Abstract
The recent solar cycles 23 and 24 are thought to be unusually quiet with more prolonged periods. Both sunspot groups and solar soft X-ray (SXR) flares show a decline in numbers comparable to cycles 21 and 22. In order to understand the periodic variations and distributions of solar flares with the sunspot group numbers in these cycles, this study investigates the periodicities and distributions of the solar SXR flares, 36354 in total (B (13351) 36.7%, C (20699) 56.9%, M (2141) 5.9%, and X (163) 0.45%) between 1996 July and 2016 December. The continuous wavelet transforms and cross-correlation methods were used to carry out the study. First, we found that the B- class flare number is asynchronous and negatively correlated with the sunspot group numbers. The flare class exhibits deviation when sunspot group numbers rise or fall around 100. The other class flares are in phase, synchronous with the sunspot group numbers. The C-class flares show the highest level of correlation of 0.868 with sunspot group numbers. A different number of short and intermediate periodicities was also noticed among the flare classes. Notable 256-day periodicity is found for B flares, 7, 64, and 300 days for C, 32, 64, and 256 days for M flares, and 40, 32, and 25 days for X flares. The difference in periodic variations of the flare classes could be attributed to the magnetic flux system of sunspot groups producing them.