About 10 TeV \gamma -ray emission within 10 pc region from the Galactic Center had been reported by 4 independent groups .
Considering that this TeV \gamma -ray emission is produced via a hadronic model , and the relativistic protons came from the tidal disruption of stars by massive black holes , we investigate the spectral nature of the injected relativistic protons required by the hadronic model .
The calculation was carried on the tidal disruption of the different types of stars and the different propagation mechanisms of protons in the interstellar medium .
Compared with the observation data from HESS , we find for the best fitting that the power-law index of the spectrum of the injected protons is about -1.9 , when a red giant star is tidally disrupted , and the effective confinement of protons diffusion mechanism is adopted .