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We compare the measured angular cross-correlation between the Fermi-LAT gamma-ray sky and catalogues of extra-galactic objects with the expected signal induced by weakly interacting massive particle (WIMP) dark matter (DM). We include a detailed description of the contribution of astrophysical gamma-ray emitters such as blazars, misaligned AGN and star forming galaxies, and perform a global fit to the measured cross-correlation. Five catalogues are considered: SDSS-DR6 quasars, 2MASS galaxies, NVSS radio galaxies, SDSS-DR8 Luminous Red Galaxies and SDSS-DR8 main galaxy sample. To model the cross-correlation signal we use the halo occupation distribution formalism to estimate the number of galaxies of a given catalogue in DM halos and their spatial correlation properties. We discuss uncertainties in the predicted cross-correlation signal arising from the DM clustering and WIMP microscopic properties, which set the DM gamma-ray emission. The use of different catalogues probing objects at different redshifts reduces significantly, though not completely, the degeneracy among the different gamma-ray components. We find that the presence of a significant WIMP DM signal is allowed by the data but not significantly preferred by the fit, although this is mainly due to a degeneracy with the misaligned AGN component. With modest substructure boost, the sensitivity of this method excludes thermal annihilation cross sections at 95% C.L. for WIMP masses up to few tens of GeV. Constraining the low-redshift properties of astrophysical populations with future data will further improve the sensitivity to DM.
Cuoco et al. (2015) studied this question.