The Galactic Isotropic $\gamma$-ray Background and Implications for Dark Matter

We present an analysis of the radial angular profile of the galacto-isotropic (GI) $\gamma$-ray flux--the statistically uniform flux in circular annuli about the Galactic center. Two different approaches are used to measure the GI flux profile in 85 months of Fermi-LAT data: the BDS statistic method which identifies spatial correlations, and a new Poisson ordered-pixel method which identifies non-Poisson contributions. Both methods produce similar GI flux profiles. The GI flux profile is well-described by an existing model of bremsstrahlung, $\pi^0$ production, inverse Compton scattering, and the isotropic background. Discrepancies with data in our full-sky model are not present in the GI component, and are therefore due to mis-modeling of the non-GI emission. Dark matter annihilation constraints based solely on the observed GI profile are close to the thermal WIMP cross section below 100 GeV, for fixed models of the dark matter density profile and astrophysical $\gamma$-ray foregrounds. Refined measurements of the GI profile are expected to improve these constraints by a factor of a few.