Revisiting Empirical Solar Energetic Particle Scaling Relations I. Solar flares

TL;DR

This study investigates the relationship between solar flare intensity and solar energetic particle events over 34 years, deriving scaling laws to estimate maximum particle fluxes and fluences, with implications for extreme space weather events.

Contribution

It introduces new empirical scaling laws linking solar flare soft X-ray flux to SEP peak flux and fluence, extending understanding of extreme space weather potential.

Findings

Scaling law: $I_P$ and $F_P$ scale as $F_{SXR}^{5/6}$.

Estimated upper limits for SEP events related to the strongest GLE.

Consistent with cosmogenic radionuclide event of AD774/775.

Abstract

Aims The possible influence of solar superflares on the near-Earth space radiation environment are assessed through the investigation of scaling laws between the peak proton flux and fluence of Solar Energetic Particle (SEP) events with the solar flare soft X-ray peak photon flux. Methods We compiled a catalog of 65 well-connected (W20-90) SEP events during the last three solar cycles covering a period of $\sim$34 years (1984-2020) that were associated with flares of class $\geq$C6.0 and investigated the statistical relations between the recorded peak proton fluxes ($I_{P}$) and the fluences ($F_{P}$) at a set of integral energies from E $>$10; $>$30; $>$60; to $>$100 MeV versus the associated solar flare peak soft X-ray flux in the 1$-$8 A band ($F_{SXR}$). Based on the inferred relations, we calculate the integrated energy dependence of the peak proton flux ($I_{P}$) and fluence ($F_{P}$) of the SEP events, assuming that they follow an inverse power-law with respect to energy. Finally, we make use of simple physical assumptions, combining our derived scaling laws, and estimate the upper limits for $I_{P}$ and $F_{P}$ focusing on the flare associated with the strongest GLE yet directly observed (GLE 05 on 23 February 1956), and that inferred for the cosmogenic radionuclide based SEP event of AD774/775. Results A scaling law relating $I_{P}$ and $F_{P}$ to the solar soft X-ray peak intensity ($F_{SXR}$) as $\propto$~$F_{SXR}^{5/6}$ for a flare with a $F_{SXR}$ = X600 (in the revised scale) is consistent with values of $F_{P}$ inferred for the cosmogenic nuclide event of AD774/775.