Radio emission and nonlinear diffusive shock acceleration of cosmic rays in the supernova SN 1993J

Aims. The extensive observations of the supernova SN 1993J at radio wavelengths make this object a unique target for the study of particle acceleration in a supernova shock. Methods. To describe the radio synchrotron emission we use a model that couples a semianalytic description of nonlinear diffusive shock acceleration with self-similar solutions for the hydrodynamics of the supernova expansion. The synchrotron emission, which is assumed to be produced by relativistic electrons propagating in the postshock plasma, is worked out from radiative transfer calculations that include the process of synchrotron self-absorption. The model is applied to explain the morphology of the radio emission deduced from high-resolution VLBI imaging observations and the measured time evolution of the total flux density at six frequencies. Results. Both the light curves and the morphology of the radio emission indicate that the magnetic field was strongly amplified in the blast wave region shortly after the explosion, possibly via the nonresonant regime of the cosmic-ray streaming instability operating in the shock precursor. The amplified magnetic field immediately upstream from the subshock is determined to be $B_u \approx 50 (t/1 {\rm~day})^{-1}$ G. The turbulent magnetic field was not damped behind the shock but carried along by the plasma flow in the downstream region. Cosmic-ray protons were efficiently produced by diffusive shock acceleration at the blast wave. We find that during the first ~8.5 years after the explosion, about 19% of the total energy processed by the forward shock was converted to cosmic-ray energy. However, the shock remained weakly modified by the cosmic-ray pressure. The high magnetic field amplification implies that protons were rapidly accelerated to energies well above 1015 eV. The results obtained for this supernova support the scenario that massive stars exploding into their former stellar wind are a major source of Galactic cosmic-rays of energies above ~1015 eV. We also calculate the flux from SN 1993J of gamma-rays arising from collisions of accelerated cosmic rays with ambient material and the result suggests that type II supernovae could be detected in $\pi^0$-decay gamma-rays with the Fermi Gamma-ray Space Telescope out to a maximum distance of only ~1 Mpc