Power Laws in Solar Flares: Self-Organized Criticality or Turbulence?

Abstract

We study the time evolution of Solar Flares activity by looking at the statistics of quiescent times ${\tau }_L$ between successive bursts. The analysis of 20 years of data reveals a power law distribution with exponent $\alpha \simeq 2.4$ which is an indication of complex dynamics with long correlation times. The observed scaling behavior is in contradiction with the Self-Organized Criticality models of Solar Flares which predict Poisson-like statistics. Chaotic models, including the destabilization of the laminar phases and subsequent restabilization due to nonlinear dynamics, are able to reproduce the power law for the quiescent times. In the case of the more realistic Shell Model of MHD turbulence we are able to reproduce all the observed distributions.

4 pages, 4 postscript figures. Submitted to Physical Review Letters

Cited by in corpus (110)

• Grand minima and maxima of solar activity: New observational constraints
• Cascades and transitions in turbulent flows
• Power laws and Self-Organized Criticality in Theory and Nature
• 25 Years of Self-Organized Criticality: Solar and Astrophysics
• 25 Years of Self-Organized Criticality: Concepts and Controversies
• The Origin of the Solar Flare Waiting-Time Distribution
• Recurrence time analysis, long-term correlations, and extreme events
• Universality in solar flare and earthquake occurrence
• Power-law size distributions in geoscience revisited
• Inter-occurrence Times in the Bak-Tang-Wiesenfeld Sandpile Model: A Comparison with the Turbulent Statistics of Solar Flares
• Intensity Thresholds and the Statistics of the Temporal Occurrence of Solar Flares
• Flare Heating in Stellar Coronae
• q-exponential, Weibull, and q-Weibull distributions: an empirical analysis
• Solar Flares as Cascades of Reconnecting Magnetic Loops
• Structures in magnetohydrodynamic turbulence: detection and scaling
• Reconciliation of Waiting Time Statistics of Solar Flares Observed in Hard X-Rays
• City Size Distributions For India and China
• q-Exponential Distribution in Urban Agglomeration
• Solar Flare Intermittency and the Earth's Temperature Anomalies
• Coexistence of Self-Organized Criticality and Intermittent Turbulence in the Solar Corona
• Shell-models of RMHD turbulence and the heating of solar coronal loops
• Diffusion entropy and waiting time statistics of hard x-ray solar flares
• Threshold driven contagion on weighted networks
• Power law burst and inter-burst interval distributions in the solar wind: turbulence or dissipative SOC ?
• The coronal mass ejection waiting-time distribution
• A Goldilocks principle for modeling radial velocity noise
• 1/f noise from correlations between avalanches in self-organized criticality
• Statistical Modeling of Solar Flare Activity from Empirical Time Series of Soft X-ray Solar Emission
• Scaling and correlations in the dynamics of forest-fire occurrence
• Clustering of Intermittent Magnetic and Flow Structures near Parker Solar Probe's First Perihelion -- A Partial-Variance-of-Increments Analysis
• The clustering of polarity reversals of the geomagnetic field
• Avalanching and Self Organised Criticality, a paradigm for geomagnetic activity?
• Regularities in football goal distributions
• To what extent can dynamical models describe statistical features of turbulent flows?
• 25 Years of Self-Organized Criticality: Numerical Detection Methods
• Scaling and singularity characteristics of solar wind and magnetospheric fluctuations
• Scaling in the Timing of Extreme Events
• Self-Organized Criticality and Stock Market Dynamics: an Empirical Study
• A common stochastic process rules gamma-ray burst prompt emission and X-ray flares
• Temporal Intermittency of Energy Dissipation in Magnetohydrodynamic Turbulence
• Data-Driven Prediction of Thresholded Time Series of Rainfall and SOC models
• Memory in Self Organized Criticality
• The Energetics of a Flaring Solar Active Region, and Observed Flare Statistics
• Turbulent self-organized criticality
• Evidence for departure from a power-law flare size distribution for a small solar active region
• A simplified numerical model of coronal energy dissipation based on reduced MHD
• Universal Scaling Laws for Solar and Stellar Atmospheric Heating
• Modeling a coronal loop heated by MHD-turbulence nanoflares
• A new catalogue of solar flare events from soft x-ray GOES signal in the period 1986-2020
• Power-law distributions and fluctuation-dissipation relation in the stochastic dynamics of two-variable Langevin equations
• Solar Flare Index Prediction Using SDO/HMI Vector Magnetic Data Products with Statistical and Machine Learning Methods
• A Self-Organized-Criticality model consistent with statistical properties of edge turbulence in a fusion plasma
• Temporal Analysis of Dissipative Structures in Magnetohydrodynamic Turbulence
• Rain, power laws, and advection
• Testing the SOC hypothesis for the magnetosphere
• Influence of the definition of dissipative events on their statistics
• Scale-free avalanche dynamics in the stock market
• Multiscale self-organized criticality and powerful X-ray flares
• Principle of Minimum Energy in Magnetic Reconnection in a Self-Organized Critical Model for Solar Flares
• Persistent dynamic correlations in self-organized critical systems away from their critical point
• Kramers escape rate in overdamped systems with the power-law distribution
• The viscosity of charged particles in the weakly ionized plasma with power-law distributions
• Distribution of Return Intervals of Extreme Events
• The Effect of Limited Sample Sizes on the Accuracy of the Estimated Scaling Parameter for Power-Law-Distributed Solar Data
• Universal Scaling Laws for Large Events in Driven Nonequilibrium Systems
• Energy Balance in Avalanche Models for Solar Flares
• Modelling the influence of photospheric turbulence on solar flare statistics
• The Poissonian Origin of Power Laws in Solar Flare Waiting Time Distributions
• Fluctuating landscapes and heavy tails in animal behavior
• Time-energy correlations in solar flare occurrence
• The Solar Memory From Hours to Decades
• Identification of criticality in neuronal avalanches: II. A theoretical and empirical investigation of the driven case
• Scale-free vortex cascade emerging from random forcing in a strongly coupled system
• Realistic time correlations in sandpiles
• Monte-Carlo Simulation of Solar Active-Region Energy
• Are power-law distributions an equilibrium distribution or a stationary nonequilibrium distribution?
• Correlation of the sunspot number and the waiting time distribution of solar flares, coronal mass ejections, and solar wind switchback events observed with the Parker Solar Probe
• The mean first passage time in an energy-diffusion controlled regime with power-law distributions
• Statistical Models for Solar Flare Interval Distribution in Individual Active Regions
• Macroscopic control parameter for avalanche models for bursty transport
• Escape rate for the power-law distribution in low-to-intermediate damping
• Effect of magnetic field on viscosity in the weakly ionized and magnetized plasma with power-law q-distributions in nonextensive statiostics
• Quiet Sun coronal heating: statistical model
• Apparent universality of $1/f$ spectra as an artifact of finite-size effects
• Power-law behaviors from the two-variable Langevin equation: Ito's and Stratonovich's Fokker-Planck equations
• Solar Flare Occurrence Rate and Waiting Time Statistics
• Self Similar Properties of Avalanche Statistics in a Simple Turbulent Model
• Scaling and Universality in the Temporal Occurrence of Repeating FRBs
• Evolving Powergrids in Self-Organized Criticality: An analogy with Sandpile and Earthquakes
• Inducing Self-Organized Criticality in a network toy model by neighborhood assortativity
• The current density and transport coefficients in the fully ionized plasma with q-distributions in nonextensive statistics
• What can we infer about the underlying physics from burst distributions observed in an RMHD simulation ?
• Long-time behavior of MHD shell models
• Fractal dimensions of umbral and penumbral regions of sunspots
• Underestimating extreme events in power-law behavior due to machine-dependent cutoffs
• Correlated flares in models of a magnetized "canopy"
• Statistical Study of Short Quiescent Times Between Flares
• Evolution of Zipf's Law for Indian Urban Agglomerations vis-à-vis Chinese Urban Agglomerations
• Role of the Solar Minimum in the Waiting Time Distribution Throughout the Heliosphere
• Time-dependent Stochastic Modeling of Solar Active Region Energy
• Avalanches impede synchronization of jammed oscillators
• Scale-free avalanches in the multifractal random walk
• A statistical search for a uniform trigger threshold in solar flares from individual active regions
• Model for the spatio-temporal intermittency of the energy dissipation in turbulent flows
• A stochastic theory for temporal fluctuations in self-organized critical systems
• Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations
• Analysis of music: controlled random music and probability distribution function of recurrence time of amplitude peaks
• Statistics of Extreme Values in Time Series with Intermediate-Term Correlations
• Quantification of Sleep Fragmentation Through the Analysis of Sleep-Stage Transitions
• A Self-Organized Model for the Flicker Noise in Interacting Two-Dimensional Electron Gas