dorsal/arxiv
View SchemaThe Energy-Duration Relationship in Astrophysical Self-Organized Criticality Systems
| Authors | Markus J. Aschwanden, Alexandre Araujo |
|---|---|
| Categories | |
| ArXiv ID | 2601.06277vv1 |
| URL | https://arxiv.org/abs/2601.06277 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
Scaling laws in astrophysical systems that involve the energy, the geometry, and the spatio-temporal evolution, provide the theoretical framework for physical models of energy dissipation processes. A leading model is the standard fractal-diffusive self-organized criticality (FD-SOC) model, which is built on four fundamental assumptions: (i) the dimensionality $d=3$, (ii) the fractal dimension $D_V=d-1/2=2.5$, (iii) classical diffusion $L \propto T^{(1/2)}$, and (iv) the proportionality of the dissipated energy to the fractal volume $E \propto V$. Based on these assumptions, the FD-SOC model predicts a scaling law of $T \propto E^k \propto E^{(4/5)} = E^{0.8}$. On the observational side, we find empirical scaling laws of $T \propto E^{0.81\pm0.03}$ by Peng et al.~(2023) and $T \propto E^{0.86\pm0.03}$ by Araujo \& Valio (2021) that are self-consistent with the theoretical prediction of the FD-SOC model. However, cases with a small time range $q_T = \log{(T_{max}/T_{min})} \lapprox 2$ have large statistical uncertainties and systematic errors, which produces smaller scaling law exponents ($k \approx 0.3, ..., 0.6$) as a consequence. The close correlation of the scaling exponent $k$ with the truncation bias $q_T$ implies that the dispersion of k-values is an observational effect, rather than a physical property.
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"abstract": "Scaling laws in astrophysical systems that involve the energy, the geometry, and the spatio-temporal evolution, provide the theoretical framework for physical models of energy dissipation processes. A leading model is the standard fractal-diffusive self-organized criticality (FD-SOC) model, which is built on four fundamental assumptions: (i) the dimensionality $d=3$, (ii) the fractal dimension $D_V=d-1/2=2.5$, (iii) classical diffusion $L \\propto T^{(1/2)}$, and (iv) the proportionality of the dissipated energy to the fractal volume $E \\propto V$. Based on these assumptions, the FD-SOC model predicts a scaling law of $T \\propto E^k \\propto E^{(4/5)} = E^{0.8}$. On the observational side, we find empirical scaling laws of $T \\propto E^{0.81\\pm0.03}$ by Peng et al.~(2023) and $T \\propto E^{0.86\\pm0.03}$ by Araujo \\\u0026 Valio (2021) that are self-consistent with the theoretical prediction of the FD-SOC model. However, cases with a small time range $q_T = \\log{(T_{max}/T_{min})} \\lapprox 2$ have large statistical uncertainties and systematic errors, which produces smaller scaling law exponents ($k \\approx 0.3, ..., 0.6$) as a consequence. The close correlation of the scaling exponent $k$ with the truncation bias $q_T$ implies that the dispersion of k-values is an observational effect, rather than a physical property.",
"arxiv_id": "2601.06277",
"authors": [
"Markus J. Aschwanden",
"Alexandre Araujo"
],
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],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "The Energy-Duration Relationship in Astrophysical Self-Organized Criticality Systems",
"url": "https://arxiv.org/abs/2601.06277",
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