Clustering in the Phase Space of Dark Matter Haloes. II. Stable
  Clustering and Dark Matter Annihilation
  We present a model for the structure of the particle phase space average
density ($P^2SAD$) in galactic haloes, introduced recently as a novel measure
of the clustering of dark matter. Our model is based on the stable clustering
hypothesis in phase space, the spherical collapse model, and tidal disruption
of substructures, which is calibrated against the Aquarius simulations. Using
this model, we can predict the behaviour of $P^2SAD$ in the numerically
unresolved regime, down to the decoupling mass limit of generic WIMP models.
This prediction can be used to estimate signals sensitive to the small scale
structure of dark matter. For example, the dark matter annihilation rate can be
estimated for arbitrary velocity-dependent cross sections in a convenient way
using a limit of $P^2SAD$ to zero separation in physical space. We illustrate
our method by computing the global and local subhalo annihilation boost to that
of the smooth dark matter distribution in a Milky-Way-size halo. Two cases are
considered, one where the cross section is velocity independent and one that
approximates Sommerfeld-enhanced models. We find that the global boost is
$\sim10-30$, which is at the low end of current estimates (weakening
expectations of large extragalactic signals), while the boost at the solar
radius is below the percent level. We make our code to compute $P^2SAD$
publicly available, which can be used to estimate various observables that
probe the nanostructure of dark matter haloes.
