The Statistical Flare


Solar and stellar flares are interpreted so far as an instability of a large scale magnetic neutral sheet. In this article, however, we assume that the active region is highly inhomogeneous: a large number of magnetic loops are simultaneously present interacting and randomly forming discontinuities in many independent points in space. These magnetic discontinuities release energy and force weaker discontinuities in their neighbourhood to release energy as well. This complex dynamical system releases constantly energy in the form of small and large scale explosions. Clustering of many discontinuities in the same area has the effect of larger scale explosions (flares). This type of flare with spatiotemporal fragmentation and clustering in small and large scale structures will be called here the statistical flare . The statistical flare is simulated using avalanche models originally introduced by Bak, Tang and Wiesenfeld (1988). Avalanche models applied so far to solar flares (Lu and Hamilton 1991) were isotropic (the field was distributed equally to the closest neighbours of an unstable point). These models simulate realtively large events (microflares and flares). Here we introduce a more refined isotropic avalanche model as well as an anisotropic avalanche model (energy is distributed only among the unstable point and those neighbours that develop gradients higher than a critical value). The anisotropic model simulates better the smaller events (nanoflares): in contrast to the well-known results of the isotropic model (a power law with index -1.8 in the peak-luminosity distribution), the anisotropic model produces a much steeper power law with index -3.5. Finally, we introduce a mixed model (a combination of isotropic and anisotropic models) which gives rise to two distinct power-law regions in the peak-luminosity distribution, one with index -3.5 accounting for the small events, and one with index -1.8 accounting for large events. This last model therefore explains coronal heating as well as flaring. The three models introduced in this paper show length-scale invariant behaviour. Model-dependent memory effects are detected in the peak-luminosity time series produced by these models.

Subject Headings: Sun: activity - Sun: corona - Sun:flare-Sun: magnetic fields - Stars: activity - Stars: flare

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