Waldmeier relations and the solar cycle dynamics by the mean-field dynamos

Abstract. The long-term variability of the sunspot cycle, as recorded by the Wolf numbers, are imprinted in different kinds of statistical relations which relate the cycle amplitudes, duration and shapes. This subject always gets a special attention because it is important for the solar activity forecast. We discuss statistical properties of the mean-field dynamo model with the fluctuating α-effect. Also, we estimate dynamical properties of the model for the long and short time-scale and compare it with the dynamics of the sunspot numbers data sets. Keywords. Solar activity, Sun: magnetic field Figure 1. The Waldmeier relations for the model (the left and the middle panel); squares show data for individual cycles, while the solid line gives the correlation, the dashed line shows these relations obtained from the actual sunspot number(SSN) data. The circles on the right panel mark the results of the Wilcox Solar Observatory (WSO) observations. 1. Waldmeier relations by the mean-field dynamos Recently, Pipin & Kosovichev (2011) showed that the Waldmeier relations can be explained by the mean field dynamo model with a variable magnitude of the α-effect. The idea was elaborated further by Pipin & Sokoloff (2011) and Pipin et al. (2012) for dynamo models that take into account the fluctuating α-effect. Figure 1 shows some of the results obtained in those papers. Note, that the model reproduces the Gnevyshev-Ohl rule as well (Pipin et al, 2012). We suggest that the obtained statistical relations can be interpreted as an evidence for the solar cycle to be a nonlinear self-excited oscillation that tends to preserve the property of the attractor under random perturbations. The strength of the link between the parameters of the subsequent cycles is controlled by the 1 a