Recent HESS observations of the ~200 pc scale diffuse gamma-ray emission from the central molecular zone (CMZ) suggest the presence of a PeV cosmic-ray accelerator (PeVatron) located in the inner 10 pc region of the Galactic Center. Interestingly, the gamma-ray spectrum of the point-like source (HESS J1745-290) in the Galactic Center shows a cutoff at ~10 TeV, implying a cutoff around 100 TeV in the cosmic-ray proton spectrum. Here we propose that the gamma-ray emission from the inner and the outer regions may be explained self-consistently by run-away protons from a single, yet fading accelerator. In this model, gamma rays from the CMZ region are produced by protons injected in the past, while gamma rays from the inner region are produced by protons injected more recently. We suggest that the blast wave formed in a tidal disruption event (TDE) caused by the supermassive black hole (Sgr A*) could serve as such a fading accelerator. With typical parameters of the TDE blast wave, gamma-ray spectra of both the CMZ region and HESS J1745-290 can be reproduced simultaneously. Meanwhile, we find that the cosmic-ray energy density profile in the CMZ region may also be reproduced in the fading accelerator model when appropriate combinations of the particle injection history and the diffusion coefficient of cosmic rays are adopted.
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