Long–Term Variations in Solar Differential Rotation and Sunspot Activity, II: Differential Rotation Around the Maxima and Minima of Solar Cycles 12 – 24

Studies of variations in the solar differential rotation are important for understanding the underlying mechanism of solar cycle and other variations of solar activity. We analyzed the sunspot-group daily data that were reported by Greenwich Photoheliographic Results (GPR) during the period 1874 – 1976 and Debrecen Photoheliographic Data (DPD) during the period 1977 – 2017. We determined the equatorial rotation rate [ $A$ ] and the latitude gradient [ $B$ ] components of the solar differential rotation by fitting the data in each of the 3-year moving time intervals (3-year MTIs) successively shifted by one year during the period 1874 – 2017 to the standard law of differential rotation. The values of $A$ and $B$ around the years of maxima and minima of Solar Cycles 12 – 24 are obtained from the 3-year MTIs series of $A$ and $B$ and studied the long-term cycle-to-cycle modulations in these coefficients. Here we have used the epochs of the maxima and minima of the Solar Cycles 12 – 24 that were recently determined from the revised Version-2 international sunspot-number series. We find that there exits a considerably significant secular decreasing-trend in $A$ around the maxima of solar cycles. There exist no secular trends in both $A$ and $B$ around the minima of solar cycles. The secular trend in $B$ around the maxima of solar cycles is also found to be statistically insignificant. We fitted a cosine function to the values of $A$ , and also to those of $B$ , after removing the corresponding linear trends. The cosine-fits suggest that there exist ≈54-year (≈94-year) and ≈82-year (≈79-year) periodicities in $A$ ( $B$ ) around the maxima and minima of solar cycles, respectively. The amplitude of the cosine-profile of $A$ ( $B$ ) around the minima of solar cycles is about 41% (65%) larger than that of $A$ ( $B$ ) around the maxima. In addition, the cosine profiles of $A$ and $B$ suggest a large (up to $180^{\circ }$ ) phase difference between the long-term variations of $A$ , and also between those of $B$ , around maxima and minima of solar cycles. Implications of all these results are discussed briefly.