Observations from the radio to the gamma-ray wavelengths indicate that supernova remnant (SNR) shocks are sites of effective particle acceleration. It has been proposed that the presence of dense clumps in the environment where supernovae explode might have a strong impact in shaping the hadronic gamma-ray spectrum. Here we present a detailed numerical study about the penetration of relativistic protons into clumps which are engulfed by a SNR shock, taking into account the magneto-hydrodynamical properties of the background plasma. 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 formation of the spectrum of hadronic gamma rays, which does not reflect anymore the acceleration spectrum of protons, resulting substantially modified inside the clumps due to propagation effects. For the Galactic SNR RX J1713.7-3946, we show that a hadronic scenario including dense clumps inside the remnant shell is able to reproduce the broadband gamma-ray spectrum from GeV to TeV energies. Moreover, we argue that small clumps crossed by the shock could provide a natural explanation to the non-thermal X-ray variability observed in some hot spots of RX J1713.7-3946. Finally we discuss the detectability of gamma-ray emission from clumps with the upcoming Cherenkov Telescope Array and the possible detection of the clumps themselves through molecular lines.
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