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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 and .
Both the WTDs of solar electron events (SEEs) and solar proton events (SPEs)
display a power-law tail . The SEEs display a broken
power-law WTD. The power-law index is 0.99 for the short waiting
times (100
hours). The break of the WTD of SEEs is probably due to the modulation of the
corotating interaction regions (CIRs). The power-law index 1.82
is derived for the WTD of SPEs that 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 (Wheatland 2000; Aschwanden McTiernan
2010). We generalize the method and find that, if the SEP event rate varies as the time distribution of event rate , the time-dependent Poisson distribution
can produce a power-law tail WTD , where .Comment: 10 pages, 4 figures, accepted for publication in ApJ Letter
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