Anisotropy of the cosmic gamma-ray background from dark matter annihilation

High-energy photons from pair annihilation of dark matter particles contribute to the cosmic gamma-ray background (CGB) observed in a wide energy range. Since dark matter particles are weakly interacting, annihilation can happen only in high density regions such as dark matter halos. The precise shape of the energy spectrum of CGB depends on the nature of dark matter particles-their mass and annihilation cross section, as well as the cosmological evolution of dark matter halos. In order to discriminate between the signals from dark matter annihilation and other astrophysical sources, however, the information from the energy spectrum of CGB may not be sufficient. We show that dark matter annihilation not only contributes to the mean CGB intensity, but also produces a characteristic anisotropy, which provides a powerful tool for testing the origins of the observed CGB. We develop the formalism based on a halo model approach to analytically calculate the three-dimensional power spectrum of dark matter clumping, which determines the power spectrum of annihilation signals. We show that the expected sensitivity of future gamma-ray detectors such as the Gamma Ray Large Area Space Telescope (GLAST) should allow us to measure the angular power spectrum of CGB anisotropy, if dark matter particles are supersymmetric neutralinos and they account for most of the observed mean intensity of CGB in GeV region. On the other hand, if dark matter has a relatively small mass, on the order of 20 MeV, and accounts for most of the CGB in MeV region, then the future Advanced Compton Telescope (ACT) should be able to measure the angular power spectrum in MeV region. As the intensity of photons from annihilation is proportional to the density squared, we show that the predicted shape of the angular power spectrum of gamma rays from dark matter annihilation is different from that due to other astrophysical sources such as blazars and supernovae, whose intensity is linearly proportional to density. Therefore, the angular power spectrum of the CGB provides a smoking-gun signature of gamma rays from dark matter annihilation. While the mean CGB intensity expected from dark matter halos with smooth density profiles is smaller than observed, the dark matter substructure within halos may provide the origin of additional boost factors for the annihilation signal. Our formalism can be used for any other radiation processes that involve collision of particles.