Revisiting empirical solar energetic particle scaling relations

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