Do Cellular Automaton Avalanche Models Simulate the Quasi-periodic Pulsations of Solar Flares?

Abstract

Quasi-periodic pulsations (QPPs) with various periods that originate in the underlying magnetohydrodynamic processes of flaring structures are detected repeatedly in solar flare emissions. We apply a 2D cellular automaton (CA) avalanche model to simulate QPPs as a result of a repetitive load/unload mechanism. We show that the frequent occurrence of magnetic reconnections in a flaring loop could induce quasi-periodic patterns in the detected emissions. We find that among 21,070 simulated flares, 813 events last over 50 s, scaled with the temporal resolution of the Yohkoh Hard X-ray Telescope, and about 70% of these rather long-lasting events exhibit QPPs. We also illustrate that the applied CA model provides a wide range of periodicities for QPPs. Furthermore, we observe the presence of multiple periods in nearly 50% of the cases by applying the Lomb–Scargle periodogram. A lognormal distribution is fitted to the unimodal distribution of the periods as a manifestation of an underlying multiplicative mechanism that typifies the effect of the system’s independently varying parameters. The global maximum of the periods’ lognormal distribution is located at 29.29 ± 0.67 s. We compare statistics of the simulated QPPs with parameters of the host flares and discuss the impacts of flare properties on the periods of QPPs. Considering the intrinsic characteristic of CA models, namely the repetitive load/unload mechanism, and the obtained pieces of evidence, we suggest that CA models may generate QPPs. We also examine the applicability of autoregressive integrated moving average models to describe the simulated and observed QPPs.