Intrinsic nonlinearity of the solar cycles Original Research Article

The solar cycles represented by the monthly averaged sunspot numbers show characteristic nonlinear manifestations: a) non-sinusoidal time dependence with shorter rising phases and longer declining phases of moderate and strong cycles; b) smoother minima than maxima. In addition, stronger solar cycles are shorter, as a rule. We have found the approximate empirical formula τ = 45W−12M which relates the duration of the rising phase τ (years) and the maximal sunspot numbers WM of a given solar cycle. The formula is valid for the past 22 solar cycles with the precision of 30% and does not contradict previous empirical relations obtained by Waldmeier and King-Hele. Nonlinear self-gravitation oscillations of the subphotospheric layers on the Sun coupled to luminosity variations are considered as a hypothetical physical mechanism responsible for this empirical relation.