Excess GeV radiation and cosmic ray origin

Particle acceleration at supernova remnant (SNR) shock waves is regarded as the most probable mech- anism for providing Galactic cosmic rays at energies below 10 15 eV. The Galactic cosmic ray hadron component would in this picture result from the injection of relativistic particles from many SNRs. It is well known that the superposition of individual power law source spectra with dispersion in the spectral index value, which behaviour is observed in the synchrotron radio spectra of shell SNR, displays a positive curvature in the total spectrum and in particular shows a hardening at higher energies. Recent observations made with the EGRET instrument on the Compton Gamma-Ray Observatory of the diuse Galactic -ray emission reveal a spectrum which is incompati- ble with the assumption that the cosmic ray spectra measured locally hold throughout the Galaxy: the spectrum above 1 GeV, where the emission is supposedly dominated by 0 -decay, is harder than that derived from the local cosmic ray proton spectrum. We demonstrate that in case of a SNR origin of cosmic ray nucleons part of this -ray excess may be attributed to the dispersion of the spectral indices in these objects. In global averages, as are -ray line-of-sight integrals, this dispersion leads to a positive curvature in the composite spectrum, and hence to modied 0 -decay -ray spectra.