caa a22 4500 445346795 CHVBK 20180317142831.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s11207-011-9835-1 doi (NATIONALLICENCE)springer-10.1007/s11207-011-9835-1 Aschwanden Markus Lockheed Martin Advanced Technology Center, Dept. ADBS, Solar and Astrophysics Laboratory, Bldg. 252, 3251 Hanover St., 94304, Palo Alto, CA, USA aut The State of Self-organized Criticality of the Sun during the Last Three Solar Cycles. II. Theoretical Model [Elektronische Daten] [Markus Aschwanden] 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. Springer Science+Business Media B.V., 2011 Sun: hard X-rays nationallicence Sun: flares nationallicence Solar cycle nationallicence Solar Physics Springer Netherlands 274/1-2(2011-12-01), 119-129 0038-0938 274:1-2<119 2011 274 11207 https://doi.org/10.1007/s11207-011-9835-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11207-011-9835-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Aschwanden Markus Lockheed Martin Advanced Technology Center, Dept. ADBS, Solar and Astrophysics Laboratory, Bldg. 252, 3251 Hanover St., 94304, Palo Alto, CA, USA aut NATIONALLICENCE 773 0- Solar Physics Springer Netherlands 274/1-2(2011-12-01), 119-129 0038-0938 274:1-2<119 2011 274 11207 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 445346795 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer