Double-power-law feature of energetic particles accelerated at coronal shocks

TL;DR

This study models particle acceleration at coronal shocks, revealing a double power-law energy spectrum whose break depends on ion charge-to-mass ratio, explaining observed SEP spectral features and variability.

Contribution

It introduces a numerical model showing double power-law spectra from coronal shocks and links the break energy to ion charge-to-mass ratio, advancing understanding of SEP spectral shapes.

Findings

Double power-law spectra are produced for all ion species.

Break energy scales with charge-to-mass ratio as E_B ∼ (Q/A)^α.

Spectral forms vary along the shock front, influenced by particle diffusion.

Abstract

Recent observations have shown that in many large solar energetic particle (SEP) events the event-integrated differential spectra resemble double power laws. We perform numerical modeling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation, including protons and heavier ions. We find that for all ion species the energy spectra integrated over the simulation domain can be described by a double power law, and the break energy depends on the ion charge-to-mass ratio as $E_B \sim (Q/A)^\alpha$, with $\alpha$ varying from 0.16 to 1.2 by considering different turbulence spectral indices. We suggest that the double power law distribution may emerge as a result of the superposition of energetic particles from different source regions where the acceleration rates differ significantly due to particle diffusion. The diffusion and mixing of energetic particles could also provide an explanation for the increase of Fe/O at high energies as observed in some SEP events. Although further mixing processes may occur, our simulations indicate that either power-law break or rollover can occur near the Sun and predict that the spectral forms vary significantly along the shock front, which may be examined by upcoming near-Sun SEP measurements from Parker Solar Probe and Solar Orbiter.