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 $GOES$. 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 $0 leq alpha < 2$.

Solar source of energetic particles in interplanetary space during the 2006 December 13 event

An X3.4 solar flare and a fast halo coronal mass ejection (CME) occurred on 2006 December 13, accompanied by a high flux of energetic particles recorded both in near-Earth space and at ground level. Our purpose is to provide evidence of flare acceleration in a major solar energetic particle (SEP) event. We first present observations from ACE/EPAM, GOES, and the Apatity neutron monitor. It is found that the initial particle release time coincides with the flare emission and that the spectrum becomes softer and the anisotropy becomes weaker during particle injection, indicating that the acceleration source changes from a confined coronal site to a widespread interplanetary CME-driven shock. We then describe a comprehensive study of the associated flare active region. By use of imaging data from HINODE/SOT and SOHO/MDI magnetogram, we infer the flare magnetic reconnection rate in the form of the magnetic flux change rate. This correlates in time with the microwave emission, indicating a physical link between the flare magnetic reconnection and the acceleration of nonthermal particles. Combining radio spectrograph data from Huairou/NOAC, Culgoora/IPS, Learmonth/RSTN, and WAVES/WIND leads to a continuous and longlasting radio burst extending from a few GHz down to several kHz. Based on the photospheric vector magnetogram from Huairou/NOAC and the nonlinear force free field (NFFF) reconstruction method, we derive the 3D magnetic field configuration shortly after the eruption. Furthermore, we also compute coronal field lines extending to a few solar radii using a potential-field source-surface (PFSS) model. Both the so-called type III-l burst and the magnetic field configuration suggest that open-field lines extend from the flare active region into interplanetary space, allowing the accelerated and charged particles escape.