  We perform a composite likelihood analysis of subdivided regions within the
central $26^\circ\times20^\circ$ of the Milky Way, with the aim of
characterizing the spectrum of the gamma-ray galactic center excess in regions
of varying galactocentric distance. Outside of the innermost few degrees, we
find that the radial profile of the excess is background-model dependent and
poorly constrained. The spectrum of the excess emission is observed to extend
upwards of 10 GeV outside $\sim5^\circ$ in radius, but cuts off steeply between
10--20 GeV only in the innermost few degrees. If interpreted as a real feature
of the excess, this radial variation in the spectrum has important implications
for both astrophysical and dark matter interpretations of the galactic center
excess. Single-component dark matter annihilation models face challenges in
reproducing this variation; on the other hand, a population of unresolved
millisecond pulsars contributing both prompt and secondary inverse Compton
emission may be able to explain the spectrum as well as its spatial dependency.
We show that the expected differences in the photon-count distributions of a
smooth dark matter annihilation signal and an unresolved point source
population are an order of magnitude smaller than the fluctuations in residuals
after fitting the data, which implies that mismodeling is an important
systematic effect in point source analyses aimed at resolving the gamma-ray
excess.
