Supernova remnants in clumpy media: propagation of accelerated particles into clumps

Supernova remnant (SNR) shocks are sites of particle acceleration, as indicated by observations from the radio to the gamma-ray domain. In particular, gamma-rays can be produced as the result of the interaction between particles accelerated at the SNR shock and the ambient matter and/or radiation. Both protons and electrons can contribute to the observed gamma-ray emission from SNRs, through neutral pion decay and inverse Compton (IC) scattering, respectively. Ascribing the origin of the SNR gamma-ray emission to either hadronic or leptonic processes remains, in most cases, an open problem, and its solution would constitute a crucial step in the quest for cosmic-ray (CR) sources. It has been proposed that the presence of dense clumps in the environment where supernovae explode can have a dramatic impact in shaping the hadronic gamma-ray spectrum. This is because the high-energy protons accelerated at the SNR shock are able to penetrate the dense clumps while low-energy ones cannot, and thus probe the diffuse inter-clump medium only. Here we present a numerical study of the penetration of relativistic protons into clumps which are engulfed by a SNR shock. We show that the spectrum of protons inside clumps is much harder than that in the diffuse inter-clump medium and we discuss the implications for the production of hadronic gamma-rays.