Milky Way mass constraints from the Galactic satellite gap

We use the distribution of maximum circular velocities, Vmax, of satellites in the Milky Way (MW) to constrain the virial mass, M200, of the Galactic halo under an assumed prior of a Λ cold dark matter universe. This is done by analysing the subhalo populations of a large sample of haloes found in the Millennium II cosmological simulation. The observation that the MW has at most three subhaloes with Vmax ≥ 30 km s−1 requires a halo mass M200 ≤ 1.4 × 1012 M⊙, while the existence of the Magellanic Clouds (assumed to have Vmax ≥ 60 km s−1) requires M200 ≥ 1.0 × 1012 M⊙. 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 ≤ M200/(1012 M⊙) ≤ 1.4 at 90 per cent confidence. The gap in the abundance of Galactic satellites between 30 km s−1 ≤ Vmax ≤ 60 km s−1 places our galaxy in the tail of the expected satellite distribution.