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We apply the non-linear diffusive shock acceleration theory in order todescribe the properties of two supernova remnants, SN 1572 (Tycho) and SN 1604(Kepler). By analyzing the multi-wavelength spectra, we infer that both Tycho'sand Kepler's forward shocks are accelerating protons up to ~500 TeV, channelinginto cosmic rays more than 10 per cent of their kinetic energy. We find thatthe streaming instability induced by cosmic rays is consistent with the X-raymorphology of the remnants, indicating a very efficient magnetic fieldamplification (up to ~300 microG). In the case of Tycho we explain thegamma-ray spectrum from the GeV up to the TeV band as due to pion decayproduced in nuclear collisions by accelerated nuclei scattering against thebackground gas. On the other hand, due to the larger distance, the gamma-rayemission from Kepler is not detected, being below the sensitivity of thepresent detectors, but it should be detectable by the Cerenkov Telescope Array.

Nonlinear shock acceleration and gamma-ray emission from Tycho and Kepler