Energy Balance in Avalanche Models for Solar Flares

TL;DR

This study evaluates whether avalanche models can simultaneously describe the energy and waiting time distributions of solar flares, revealing that transition rates influence energy distribution and waiting times follow a q-exponential distribution.

Contribution

It demonstrates that avalanche models can account for both energy and waiting time distributions of solar flares, highlighting the role of transition rates in power-law behavior.

Findings

Power law in flare energies stems from transition rate distribution.

Waiting times follow a q-exponential distribution approximating Poisson.

Avalanche models can describe both energy and timing of solar flares.

Abstract

The distributions of solar flare energies and waiting times have not been described simultaneously by a single physical model, yet. In this research, we investigate whether recent avalanche models can describe the distributions for both the released energies and waiting times of flares in an active region. Flaring events are simulated using the modified Lu and Hamilton model (Lu and Hamilton (1991), ApJ, 380, 89) and also the optimized model (Farhang et al. (2018), ApJ, 859, 41). Applying a probability balance equation approach, we study the statistics of the simulated flaring events and investigate the origin of the observed power law in the flare frequency-size distribution. The results indicate that the power law originates in the distribution of transition rates (the distribution of the probabilities of transitions between different energies) rather than the distribution of the energy of the active region. It is also observed that the waiting-time distribution of simulated flaring events follows a q-exponential function which approximates a simple Poisson distribution.