Phase Relationship between Polar Faculae and Sunspot Numbers Revisited: Wavelet Transform Analyses

Cross-correlation analysis and wavelet transform methods are proposed to investigate the phase relationship between the polar faculae (PF) and the sunspot numbers (SNs). It was found that: (1) the PF begin 52 months earlier than the SNs on the average of the considered time interval, which should lead to phase asynchrony between them; (2) the length of the Schwabe cycle for the PF obviously differs from that for the SNs at all time points, and the mean length of the Schwabe cycle of the PF (10.28 yr) is slightly smaller than that of the SNs (10.37 yr); (3) the phase relationship between the PF and the SNs is not only time-dependent but also frequency-dependent.

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