Number of solar particle 1 AU crossings and implications on the analysis of long duration gamma-ray flares

Abstract:

Energetic protons released during solar eruptive events experience scattering during their interplanetary propagation and may cross 1 AU several times. Knowledge of <N_cross>, the average number of 1 AU crossings per particle, is important to deduce the total number of relativistic solar protons at 1 AU, for comparison with the number of interacting protons at the Sun derived from gamma-ray flare observations. We show that <N_cross> obtained from 3D test particle simulations agrees well with the value from a formula involving the outward and forward fluences at 1 AU, derived from the continuity equation, when the fluences are obtained from counts over the entire 1 AU sphere. We demonstrate that the commonly used version of the formula is incorrect by a factor of 2. We discuss application of the corrected formula to neutron monitor observations for specific recent GLE events and show that even then it underestimates <N_cross> significantly. We comment on the implications of these findings on the debate about sources of particle acceleration in long duration gamma-ray flares.