Modelling of proton transport in application to solar long-duration gamma-ray events

Alexandr Afanasiev, University of Turku

The discovery of solar >100 MeV gamma-ray events lasting for many hours has questioned the origin of high-energy ions required for the gamma-ray production, which was conventionally attributed to flares. The long-duration gamma-ray events are also associated with fast coronal mass ejections (CMEs), so an idea that the interacting ions can be accelerated in a CME-driven shock came into consideration. In this hypothesis, ions must be able to propagate from the shock downstream back to the solar surface. This point being under strong debate in the community requires thorough modelling. In this study, we model the transport of protons from the shock towards the Sun, assuming that it is diffusive. Application of a one-dimensional (1-D) model including only parallel (along magnetic field line) spatial diffusion shows that the proton transport is governed by the flux tube expansion parameter, controlling the mirroring of particles close to the solar surface, and the proton mean free path in the flux tube. For the cases considered, a larger flux tube expansion parameter and a shorter mean free path both lead to a smaller number of precipitating protons. We also apply a new 2-D transport model that includes perpendicular diffusion and a highly turbulent sheath behind the shock that can serve as a particle reservoir.