Slow Diffusion of Cosmic-Rays around a Supernova Remnant

We study the escape of cosmic-ray protons accelerated at a supernova remnant (SNR). We are interested in their propagation in interstellar medium (ISM) after they leave the shock neighborhood where they are accelerated, but when they are still near the SNR with their energy density higher than that in the average ISM. Using Monte-Carlo simulations, we found that the cosmic-rays with energies of <~TeV excite Alfven waves around the SNR on a scale of the SNR itself if the ISM is highly ionized. Thus, even if the cosmic-rays can leave the shock, scattering by the waves prevents them from moving further away from the SNR. The cosmic-rays form a slowly expanding cosmic-ray bubble, and they spend a long time around the SNR. This means that the cosmic-rays cannot actually escape from the SNR until a fairly late stage of the SNR evolution. This is consistent with some results of Fermi and H.E.S.S. observations.