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.
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