Statistical Analysis of Solar Flare Properties from 1975 to 2017

Introduction: Solar flares are among the most powerful manifestations of magnetic activity, characterized by sudden, violent eruptions in the solar atmosphere, ranging from 10¹⁹ erg in nanoflares up to 10³² erg in large two-ribbon flares. Since their first detection (Peterson and Winckler, 1959), a significant body of data have been collected, thanks to the advent of spacecraft observations of solar flares (e.g. OSO 7, Explorer, SMM, GRANAT, ICE/ISEE 3, GOES). The latter enabled detailed statistical investigations of flare properties and underlying physical mechanisms (e.g., Temmer et al. 2001; Veronig et al. 2002; Lee et al. 2012; Joshi et al. 2015).

This work presents a comprehensive statistical analysis of the size and temporal characteristics of soft X-ray (SXR) flares across four solar cycles (SC21–SC24), covering the period from September 1975 to June 2017. More in detail, we investigate the distribution characteristics of solar flares, shedding light on their statistical properties and their relationship with the solar activity. Our analysis provides valuable insights into the distribution patterns, offers estimates for the occurrence of intense solar flare events, and proposes a monitoring framework.

Results: Flare data were obtained from the GOES satellite archive, using the 1–8 Å flux channel to identify start, peak, and end times.

We first explore the relationship between flare occurrence rates and solar activity. Temporal properties (duration, waiting time) and energetic properties (peak flux) are analyzed through their frequency distributions. Results indicate a clear correlation between flare duration and peak intensity with the level of solar activity, while waiting time appears largely uncorrelated.

Additionally, we investigate correlations among these parameters, confirming that flare duration increases with flare importance class. Notably, the distribution of durations for X-class flares reveals a secondary peak at ∼100 minutes for SC21 and SC22 and ∼80 minutes for SC23 and SC24 (Figure 1), referring to extremely long duration events (LDE).

Figure 1. Probability density functions (PDFs) of the observed flare duration data, during SC23 and SC24, compared with fitted unimodal and bimodal distribution models. The red solid line represents the fitted bimodal Gaussian mixture model.

Finally, we assess time–energy correlations in flare sequences to test the hypothesis, proposed by Rosner and Vaiana (1978), that energy builds up progressively prior to major events. Analyzing precursor flares from the same active region preceding X-class events, we find no monotonic increase in energy, suggesting a limited role for precursors in triggering major flares. Overall, no significant correlation is found between waiting time and peak intensity for flares in SC23 and SC24 (Figure 2).

Figure 2. Correlation scatter plot of flare peak-intensity and the waiting time for SC23 (red dots) and SC24 (blue dots).

This study highlights key statistical features of solar flare behavior that may constrain the plausible physical mechanism that generated them. Future work will focus on linking these statistical signatures to the underlying physical processes responsible for flare generation.

References: Joshi, B., Bhattacharyya, R., Pandey, K.K., Kushwaha, U., Moon, Y.-J.: 2015, Evolutionary aspects and north-south asymmetry of soft X-ray flare index during solar cycles 21, 22, and 23. Astron. Astrophys. 582, A4.

Lee, K., Moon, Y.-J., Lee, J.-Y., Lee, K.-S., Na, H.: 2012, Solar Flare Occurrence Rate and Probability in Terms of the Sunspot Classification Supplemented with Sunspot Area and Its Changes. Sol. Phys. 281, 639.

Rosner, R., Vaiana, G.S.: 1978, Cosmic flare transients: constraints upon models for energy storage and release derived from the event frequency distribution. Astrophys. J. 222, 1104.

Temmer, M., Veronig, A., Hanslmeier, A., Otruba, W., Messerotti, M.: 2001, Statistical analysis of solar Hα flares. Astron. Astrophys. 375, 1049.

Veronig, A., Temmer, M., Hanslmeier, A., Otruba, W., Messerotti, M.: 2002, Temporal aspects and frequency distributions of solar soft X-ray flares. Astron. Astrophys. 382, 1070.

Acknowledgements We acknowledge support by the INAF with the mini-grant, ‘Space WEather Analysis of Rogue events (SWEAR)’ (F.O. 1.05.23.04.03).