We develop a theoretical framework for describing the hierarchical structure of the phase space of cold dark matter haloes, due to gravitationally bound substructures. Because it includes the full hierarchy of the cold dark matter initial conditions and is hence complementary to the halo model, the stable clustering hypothesis is applied for the first time here to the small-scale phase-space structure. As an application, we show that the particle dark matter annihilation signal could be up to 2 orders of magnitude larger than that of the smooth halo within the Galactic virial radius. The local boost is inversely proportional to the smooth halo density, and thus is $\mathcal{O}(1)$ within the solar radius, which could translate into interesting signatures for dark matter direct detection experiments: The temporal correlation of dark matter detection can change by a factor of 2 in the span of 10 years, while there will be significant correlations in the velocity space of dark matter particles. This can introduce $\mathcal{O}(1)$ uncertainty in the direction of local dark matter wind, which was believed to be a benchmark of directional dark matter searches or the annual modulation signal.

• Received 2 November 2009

DOI:https://doi.org/10.1103/PhysRevD.81.101301