Self‐organized Critical Model of Energy Release in an Idealized Coronal Loop

Abstract

We present and discuss a new avalanche model for solar flares, based on an idealized representation of a coronal loop as a bundle of magnetic flux strands wrapping around one another. The model is based on a two-dimensional cellular automaton with anisotropic connectivity, where linear ensembles of interconnected nodes define the individual strands collectively making up the coronal loop. The system is driven by random deformation of the strands, and a form of reconnection is assumed to take place when the angle subtended by two strands crossing at the same lattice site exceed some preset threshold. Driven in this manner, the cellular automaton produces avalanches of reconnection events characterized by scale-free size distributions that compare favorably with the corresponding size distribution of solar flares, as inferred observationally. Although lattice-based and highly idealized, the model satisfies the constraints Δ B = 0 by design and is defined in such a way as to be readily mapped back onto coronal loops with set physical dimensions. Carrying this exercise for a generic coronal loop of length 1010 cm and diameter 108 cm yields flare energies ranging from 1023 to 1029 erg, for an instability threshold angle of 11° between contiguous magnetic flux strands. These figures square well with both observational determinations and theoretical estimates.