Features of the Gnevyshev-Waldmeier Rule for Various Lifetimes and Areas of Sunspot Groups

Abstract

Based on a sample of 7696 nonrecurrent and 566 recurrent sunspot groups, we have investigated the Gnevyshev–Waldmeier rule using the Catalogue of Solar Activity by R.S. Gnevysheva (1954–1978). The maximum recorded sunspot group lifetime is 160 days. The general Gnevyshev–Waldmeier rule for all lifetimes is A_max = (12.1 ± 0.70)LT (A_max is the maximum sunspot group area during the lifetime and LT is the sunspot group lifetime). However, the general rule has turned out to deviate from the derived linear form for the population of small short-living sunspot groups (SSG): it has a significant nonlinear scaling form A_max = (8.02 ± 0.41)LT^{(1.105±0.022)}. For the population of large long-living sunspot groups (LLG) there is a linear form A_max = (12.9 ± 1.1)LT. Allowance only for recurrent sunspot groups with lifetimes more than 40 days gives A_max = (13.93 ± 0.41)LT.