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Probing a dark matter density spike at the Galactic Center

The dark matter halo profile in the inner Galaxy is very uncertain. Yet its radial dependence toward the Galactic Center is of crucial importance for the determination of the gamma-ray and radio fluxes originating from dark matter annihilations. Here we use synchrotron emission to probe the dark matter energy distribution in the inner Galaxy. We first solve the problem of the cosmic ray diffusion on very small scales, typically smaller than 10^{-3} pc, by using a Green's function approach and use this technique to quantify the effect of a spiky profile (rho(r) ~ r^{-7/3}) on the morphology and intensity of the synchrotron emission expected from dark matter. We illustrate our results using 10 and 800 GeV candidate weakly interacting dark matter particles annihilating directly into e+ e-. Our most critical assumptions are that the dark matter is heavier than a few GeV and directly produces a reasonable amount of electrons and positrons in the Galaxy. We conclude that dark matter indirect detection techniques (including the Planck experiment) could be used to shed light on the dark matter halo profile on scales that lie beyond the capability of any current numerical simulations.