Constraints on dark matter cores from the tidal evolution of Milky Way satellites

As dark matter substructures get accreted onto larger host haloes, they lose mass through tidal forces, and their sizes decrease. The details of this evolution are crucially dependent on the shape of the substructures' dark matter density profiles. Substructures with centrally-divergent density cusps are very resilient to tidal stripping and give rise to a population of dense, low-mass "tidal remnants", with well-defined structural properties. In contrast, substructures with constant-density cores may be fully disrupted by tides, resulting in a very smooth distribution of dark matter within the host halo. This divergent evolution places strong constraints on the largest possible sizes of dark matter cores in Milky Way dwarf galaxies: A satellite like Tucana 3, with pericentre ~3.5 kpc, must have a core size smaller than ~2 pc to survive just three orbital periods on its current orbit. We find that the core sizes expected in self-interacting dark matter (SIDM) models with a cross section of >= 1 cm^2/g seem incompatible with the survival of Milky Way ultra-faint satellites.