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Abstract. The observations of high energy γ-ray emission from the Galactic center (GC) by HESS, and recently by Fermi, suggest the cosmic ray acceleration in the GC and possibly around the supermassive black hole. In this work we propose a leptonhadron hybrid model to explain simultaneously the GeV-TeV γ-ray emission. Both electrons and hadronic cosmic rays were accelerated during the past activity of the GC. Then these particles would diffuse outwards and interact with the interstellar gas and background radiation field. The collisions between hadronic cosmic rays with gas is responsible to the TeV γ-ray emission detected by HESS. With fast cooling in the strong radiation field, the electrons would cool down and radiate GeV photons through inverse Compton scattering off the soft background photons. This scenario provides a natural explanation of the observed GeV-TeV spectral shape of γ-rays.

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