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 W IND and GOES. Both the WTDs of solar electron events (SEEs) and solar proton events (SPEs) display a power-law tail ∼ ∆t −γ . The SEEs display a broken power-law WTD. The powerlaw index is γ 1 = 0.99 for the short waiting times (<70 hours) and γ 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 γ ∼ 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 λ = 1/∆t varies as the time distribution of event rate f (λ) = Aλ −α exp(−βλ), the timedependent Poisson distribution can produce a power-law tail WTD ∼ ∆t α−3 , where 0 ≤ α < 2.

Coronal Mass Ejections over Solar Cycles 23 and 24

“…18 displays the histograms of the distribution of WTDs together with different fitted models: Poisson, Weibull, and power law. In addition, in the case of ARTEMIS, we include the non-stationary Poisson model introduced by Li et al (2014) in their analysis of the WTD of solar energetic particles where the event rate f (λ) follows an exponential law via:…”

Automated Detection of Small-scale Magnetic Flux Ropes in the Solar Wind: First Results from the Wind Spacecraft Measurements

“…Many models on solar eruptive processes predict definitive WTDs, so the WTD analysis based on observational data is a powerful tool to validate these models. The WTD analysis is widely used in analyzing space plasma processes such as CMEs (Li et al 2016), solar flares (Wheatland et al 1998;Li et al 2016), current sheets (Miao et al 2011), gamma ray burst (Wang & Dai 2013), and solar energetic particles (Li et al 2014), and also in other discrete time random processes such as earthquakes (Sotolongo-Costa et al 2000). In this section, we apply the WTD analysis on the occurrence of small-scale magnetic flux ropes, in order to investigate the underlying mechanism governing the flux rope origination process.…”

“…Li et al (2016) investigated the statistical properties of CMEs and solar flares during solar cycle 23. They adopted the non-stationary Poisson distribution functions from Li et al (2014) and Guidorzi et al (2015) to fit the WTDs of solar flares and CMEs, and obtained good fitting results. In Li et al (2014); Guidorzi et al (2015) the non-stationary Poisson distribution functions and the asymptotic behavior of the longer waiting time near the tail lead to power law functions.…”

Dynamic SEP event probability forecasts

“…The compilation of waiting time distributions (WTDs), the times δ t between successive flare occurrences, has been used to test that assumption, with the result that the flaring process is understood to be a nonstationary or intermittent Poisson process with a temporal variation in the flare rate λ [ Wheatland , ; Aschwanden and McTiernan , ]. Recent investigations of WTDs using the NOAA [ Li et al , ] and other SEP event lists [ Jiggens and Gabriel , ] have shown clearly that the SEP events are also a time‐dependent process characterized by clustering of events. In principle, the SEP WTD could provide an additional forecasting tool, but it appears that for the 10 pfu events of this study, the time interval needed to determine a valid SEP event rate λ , perhaps 2 weeks for disk passage of an AR complex, would include too few SEP events to be practical.…”