The G-O Rule and Waldmeier Effect in the Variations of the Numbers of Large and Small Sunspot Groups

TL;DR

This study analyzes sunspot group data from 1874-2011, revealing patterns consistent with the G-O rule, a reverse G-O rule for small groups, and variations in cycle peak timings, contributing to understanding solar cycle behaviors.

Contribution

It provides a detailed analysis of sunspot group variations across multiple cycles, highlighting violations of the G-O rule and differences in cycle peak timings based on group size.

Findings

G-O rule holds for large groups in most cycles

Reverse G-O rule observed for small groups in certain cycles

Cycle peak timings vary with group size and cycle number

Abstract

We have analysed 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, large and big sunspot groups (these classifications are made on the basis of the maximum areas of the sunspot 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 or G-O rule of solar cycles, generally described by using the Zurich sunspot number (Rz). 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 Rz. This behaviour of the variations in the small groups is largely responsible for the anomalous behaviour of Rz 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 can be called as `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 Rz peaks. In the case of cycle 23, the corresponding cycles of the small and large groups are largely symmetric/less asymmetric (Waldmeier effect is weak/absent) with their maxima taking place two years later than that of Rz. 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 Rz.