The Gamma-Ray-Flux Probability Distribution Function from Galactic Halo Substructure

One of the targets of the recently launched Fermi Gamma-ray Space Telescope is a diffuse gamma-ray background from dark-matter annihilation or decay in the Galactic halo. N-body simulations and theoretical arguments suggest that the dark matter in the Galactic halo may be clumped into substructure, rather than smoothly distributed. Here we propose the gamma-ray-flux probability distribution function (PDF) as a probe of substructure in the Galactic halo. We calculate this PDF for a phenomenological model of halo substructure and determine the regions of the substructure parameter space in which the PDF may be distinguished from the PDF for a smooth distribution of dark matter. In principle, the PDF allows a statistical detection of substructure, even if individual halos cannot be detected. It may also allow detection of substructure on the smallest microhalo mass scales, $\sim M_\oplus$, for weakly-interacting massive particles (WIMPs). Furthermore, it may also provide a method to measure the substructure mass function. However, an analysis that assumes a typical halo substructure model and a conservative estimate of the diffuse background suggests that the substructure PDF may not be detectable in the lifespan of Fermi in the specific case that the WIMP is a neutralino. Nevertheless, for a large range of substructure, WIMP annihilation, and diffuse background models, PDF analysis may provide a clear signature of substructure.