The Second Waldmeier Rule and the Form of the 11-Year Cycle

Abstract

It is known that the form of the 11-year solar-activity cycle can be approximately described by its amplitude A and the arrangement of three characteristic moments: the moment of the minimum (T_min), maximum (T_max), and the subsequent minimum (T_min2). According to the classical Waldmeier rule, there is an anticorrelation between the maximum activity value (amplitude) of cycle A and the duration of its ascending branch T_max – T_min, while the correlation between A and the length of the downward branch of the cycle T_min2 – T_max is much lower. Following Waldmeier, the moment T_V can be entered near the end of the downward branch of the cycle, in which the activity falls within a certain (low) specified level V. The relationship between the length of the corresponding phase of cycle T_V – T_max and the amplitude of this cycle is quite strong. We demonstrate that this connection, which can be called the “second Waldmeier rule,” agrees well with the fact that the downward branch of the cycle has a universal appearance. Thus, one parameter, its value is at the maximum, is enough for an approximate qualitative description of the form of a single 11-year cycle that takes into account the two Waldmeier rules.