  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.
