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

Abstract

Waiting time distributions of solar flares and {\sl coronal mass ejections (CMEs)} exhibit power law-like distribution functions with slopes in the range of ${\alpha }_{\tau }\approx 1.4-3.2$, as observed in annual data sets during 4 solar cycles (1974-2012). We find a close correlation between the waiting time power law slope ${\alpha }_{\tau }$ and the {\sl sunspot number (SN)}, i.e., ${\alpha }_{\tau }$ = 1.38 + 0.01 $\times$ SN. The waiting time distribution can be fitted with a Pareto-type function of the form $N(\tau )=N_0$ $({\tau }_0+\tau {)}^{-{\alpha }_{\tau }}$, where the offset ${\tau }_0$ depends on the instrumental sensitivity, the detection threshold of events, and pulse pile-up effects. The time-dependent power law slope ${\alpha }_{\tau }(t)$ of waiting time distributions depends only on the global solar magnetic flux (quantified by the sunspot number) or flaring rate, independent of other physical parameters of {\sl self-organized criticality (SOC)} or {\sl magneto-hydrodynamic (MHD)} turbulence models. Power law slopes of ${\alpha }_{\tau }\approx 1.2-1.6$ were also found in solar wind switchback events, as observed with the {\sl Parker Solar Probe (PSP)}. We conclude that the annual variability of switchback events in the heliospheric solar wind is modulated by flare and CME rates originating in the photosphere and lower corona.

arXiv comment12 pages, 8 figures

References in corpus (19)

• 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
• Automated Solar Flare Statistics in Soft X-rays over 37 Years of GOES Observations - The Invariance of Self-Organized Criticality during Three Solar Cycles
• Magnetic field kinks and folds in the solar wind
• 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
• A Macroscopic Description of a Generalized Self-Organized Criticality System: Astrophysical Applications
• Diffusion entropy and waiting time statistics of hard x-ray solar flares
• Thresholded Power Law Size Distributions of Instabilities in Astrophysics
• The coronal mass ejection waiting-time distribution
• Self-Organized Criticality in Stellar Flares
• The State of Self-Organized Criticality of the Sun During the Last 3 Solar Cycles. I. Observations
• Simulated Encounters of Parker Solar Probe with A Coronal-Hole Jet
• Self-Organized Criticality in Solar and Stellar Flares: Are Extreme Events Scale-Free ?
• Multiscale dynamics of solar magnetic structures
• Global Energetics of Solar Flares. XII. Energy Scaling Laws
• Non-Stationary Fast-Driven Self-Organized Criticality in Solar Flares

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• Scaling and Universality in the Temporal Occurrence of Repeating FRBs
• Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations