Waiting time distribution of solar flares from a global perspective

Abstract

The waiting time statistics of solar flares provides clues for the underlying physical mechanisms. However, flares occurring on the far-side have been missing in the statistics. In the 2024 May and June, the Solar Orbiter (SolO) spacecraft orbiting behind the Sun, together with near-Earth spacecrafts, provides a unique opportunity to study one of the most flare-productive active regions, NOAA \sar, over its lifetime, as well as the flare occurrence over the entire solar globe. Derived from time intervals between flare peak times, the waiting time distribution (WTD) is fitted by exponential, log-normal, power-law, and \levy functions with the maximum likelihood estimation method. The goodness of fit is evaluated by the Kolmogorov-Smirnov test, and the statistical models are discriminated by information criteria. The major statistical results are: the WTD of flares in the \sar leans towards the log-normal function, while that in the `normal' \rar towards the \levy function; the WTD of global flares defies the local Poisson hypothesis, and its overall profile cannot be reasonably fitted by any of the four candidate distributions, but its power-law tail $Δt^{-α}$ is steeper ($α>3$) than the theoretical expectations ($α\le3$), due to the decreased number of long waiting times ($>10^4$ s) and the increased number of shorter waiting times when the far-side flares are taken into account. These results highlight the importance of studying the flare WTD from a global perspective, and suggest that the long-range magnetic connections in the corona may play a role in the flare occurrences.

Figures (3)

• Figure 1: Overview of global flares occurring during the SAR 13664/13697 lifetime. Panels (a) and (b) shows the flare magnitude and count number of flares on a daily basis with flares within (outside) SAR 13664/13697 in pink (black) colors. The light-blue and light-orange shades indicate the time interval during which SAR 13664/13697 was on the near-side (observed by GOES) and far-side of the Sun (observed by STIX), respectively. The blue dashed curve plots the percentage of the global area covered by the joint perspective of GOES and SolO. The fraction number on the top of bars in (b) gives the daily percentage of SAR 13664/13697 flares over all the flares. The inset illustrates in the ecliptic plane the relative positions of the Sun (orange), Earth (blue) and SolO (purple) as well as its trajectory during the SAR 13664/13697 lifetime. Panels (c) and (d) show the spatial distribution of flares occurred during the Carrington rotation 2284 (2024 May 6--June 2) and 2285 (June 2--29), respectively. The 'o' ('x') symbol marks flares within (outside) SAR 13664/13697. The flare magnitude is color-coded, from strong (purple) to weak (red). The yellow (blue) box marks the range of SAR 13664/13697 (AR 13679/13711).
• Figure 2: WTDs of flares within individual ARs. Panels (a & b) show the WTD of flares within SAR 13664/13697; the tail portion is fitted in (a) and the overall profile in (b). The vertical dashed line indicating $x_{\min}$ as determined by minimizing the KS distance for power-law. The $p$-values of the KS tests are shown with subscripts 'l', 'e', 'p'/'mp', and 'v', indicating log-normal (pink), exponential (green), power-law (gold), and Lévy (blue) functions, respectively. (c & d) show the WTD of flares within AR 13679/13711 in the same style as (a & b).
• Figure 3: WTDs of global flares. The format is the same as Figure \ref{['F-local']}. For the WTD in the same row, left (right) panel shows the fitting of the tail portion (overall profile). In the left column, the corresponding WTD of near-side flares observed by GOES is shown in gray; its tail, starting from the same $x_{\min}$ as that of the global WTD, is fitted by power law, and the resultant $p$-value and power-law index are annotated.