Improved Cosmic-Ray Injection Models and the Galactic Center Gamma-Ray
  Excess
  Fermi-LAT observations of the Galactic Center (GC) have revealed a
spherically- symmetric excess of GeV gamma rays extending to at least 10 deg
from the dynamical center of the Galaxy. A critical uncertainty in extracting
the intensity, spectrum, and morphology of this excess concerns the accuracy of
astrophysical diffuse gamma-ray emission models near the GC. Recently, it has
been noted that many diffuse emission models utilize a cosmic-ray injection
rate far below that predicted based on the observed star formation rate in the
Central Molecular Zone. In this study, we add a cosmic-ray injection component
which non-linearly traces the Galactic H2 density determined in
three-dimensions, and find that the associated gamma-ray emission is degenerate
with many properties of the GC gamma-ray excess. In models that utilize a large
sideband (40x40 deg surrounding the GC) to normalize the best-fitting diffuse
emission models, the intensity of the GC excess decreases by a factor of 2, and
the morphology of the excess becomes less peaked and less spherically
symmetric. In models which utilize a smaller region of interest (15x15 deg) the
addition of an excess template instead suppresses the intensity of the best-fit
astrophysical diffuse emission, and the GC excess is rather resilient to
changes in the details of the astrophysical diffuse modeling. In both analyses,
the addition of a GC excess template still provides a statistically significant
improvement to the overall fit to the gamma-ray data. We also implement
advective winds at the GC, and find that the Fermi-LAT data strongly prefer
outflows of order several hundred km/s, whose role is to efficiently advect
low-energy cosmic rays from the Galactic center. Finally, we perform numerous
tests of our models, and conclude that they significantly improve our
understanding of multi-wavelength non-thermal emission from the GC.
