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

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.