Astrophysical and Dark Matter Interpretations of Extended Gamma-Ray
  Emission from the Galactic Center
  We construct empirical models of the diffuse gamma-ray background toward the
Galactic Center. Including all known point sources and a template of emission
associated with interactions of cosmic rays with molecular gas, we show that
the extended emission observed previously in the Fermi Large Area Telescope
data toward the Galactic Center is detected at high significance for all
permutations of the diffuse model components. However, we find that the fluxes
and spectra of the sources in our model change significantly depending on the
background model. In particular, the spectrum of the central Sgr A$^\ast$
source is less steep than in previous works and the recovered spectrum of the
extended emission has large systematic uncertainties, especially at lower
energies. If the extended emission is interpreted to be due to dark matter
annihilation, we find annihilation into pure $b$-quark and $\tau$-lepton
channels to be statistically equivalent goodness of fits. In the case of the
pure $b$-quark channel, we find a dark matter mass of
$39.4\left(^{+3.7}_{-2.9}\rm\ stat.\right)\left(\pm 7.9\rm\ sys.\right)\rm\
GeV$, while a pure $\tau^{+} \tau^{-}$-channel case has an estimated dark
matter mass of $9.43\left(^{+0.63}_{-0.52}\rm\ stat.\right)(\pm 1.2\rm\ sys.)\
GeV$. Alternatively, if the extended emission is interpreted to be
astrophysical in origin such as due to unresolved millisecond pulsars, we
obtain strong bounds on dark matter annihilation, although systematic
uncertainties due to the dependence on the background models are significant.
