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

Abstract

The observed power-law distributions of solar-flare parameters can be interpreted in terms of a nonlinear dissipative system in a state of self-organized criticality (SOC). We present a universal analytical model of an 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 also includes 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 parameters 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 power-law slopes of flare-frequency distributions can be used to diagnose the thresholds and growth rates of magnetic instabilities responsible for solar flares.

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Correspondence to Markus J. Aschwanden.

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The Sun – Earth Connection near Solar Minimum

Guest Editors: M.M. Bisi, B.A. Emery, and B.J. Thompson.

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Aschwanden, M.J. The State of Self-organized Criticality of the Sun during the Last Three Solar Cycles. II. Theoretical Model. Sol Phys 274, 119–129 (2011). https://doi.org/10.1007/s11207-011-9835-1

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  • DOI: https://doi.org/10.1007/s11207-011-9835-1

Keywords

  • Sun: hard X-rays
  • Sun: flares
  • Solar cycle