Revisiting empirical solar energetic particle scaling relations

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 ∼34 yr (1984–2020) that were associated with flares of class ≥C6.0, and investigated the statistical relations between the recorded peak proton fluxes (IP) and the fluences (FP) at a set of integral energies from E > 10, > 30, and > 60 to > 100 MeV versus the associated solar flare peak soft X-ray flux in the 1–8 Å band (FSXR). Based on the inferred relations, we calculated the integrated energy dependence of the peak proton flux (IP) and fluence (FP) of the SEP events, assuming that they follow an inverse power law with respect to energy. Finally, we made use of simple physical assumptions, combining our derived scaling laws, and estimated the upper limits for IP and FP focusing on the flare associated with the strongest ground level enhancement (GLE) directly observed to date (GLE 05 on 23 February 1956), and that inferred for the cosmogenic radionuclide-based SEP event of AD774/775. Results. A scaling law relating IP and FP to the solar soft X-ray peak intensity (FSXR) as ∝ $ {F}_{\mathrm{SXR}}^{5/6} $ for a flare with a FSXR = X600 (in the revised scale) is consistent with values of FP inferred for the cosmogenic nuclide event of AD774/775