Full calculation of clumpiness boost factors for antimatter cosmic rays in the light of Lambda-CDM N-body simulation results

Anti-proton and positron Galactic cosmic ray spectra are among the key targets for indirect detection of dark matter. The boost factors, corresponding to an enhancement of the signal and linked to the clumpiness properties of the dark matter distribution, have been taken as high as thousands in the past. The dramatic impact of these boost factors for indirect detection of antiparticles, for instance with the PAMELA satellite or the coming AMS-02 experiment, asks for their detailed calculation. We take into account the results of high resolution N-body dark matter simulations to calculate the most likely energy dependent boost factors linked to the cosmic ray propagation properties, for anti-protons and positrons. Starting from the mass and space distributions of sub-halos, the anti-proton and positron propagators are used to calculate the mean value and the variance of the boost factor for the primary fluxes. We take advantage of the statistical method introduced in Lavalle et al. (2007) and cross-check the results with Monte Carlo computations. By spanning some extreme configurations of sub-halo and propagation properties, we find that the average contribution of the clumps is negligible compared to that of the smooth dark matter component. Sub-halos do not lead to enhancement of the signals, unless they are taken with some extreme (unexpected) properties. This result is independent of the nature of the self-annihilating dark matter candidate considered, and provides precise estimates of the theoretical and the statistical uncertainties of the antimatter flux from dark matter substructures. Spectral distortions can still be expected in antimatter flux measurements, but scenarios invoking large and even mild clumpiness boost factors are strongly disfavoured by our analysis.