Stochastic acceleration of charged particles interacting resonantly with a turbulent magnetic field in a small accretion torus appears to be the likely mechanism responsible for much of Sagittarius A*'s mm and shorter wavelength spectrum. The longer wavelength radiation is produced at larger radii by electrons either diffusing from smaller scales or accelerated in situ. An important prediction of this model is the ejection of a significant flux of relativistic protons from a magnetic-field-dominated acceleration site into the wind-shocked medium surrounding the black hole. Recently, several air \v Cerenkov telescopes, notably HESS, have detected TeV emission from within 1' of the Galactic Center, with characteristics hinting at a pp-induced pion decay process for the gamma -ray emission. Given (i) that we now know the size of this acceleration region, where Sagittarius A*'s 7-mm wavelength emission originates, and (ii) that we can now map the wind-injected ISM within 3 pc of the nucleus using the diffuse X- rays detected with Chandra, it is feasible to test the idea that protons accelerated within 20 Schwarzschild radii of the black hole produce the TeV emission farther out. We show that the diffusion length of these particles away from their source guarantees a majority of TeV protons scattering at least once within 3 pc of Sagittarius A*, and we demonstrate that the proton power ( 1037 ergs s-1) produced in concert with the 7-mm radio emission matches the TeV luminosity well. The particle cascade generated by the pp scatterings produces GeV gamma -rays from \pi0 decays, and bremsstrahlung, inverse Compton, and synchrotron emission at longer wavelengths from secondary particles. We compare these with current measurements and demonstrate that GLAST will detect this source during its one-year all-sky survey. This model explains why the TeV source is unresolved, yet does not vary on a time scale of a year or less, and it also accounts for the high-energy emission while retaining consistency with Sgr A*'s well- studied cm and mm characteristics.
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