The Solar Memory From Hours to Decades

Abstract

Waiting time distributions allow us to distinguish at least three different types of dynamical systems, such as (i) linear random processes (with no memory); (ii) nonlinear, avalanche-type, nonstationary Poisson processes (with memory during the exponential growth of the avalanche rise time); and (iii) chaotic systems in the state of a nonlinear limit cycle (with memory during the oscillatory phase). We describe the temporal evolution of the flare rate $\lambda (t)\propto t^p$ with a polynomial function, which allows us to distinguish linear ($p\approx 1$) from nonlinear ($p \gapprox 2$) events. The power law slopes $\alpha$ of observed waiting times (with full solar cycle coverage) cover a range of $\alpha =2.1-2.4$, which agrees well with our prediction of $\alpha =2.0+1/p=2.3-2.5$. The memory time can also be defined with the time evolution of the logistic equation, for which we find a relationship between the nonlinear growth time ${\tau }_G={\tau }_{rise}/(4p)$ and the nonlinearity index $p$. We find a nonlinear evolution for most events, in particular for the clustering of solar flares ($p=2.2\pm 0.1$), partially occulted flare events ($p=1.8\pm 0.2$), and the solar dynamo ($p=2.8\pm 0.5$). The Sun exhibits memory on time scales of $\lapprox$2 hours to 3 days (for solar flare clustering), 6 to 23 days (for partially occulted flare events), and 1.5 month to 1 year (for the rise time of the solar dynamo).

arXiv comment11 pages, 1 Table, 5 Figures

References in corpus (32)

• Power laws, Pareto distributions and Zipf's law
• Problems with Fitting to the Power-Law Distribution
• Grand minima and maxima of solar activity: New observational constraints
• Kepler Flares I. Active and Inactive M dwarfs
• Power Laws in Solar Flares: Self-Organized Criticality or Turbulence?
• 25 Years of Self-Organized Criticality: Solar and Astrophysics
• Switchbacks in the near-Sun magnetic field: long memory and impact on the turbulence cascade
• The Origin of the Solar Flare Waiting-Time Distribution
• Parameter estimation for power-law distributions by maximum likelihood methods
• Automated Solar Flare Statistics in Soft X-rays over 37 Years of GOES Observations - The Invariance of Self-Organized Criticality during Three Solar Cycles
• Comprehensive study of the X-ray flares from gamma-ray bursts observed by Swift
• A Statistical Fractal-Diffusive Avalanche Model of a Slowly-Driven Self-Organized Criticality System
• Reconciliation of Waiting Time Statistics of Solar Flares Observed in Hard X-Rays
• Diffusion entropy and waiting time statistics of hard x-ray solar flares
• Understanding solar cycle variability
• The coronal mass ejection waiting-time distribution
• Turbulence characteristics of switchbacks and non-switchbacks intervals observed by \emph{Parker Solar Probe}
• A common stochastic process rules gamma-ray burst prompt emission and X-ray flares
• Self-Organized Criticality in Solar and Stellar Flares: Are Extreme Events Scale-Free ?
• Universal Behavior of X-ray Flares from Black Hole Systems
• On the Brightness and Waiting-time Distributions of a Type III Radio Storm observed by STEREO/WAVES
• Waiting Times of Quasi-homologous Coronal Mass Ejections from Super Active Regions
• Cosmic-Ray Interactions in the Solar Atmosphere
• The Spatio-Temporal Evolution of Solar Flares Observed with AIA/SDO: Fractal Diffusion, Sub-Diffusion, or Logistic Growth ?
• Self-organized criticality in type I X-ray bursts
• Waiting time distribution of solar energetic particle events modeled with a non-stationary Poisson process
• A Model of Sunspot Number with Modified Logistic Function
• 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
• Non-Stationary Fast-Driven Self-Organized Criticality in Solar Flares
• Solar Flare Occurrence Rate and Waiting Time Statistics
• Role of the Solar Minimum in the Waiting Time Distribution Throughout the Heliosphere
• Departure from Gaussian: The Waiting time Statistics of X-Ray Solar Flares