Diffusion entropy and waiting time statistics of hard x-ray solar flares

Abstract

We analyze the waiting time distribution of time distances $\tau$ between two nearest-neighbor flares. This analysis is based on the joint use of two distinct techniques. The first is the direct evaluation of the distribution function $\psi (\tau )$, or of the probability, $\Psi (tau)$, that no time distance smaller than a given $\tau$ is found. We adopt the paradigm of the inverse power law behavior, and we focus on the determination of the inverse power index $\mu$, without ruling out different asymptotic properties that might be revealed, at larger scales, with the help of richer statistics. The second technique, called Diffusion Entropy (DE) method, rests on the evaluation of the entropy of the diffusion process generated by the time series. The details of the diffusion process depend on three different walking rules, which determine the form and the time duration of the transition to the scaling regime, as well as the scaling parameter $\delta$. With the first two rules the information contained in the time series is transmitted, to a great extent, to the transition, as well as to the scaling regime. The same information is essentially conveyed, by using the third rules, into the scaling regime, which, in fact, emerges very quickly after a fast transition process. We show that the significant information hidden within the time series concerns memory induced by the solar cycle, as well as the power index $\mu$. The scaling parameter $\delta$ becomes a simple function of $\mu$, when memory is annihilated. Thus, the three walking rules yield a unique and precise value of $\mu$ if the memory is wisely taken under control, or cancelled by shuffling the data. All this makes compelling the conclusion that $\mu =2.138\pm 0.01$.

23 pages, 13 figures

References in corpus (1)

• Effect of Trends on Detrended Fluctuation Analysis

Cited by in corpus (26)

• 25 Years of Self-Organized Criticality: Solar and Astrophysics
• Scaling detection in time series: diffusion entropy analysis
• 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
• Reconciliation of Waiting Time Statistics of Solar Flares Observed in Hard X-Rays
• Solar Flare Intermittency and the Earth's Temperature Anomalies
• Multi-Scaling Comparative Analysis of Time Series and a Discussion on "Earthquake Conversations" in California
• Compression and diffusion: a joint approach to detect complexity
• A Trade-Investment Model for Distribution of Wealth
• Temporal Series Analysis Approach to Spectra of Complex Networks
• Diffusion entropy analysis on the scaling behavior of financial markets
• Scaling Behavior of the Portevin-Le Chatelier Effect in an Al-2.5%Mg Alloy
• Evaluation of Scale-Invariance In Physiological Signals By Means Of Balanced Estimation Of Diffusion Entropy
• Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion
• The Spatio-Temporal Evolution of Solar Flares Observed with AIA/SDO: Fractal Diffusion, Sub-Diffusion, or Logistic Growth ?
• Lévy statistics in coding and non-coding nucleotide sequences
• Diffusion entropy analysis on the stride interval fluctuation of human gait
• Is there long-range memory in solar activity on time scales shorter than the sunspot period?
• The Solar Memory From Hours to Decades
• Scaling in Non-stationary time series I
• Scaling Analysis on Indian Foreign Exchange Market
• Vortex dynamics in evolutive flows: a weakly chaotic phenomenon
• 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
• Correlation regimes in fluctuations of fatigue crack growth
• Scaling Behaviour and Complexity of the Portevin-Le Chatelier Effect
• A study of Complexity in Gamma Ray Burst using the Diffusion Entropy Approach