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The sum of sunspot numbers over an odd-numbered 11-yr sunspot cycle exceeds that of its preceding even-numbered cycle, and it is well known as Gnevyshev and Ohl rule (or G-O rule) after the names of the authors who discovered it in 1948. The G-O rule can be used to predict the sum of sunspot numbers of a forthcoming odd cycle from that of its preceding even cycle. However, this is not always possible because occasionally the G-O rule is violated. So far, no plausible reason is known either for the G-O rule or for the violation of this rule. Here, we show the epochs of the violation of the G-O rule are close to the epochs of the Sun's retrograde orbital motion about the centre of mass of the Solar system (i.e. the epochs at which the orbital angular momentum of the Sun is weakly negative). Using this result, it is easy to predict the epochs of violation of the G-O rule well in advance. We also show that the solar equatorial rotation rate determined from sunspot group data during the period 1879-2004 is correlated/anticorrelated to the Sun's orbital torque before/after 1945. We have found the existence of a statistically significant ∼17-yr periodicity in the solar equatorial rotation rate. The implications of these findings for understanding the mechanism behind the solar cycle and the solar-terrestrial relationship are discussed.

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The solar equatorial rotation rate, determined from sunspot group data during the period 1879-2004, decreased over the last century, whereas the level of activity has increased considerably. The latitude gradient term of the solar rotation shows a significant modulation of about 79 year, which is consistent with what is expected for the existence of the Gleissberg cycle. Our analysis indicates that the level of activity will remain almost the same as the present cycle during the next few solar cycles (i.e., during the current double Hale cycle), while the length of the next double Hale cycle in Sunspot activity is predicted to be longer than the Current one. We find evidence for the existence of a weak linear relationship between the equatorial rotation rate and the length of sunspot cycle. Finally, we find that the length of the current cycle will be as short as that of cycle 22, indicating that the present Hale cycle may be a combination of two shorter cycles. Abstract. The solar equatorial rotation rate, determined from sunspot group data during the period 1879-2004, decreased over the last century, whereas the level of activity has increased considerably. The latitude gradient term of the solar rotation shows a significant modulation of about 79 year, which is consistent with what is expected for the existence of the Gleissberg cycle. Our analysis indicates that the level of activity will remain almost the same as the present cycle during the next few solar cycles (i.e., during the current double Hale cycle), while the length of the next double Hale cycle in sunspot activity is predicted to be longer than the current one. We find evidence for the existence of a weak linear relationship between the equatorial rotation rate and the length of sunspot cycle. Finally, we find that the length of the current cycle will be as short as that of cycle 22, indicating that the present Hale cycle may be a combination of two shorter cycles.

We have used the daily values of the equatorial rotation rate determined from the Mt. Wilson daily Doppler-velocity measurements during the period 3 December 1985 -5 March 2007 to search for periodicities in the solar equatorial rotation rate on time scales shorter than 11 years. After the daily values have been binned into 61-day intervals, a cosine fit with a period of one year was applied to the sequence to remove any seasonal trend. The spectral properties of this sequence were then investigated by using standard Fourier analysis, maximum-entropy methods, and a Morlet-wavelet analysis. From the analysis of the Fourier power spectrum we detected peaks with periodicities around 7.6, 2.8, and 1.47 years and 245, 182, and 158 days, but none of them were at a statistically significant level. In the Morlet-wavelet analysis the ≈1.47-year periodicity is detected only for 1990 (i.e., near the maximum of cycle 22) and near the end of cycle 22 in 1995. From the same wavelet analysis we found some evidence for the existence of a 2.8-year periodicity and a 245-day periodicity in the equatorial rotation rate around the years 1990 and 1992, respectively. In the data taken during the period 1996 -2007, when the Mt. Wilson spectrograph instrumentation was more stable, we were unable to detect any signal from the wavelet analysis. Thus, the detected periodicities during the period before 1996 could be artifacts of frequent changes in the Mt. Wilson spectrograph instrumentation. However, the temporal behavior of most of the activity phenomena during cycles 22 (1986 -1996) and 23 (after 1997) is considerably different. Therefore, the presence of the aforementioned short-term periodicities during the last cycle and absence of them in the current cycle may, in principle, be real temporal behavior of the solar rotation during these cycles.