2021/01/08 by Markus J. Aschwanden
Earth and Planetary Sciences · Physics and Astronomy · #Dissipation #Earthquake Detection and Analysis #Flare #Limit (mathematics) #Line (geometry) #Nonlinear system #Solar and Space Plasma Dynamics #Solar flare #Stars #Statistical Mechanics and Entropy #astro-ph.SR
paper · pdf · doi:10.3847/1538-4357/abda48
published as (2021), ApJ 909:69 · 21 pages, 10 Figures
arxiv created 2021/01/08 · openalex created_date 2021/01/18 · openalex publication_date 2021/03/01 · arxiv updated 2021/06/14 · openalex updated_date 2026/08/06
Abstract We explore upper limits for the largest avalanches or catastrophes in nonlinear energy dissipation systems governed by self-organized criticality. We generalize the idealized “straight” power-law size distribution and Pareto distribution functions in order to accommodate incomplete sampling, limited instrumental sensitivity, finite system-size effects, and “Black Swan” and “Dragon King” extreme events. Our findings are as follows. (i) Solar flares show no finite system-size limits up to L ≲ 200 Mm, but solar flare durations reveal an upper flare duration limit of ≲6 hr. (ii) Stellar flares observed with Kepler exhibit inertial ranges of E ≈ 10 34 –10 37 erg, finite system-size ranges of E ≈ 10 37 –10 38 erg, and extreme events at E ≈ (1–5) × 10 38 erg. (iii) The maximum flare energies of different spectral type stars (M, K, G, F, A, giants) reveal a positive correlation with the stellar radius, which indicates a finite system-size limit imposed by the stellar surface area. Fitting our finite system-size models to terrestrial data sets (earthquakes, wildfires, city sizes, blackouts, terrorism, words, surnames, web links) yields evidence (in half of the cases) for finite system-size limits and extreme events, which can be modeled with dual power-law size distributions.