Distinct Solar Energetic Particle Shock Intensity–Diffusion Coefficient Relationships in the Inner Heliosphere

Abstract

It has been inferred from theory that the spatial diffusion coefficient (κ) upstream of shocks is anticorrelated with the intensity of solar energetic particles (SEPs) at the shock (j<inf>shock</inf>) motivated by quasi-linear theory (QLT). This is because a lower κ along the magnetic field (κ<inf>∥</inf>) implies that particles are trapped for longer, providing more acceleration and resulting in a higher j<inf>shock</inf>. However, the simplest version of DSA predicts that j<inf>shock</inf> is determined by the source of the injected population at the shock and plasma density jump with no relation to κ for low-energy SEPs. Here, we identify the relationship between κ and j<inf>shock</inf>, whose form is unknown, using Parker Solar Probe observations of eight shocks within 1 au. We estimate a characteristic κ<inf>fit</inf> along the shock normal by fitting the upstream SEP intensity profiles with a 1D steady-state transport model for acceleration and escape assuming pitch-angle isotropy in the plasma frame. Also, we estimate κ<inf>∥</inf> based on the magnetic power spectral density using QLT for comparison with κ<inf>fit</inf>. Our results show that both quantities are anticorrelated with j<inf>shock</inf>. Instead of a uniform relationship between κ and j<inf>shock</inf>, we find distinct relationships appearing as potential power laws manifested across SEP events with no obvious radial dependence from 0.07 to 0.74 au. These relationships may be grouped by similar shock parameters (in terms of speed, strength, and orientation). Our findings raise questions about SEP transport and its radial dependence within 1 au and provide important observational constraints for models of shock-accelerated particles.