Periodic variation and phase analysis of grouped solar flare with sunspot activity

Studies on the periodic variation and the phase relationship between different solar activity indicators are useful for understanding the long-term evolution of solar activity cycles. Here we report the statistical analysis of grouped solar flare (GSF) and sunspot number (SN) during the time interval from January 1965 to March 2009. We find that, (1) the significant periodicities of both GSF and SN are related to the differential rotation periodicity, the quasi-biennial oscillation (QBO), and the eleven-year Schwabe cycle (ESC), but the specific values are not absolutely identical; (2) the ESC signal of GSF lags behind that of SN with an average of 7.8 months during the considered time interval, which implies that the systematic phase delays between GSF and SN originate from the inter-solar-cycle signal. Our results may provide evidence about the storage of magnetic energy in the corona.