Variability of the Occurrence Frequency of Solar Flares and the Statistical Flare

Abstract

Self-Organised Criticality (SOC), embedded in cellular automata models, has been so far viewed as an attractive phenomenological approach for studying the statistical behaviour of flaring activity in solar active regions. Well-known statistical properties of flares, like the robust scaling laws seen in the distribution functions of characteristic parameters of the events, as well as correlations linking those parameters, are successfully reproduced by SOC models. Recent observations, however, challenge the flexibility of SOC as they reveal a variation of the flaring power-law indices over short-time activity periods. The initial SOC models, based on a small-amplitude, constant external driver and isotropic instability criteria, appear inefficient to predict variable power-law indices. In this paper we introduce a SOC-type numerical model, with a number of modifications of the original SOC concept. We show that scaling laws and correlations between the events' characteristic parameters survive under the action of a highly variable driver. A variable driver initiates a variability in the resulting power-law indices. We reproduce qualitatively and quantitatively the statistics of flaring activity during the 154-day periodicity. Moreover, small-scale, anisotropic instability criteria imply the existence of a soft population of events, with statistical properties analogous to those attributed to the hypothetical nanoflares. We show that numerous small-scale events could be the dominant energy release mechanism in cases of quiescent coronal activity.

Subject Headings: Sun: activity - Sun: corona - Sun:flares - Sun: magnetic fields - Sun: photosphere

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