Bounds on Velocity-dependent Dark Matter-Proton Scattering from Milky Way Satellite Abundance

We use the latest measurements of the Milky Way satellite population from the Dark Energy Survey and Pan-STARRS1 to infer the most stringent astrophysical bound to date on velocity-dependent interactions between dark matter particles and protons. We model the momentum-transfer cross section as a power law of the relative particle velocity v with a free normalizing amplitude, sigma(MT) = sigma(0)v(n), to broadly capture the interactions arising within the nonrelativistic effective theory of dark matter-proton scattering. The scattering leads to a momentum and heat transfer between the baryon and dark matter fluids in the early universe, ultimately erasing structure on small physical scales and reducing the abundance of low-mass halos that host dwarf galaxies today. From the consistency of observations with the cold collisionless dark matter paradigm, using a new method that relies on the most robust predictions of the linear perturbation theory, we infer an upper limit on sigma(0) of 1.4 x 10(-23), 2.1 x 10(-19), and 1.0 x 10(-12) cm(2), for interaction models with n = 2, 4, and 6, respectively, for a dark matter particle mass of 10 MeV. These results improve observational limits on dark matter-proton scattering by orders of magnitude and thus provide an important guide for viable sub-GeV dark matter candidates.