  Observations from multiple gamma-ray telescopes have uncovered a high energy
gamma-ray source spatially coincident with the Galactic center. Recently, a
compelling model for the broad-band gamma-ray emission has been formulated
which posits that high energy protons emanating from Sgr A* could produce
gamma-rays through pion decays resulting from inelastic collisions with the
traversed interstellar gas in the region. Models of the gas distribution in the
Galactic center region imply that the resulting gamma-ray morphology would be
observed as a point source with all current telescopes, but that the upcoming
Cherenkov Telescope Array (CTA) may be able to detect an extended emission
profile with an unmistakable morphology. Here, we critically evaluate this
claim, employing a three dimensional gas distribution model and a detailed
Monte Carlo simulation, and using the anticipated effective area and angular
resolution of CTA. We find that the impressive angular resolution of CTA will
be key to test hadronic emission models conclusively against, for example,
point source or dark matter annihilation scenarios. We comment on the relevance
of this result for searches for dark matter annihilation in the Galactic center
region.
