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Self-organized criticality in solar physics and astrophysics. (English) Zbl 1231.85005

The concept of “self-organized criticality” (SOC) was introduced by P. Bak, Ch. Tang and K. Wiesenfeld [Phys. Rev. A (3) 38, No. 1, 364–374 (1988; Zbl 1230.37103)] to describe the statistics of avalanches on the surface of a sandpile with a critical slope, which produces a scale-free powerlaw size distribution of avalanches. In the meantime, SOC behavior has been identified in many nonlinear dissipative systems that are driven to a critical state. On a most general level, SOC is the statistics of coherent nonlinear processes, in contrast to the Poisson statistics of incoherent random processes. The SOC concept has been applied to laboratory experiments (of rice or sand piles), to human activities (population growth, language, economy, traffic jams, wars), to biophysics, geophysics (earthquakes, landslides, forest fires), magnetospheric physics, solar physics (flares), stellar physics (flares, cataclysmic variables, accretion disks, black holes, pulsar glitches, gamma ray bursts), and to galactic physics and cosmology.
The present paper reviews the analytical model of SOC avalanches. Using a simple model the powerlaw distribution of peak energies in nonlinear coherent processes (which have an exponential-like growth) is explained. In incoherent processes, the distribution of peak energies is identical to that of the saturation times, which is an exponential Poissonian distribution. Further it is discussed that the more physical description of a logistic avalanche with a continuous time evolution shares the same characteristic as an exponentially-growing avalanche, and thus may also be used to describe SOC processes.
Special attention is paid to the investigation of solar flares, which are probably the best studied astrophysical phenomena regarding SOC statistics. The self-similarity of flare parameters is observed over wide ranges of temperature allowing the conclusion that the solar corona is in a state of self-organized criticality. Besides, also other astrophysical SOC phenomena are briefly mentioned, for instance stellar flares which are up to two orders of magnitude more energetic than solar ones.

MSC:

85A35 Statistical astronomy
62P35 Applications of statistics to physics
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
58K35 Catastrophe theory
76E20 Stability and instability of geophysical and astrophysical flows
83F05 Relativistic cosmology

Citations:

Zbl 1230.37103
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