Orbital evolution of satellite galaxies in self-interacting dark matter models

Dark matter self-interactions can leave distinctive signatures on the properties of satellite galaxies around Milky Way--like hosts through their impact on tidal stripping, ram pressure, and gravothermal collapse. We delineate the regions of self-interacting dark matter parameter space---specified by interaction cross section and a velocity scale---where each of these effects dominates and show how the relative mass loss depends on the satellite's initial mass, density profile, and orbit. We obtain novel, conservative constraints in this parameter space using Milky Way satellite galaxies with notably high central densities and small pericenter distances. Our results for self-interacting dark matter models, in combination with constraints from clusters of galaxies, favor either velocity-dependent cross sections that lead to gravothermal core collapse in the densest satellites or small cross sections which more closely resemble cold and collisionless dark matter.