The missing ultra-faint satellites of the Milky Way

We combine the highest resolution N-body simulation of a about10 12M Λ CDM halo (Aquarius-A) with the semi-analytic model GALFORM to study the full satellite population of Milky Way (MW)-like galaxies. The model assumes that galaxies form only in subhalos whose peak circular velocity exceeds the hydrogen-cooling threshold, and predicts that the total number of satellites ever accreted into the main halo, down to arbitrarily low luminosity, should not exceed a few hundred. The model tracks satellites even after their halos become unresolved ("orphan" galaxies), and includes a novel treatment of dark matter and stellar tidal stripping which takes into account that Λ CDM subhalos survive tidal disruption because of their cuspy density profiles. Our results match the massive end of the observed MW satellite mass function and predict that many ultra-faint dwarfs (UFDs) with M V>-5 are missing from the current MW satellite census. The missing UFDs are predicted to avoid the innermost regions of the host, and have properties overlapping those of the recently-discovered ultra-faint compact MW satellites (UFCSs). If the faintest dwarfs are initially as compact as UFCSs, our results suggest that many UFCSs should be dark matter-dominated dwarfs with velocity dispersions 1-3 km/s which survived disruption because they inhabit the cusp of Λ CDM subhalos. UFCSs have predicted densities of 10 10 - 10 11,M/ kpc cubed, higher than those of more extended UFDs. If confirmed, our results provide strong support for the cuspy nature of Λ CDM halos and for the hydrogen-cooling threshold for galaxy formation.