Clustering in the phase space of dark matter haloes-II. stable clustering and dark matter annihilation

Abstract

We present a model for the structure of the particle phase space average density (P2SAD) 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 P2SAD in the numerically unresolved regime, down to the decoupling mass limit of generic weakly interacting massive particle 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 P2SAD 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-sized halo. Two cases are considered, one where the cross-section is velocity independent and one that approximates Sommerfeldenhanced models. We find that the global boost is ̃10-30, 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 P2SAD publicly available, which can be used to estimate various observables that probe the nanostructure of dark matter haloes. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.