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

Recent observations by the H.E.S.S. collaboration of the Galactic Centre region have revealed what appears to be γ-ray emission from the decay of pions produced by interactions of recently accelerated cosmic rays with local molecular hydrogen clouds. Synthesizing a 3D hydrogen cloud map from the available data and assuming a diffusion coefficient of the form κ(E) = κ0(E/E0)δ, we performed Monte Carlo simulations of cosmic ray diffusion for various propagation times and values of κ0 and δ. By fitting the model γ-ray spectra to the observed one we were able to infer the value of the diffusion coefficient in that environment (κ = 3.0 ± 0.2 kpc2 Myr−1 for E = 1012.5 eV and for total propagation time 104 yr) as well as the source spectrum (2.1 ⩽ γ ⩽ 2.3). Also, we found that proton losses can be substantial, which justifies our approach to the problem.