We characterize and provide a catalog of thirty >100 MeV sustained gamma-ray emission (SGRE) events observed by Fermi LAT. These events are temporally and spectrally distinct from the associated solar flares. Their spectra are consistent with decay of pions produced by >300 MeV protons and are not consistent with electron bremsstrahlung. SGRE start times range from CME onset to two hours later. Their durations range from about four minutes to twenty hours and appear to be correlated with durations of >100 MeV SEP proton events. The >300 MeV protons producing SGRE have spectra that can be fit with power laws with a mean index of ~4 and RMS spread of 1.8. Gamma-ray line measurements indicate that SGRE proton spectra are steeper above 300 MeV than they are below 300 MeV. The number of SGRE protons >500 MeV is on average about ten times more than then the number in the associated flare and about fifty to one hundred times less than the number in the accompanying SEP. SGRE can extend tens of degrees from the are site. Sustained bremsstrahlung from MeV electrons was observed in one SGRE event. Flare >100 keV X-ray emission appears to be associated with SGRE and with intense SEPs. From this observation, we provide arguments that lead us to propose that sub-MeV to MeV protons escaping from the flare contribute to the seed population that is accelerated by shocks onto open field lines to produce SEPs and onto field lines returning to the Sun to produce SGRE.
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