The isotropic gamma-ray background arises from the contribution of unresolved sources, including members of confirmed source classes and proposed gamma-ray emitters such as the radiation induced by dark matter annihilation and decay. Clues about the properties of the contributing sources are imprinted in the anisotropy characteristics of the gamma-ray background. We use 81 months of Pass 7 Reprocessed data from the Fermi Large Area Telescope to perform a measurement of the anisotropy angular power spectrum of the gamma-ray background. We analyze energies between 0.5 and 500 GeV, extending the range considered in the previous measurement based on 22 months of data. We also compute, for the first time, the cross-correlation angular power spectrum between different energy bins. We find that the derived angular spectra are compatible with being Poissonian, i.e. constant in multipole. Moreover, the energy dependence of the anisotropy suggests that the signal is due to two populations of sources, contributing, respectively, below and above 2 GeV. Finally, using data from state-of-the-art numerical simulations to model the dark matter distribution, we constrain the contribution from dark matter annihilation and decay in Galactic and extragalactic structures to the measured anisotropy. These constraints are competitive with those that can be derived from the average intensity of the isotropic gamma-ray background. Data are available at https://www-glast.stanford.edu/pub_data/552.
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