Gamma-ray production in supernova remnants

The bulk of the cosmic rays up to about 100 TeV are thought to be accelerated by the 1st order Fermi mechanism at supernova shocks, producing a power-law spectrum. Both electrons and protons should be accelerated, but their ratio on acceleration is not well known. Recently, the EGRET instrument on the Compton Gamma Ray Observatory has observed supernova remnants IC 443 and $\gamma$ Cygni at GeV energies. On the assumption that the observed gamma-rays are produced by accelerated particles in the remnants (rather than, for example, from a central compact object) we model the contributions due to pion production, bremsstrahlung, and inverse Compton scattering on the cosmic microwave, diffuse galactic radiation, and locally produced radiation fields. In the case of the same spectral index for both electrons and nuclei, and a cut-off at 80 TeV, we find that a spectral index of accelerated particles close to 2.4, and a ratio of electrons to protons in the range 0.2 to 0.3, gives a good fit to the observed spectra. For lower cut-off energies flatter spectra are possible. We also investigate the case where the electron spectrum is steeper than that of nuclei. We discuss the implications of our results for observations at air shower energies, and for the propagation of cosmic rays.