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Ground-based gamma ray observations of the Galactic Center region haverevealed a high energy gamma ray source spatially coincident with thegravitational centroid of our Galaxy. The pointlike emission detected byH.E.S.S. exhibits an energy cut-off at about 10 TeV. We identify the parametersof the best fit of the exponential and the super-exponential cutoff models tothe spectrum of the pointlike source and find that super-exponential oneprovides a similar quality of the fit to the spectrum of the pointlike sourceas the best-fit exponential cutoff model, while a dark matter interpretationdoes not provide as good a fit in the whole energy range of the signal. Basedon the magnitude of the flux we derive constraints in the plane of the slope ofthe density profile $\gamma$ and the critical radius, below which the densityis assumed to be constant, $r_c$. Motivated by recent results on the spectrumand morphology from H.E.S.S. and by the possible observation of asuper-exponential cutoff, we forecast the observations of super-exponentialversus exponential cut-offs by the upcoming Cherenkov Telescope Array (CTA). Wederive a formula for $J$-factor in the small angle approximation and proposeapproximate morphological constraints on the central source.

Study of the very high energy gamma-ray spectrum from the Galactic Center and future prospects