_{max}\ge60 km/s$) requires$M_{200}\ge1.0\times10^{12} M_\odot$. The first of these conditions isnecessary to avoid the "too-big-to-fail" problem highlighted by Boylan-Kolchinet al., while the second stems from the observation that massive satelliteslike the Magellanic Clouds are rare. When combining both requirements, we findthat 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 satellitesbetween $30 km/s\le V_{max} \le 60 km/s$ places our galaxy in the tail of theexpected satellite distribution.

Milky Way mass constraints from the Galactic satellite gap