Peak-Size Distributions of Proton Fluxes and Associated Soft X-Ray Flares

Abstract

A database combining information about solar proton enhancements (SPEs) near the Earth and soft X-ray flares (GOES measurements) has been used for the study of different correlations through the period from 1975 to May 2006. The emphasis of this work is on the treatment of peak-size distributions of SXR flares and SPEs. The frequency of SXR flares and solar proton events (>10 and >100 MeV, respectively) for the past three solar cycles has been found to follow mainly a power-law distribution over three to five orders of magnitude of fluxes, which is physically correct beyond the "sensitivity" problem with the smallest peak values. The absence of significant spectral steepening in the domain of the highest peak values demonstrates that during the period considered, lasting 30 years, the limit of the highest flare's energy release has not yet been achieved. The power-law exponents were found to be −2.19 ± 0.04, −1.34 ± 0.02, and −1.46 ± 0.04, for the total SXR flare distribution and the total SPE distributions (for both E P > 10 MeV and E P > 100 MeV), respectively. For SPEs associated with flares located to the West of 20°W, the exponents are −1.22 ± 0.05 (E P > 10 MeV) and −1.26 ± 0.03 (E P > 100 MeV). The size distribution for corresponding flares follows a power law with a slope of −1.29 ± 0.12. Thus, X-ray and proton fluxes produced in the same solar events have very similar distribution shapes. Moreover, the derived slopes are not incompatible with a linear dependence between X-ray flare power and proton fluxes near the Earth. A similar statistical relation is obtained independently from the direct comparison of the X-ray and proton fluxes. These all argue for a statistically significant relationship between X-ray and proton emissions.

Large gradual solar energetic particle events

“…The size distribution of SEP events has often been characterized in terms of a powerlaw in the peak proton flux or fluence and then compared to the peak soft X-ray (SXR) flux in flares (see, e.g., Hudson 1978;Belov et al 2007;, and references therein). However, the power-law characterizing SEP size is significantly flatter than that of the SXR flux.…”

The MUSCLES Treasury Survey. IV. Scaling Relations for Ultraviolet, Ca ii K, and Energetic Particle Fluxes from M Dwarfs

“…Energetic particles from stellar eruptive events are not frequently included in these energy budgets, because there are no observational constraints for stars other than the Sun. Existing solar correlations between SXRs and protons detected near Earth (i.e., Belov et al 2007;Cliver et al 2012) cannot be directly applied to HSTʼs UV flares, because we do not know the energy partition between stellar UV emission lines and SXRs during flares. Thus, we have developed a new scaling relation between energetic protons detected near Earth and UV flares from the Sun.…”

Energetic Particle Acceleration and Propagation in Strong CME-Less Flares

“…Despite the widespread belief that large SEP events result from particle acceleration at CME shocks, soft X-ray burst characteristics play an important part in operational models used for SEP forecasting (Garcia, 2004;Balch, 2008). Indeed Belov et al (2007) showed that the probability of an SEP event rises with the peak soft X-ray flux of the flare. But they also demonstrated (their Figure 3) that more than 30% of GOES X class flares westward of longitude E 20 • have no SEP event associated with them.…”