Obtaining cosmic-ray propagation parameters from diffuse very high energy gamma-ray emission from the galactic center ridge

The recent discovery of diffuse, very high energy (VHE) gamma-radiation from the Galactic center ridge by the HESS telescope allows for the first time the direct determination of the parameters of Galactic cosmic-ray propagation models. Whereas this discovery showed that the diffuse gamma-radiation can be explained by the interaction of VHE cosmic-ray (CR) protons with the interstellar gas located in several giant molecular clouds, we show in this paper that the associated diffusion coefficient for the protons depends on the epoch of activity of the central source of protons: Assuming that the supernova remnant (SNR) Sgr A East was responsible for the particle acceleration, we infer a diffusion coefficient for the Galactic center region of kappa = 1-5 kpc(2) Myr(-1) for a mean proton energy of similar to 3 TeV. More specifically, for impulsive injection in a 5-10 kyr SNR, we infer a value of kappa = 1-2 kpc(2) Myr(-1), whereas for source activity time-scales equal to the age of the SNR, the diffusion coefficient would increase to kappa similar to 5 kpc(2) Myr(-1). These values are smaller than those inferred from local CR abundances. Finally, the above-mentioned values of kappa for impulsive injection are equally valid if the required transient source of protons was due to an earlier epoch of stellar infall into the black hole Sgr A*.