The State of Self-Organized Criticality of the Sun During the Last Three Solar Cycles. II. Theoretical Model

TL;DR

This paper introduces a universal analytical model for self-organized criticality in solar flares, capturing observed distributions and cycle modulations more efficiently than cellular automaton simulations.

Contribution

It presents a generalized randomized exponential-growth model for SOC, enabling faster Monte-Carlo simulations of solar flare distributions and correlations.

Findings

Model reproduces observed powerlaw distributions.

Incorporates cycle-dependent modulation of flare distributions.

Allows efficient simulation of SOC processes in solar activity.

Abstract

The observed powerlaw distributions of solar flare parameters can be interpreted in terms of a nonlinear dissipative system in the state of self-organized criticality (SOC). We present a universal analytical model of a SOC process that is governed by three conditions: (i) a multiplicative or exponential growth phase, (ii) a randomly interrupted termination of the growth phase, and (iii) a linear decay phase. This basic concept approximately reproduces the observed frequency distributions. We generalize it to a randomized exponential-growth model, which includes also a (log-normal) distribution of threshold energies before the instability starts, as well as randomized decay times, which can reproduce both the observed occurrence frequency distributions and the scatter of correlated parametyers more realistically. With this analytical model we can efficiently perform Monte-Carlo simulations of frequency distributions and parameter correlations of SOC processes, which are simpler and faster than the iterative simulations of cellular automaton models. Solar cycle modulations of the powerlaw slopes of flare frequency distributions can be used to diagnose the thresholds and growth rates of magnetic instabilities responsible for solar flares.