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Constraints on WIMP annihilation for contracted dark matter in the inner Galaxy with the Fermi-LAT

We derive constraints on parameters of generic dark matter candidates by comparing theoretical predictions with the gamma-ray emission observed by the Fermi-LAT from the region around the Galactic Center. Our analysis is conservative since it simply requires that the expected dark matter signal does not exceed the observed emission. The constraints obtained in the likely case that the collapse of baryons to the Galactic Center is accompanied by the contraction of the dark matter are strong. In particular, we find that for bb̄ and τ+τ− or W+W− dark matter annihilation channels, the upper limits on the annihilation cross section imply that the thermal cross section is excluded for a Weakly Interacting Massive Particle (WIMP) mass smaller than about 700 and 500 GeV, respectively. For the μ+μ− channel, where the effect of the inverse Compton scattering is important, depending on models of the Galactic magnetic field the exclusion of the thermal cross-section is for a WIMP mass smaller than about 150 to 400 GeV. The upper limits on the annihilation cross section of dark matter particles obtained are two orders of magnitude stronger than without contraction. In the latter case our results are compatible with the upper limits from the Galactic halo analysis reported by the Fermi-LAT collaboration for the case in which the same conservative approach without modeling of the astrophysical background is employed.