Shape of the 11-Year Cycle of Solar Activity and the Evolution of Latitude Characteristics of the Sunspot Distribution

Abstract

The solar activity index and parameters of the spatial distribution of sunspots are known to be related. Using these relationships, we propose interrelated approximations for the sunspot number (SN) and the two key latitude characteristics of their distribution in the cycle: the mean latitude of sunspots and the standard deviation of their latitudes. The two parameters of these approximations are the cycle amplitude SN_max and the drift of its downward branch relative to the cycle beginning t₀. These approximations specifically take into account the relationship between amplitudinal and spatial properties of the 11-year solar cycle, as well as the universality of the behavior of the activity and mean latitude of sunspots in the declining phase of the cycle. We demonstrate that the pair of parameters SN_max and t₀ allows approximation of both the shape of the cyclic curve and the latitude–time diagram for sunspots of this cycle (“Maunder’s butterfly”).