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 $\sim \Delta t^{-\gamma }$. The SEEs display a broken power-law WTD. The power-law index is ${\gamma }_1=$ 0.99 for the short waiting times ($<$70 hours) and ${\gamma }_2=$ 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 $\gamma \sim$ 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 $\lambda =1/\Delta t$ varies as the time distribution of event rate $f(\lambda )=A{\lambda }^{-\alpha }exp(-\beta \lambda )$, the time-dependent Poisson distribution can produce a power-law tail WTD $\sim \Delta t^{\alpha -3}$, where $0\le \alpha <2$.

arXiv comment10 pages, 4 figures, accepted for publication in ApJ Letters

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