Beyond collisionless dark matter: Particle physics dynamics for dark matter halo structure

Dark matter (DM) self-interactions have important implications for the formation and evolution of structure, from dwarf galaxies to clusters of galaxies. We study the dynamics of self-interacting DM via a light mediator, focusing on the quantum resonant regime where the scattering cross section has a nontrivial velocity dependence. While there are long-standing indications that observations of small scale structure in the Universe are not in accord with the predictions of collisionless DM, theoretical study and simulations of DM self-interactions have focused on parameter regimes with simple analytic solutions for the scattering cross section, with constant or classical velocity (and no angular) dependence. We devise a method that allows us to explore the velocity and angular dependence of self-scattering more broadly, in the strongly coupled resonant and classical regimes where many partial modes are necessary for achieving the result. We map out the entire parameter space of DM self-interactions---and implications for structure observations---as a function of the coupling and the DM and mediator masses. We derive a new analytic formula for describing resonant s-wave scattering. Finally, we show that DM self-interactions can be correlated with observations of Sommerfeld enhancements in DM annihilation through indirect detection experiments.