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,
$\sigma_\text{MT}=\sigma_0 v^n$, to broadly capture the interactions arising
within the non-relativistic 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 $1.4\times10^{-23}$, $2.1\times10^{-19}$, and
$1.0\times10^{-12}\ \mathrm{cm}^2$, for interaction models with $n=2,4,6$,
respectively, for a dark matter particle mass of $10\ \mathrm{MeV}$. 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.
