Motivations for a Large Self-Interacting Dark Matter Cross Section from Milky Way Satellites

We explore the properties of Milky Way subhalos in self-interacting dark matter models for moderate cross sections of 1 to 5 cm$^2$g$^{-1}$ using high-resolution zoom-in N-body simulations. We include the gravitational potential of a baryonic disk and bulge matched to the Milky Way, which is critical for getting accurate predictions. The predicted number and distribution of subhalos within the host halo are similar for 1 and 5 cm$^2$g$^{-1}$ models, and they agree with observations of Milky Way satellite galaxies only if subhalos with peak circular velocity over all time > 4.5 km/s are able to form galaxies. We do not find distinctive signatures in the pericenter distribution of the subhalos that could help distinguish the models. Using an analytic model to extend the simulation results, we are able to show that subhalos in models with cross sections between 1 and 5 cm$^2$g$^{-1}$ are not dense enough to match the densest ultra-faint and classical dwarf spheroidal galaxies in the Milky Way. This motivates velocity-dependent cross sections with values larger than 5 cm$^2$g$^{-1}$ at the velocities relevant for the satellites such that core collapse would occur in some of the ultra-faint and classical dwarf spheroidals.