The Common Origin of High-energy Protons in Solar Energetic Particle Events and Sustained Gamma-Ray Emission from the Sun

We report that the number of > 500 MeV protons (Ng) inferred from sustained gamma ray emission (SGRE) Sun is significantly correlated with propagating into space (NSEP) as solar energetic particles (SEPs). Under shock paradigm for SGRE, shocks driven by coronal mass ejections (CMEs) accelerate high-energy sending them toward to produce SGRE interacting atmospheric particles. Particles also escape away be detected SEP events. Therefore, significant NSEP vs. Ng correlation (correlation coefficient 0.77) consistent common origin two proton populations. Furthermore, underlying CMEs have properties akin those involved in ground level enhancement (GLE) events indicating presence (up GeV) required SGRE. show observed gamma-ray flux an underestimate limb (central meridian distance 60 degrees) because sources are partially occulted when spatially extended. With assumption spectrum at nose hard and 100 accelerated throughout surface (half width range 120 we find latitudinal widths distributions energy dependent smallest highest energies. Not using energy-dependent results occurring relatively higher latitudes. Taking these effects account removes apparent lack - reported previous studies.