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.
