Solar activity secular cycles

Long-term variations in solar activity secular cycles have been studied using a method for the expansion of reconstructed sunspot number series Sn(t) for 11400 years in terms of natural orthogonal functions. It has been established that three expansion components describe more than 98% of all Sn(t) variations. In this case, the contribution of the first expansion component is about 92%. The averaged form of the 88year secular cycle has been determined based on the form of the first expansion coordinate function. The quasi-periodicities modulating the secular cycle have been revealed based on the time function conjugate to the first function. The quasi-periodicities modulating the secular cycle coincide with those observed in the Sn(t) series spectrum. A change in the secular cycle form and the time variations in this form are described by the second and third expansion components, the contributions of which are about 4 and 2%, respectively. The variations in the steepness of the secular cycle branches are more pronounced in the 200-year cycle, and the secular cycle amplitude varies more evidently in the 2300-year cycle.