Reconciling Power Law Slopes in Solar Flare and Nanoflare Size Distributions

TL;DR

This paper unifies solar flare and nanoflare energy distributions using models based on fractal dimensions, showing that nanoflares likely do not have enough energy to heat the corona significantly.

Contribution

It introduces three models predicting power law slopes for flare energies, aligning theoretical predictions with observational data and challenging nanoflares' role in coronal heating.

Findings

Theoretical slopes match observed values within uncertainties.

Nanoflares' energy distribution does not diverge at small energies.

Results argue against nanoflares being the primary coronal heating mechanism.

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 $\alpha_E$ of flare energies defined in terms of the 2-D and 3-D fractal dimensions ($D_A, D_V$): (i) The spatio-temporal standard SOC model, defined by the power law slope $\alpha_{E1}=1+2/(D_V+2)=(13/9)\approx 1.44$; (ii) the 2-D thermal energy model, $\alpha_{E2}=1+2/D_A=(7/3)\approx 2.33$, and (iii) the 3-D thermal energy model, $\alpha_{E3}=1+2/D_V=(9/5)\approx 1.80$. The theoretical predictions of energies are consistent with the observational values of these three groups, i.e., $\alpha_{E1}=1.47 \pm 0.07$; $\alpha_{E2}=2.38 \pm 0.09$, and $\alpha_{E3}=1.80 \pm 0.18$. These results corroborate that the energy of nanoflares does not diverge at small energies, since $(\alpha_{E1}<2$) and $(\alpha_{E3}<2)$, except for the unphyiscal 2-D model $(\alpha_{E2}>2)$. This conclusion adds an additional argument against the scenario of coronal heating by nanoflares.