Hidden Sector Hydrogen as Dark Matter: Small-scale Structure Formation
  Predictions and the Importance of Hyperfine Interactions
  We study the atomic physics and the astrophysical implications of a model in
which the dark matter is the analog of hydrogen in a secluded sector. The self
interactions between dark matter particles include both elastic scatterings as
well as inelastic processes due to a hyperfine transition. The self-interaction
cross sections are computed by numerically solving the coupled Schr\"{o}dinger
equations for this system. We show that these self interactions exhibit the
right velocity dependence to explain the low dark matter density cores seen in
small galaxies while being consistent with all constraints from observations of
clusters of galaxies. For a viable solution, the dark hydrogen mass has to be
in 10--100 GeV range and the dark fine-structure constant has to be larger than
0.02. Precisely for this range of parameters, we show that significant cooling
losses may occur due to inelastic excitations to the hyperfine state and
subsequent decays, with implications for the evolution of low-mass halos and
the early growth of supermassive black holes. Cooling from excitations to
higher $n$ levels of dark hydrogen and subsequent decays is possible at the
cluster scale, with a strong dependence on halo mass. Finally, we show that the
minimum halo mass is in the range of $10^{3.5}$ to $10^7 M_\odot$ for the
viable regions of parameter space, significantly larger than the typical
predictions for weakly-interacting dark matter models. This pattern of
observables in cosmological structure formation is unique to this model, making
it possible to rule in or rule out hidden sector hydrogen as a viable dark
matter model.
