Revisiting empirical solar energetic particle scaling relations

I. Solar flares

¹ Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing (IAASARS), National Observatory of Athens, I. Metaxa & Vas. Pavlou St., 15236 Penteli, Greece
e-mail: atpapaio@astro.noa.gr
² Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, 24118 Kiel, Germany
³ Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, 24118 Kiel, Germany
⁴ National Solar Observatory, 3665 Discovery Drive, Boulder, CO 80303, USA
⁵ NASA, Goddard Space Flight Center, Heliophysics Science Division, Greenbelt, MD 20771, USA
⁶ Institute of Physics & Kanzelhöhe Observatory for Solar and Environmental Research, University of Graz, 8010 Graz, Austria

Received: 23 February 2022
Accepted: 2 December 2022

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 ∼34 yr (1984–2020) that were associated with flares of class ≥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, and > 60 to > 100 MeV versus the associated solar flare peak soft X-ray flux in the 1–8 Å band (F_SXR). Based on the inferred relations, we calculated 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 made use of simple physical assumptions, combining our derived scaling laws, and estimated the upper limits for I_P and F_P 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 I_P and F_P to the solar soft X-ray peak intensity (F_SXR) as ∝ $F_{\mathrm{SXR}}^{5/6}$ for a flare with a F_SXR = X600 (in the revised scale) is consistent with values of FP inferred for the cosmogenic nuclide event of AD774/775.