Context: Cosmic rays are thought to be accelerated at supernova remnant (SNR) shocks, but conclusive evidence is lacking. Aims: New data from ground-based gamma-ray telescopes and the Large Area Telescope on the Fermi Gamma-ray Space Telescope are used to test this hypothesis. A simple model for gamma-ray production efficiency is compared with measured gamma-ray luminosities of SNRs, and the GeV to TeV fluxes ratios of SNRs are examined for correlations with SNR ages. Methods: The supernova explosion is modeled as an expanding spherical shell of material that sweeps up matter from the surrounding interstellar medium (ISM). The accumulated kinetic energy of the shell, which provides the energy available for nonthermal particle acceleration, changes when matter is swept up from the ISM and the SNR shell decelerates. A fraction of this energy is assumed to be converted into the energy of cosmic-ray electrons or protons. Three different particle radiation processes---nuclear pion-production interactions, nonthermal electron bremsstrahlung, and Compton scattering---are considered. Results: The efficiencies for gamma-ray production by these three processes are compared with gamma-ray luminosities of SNRs. Our results suggest that SNRs become less gamma-ray luminous at >~ 10^4 yr, and are consistent with the hypothesis that supernova remnants accelerate cosmic rays with an efficiency of ~10% for the dissipation of kinetic energy into nonthermal cosmic rays. Weak evidence for an increasing GeV to TeV flux ratio with SNR age is found.
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