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We present a model for the structure of the particle phase space averagedensity ($P^2SAD$) in galactic haloes, introduced recently as a novel measureof the clustering of dark matter. Our model is based on the stable clusteringhypothesis in phase space, the spherical collapse model, and tidal disruptionof substructures, which is calibrated against the Aquarius simulations. Usingthis model, we can predict the behaviour of $P^2SAD$ in the numericallyunresolved regime, down to the decoupling mass limit of generic WIMP models.This prediction can be used to estimate signals sensitive to the small scalestructure of dark matter. For example, the dark matter annihilation rate can beestimated for arbitrary velocity-dependent cross sections in a convenient wayusing a limit of $P^2SAD$ to zero separation in physical space. We illustrateour method by computing the global and local subhalo annihilation boost to thatof the smooth dark matter distribution in a Milky-Way-size halo. Two cases areconsidered, one where the cross section is velocity independent and one thatapproximates Sommerfeld-enhanced models. We find that the global boost is$\sim10-30$, which is at the low end of current estimates (weakeningexpectations of large extragalactic signals), while the boost at the solarradius is below the percent level. We make our code to compute $P^2SAD$publicly available, which can be used to estimate various observables thatprobe the nanostructure of dark matter haloes.

Clustering in the Phase Space of Dark Matter Haloes. II. Stable Clustering and Dark Matter Annihilation