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).

11 pages, 1 Table, 5 Figures

References in corpus (13)

• Kepler Flares I. Active and Inactive M dwarfs
• 25 Years of Self-Organized Criticality: Solar and Astrophysics
• Switchbacks in the near-Sun magnetic field: long memory and impact on the turbulence cascade
• 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
• Understanding solar cycle variability
• A common stochastic process rules gamma-ray burst prompt emission and X-ray flares
• Universal Behavior of X-ray Flares from Black Hole Systems
• Cosmic-Ray Interactions in the Solar Atmosphere
• Self-organized criticality in type I X-ray bursts
• Waiting time distribution of solar energetic particle events modeled with a non-stationary Poisson process
• 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
• Role of the Solar Minimum in the Waiting Time Distribution Throughout the Heliosphere