  Small-scale structure is studied in the context of dissipative dark matter,
arising for instance in models with a hidden unbroken Abelian sector, so that
dark matter couples to a massless dark photon. The dark sector interacts with
ordinary matter via gravity and photon-dark photon kinetic mixing. Mirror dark
matter is a theoretically constrained special case where all parameters are
fixed except for the kinetic mixing strength, $\epsilon$. In these models, the
dark matter halo around spiral and irregular galaxies takes the form of a
dissipative plasma which evolves in response to various heating and cooling
processes. It has been argued previously that such dynamics can account for the
inferred cored density profiles of galaxies and other related structural
features. Here we focus on the apparent deficit of nearby small galaxies
("missing satellite problem"), which these dissipative models have the
potential to address through small-scale power suppression by acoustic and
diffusion damping. Using a variant of the extended Press-Schechter formalism,
we evaluate the halo mass function for the special case of mirror dark matter.
Considering a simplified model where $M_{\text{baryons}} \propto
M_{\text{halo}}$, we relate the halo mass function to more directly observable
quantities, and find that for $\epsilon/10^{-10} \approx 2$ such a simplified
description is compatible with the measured galaxy luminosity and velocity
functions. On scales $M_{\text{halo}} \lesssim 10^8 \ M_\odot$, diffusion
damping exponentially suppresses the halo mass function, suggesting a
nonprimordial origin for dwarf spheroidal satellite galaxies, which we
speculate were formed via a top-down fragmentation process as the result of
nonlinear dissipative collapse of larger density perturbation. This could
explain the planar orientation of satellite galaxies around Andromeda and the
Milky Way.
