Recently , HESS and other air Čerenkov telescopes have detected a source of TeV \gamma -rays coincident with the Galactic center .
It is not yet clear whether the \gamma -rays are produced via leptonic or hadronic processes , so it is important to consider possible acceleration sites for the charged particles which produce the \gamma -rays .
One exciting possibility for the origin of these particles is the central black hole , Sgr A* , where the turbulent magnetic fields close to the event horizon can accelerate protons to TeV energies .
Using a realistic model of the density distribution in a 6 pc \times 6 pc \times 6 pc cube at the Galactic center , we here calculate the trajectories followed by these TeV protons as they gyrate through the turbulent medium surrounding Sgr A* .
Diffusing out from the black hole , the protons produce TeV \gamma -rays via \pi ^ { 0 } decay following a collision with a proton in the surrounding medium .
After following over 222,000 such trajectories , we find that the circumnuclear ring around Sgr A* can reproduce the observed 0.1–100 TeV HESS spectrum and flux if the protons are injected into this medium with an effective power-law index \approx 0.75 , significantly harder than the observed photon index of 2.25 .
The total energy in the steady-state 1 – 40 TeV proton population surrounding Sgr A* is inferred to be \approx 5 \times 10 ^ { 45 } ergs .
Only 31 % of the emitted 1–100 TeV protons encounter the circumnuclear torus , leaving a large flux of protons that diffuse outward to contribute to the Galactic ridge emission observed by HESS on scales of \gtrsim 1 ^ { \circ } .