New Trends in Astrophysical Self-Organized Criticality

TL;DR

This review updates the landscape of self-organized criticality in astrophysics from 2015 to 2025, emphasizing the fractal-diffusive SOC (FD-SOC) model as a unifying framework. It synthesizes solar, heliospheric, planetary, stellar, and galactic phenomena, showing that many observed size, energy, and waiting-time distributions conform to FD-SOC predictions (e.g., $\\alpha_F=1.80$, $\\alpha_E=1.67$, $\\alpha_T=2$ in 3D), while also detailing systematic deviations due to thresholds, incomplete sampling, and finite system sizes. The review highlights how non-stationary drivers, multifractal geometry, complex networks, and reconnection-based energetics shape SOC signatures across scales, from nanoflares to FRBs and black-hole systems. Collectively, these findings support SOC as a robust, scale-invariant paradigm in astrophysics, with practical implications for predicting extreme events and understanding energy partitioning in diverse cosmic environments.

Abstract

This review is focused on recent {\sl Self-Organized Criticality (SOC)} literature of astrophysical phenomena, covering the last decade of (2015-2025), while previous SOC literature (1987-2014) is reviewed elsewhere. The selection of literature is mostly based on searches with the NASA-supported {\sl Astrophysics Data System (ADS)}. The discussed astrophysical SOC phenomena are subdivided into solar flares, solar atmosphere (photosphere, chromosphere, corona), heliospheric systems (coronal mass ejections, solar wind, solar energetic particles), planetary systems (asteroids and small bodies, lunar cratering, Saturnian ring systems, magnetospheric systems), stellar flares, and galactic systems (pulsar glitches, gamma ray bursts, soft gamma-ray repeaters, supergiant fast X-ray transients, fast transient radio bursts, magnetars, blazars, black holes).

Figures (6)

• Figure 1: Size distributions of the physical parameters $L, V, T_w, n_e, EM$ and $E_{th}$ for 391 analyzed M and X-class flares. A powerlaw function is fitted in the range indicated with dotted vertical lines. The reduced $\chi^2$ distribution is characterized with a median value of $\chi^2 = 1.3$ (Aschwanden et al. 2015a).
• Figure 2: Synopsis of three power law models: (PM) = Pareto distribution model $[x_1, x_0]$, (EM) = Extreme events model $[x_3, x_2$], and (FM) = Finite system-size model $[\hbox{$\;\buildrel >\over{\sim}\;$} x_3]$. The inertial range covers $[\hbox{$\;\buildrel >\over{\sim}\;$} x_0, \hbox{$\;\buildrel <\over{\sim}\;$} x_3$]. The data used here are from a stellar flare catalog observed with Kepler (Aschwanden 2021).
• Figure 3: Overview of waiting time distributions for slow-driven and fast-driven, stationary and non-stationary SOC models: Stationary models imply exponential WTD functions, while nonstationary models produce power law size distributions (Aschwanden 2019c).
• Figure 4: Schematic diagram of energy input (free magnetic energy $E_{\rm mag}$), primary energy dissipation processes (electron acceleration $E_{nt,e}$, ion acceleration $E_{nt,i}$, direct heating $E_{dir}$, and launching of CME $E_{\rm CME}$), and secondary energy dissipation processes (thermal energy $E_{th}$, solar energetic particles $E_{\rm SEP}$, and bolometric luminosity $E_{\rm bol}$, with radiative energies observed in white light $E_{\rm WL}$, and soft X-rays and EUV $E_{\rm rad}$), (Aschwanden et al. 2017).
• Figure 5: Cumulative size distribution of Saturn ring particles, near-Earth objects, Jovian Trojans, asteroids, Neptunian Trojans, lunar craters, Kuijper belt objects, Neptune Trojans,and Earth-sized extra-solar planets. The grey diagonal lines indicate the prediction of the FD-SOC model, with a power law slope of $\alpha_L^{cum} = 2$ for the cumulative size distribution, corresponding to a power law slope of $\alpha_L =\alpha_L^{cum}+1=3$ for the differential occurrence frequency distribution. References are given in Aschwanden et al. (2016b).