Obtaining the diffusion coefficient for cosmic ray propagation in the Galactic Centre Ridge through time-dependent simulations of their gamma-ray emission

Recent observations by the H.E.S.S. collaboration of the Galactic Centre region have revealed what appears to be gamma-ray emission from the decay of pions produced by interactions of recently accelerated cosmic rays with local molecular hydrogen clouds. Synthesizing a 3-D hydrogen cloud map from the available data and assuming a diffusion coefficient of the form kappa(E) = kappa_0(E/E0)^delta, we performed Monte Carlo simulations of cosmic ray diffusion for various propagation times and values of kappa_0 and delta. By fitting the model gamma-ray spectra to the observed one we were able to infer the value of the diffusion coefficient in that environment (kappa = 3.0 +/- 0.2 kpc^2 Myr^-1 for E = 10^12.5 eV and for total propagation time 10^4 yr) as well as the source spectrum (2.1 < gamma < 2.3). Also, we found that proton losses can be substantial, which justifies our approach to the problem.