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25 Years of Self-Organized Criticality: Solar and Astrophysics

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25 Years of Self-Organized Criticality: Solar and Astrophysics Space Sci Rev (2016) 198:47–166 DOI 10.1007/s11214-014-0054-6 25 Years of Self-Organized Criticality: Solar and Astrophysics Markus J. Aschwanden · Norma B. Crosby · Michaila Dimitropoulou · Manolis K. Georgoulis · Stefan Hergarten · James McAteer · Alexander V. Milovanov · Shin Mineshige · Laura Morales · Naoto Nishizuka · Gunnar Pruessner · Raul Sanchez · A. Surja Sharma · Antoine Strugarek · Vadim Uritsky Received: 24 March 2014 / Accepted: 30 May 2014 / Published online: 15 July 2014 © The Author(s) 2014. This article is published with open access at Springerlink.com 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, M.J. Aschwanden (B) Lockheed Martin, Solar and Astrophysics Laboratory (LMSAL), Advanced Technology Center (ATC), A021S, Bldg. 252, 3251 Hanover St., Palo Alto, CA 94304, USA e-mail: [email protected] N.B. Crosby Belgian Institute for Space Aeronomy, Ringlaan-3-Avenue Circulaire, 1180 Brussels, Belgium M. Dimitropoulou Dept. Physics, Kapodistrian University of Athens, 15483 Athens, Greece M.K. Georgoulis Research Center Astronomy and Applied Mathematics, Academy of Athens, 4 Soranou Efesiou St., 11527 Athens, Greece S. Hergarten Institute für Geo- und Umweltnaturwissenschaften, Albert-Ludwigs-Universität Freiburg, Albertstr. 23B, 79104 Freiburg, Germany J. McAteer Dept. Astronomy, New Mexico State University, P.O. Box 30001, 4500 Las Cruces, USA A.V. Milovanov ENEA National Laboratory, Centro Ricerche Frascati, Via Enrico Fermi 45, C.P.-65, 00044 Frascati, Rome, Italy A.V. Milovanov Space Research Institute, Russian Academy of Sciences, Profsoyuznaya Str. 84/32, 117997 Moscow, Russia A.V. Milovanov Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, 01187 Dresden, Germany 48 M.J. Aschwanden et al. 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 magneto- spheric 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 per- formed 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 dis- cretization 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 com- plexity 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. Keywords Instabilities · Methods: statistical · Sun: flare · Stars: flare · Planets and satellites: rings · Cosmic rays Acronyms 1D, 2D, 3D 1-, 2-, 3-dimensional ACE Advanced Composition Explorer (spacecraft) AE Auroral Electron jet index AGILE Astro-Rivelatore Gamma a Immagini LEggero (spacecraft) S. Mineshige Dept. Astronomy, Kyoto University, 606-8602 Kyoto, Japan L. Morales Canadian Space Agency, Space Science and Technology Branch, 6767 Route de l’Aeroport, Saint Hubert, QC J3Y8Y9, Canada N. Nishizuka National Institute of Information and Communications Technology, 4-2-1 Nukui-Kitamachi Koganei, 184-8795 Tokyo, Japan G. Pruessner Dept. Mathematics, Imperial College London, 180 Queen’s Gate, SW7 2AZ London, United Kingdom R. Sanchez Dept. Fisica, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganes, Madrid, Spain A.S. Sharma Dept. Astronomy, University of Maryland, College Park, MD 20740, USA A. Strugarek Dept. de Physique, University of Montreal, C.P. 6128 Succ. Centre-Ville, Montreal, QC H3C-3J7, Canada V. Uritsky NASA Goddard Space Flight Center, Code 671.0, Greenbelt, MD 20771, USA 25 Years of Self-Organized Criticality: Solar and Astrophysics 49 AGN Active Galactic Nuclei AIA Atmospheric Imaging Assembly (on SDO) AlMg Aluminium-Magnesium filter (on Yohkoh spacecraft) AU Auroral Upper geomagnetic index AU Astronomical Unit (Sun-Earth distance) BATSE Burst And Transient Source Experiment (on CGRO) BC Box Counting (fractal dimension) BCS Bent Crystal Spectrograph (on SMM) BTW Bak, Tang, and Wiesenfeld (SOC model) COBE COsmic Background Explorer (spacecraft) CGRO Compton Gamma Ray Observatory (spacecraft) CLUSTER Magnetospheric mission with 4 spacecraft CME Coronal Mass Ejection DCIM-P Decimetric pulsation radio burst DCIM-S Decimetric spike radio burst DNL Distant Neutral Line (in geotail) EIT Extreme ultra-violet Imager Telescope (on SOHO) EM Emission Measure ESA European Space Agency EUV Extreme Ultra-Violet EUVE Extreme Ultra-Violet Explorer (spacecraft) EXOSAT European X-ray Observatory SATellite FD-SOC Fractal-Diffusive Self-Organized Criticality model Fermi Hard X-ray spacecraft FSOC Forced Self-Organized Criticality GEOTAIL Magnetospheric mission (spacecraft) GOES Geostationary Orbiting Earth Satellite (spacecraft) GRANAT Gamma Ray Astronomical observatory (Russian spacecraft) HSP High Speed Photometer (instrument on HST) HST Hubble Space Telescope HXR Hard X-Rays HXRBS Hard X-Ray Burst Spectrometer (on SMM) ICE International Cometary Explorer (spacecraft) IMAGE Magnetospheric spacecraft IMF Interplanetary Magnetic Field IMP Interplanetary Monitoring Platform (spacecraft) ISEE-3 International Cometary Explorer (spacecraft) ISSI International Space Science Institute, Bern, Switzerland IT Intermittent Turbulence keV Kilo electron Volt LA Linear size vs. Area method (fractal dimension) LASCO Large-Angle Solar COronagraph (on SOHO) LIM Local Intermittency Measure (method) MHD Magneto-HydroDynamics MeV Mega electron Volt MG Magnetogram MK Mega Kelvin MW Microwave Burst MW-S Microwave Burst Synchrotron emission 50 M.J. Aschwanden et al. NASA National Aeronautics and Space Administration NOAA National Oceanic and Atmospheric Administration OFC Olami–Feder–Christensen (SOC model) OGO Orbiting Geophysical Observatory (spacecraft) OSO Orbiting Solar Observatory (spacecraft) PA Perimeter versus Area (fractal dimension) PDF Probability Distribution Function PHEBUS Gamma ray burst instrument (on GRANAT) POLAR Magnetospheric mission (spacecraft) PSR Pulsar RHESSI Ramaty High Energy Solar Spectroscopic Imager (spacecraft) RTV Rosner–Tucker–Vaiana model (coronal heating) RXTE Rossi X-ray Timing Explorer (spacecraft) SDF Surviving Distribution Function SGR Soft Gamma-ray Repeaters SDO Solar Dynamics Observatory (spacecraft) SEP Solar Energetic Particle event SMM Solar Maximum Mission (spacecraft) SOBP Self-Organized Branching Process SOC Self-Organized Criticality SOHO SOlar and Heliospheric Observatory (spacecraft) SST Swedish Solar Telescope (observatory) STEREO Sun TErrestrial RElations Observatory (spacecraft) SuperDARN Super Dual Auroral Radar Network SXR Soft X-Rays SXT Soft X-ray Telescope (on Yohkoh spacecraft) TGF Terrestrial Gamma-ray Flashes TRACE TRAnsition region and Coronal Explorer (spacecraft) TV TeleVision (camera) UCB University of California, Berkeley ULYSSES Interplanetary mission (spacecraft) UV Ultra-Violet UVI Ultra-Violet Image (on POLAR spacecraft) WATCH Wide Angle Telescope of Cosmic Hard X-rays (on GRANAT) XMM X-ray Multi-Mirror mission (spacecraft) WIC Wideband Imaging Camera (on IMAGE spacecraft) WL White Light WMAP Wilkinson Microwave Anisotropy Probe (spacecraft) WTD Waiting Time Distribution function Yohkoh Japanese Solar-A mission (spacecraft) Contents 1 Introduction ....................................... 52 2 Basics of Self-Organized Criticality Systems ..................... 54 2.1SOCDefinitions.................................. 54 2.2TheDriver..................................... 55 2.3 Instability and Criticality . ........................... 56 25 Years of Self-Organized Criticality: Solar and Astrophysics 51 2.4Avalanches..................................... 56 2.5MicroscopicStructureandComplexity..................... 57 2.6 The Scale-Free Probability Conjecture ..................... 58 2.7GeometricScalingLaws............................. 59 2.8FractalGeometry................................. 60 2.9Spatio-TemporalEvolutionandTransportProcess............... 61 2.10FluxandEnergyScaling............................. 62 2.11CoherentandIncoherentRadiation....................... 65 2.12 Waiting Times and Memory ........................... 66 2.12.1StationaryPoissonProcesses....................... 66 2.12.2Non-stationaryPoissonProcesses.................... 67 2.12.3 Waiting Time Probabilities in the Fractal-Diffusive SOC Model . 69 2.12.4WeibullDistributionandProcesseswithMemory........... 70 2.13TheSeparationofTimeScales.......................... 72 2.14CellularAutomatonModels........................... 73 3AstrophysicalApplications............................... 75 3.1SolarPhysics:Observations........................... 76 3.1.1StatisticsofSolarFlareHardX-Rays.................
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