Geometric Effects in Avalanche Models of Solar Flares: Implications for Coronal Heating

Open Access
Publisher Website
Google Scholar
Abstract
Observational inferences of the power-law frequency distribution of energy release by solar flares, and in particular its logarithmic slope αE, depend critically on the geometric relationship assumed to relate the observed emitting area A and the underlying emitting volume V. Recent results on the fractal nature of avalanches in self-organized critical models for solar flares indicate that this relationship is a power law V ∝ Aγ with index γ = 1.41(±0.04). We show that when proper account is made for the fractal geometry of the flaring volume, hitherto discrepant observational inferences of αE are brought in much closer agreement. The resulting values of αE lie tantalizingly close, but still below the critical value αE = 2.0, beyond which Parker's conjecture of coronal heating by nanoflares is tenable.