  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.
