Diffuse gamma-ray constraints on dark matter revisited I: the impact of subhalos

We make a detailed analysis of the indirect diffuse gamma-ray signals from dark matter annihilation in the Galaxy. We include the prompt emission, as well as the emission from inverse Compton scattering whenever the annihilation products contain light leptons. We consider both the contribution from the smooth dark matter halo and that from substructures. The main parameters for the latter are the mass function index and the minimal subhalo mass. We use recent results from N-body simulations to set the most reasonable range of parameters, and find that the signal can be boosted by a factor ranging from 2 to 15 towards the Galactic poles, slightly more towards the Galactic anticenter, with an important dependence on the subhalo mass index. This uncertainty is however much less than that of the extragalactic signal studied in the literature. We derive upper bounds on the dark matter annihilation cross section using the isotropic gamma-ray emission measured by Fermi-LAT, for two directions in the sky, the Galactic anticenter and the Galactic pole(s). The former represents the lowest irreducible signal from dark matter annihilation, and the latter is robust as the astrophysical background, dominated by the hadronic contribution, is rather well established in that direction. Finally, we show how the knowledge of the minimal subhalo mass, which formally depends on the dark matter particle interactions with normal matter, can be used to derive the mass function index.