Influence of the Gleissberg Cycle on Variations of the 11-Year Cycle of Solar Activity in 1700–2021

Abstract

The wavelet analysis was used to study the spectral composition of the sunspot numbers SN during1700–2021. In addition to the dominant 11-year component, two powerful components of the Gleissbergcycle can be traced in the spectrum: before 1880, a branch with a period of ~60 years; from 1850 a branch of~115 years is found. It is found that the series of lengths and amplitudes of the solar cycle as a whole areinversely related (correlation coefficient k = –0.5–0.63). The interval between the series at which the maximumanticorrelation is reached depends on time. In the 18th and early 19th centuries, the lag was equal toone cycle, in the 19th century it was two cycles, and from 1950 to our time the lag decreased to 2 years. Quasiperiodicstructures, which are typical for long periods of low solar activity, have been identified. Such a spectralfeature in ~1800 (Dalton minimum) was caused by the influence of the 60-year branch, while the onethat has been forming since the beginning of the 21st century is due to the weaker influence of the circa-centenarybranch. Therefore, it should be expected that the next solar cycles will be higher and shorter thanduring the period of the Dalton minimum. It has been shown that solar cycle length variations for the last321 years can be described within the framework of the model, which is an 11-year oscillation that is subjectto frequency modulation by the branches of the Gleisberg cycle (60 and 115 years) with time-varying influencesof the modulator