  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.
