Abstract
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.
Publisher
American Astronomical Society
Subject
Space and Planetary Science,Astronomy and Astrophysics
Cited by
3 articles.
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