There's no place like home? Statistics of Milky Way-mass dark matter haloes

We present an analysis of the distribution of structural properties for Milky Way-mass haloes in the Millennium-II Simulation (MS-II). This simulation of structure formation within the standard ΛCDM cosmology contains thousands of Milky Way-mass haloes and has sufficient resolution to properly resolve many subhaloes per host. It thus provides a major improvement in the statistical power available to explore the distribution of internal structure for haloes of this mass. In addition, the MS-II contains lower-resolution versions of the Aquarius Project haloes, allowing us to compare our results to simulations of six haloes at a much higher resolution. We study the distributions of mass assembly histories, of subhalo mass functions and accretion times and of merger and stripping histories for subhaloes capable of impacting discs at the centres of haloes. We show that subhalo abundances are not well described by Poisson statistics at low mass, but rather are dominated by intrinsic scatter. Using the masses of subhaloes at infall and the abundance-matching assumption, there is less than a 10 per cent chance that a Milky Way halo with M_vir = 10¹² M_solar will host two galaxies as bright as the Magellanic Clouds. This probability rises to ~25 per cent for a halo with M_vir = 2.5 × 10¹² M_solar. The statistics relevant for disc heating are very sensitive to the mass range that is considered relevant. Mergers with infall mass : redshift zero virial mass greater than 1:30 could well impact a central galactic disc and are a near inevitability since z = 2, whereas only half of all haloes have had a merger with infall mass : redshift zero virial mass greater than 1:10 over this same period.