Distribution of extreme solar energetic proton fluxes

The knowledge of the high intensity tails of probability distributions that determine the rate of occurrence of extreme events of solar energetic particles is a critical element in the evaluation of hazards for human and robotic space missions. Here instead of the standard approach based on fitting a selected distribution function to the observed data we investigate a different approach, which is based on a study of the scaling properties of the maximum particle flux in time intervals of increasing length. To find the tail of the probability distributions we apply the “Max-Spectrum” method (Stoev, S.A., Michailidis, G., 2006. On the estimation of the heavy-tail exponent in time series using the Max-Spectrum. Technical Report 447, Department of Statistics, University of Michigan) to 1973–1997 IMP-8 proton data and the 1987–2008 GOES data, which cover a wide range of proton energies. We find that both data sets indicate a power-law tail with the power exponents close to 0.6 at least in the energy range 9–60 MeV. The underlying probability distribution is consistent with the Fréchet type (power-law behavior) extreme value distribution. Since the production of high fluxes of energetic particles is caused by fast Coronal Mass Ejections (CMEs) this heavy-tailed distribution also means that the Sun generates more fast CMEs than would be expected from a Poissonian-type process.