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

Ground-based gamma ray observations of the Galactic Center region have revealed a high energy gamma ray source spatially coincident with the gravitational centroid of our Galaxy. The pointlike emission detected by H.E.S.S. exhibits an energy cut-off at about 10 TeV. We identify the parameters of the best fit of the exponential and the super-exponential cutoff models to the spectrum of the pointlike source and find that super-exponential one provides a similar quality of the fit to the spectrum of the pointlike source as the best-fit exponential cutoff model, while a dark matter interpretation does not provide as good a fit in the whole energy range of the signal. Based on the magnitude of the flux we derive constraints in the plane of the slope of the density profile $\gamma$ and the critical radius, below which the density is assumed to be constant, $r_c$. Motivated by recent results on the spectrum and morphology from H.E.S.S. and by the possible observation of a super-exponential cutoff, we forecast the observations of super-exponential versus exponential cut-offs by the upcoming Cherenkov Telescope Array (CTA). We derive a formula for $J$-factor in the small angle approximation and propose approximate morphological constraints on the central source.