The phase relation between sunspot numbers and soft X-ray flares

TL;DR

This study analyzes the timing and correlation between sunspot numbers and soft X-ray flares across solar cycles 21 to 23, revealing cycle-dependent time lags and correlations that could aid in flare prediction and understanding solar energy processes.

Contribution

It provides a detailed statistical analysis of the phase relations between sunspot activity and soft X-ray flares over multiple solar cycles, highlighting cycle-specific lag patterns and correlation strengths.

Findings

Significant time lags between sunspots and flare classes vary by cycle.

Correlation coefficients are higher in cycle 22 than in cycles 21 and 23.

Cycle-dependent differences in flare-sunspot phase relations may improve flare prediction.

Abstract

To better understand long-term flare activity, we present a statistical study on soft X-ray flares from May 1976 to May 2008. It is found that the smoothed monthly peak fluxes of C-class, M-class, and X-class flares have a very noticeable time lag of 13, 8, and 8 months in cycle 21 respectively with respect to the smoothed monthly sunspot numbers. There is no time lag between the sunspot numbers and M-class flares in cycle 22. However, there is a one-month time lag for C-class flares and a one-month time lead for X-class flares with regard to sunspot numbers in cycle 22. For cycle 23, the smoothed monthly peak fluxes of C-class, M-class, and X-class flares have a very noticeable time lag of one month, 5 months, and 21 months respectively with respect to sunspot numbers. If we take the three types of flares together, the smoothed monthly peak fluxes of soft X-ray flares have a time lag of 9 months in cycle 21, no time lag in cycle 22 and a characteristic time lag of 5 months in cycle 23 with respect to the smoothed monthly sunspot numbers. Furthermore, the correlation coefficients of the smoothed monthly peak fluxes of M-class and X-class flares and the smoothed monthly sunspot numbers are higher in cycle 22 than those in cycles 21 and 23. The correlation coefficients between the three kinds of soft X-ray flares in cycle 22 are higher than those in cycles 21 and 23. These findings may be instructive in predicting C-class, M-class, and X-class flares regarding sunspot numbers in the next cycle and the physical processes of energy storage and dissipation in the corona.