  Recently, detections of a high-energy gamma-ray source at the position of the
Galactic center have been reported by multiple gamma-ray telescopes, spanning
the energy range between 100 MeV and 100 TeV. Analysis of these signals
strongly suggests the TeV emission to have a morphology consistent with a point
source up to the angular resolution of the HESS telescope (approximately 3 pc),
while the point-source nature of the GeV emission is currently unsettled, with
indications that it may be spatially extended. In the case that the emission is
hadronic and in a steady state, we show that the expected gamma-ray morphology
is dominated by the distribution of target gas, rather than by details of
cosmic-ray injection and propagation. Specifically, we expect a significant
portion of hadronic emission to coincide with the position of the
circum-nuclear ring, which resides between 1-3 pc from the Galactic center. We
note that the upcoming Cherenkov Telescope Array (CTA) will be able to observe
conclusive correlations between the morphology of the TeV gamma-ray source and
the observed gas density, convincingly confirming or ruling out a hadronic
origin for the gamma-ray emission.
