  Employing data collected during the first 25 months' observations by the
Fermi-LAT, we describe and subsequently seek to model the very high energy
(>300 MeV) emission from the central few parsecs of our Galaxy. We analyze the
morphological, spectral and temporal characteristics of the central source,
1FGL J1745.6-2900. Remarkably, the data show a clear, statistically significant
signal at energies above 10 GeV, where the Fermi-LAT has an excellent angular
resolution comparable to the angular resolution of HESS at TeV energies, which
makes meaningful the joint analysis of the Fermi and HESS data. Our analysis
does not show statistically significant variability of 1FGL J1745.6-2900. Using
the combination of Fermi data on 1FGL J1745.6-2900 and HESS data on the
coincident, TeV source HESS J1745-290, we show that the spectrum of the central
gamma-ray source is inflected with a relatively steep spectral region matching
between the flatter spectrum found at both low and high energies. We seek to
model the gamma-ray production in the inner 10 pc of the Galaxy and examine, in
particular, cosmic ray (CR) proton propagation scenarios that reproduce the
observed spectrum of the central source. We show that a model that instantiates
a transition from diffusive propagation of the CR protons at low energy to
almost rectilinear propagation at high energies (given a reasonable
energy-dependence of the assumed diffusion coefficient) can well explain the
spectral phenomenology. In general, however, we find considerable degeneracy
between different parameter choices which will only be broken with the addition
of morphological information that gamma-ray telescopes cannot deliver given
current angular resolution limits.We argue that a future analysis done in
combination with higher-resolution radio continuum data holds out the promise
of breaking this degeneracy.
