Revisiting Empirical Solar Energetic Particle Scaling Relations I Solar flares by Athanasios Papaioannou et al. on Tuesday 29 November

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 We show that $I_{P}$ and $F_{P}$ scale with the solar flare SXR flux

as $\propto$~$F_{SXR}^{5/6}$. For the AD774/775 event (with a re-scaled upper

limit $F_{SXR}$ = X600) these scaling laws yield values of $F_{P}$ at E$>$200

MeV of $\sim$10$^{10}$ cm$^{-2}$ and $\sim$1.5 $\times$ 10$^{9}$ cm$^{-2}$ at

E$>$430 MeV that are consistent with values inferred from the measurements of

$^{14}$C and $^{10}$Be.

arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2211.15312v1