  Observations by the Fermi-LAT have uncovered a bright, spherically symmetric
excess surrounding the center of the Milky Way galaxy. The spectrum of the
gamma-ray excess peaks sharply at an energy ~2 GeV, exhibiting a hard spectrum
at lower energies, and falls off quickly above an energy ~5 GeV. The spectrum
of the excess above ~10 GeV is potentially an important discriminator between
different physical models for its origin. We focus our study on observations of
the gamma-ray excess at energies exceeding 10 GeV, finding: (1) a statistically
significant excess remains in the energy range 9.5-47.5 GeV, which is not
degenerate with known diffuse emission templates such as the Fermi Bubbles, (2)
the radial profile of the excess at high energies remains relatively consistent
with data near the spectral peak, (3) the data above ~5 GeV prefer a slightly
greater ellipticity with a major axis oriented perpendicular to the Galactic
plane. Using the recently developed non-Poissonian template fit, we find mild
evidence for a point-source origin for the high-energy excess, although given
the statistical and systematic uncertainties we show that a smooth origin of
the high-energy emission cannot be ruled out. We discuss the implication of
these findings for pulsar and dark matter models of the gamma-ray excess.
Finally we provide a number of updated measurements of the gamma-ray excess,
utilizing novel diffuse templates and the Pass 8 dataset.
