Avalanche models for solar flares (Invited Review)

This paper is a pedagogical introduction to avalanche models of solar flares, including a comprehensive review of recent modeling efforts and directions. This class of flare model is built on a recent paradigm in statistical physics, known as self-organized criticality. The basic idea is that flares are the result of an ‘avalanche’ of small-scale magnetic reconnection events cascading through a highly stressed coronal magnetic structure, driven to a critical state by random photospheric motions of its magnetic footpoints. Such models thus provide a natural and convenient computational framework to examine Parker's hypothesis of coronal heating by nanoflares.

[1]  Loukas Vlahos,et al.  Coronal Heating by Nanoflares and the Variability of the Occurrence Frequency in Solar Flares , 1996 .

[2]  E. Lu.  The Statistical Physics of Solar Active Regions and the Fundamental Nature of Solar Flares , 1995 .

[3]  Loukas Vlahos,et al.  Derivation of Solar Flare Cellular Automata Models from a Subset of the Magnetohydrodynamic Equations , 1998 .

[4]  George Sugihara,et al.  Fractals: A User's Guide for the Natural Sciences , 1993 .

[5]  Sam Krucker,et al.  Are Heating Events in the Quiet Solar Corona Small Flares? Multiwavelength Observations of Individual Events , 2000 .

[6]  Guido Boffetta,et al.  Power Laws in Solar Flares: Self-Organized Criticality or Turbulence? , 1999, chao-dyn/9904043.

[7]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[8]  Hsueh-Chia Chang,et al.  Traveling waves on fluid interfaces: Normal form analysis of the Kuramoto–Sivashinsky equation , 1986 .

[9]  Turbulent Coronal Heating and the Distribution of Nanoflares , 1997, astro-ph/9705050.

[10]  Säm Krucker,et al.  Energy Distribution of Heating Processes in the Quiet Solar Corona , 1998 .

[11]  Drossel,et al.  Self-organized critical forest-fire model. , 1992, Physical review letters.

[12]  Y. Chou.  The Effect of Helicity Dissipation on the Critical State of an Avalanche Model for Solar Flares , 2001 .

[13]  R. Rosner,et al.  Erratum: Cosmic Flare Transients: Constraints upon Models for Energy Storage and Release Derived from the Event Frequency Distribution , 1978 .

[14]  Harry P. Warren,et al.  Time Variability of the “Quiet” Sun Observed with TRACE. II. Physical Parameters, Temperature Evolution, and Energetics of Extreme-Ultraviolet Nanoflares , 2000 .

[15]  Y. Chou,et al.  What Affects the Power-Law Distribution of the X-Ray Solar Flares? A Theoretical Study Based on a Model of Uniform Normal Field , 1999 .

[16]  Axel Brandeburg.  Spontaneous current sheets in magnetic fields (with applications to stellar x-rays) , 1996 .

[17]  E. Parker.  Nanoflares and the solar X-ray corona , 1988 .

[18]  Solar Flare Statistics with a One-Dimensional Mhd Model , 1998 .

[19]  Flare Frequency-Size Distributions for Individual Active Regions , 2000 .

[20]  Karen L. Harvey,et al.  Microflares in the solar magnetic network , 1987 .

[21]  M. Shimojo,et al.  Occurrence Rate of Microflares in an X-Ray-bright Point within an Active Region , 1999 .

[22]  D. Sornette.  Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools , 2000 .

[23]  M. Velli,et al.  The distribution of flares, statistics of magnetohydrodynamic turbulence and coronal heating , 1999 .

[24]  Willi-Hans Steeb,et al.  The Nonlinear Workbook , 2005 .

[25]  D. Turcotte,et al.  Self-organized criticality , 1999 .

[26]  R. Osten,et al.  Extreme Ultraviolet Explorer Photometry of RS Canum Venaticorum Systems: Four Flaring Megaseconds , 1999 .

[27]  Sidney R. Nagel,et al.  Instabilities in a sandpile , 1992 .

[28]  A. V. Ballegooijen,et al.  Cascade of magnetic energy as a mechanism of coronal heating , 1985 .

[29]  R. Sudan,et al.  Evolution and Statistics of Current Sheets in Coronal Magnetic Loops , 1994 .

[30]  Manolis K. Georgoulis,et al.  A comparison between statistical properties of solar X-ray flares and avalanche predictions in cellular automata statistical flare models , 2001 .

[31]  C. J. Wolfson,et al.  Time Variability of the “Quiet” Sun Observed with TRACE. I. Instrumental Effects, Event Detection, and Discrimination of Extreme-Ultraviolet Microflares , 2000 .

[32]  V. Kashyap,et al.  Extreme-Ultraviolet Flare Activity in Late-Type Stars , 2000 .

[33]  Wu,et al.  Scaling and universality in avalanches. , 1989, Physical review. A, General physics.

[34]  Y. Litvinenko.  A new model for the distribution of flare energies , 1996 .

[35]  J. McTiernan,et al.  Statistical Studies of ISEE 3/ICE Observations of Impulsive Hard X-Ray Solar Flares , 1995 .

[36]  E. N. Parker,et al.  Magnetic Neutral Sheets in Evolving Fields - Part Two - Formation of the Solar Corona , 1983 .

[37]  E. Noonan,et al.  Self-organized Criticality from Separator Reconnection in Solar Flares , 2000 .

[38]  H. Isliker,et al.  Astronomy & Astrophysics Hi 21 Cm Absorption in Low Z Damped Lyman-α Systems , 2001 .

[39]  A. Benz,et al.  A nanoflare heating model for the quiet solar corona , 2001, astro-ph/0104218.

[40]  Lu.  Avalanches in continuum driven dissipative systems. , 1995, Physical review letters.

[41]  Inversion of Thick-Target Bremsstrahlung Spectra from Nonuniformly Ionised Plasmas , 1998 .

[42]  Bai-Lian Li,et al.  Self-Organized Criticality , 2001 .

[43]  Vincenzo Carbone,et al.  Solar Flare Waiting Time Distribution: Varying-Rate Poisson or Lévy Function? , 2001 .

[44]  M. Wheatland.  DO SOLAR FLARES EXHIBIT AN INTERVAL–SIZE RELATIONSHIP? , 2000 .

[45]  M. Velli,et al.  Statistical Properties of Magnetic Activity in the Solar Corona , 1998 .

[46]  N. Shakhovskaya.  Stellar flare statistics — Physical consequences , 1989 .

[47]  J. M. McTiernan,et al.  The Waiting-Time Distribution of Solar Flare Hard X-Ray Bursts , 1998 .

[48]  William H. Press,et al.  Numerical recipes in C (2nd ed.): the art of scientific computing , 1992 .

[49]  E. Lu,et al.  Avalanches and the Distribution of Solar Flares , 1991 .

[50]  J. McTiernan,et al.  The Distribution of Flare Parameters and Implications for Coronal Heating , 1993 .

[51]  R. Kulsrud,et al.  Magnetic reconnection in a magnetohydrodynamic plasma , 1998 .

[52]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[53]  J. Zirker,et al.  Avalanche models of active region heating and flaring , 1993 .

[54]  James M. McTiernan,et al.  Solar flares and avalanches in driven dissipative systems , 1993 .

[55]  S. Galtier.  A One-dimensional Magnetohydrodynamic Model of Solar Flares: Emergence of a Population of Weak Events, and a Possible Road toward Nanoflares , 1999 .

[56]  D. Schnack,et al.  Creation of current filaments in the solar corona , 1989 .

[57]  J. Drake.  Characteristics of soft solar X-ray bursts , 1971 .

[58]  M. Wheatland,et al.  To appear in the Astrophysical Journal Letters THE ORIGIN OF THE SOLAR FLARE WAITING-TIME DISTRIBUTION , 2000 .

[59]  E. Lu.  Constraints on Energy Storage and Release Models for Astrophysical Transients and Solar Flares , 1995 .

[60]  Scott W. McIntosh,et al.  Waiting-Time Distributions in Lattice Models of Solar Flares , 2001 .

[61]  J. Duran,et al.  Sands, Powders, and Grains , 2000 .

[62]  P. Jupp,et al.  Statistical Analysis of the Energy Distribution of Nanoflares in the Quiet Sun , 2000 .

[63]  H. Hudson,et al.  OSO-7 observations of solar x-rays in the energy range 10–100 keV , 1974 .

[64]  Brian R. Dennis,et al.  Frequency distributions and correlations of solar X-ray flare parameters , 1993 .

[65]  K. Mellanby.  How Nature works , 1978, Nature.

[66]  Brian R. Dennis,et al.  Logistic Avalanche Processes, Elementary Time Structures, and Frequency Distributions in Solar Flares , 1998 .

[67]  M. Velli,et al.  Energy Release in a Turbulent Corona , 1996 .

[68]  William H. Press,et al.  Numerical recipes , 1990 .

[69]  Klaus Galsgaard,et al.  Heating and activity of the solar corona: 1. Boundary shearing of an initially homogeneous magnetic field , 1996 .

[70]  George L. Withbroe,et al.  Mass and Energy Flow in the Solar Chromosphere and Corona , 1977 .

[71]  C. Mercier,et al.  Coronal Radio Bursts: A Signature of Nanoflares? , 1997 .