The cosmic ray signature of dark matter caustics

Gravitational collapse of dark matter, merger of dark matter haloes and tidal disruption of satellites are among processes which lead to the formation of fine and dense dark matter shells, also known as dark matter caustics. The putative weakly interacting species which may form the dark matter are expected to strongly annihilate in these dense regions of the Milky Way halo and generate in particular antiprotons and positrons. We derive the flux of these rare antimatter particles at the Earth and show that it depends significantly on the cut-off radius of the dark matter distribution at the Galactic centre. Boost factors of similar to 30 are found with respect to a smooth Navarro, Frenk & White (NFW) profile for high-energy antiprotons and low-energy positrons if this cut-off radius is taken to be 300 pc - a somewhat extreme value though. This yields a detectable antiproton signal around hundreds of Gev in models where the annihilation cross-section today is enhanced by non-perturbative effects as in the generic case of a heavy wino. However, dark matter caustics cannot provide a better explanation for the HEAT excess reported above similar to 10 GeV than a smooth NFW or isothermal cored distribution.