Reconciling Power-law Slopes in Solar Flare and Nanoflare Size Distributions

Abstract

We unify the power laws of size distributions of solar flare and nanoflare energies. We present three models that predict the power-law slopes α E of flare energies defined in terms of the 2D and 3D fractal dimensions (D A , D V ): (i) the spatiotemporal standard self-organized criticality model, defined by the power-law slope α E1 =1 + 2/(D V + 2) = (13/9) ≈ 1.44; (ii) the 2D thermal energy model, α E2 = 1 + 2/D A = (7/3) ≈ 2.33; and (iii) the 3D thermal energy model, α E3 = 1 + 2/D V = (9/5) ≈ 1.80. The theoretical predictions of energies are consistent with the observational values of these three groups, i.e., α E1 = 1.47 ± 0.07, α E2 = 2.38 ± 0.09, and α E3 = 1.80 ± 0.18. These results corroborate that the energy of nanoflares does not diverge at small energies, since (α E1 < 2) and (α E3 < 2), except for the 2D model (α E2 > 2). Thus, while this conclusion does not support nanoflare scenarios of coronal heating from a dimensionality point of view, magnetic reconnection processes with quasi-1D or quasi-2D current sheets cannot be ruled out.