Numerical Simulation of Equal Ratio Relations for the Peak Intensities of >10 MeV Energetic Protons

Abstract

Previous studies have highlighted the significance of perpendicular diffusion in the decay phase of particle intensities for >10 MeV energetic protons. Recently, an observational study has indicated that the peak intensity ratios across different energy channels (13−64 MeV protons) remain almost constant as the spacecraft location varies in many solar proton events. This interesting phenomenon is referred to as equal ratio relations. These findings suggest that perpendicular diffusion not only affects particle intensity during the decay phase but also throughout the rising phase. In this study, we perform numerical simulations of >10 MeV energetic proton events observed by STEREO A, STEREO B, and the Solar and Heliospheric Observatory. Our findings demonstrate that perpendicular diffusion strongly affects the entire time profile of particle intensity for spacecraft not magnetically connected to the source region. The numerical simulation results indicate that in order to reproduce observations, we need to include perpendicular diffusion near the source region and in interplanetary space. Perpendicular diffusion leads to nearly uniform peak ratios at different locations and contributes to the formation of the reservoir phenomenon during the decay phase. Consequently, these numerical results support the significant role of perpendicular diffusion in the formation of the longitudinal distribution of >10 MeV proton events.