We present results from N-body simulations of self-interacting dark matter
(SIDM) subhalos, which could host ultra-faint dwarf spheroidal galaxies, inside
a Milky-Way-like main halo. We find that high-concentration subhalos are driven
to gravothermal core collapse, while low-concentration subhalos develop large
(kpc-sized) low-density cores, with both effects depending sensitively on the
satellite's orbit and the self-interaction cross section over mass $\sigma/m$.
The overall effect for $\sigma/m \gtrsim 3 \ \rm cm^2/g$ is to increase the
range of inner densities, potentially explaining the observed diversity of
Milky Way satellites, which include compact systems like Draco and Segue 1 that
are dense in dark matter, and less dense, diffuse systems like Sextans and
Crater II. We discuss possible ways of distinguishing SIDM models from
collisionless dark matter models using the inferred dark matter densities and
stellar sizes of the dwarf spheroidal galaxies.