Three-halves law in sunspot cycle shape

Abstract

Evidence is provided of a nonlinear effect consisting of a 3/2 power law in annual mean sunspot numbers since 1700. With correction for this nonlinearity, it has been possible to reproduce theoretically the well-known Waldmeier relation between rise time and maximum sunspot number, in addition to other features of the 11 yr sunspot curve such as a break in the decline of strong 11 yr cycles. Eighteenth century sunspot numbers are found to fit theoretical semicycle shapes well. The present model suggests an upward travelling 22 yr wave launched by a reciprocating magnetic oscillator deep in the sun.