25 Years of Self-Organized Criticality: Solar and Astrophysics

Abstract

Shortly after the seminal paper "Self-Organized Criticality: An explanation of 1/f noise" by Bak et al. (1987), the idea has been applied to solar physics, in "Avalanches and the Distribution of Solar Flares" by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme

Power-law Statistics of Driven Reconnection in the Magnetically Closed Corona

“…The presented statistics show that energy dissipation in our model occurs in a form of sporadic spatiotemporal activity bursts which are qualitatively similar to the statistics of solar flares obtained from observations (e.g. Crosby et al 1993;Benz & Krucker 2002;Aschwanden & Freeland 2012;Uritsky et al 2007Uritsky et al , 2013Uritsky & Davila 2014;Aschwanden et al 2016, and references therein). This behavior unfolds over transverse spatial scales of the order of several adjacent flux tubes and represents reconnection events on the misaligned field lines of these tubes.…”

“…Starting with observations of power laws in hard X-ray bursts (Datlowe et al 1974;Dennis 1985), numerous other such power laws have been observed. Solar flare hard X-rays, produced by nonthermal bremsstrahlung from accelerated coronal electrons traveling downwards toward the chomosphere, soft X-ray emission, produced by evaporated chromospheric plasma, and Extreme Ultraviolet (EUV) radiation display power-law frequency distributions in peak flux, energy, and duration (Aschwanden et al 2016, and references therein). Power-law slopes have also been measured in the distributions of solar energetic particle event fluxes (Gabriel & Feynman 1996), radio bursts (Iwai et al 2013;Das et al 1997;Ning et al 2007), and Ellerman bombs (Georgoulis et al 2002).…”

Undamped transverse oscillations of coronal loops as a self-oscillatory process

“…Such low-dimensional, conceptual models appear to be very useful in various applications, for example the self-organised criticality model (e.g. Aschwanden et al 2016). The proposed model obviously misses a number of other potentially important effects, in particular, the possibility of the excitation of multiple modes and harmonics.…”

Seismoelectromagnetism and spatio-temporal structures

“…Этот пространственно-временной скейлинг обычно характеризуется сильными, спадающими по степенному закону корре-ляциями, которые являются типичными для критических явлений [Зеленый, Милованов, 2004]. Как известно, исследования явлений подобного рода объединяются общим назва-нием «самоорганизованная критичность», позиционирующая скейлинговый контекст самоорганизации [Aschwanden et al, 2014].…”

“…Смысл СОК -эволюция таких систем к критическому состоянию без настройки каких-либо параметров. Позднее смысл термина критичность был расширен к более общему значению -критической точке [Aschwanden et al, 2014]. Суть СОК состоит в том, что по мере эволюции нелинейной дина-мической системы она неизбежно приближа-ется к критической точке (точке бифуркации).…”