A Study of Variations in Correlation Between Rotation Residual and Meridional Velocity of Sunspot Groups

We analyzed the combined 142 years sunspot-group data from Greenwich Photoheliograpic Results (GPR) and Debrecen Photoheliographic Data (DPD) and determined the yearly mean residual rotation rate and the meridional velocity of sunspot groups in different $5^{\circ }$ latitude intervals. We find that there exists a considerable latitude–time dependence in both the residual rotation and the meridional motion. The residual rotation rate is found to be −120 m s−1 to 80 m s−1. In a large number of solar cycles, the rotation is to some extent weaker during maxima than that of during minima. There exist alternate bands of equatorward and poleward meridional motions. The equatorward motion is dominant mostly around the maxima of solar cycles with velocity 8–12 m s−1, whereas the poleward motion is dominant mostly around the minima but with a relatively weak velocity, only 4–6 m s−1. The analysis of the data during Solar Cycles 12–24 that are folded according to the years from their respective epochs of maxima suggests the existence of equatorward migrating alternate bands of slower and faster than average rotation within the activity belt. This analysis suggests no clear equatorward or poleward migrating bands of meridional motions. A statistically significant anticorrelation exists between the meridional motion and residual rotation. The corresponding linear-least-squares best-fit is found to be reasonably good (slope, $-0.028 \pm 0.008$ , is about 3.5 times larger than its standard deviation). As per the sign convention used for the meridional motions, the significant negative value of the slope indicates the existence of a strong angular momentum transport toward the equator. The cross-correlation between the slopes determined from the data in 3-year moving time intervals and yearly mean sunspot number (SN) suggests that the slope leads SN by about 4 and 9 years. The Morlet wavelet spectrum of the slope suggests the existence of ≈11-year periodicity in the slope almost throughout the data window, but it was very weak during 1920–1940. We have also done cross-wavelet, wavelet-coherence, and wavelet-phase difference analyses of the slope and SN. Overall the results suggest there exists a strong relationship between the slope and amount of activity during a solar cycle. However, the correlation between the cycle-to-cycle modulations in the slope and the amplitude of solar cycle is found to be insignificant, indicating that there is no relationship between the slope and strength of activity on a long-time scale (longer than 11-year period).