The G–O rule and Waldmeier effect in the variations of the numbers of large and small sunspot groups

Abstract

We have analyzed the combined Greenwich and Solar Optical Observing Network (SOON) sunspot group data during the period of 1874 – 2011 and determined variations in the annual numbers (counts) of the small (maximum area A/subM/ < 100 millionth of solar hemisphere, msh), large (100 ≤ A/subM/< 300 msh), and big (A/subM/ ≥ 300 msh) spot groups. We found that the amplitude of an even-numbered cycle of the number of large groups is smaller than that of its immediately following odd-numbered cycle. This is consistent with the well known Gnevyshev and Ohl rule (G–O rule) of solar cycles, generally described by using the Zurich sunspot number (R/subZ/). During cycles 12 – 21 the G–O rule holds good for the variation in the number of small groups also, but it is violated by cycle pair (22, 23) as in the case of R/subZ/. This behavior of the variations in the small groups is largely responsible for the anomalous behavior of R/subZ/ in cycle pair (22, 23). It is also found that the amplitude of an odd-numbered cycle of the number of small groups is larger than that of its immediately following even-numbered cycle. This might be called the ‘reverse G–O rule’. In the case of the number of the big groups, both cycle pairs (12, 13) and (22, 23) violated the G–O rule. In many cycles the positions of the peaks of the small, large, and big groups are different, and considerably differ with respect to the corresponding positions of the R/subZ/ peaks. In the case of cycle 23, the corresponding cycles of the small and large groups are largely symmetric/ less asymmetric (the Waldmeier effect is weak/absent) with their maxima taking place two years later than that of R/subZ/. The corresponding cycle of the big groups is more asymmetric (strong Waldmeier effect) with its maximum epoch taking place at the same time as that of R/subZ/.