Statistical Relationship between Long-duration High-energy Gamma-Ray Emission and Solar Energetic Particles

Large solar eruptions are often associated with long-duration & gamma;-ray emission extending well above 100 MeV. While this phenomenon is known to be caused by high-energy ions interacting with the solar atmosphere, the underlying dominant acceleration process remains under debate. Potential mechanisms include continuous acceleration of particles trapped within large coronal loops or acceleration at coronal mass ejection (CME)-driven shocks, with subsequent back-propagation toward the Sun. As a test of the latter scenario, previous studies have explored the relationship between the inferred particle population producing the high-energy & gamma;-rays and the population of solar energetic particles (SEPs) measured in situ. However, given the significant limitations on available observations, these estimates unavoidably rely on a number of assumptions. In an effort to better constrain theories of the & gamma;-ray emission origin, we reexamine the calculation uncertainties and how they influence the comparison of these two proton populations. We show that, even accounting for conservative assumptions related to the & gamma;-ray flare, SEP event, and interplanetary scattering modeling, their statistical relationship is only poorly/moderately significant. However, though the level of correlation is of interest, it does not provide conclusive evidence for or against a causal connection. The main result of this investigation is that the fraction of the shock-accelerated protons required to account for the & gamma;-ray observations is >20%-40% for six of the 14 eruptions analyzed. Such high values argue against current CME-shock origin models, predicting a <2% back-precipitation; hence, the computed number of high-energy SEPs appears to be greatly insufficient to sustain the measured & gamma;-ray emission.