Two sunspot group populations and Gnevyshev-Waldmeier rule

Based on the materials of the Royal Greenwich Observatory catalog, the study of two different sunspot group populations continued: LLG – large long-lived, and SSG – small short-lived groups. The task of achieving a higher accuracy of the population separation parameter than before (Nagovitsyn & Pevtsov 2016, 2021) is being solved. A procedure for randomizing the lifetimes of sunspot groups observed once a day is proposed, which allows for statistical studies to achieve a higher time resolution. The form of the Gnevyshev-Waldmeier Rule is taken, which linearly connects the logarithm of the $\log S$ area and the lifetime of the sunspot group LT (over limited time intervals). It is shown that it has coefficients significantly different for SSG and LLG populations. The range of values of the group lifetime parameter separating the populations was found as ${\mathrm{LT}}^{\ast }=4.75\pm 0.53$ days, which is in agreement with the threshold values obtained earlier for the number of days of sunspot group observation: $m_{\mathrm{SSG}}⩽5$ days and $m_{\mathrm{LLG}}>5$ days. It is shown that the parameters of the bilognormal distribution of the sunspot group areas, obtained from their common grouped sample statistically by Levenberg–Marquardt method and with a preliminary division into lognormal distributions by lifetime, correspond to each other. It was clarified that, with an accuracy of up to a tenth of a day, the SSG population corresponds to the lifetimes of groups $⩽4.6$ days, and the LLG population corresponds to times $⩾4.7$ days. The results obtained make it possible to study various physical properties of SSG and LLG populations independently of each other in order to compare them and study their nature.