Revisiting Empirical Solar Energetic Particle Scaling Relations I. Solar flares

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.