Power-law distribution for solar energetic proton events

Abstract

Analyses of the time-integrated fluxes of solar energetic particle events during the period 1965–1990 show that the differential distribution of events with flux F is given by a power law, with indices between 1.2 and 1.4 depending on energy. The power law represents a good fit over three to four orders of magnitude in fluence. Similar power-law distributions have been found for peak proton and electron fluxes, X-ray flares and radio and type III bursts. At fluences greater than 109 cm−2, the slope of the distribution steepens and beyond 1010 cm−2 the power-law index is estimated to be 3.5. At energies greater than 10 MeV, the slope of the distribution was found to be essentially independent of solar cycle, when the active years of solar cycles 20, 21, and 22 were analysed. The results presented are the first for a complete period of 27 years, covering nearly 3 complete solar cycles. Other new aspects of the results include the invariance of the exponent with solar cycle and also with integral energy.