Cosmic ray lepton puzzle in the light of cosmologicalN-body simulations

The PAMELA, ATIC, and Fermi collaborations have recently reported an excess in the cosmic ray positron and electron fluxes. These lepton anomalies might be related to cold dark matter particles annihilating within a nearby dark matter clump. We outline regions of the parameter space for both the dark matter subhalo and particle model, where data from the different experiments are reproduced. We then confront this interpretation of the data with the results of the cosmological $N$-body simulation Via Lactea II. Having a sizable clump ($V_{\max }=9\mathrm{km}{\mathrm{s}}^{-1}$) at a distance of only 1.2 kpc could explain the PAMELA excess, but such a configuration has a probability of only 0.37%. Reproducing also the ATIC bump would require a very large, nearby subhalo, which is extremely unlikely ($p\simeq 3\times {10}^{-5}$). It is even less probable for the smaller Fermi bump to be caused by the presence of such an object. In either case, we predict Fermi will detect the gamma-ray emission from the subhalo. We conclude that under canonical assumptions, the cosmic ray lepton anomalies are unlikely to originate from a nearby cold dark matter subhalo.