Caustics in dark matter haloes

Cold dark matter haloes are populated by high-density structures with sharplypeaked profiles known as caustics which have not yet been resolved by 3dimensional numerical simulations. Here, we derive semi-analytic expressions for the density profiles near caustics in haloes which form by self-similar accretions of dark matter with infinitesimal velocity dispersion. A simple rescaling shows that these profiles are universal: they are valid for all caustics and irrespective of physical parameters of the halo. We derive the maximum density of the caustics and show that it depends on the velocity dispersion and the caustic location. Finally, we demonstrate that there can be a significant contribution to the emission measure from dark matter particle annihilation in the caustics.