Bounds on velocity-dependent dark matter-proton scattering from Milky Way satellite abundance

Abstract

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 $1.4\times 10^{-23}$, $2.1\times 10^{-19}$, and $1.0\times 10^{-12}{\mathrm{cm}}^2$, 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.

Comments: 8 pages, 3 figures, 1 table. Updated to correct typo in Table 1. Associated code available at https://github.com/maamari/VelocityDependentLimits