Information Theoretical Approach to Understanding Flare Waiting Times

• Published in: The Astrophysical journal 2020-08, Vol.899 (2), p.148
• Main Authors: Snelling, Jesse M., Johnson, Jay R., Willard, Jake, Nurhan, Yosia, Homan, Jonathan, Wing, Simon
• Format: Article
• Language: English
• Subjects: Astrophysics; Entropy (Information theory); GOES satellites; Poisson density functions; Poisson distribution; Solar activity; Solar cycle; Solar flares; Windows (intervals)
• ISSN: 0004-637X; 1538-4357
• DOI: 10.3847/1538-4357/aba7b9

There is not currently a consensus on the process responsible for producing the waiting time distribution of solar flares. This study presents an information theoretical approach to determining whether solar flare data are significantly distinguishable from a nonstationary Poisson process. A study of solar flares stronger than C1 class detected by the Geostationary Operational Environmental Satellite from 1975 to 2017 was performed. A sequence of waiting times (time elapsed between adjacent X-ray flare peaks) was constructed from the data. Surrogate waiting time sequences were produced using a time-varying Poisson firing rate from the Bayesian block procedure. Utilizing Shannon entropy, the mutual information of time-lagged waiting time distributions was computed for both the original data and the surrogates using a method of discretization by binning. When the entire period is considered, we see that when compared to carefully constructed surrogates, there is a significant elevation of mutual information on a timescale of approximately 30 hr, demonstrating that flares are confidently related to subsequent flares, contradicting the null hypothesis that flares are produced by a nonstationary Poisson process. When only 4 yr subsets of the data are considered, we see that at relatively small timescales (on the order of 10-30 hr), solar flare waiting times have a significant impact on subsequent flares. When corrected for the number of points in each considered time window, there is no correlation between the magnitude of significance and position in the solar cycle.