Waiting time distribution of solar energetic particle events modeled with a non-stationary Poisson process

Abstract

We present a study of the waiting time distributions (WTDs) of solar energetic particle (SEP) events observed with the spacecraft $WIND$ and $GOES$. Both the WTDs of solar electron events (SEEs) and solar proton events (SPEs) display a power-law tail $\sim \hat{I}”t^{-{\hat{I}}^3}$. The SEEs display a broken power-law WTD. The power-law index is ${\hat{I}}_1^3=$ 0.99 for the short waiting times ($<$70 hours) and ${\hat{I}}_2^3=$ 1.92 for large 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 ${\hat{I}}^3\sim$ 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 $\hat{I}»=1/\hat{I}”t$ varies as the time distribution of event rate $f(\hat{I}»)=A\hat{I}{»}^{-\hat{I}\pm }exp(-{\hat{I}}^2\hat{I}»)$, the time-dependent Poisson distribution can produce a power-law tail WTD $\sim \hat{I}”t^{\hat{I}\pm -3}$, where $0\le \hat{I}\pm <2$.

10 pages, 4 figures, accepted for publication in ApJ Letters