Is the sunspot spectrum really so complicated?

Abstract

The spectrum of the sunspot index can be qualitatively accounted for by a very simple model which the Hale 22-yr cycle dominates. The Hale cycle is amplitude modulated at the 90-yr Gleissberg period with an index of 25 percent. The square of the modulated Hale cycle reproduces all of the spectral lines of the Zurich-sunspot-index spectrum, between 90- and 8.9-yr periods, provided that a small offset is included in the Hale carrier. Without this, evidence of the 22-yr periodicity disappears because of the squaring, thus explaining the very strong 11-yr cycle which is an artifact of the modulation, as is the 45-yr line. The offset suggests a small relict magnetic field in the sun's core.