Revisiting empirical solar energetic particle scaling relations

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 (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.

On the Comprehensive 3D Modeling of the Radiation Environment of Proxima Centauri b: A New Constraint on Habitability?

“…Although these display moderate-Sunlike-bolometric flare energies, within just 52 days, three separate GLE05-type events (comparable to the strongest event directly observed at Earth) are noted, with a correspondingly significant effect on atmospheric ionization and radiation dose. Note that Evryscope observations (Howard et al 2018) have shown flares with bolometric energies of up to 10 33.5 erg (10 33.5 erg (∼3.16 × 10 −2 W m −2 , comparable to the AD774/775 event (Papaioannou et al 2023), which would have resulted in an E > 10 MeV intensity of 1.41 × 10 8 pfu at Earth, and thus, an intensity of 5.9 × 10 10 pfu at Prox Cen b, more than 4 orders of magnitudes higher than the highest intensity used in this study. However, it is currently unclear whether known solar relations hold for SXR energies above 10 −2 W m −2 ; thus, the present study confines itself to TESS-like flares.…”

“…The strongest flare observed in the TESS measurements (Vida et al 2019) utilized in this study had a bolometric energy of 1.74 × 10 32 erg. Assuming that a bolometric energy of 10 33 erg corresponds to a soft X-ray (SXR) energy of 1 × 10 −2 W m −2 (X100) (Benz 2017), this event had an SXR energy of 1.74 × 10 −3 W m −2 (X17.4), which is comparable to the flare that led to one of the strongest solar particle events ever measured as GLE event at the Earth's surface (i.e., GLE05 on 1956 February 23, X28 ± 14, see Papaioannou et al 2023). Assuming that the physical principles for these comparably low-energy flares are the same for all cool stars, known solar relations, describing the currently known upper solar limits, can be utilized to derive stellar particle intensities at the exoplanetary orbit.…”

“…Assuming that the physical principles for these comparably low-energy flares are the same for all cool stars, known solar relations, describing the currently known upper solar limits, can be utilized to derive stellar particle intensities at the exoplanetary orbit. Based on the findings in Papaioannou et al (2023), a flare intensity of X17.4 corresponds to an event-integrated E > 10 MeV flux of 2.81 × 10 7 • (1.74 × 10 −3 W m −2 ) 1.40 = 3.85 × 10 3 pfu (#/(cm 2 s sr)) at a distance of 1 au, which is less than the actual GLE05 event (∼10 4 pfu). Scaling this value with 1/r 2 to the location of Prox Cen b (i.e., 0.04857 au) thus results in an upper limit of the eventintegrated E > 10 MeV proton flux of 1.632 × 10 6 pfu.…”

Suprathermal Population Associated with Stream Interaction Regions Observed by STEREO-A: New Insights

“…Although the role of the solar flare-associated ISEP event looks promising in producing an identical spectral index, counterevidence exists in the literature. The typical time delay between the flare onset (measured by GOES X-ray fluxes) and an ISEP detection closure to the Earth is about 1 hr (e.g., Papaioannou et al 2023). In the case of SIR 12, this delay is about 9 hr.…”

Impact of Cosmic Rays on Atmospheric Ion Chemistry and Spectral Transmission Features of TRAPPIST-1e

“…Unfortunately, information on the corresponding event spectra of historical events, such as the Carrington event, is lacking. For example, to this date, it is scientifically debated whether the corresponding production rate increases around AD774/775 were caused by a single extreme event or by multiple strong events within a short amount of time (e.g., Cliver et al 2022;Papaioannou et al 2023). Thus, historical events are usually scaled with the help of measured modern-era Ground Level Enhancement (GLE) events-strong solar energetic particle events that are detected by neutron monitors at the Earth's surface-on average occurring once every year.…”