WAITING TIME DISTRIBUTION OF SOLAR ENERGETIC PARTICLE EVENTS MODELED WITH A NON-STATIONARY POISSON PROCESS

We present a study of the waiting time distributions (WTDs) of solar energetic particle (SEP) events observed with the spacecraft WIND and GOES. The WTDs of both solar electron events (SEEs) and solar proton events (SPEs) display a power-law tail of similar to Delta t (gamma). The SEEs display a broken power-law WTD. The power-law index is gamma(1) = 0.99 for the short waiting times (<70 hr) and gamma(2) = 1.92 for large waiting times (>100 hr). The break of the WTD of SEEs is probably due to the modulation of the corotating interaction regions. The power-law index, gamma similar to 1.82, is derived for the WTD of the SPEs which is consistent with the WTD of type II radio bursts, indicating a close relationship between the shock wave and the production of energetic protons. The WTDs of SEP events can be modeled with a non-stationary Poisson process, which was proposed to understand the waiting time statistics of solar flares. We generalize the method and find that, if the SEP event rate lambda = 1/Delta t varies as the time distribution of event rate integral(lambda) = A lambda(-alpha) exp(-beta lambda), the time-dependent Poisson distribution can produce a power-law tail WTD of similar to Delta t(alpha-3), where 0 <= alpha < 2.