A Model for Spectral and Compositional Variability at High Energies in Large, Gradual Solar Particle Events

Shocks driven by fast coronal mass ejections (CMEs) are generally believed to be the dominant accelerators in large, gradual solar energetic particle (SEP) events. A key challenge for this notion has been the highly variable spectral and compositional characteristics of these events above a few tens of MeV per nucleon. We have recently proposed that this variability results from the interplay of two factors: evolution in the shock-normal angle as the shock moves outward from the Sun; and a compound seed population, typically comprising at least suprathermals from the corona (or solar wind) and suprathermals from flares. We present here a simple analytical implementation of these ideas. Our calculations semiquantitatively reproduce key features of the observed variability, including spectral morphologies and energy dependence in Fe/O, 3He/4He, and mean ionic charges, in ways that are consistent with correlations in the data. The model makes a prediction for the average high-energy Fe/O enhancement that is borne out by 30 years of observations; the model also provides a quantitative explanation for the Breneman & Stone fractionation effect, a fundamental but previously unexplained aspect of SEP phenomenology. Our calculations must be bolstered by future efforts incorporating realistic CME-shock simulations and a rigorous treatment of particle transport. Suprathermal densities in the corona, as well as details of the injection process at shocks of arbitrary obliquity, require further investigation. Nevertheless, these first results suggest a comprehensive framework for understanding the complexity of high-energy variability in terms of shock physics for most, if not all, large SEP events.