The sunspot cycle revisited

The set of sunspot numbers observed since the invention of the telescope is one of the most studied time series in astronomy and yet it is also one of the most complex. Fourteen frequencies are found in the yearly mean sunspot numbers from 1700 to 2011using the Lomb-Scargle periodogram and prewhitening. All of the frequencies corresponding to shorter term periods can be matched with simple algebraic combinations of the frequency of the main 11-year period and the frequencies of the longer term periods in the periodogram. This is exactly what can be expected from amplitude and phase modulation of an 11.12-year periodicity by longer term variations. Similar, though not identical, results are obtained after correcting the sunspot number series as proposed by Svalgaard. On looking separately at the amplitude and phase modulation a clear relationship is found between the two modulations although this relationship has broken down for the last four solar cycles. The phase modulation implies that there is a definite underlying period for the solar cycle. Such a clock mechanism does seem to be a possibility in models of the solar dynamo incorporating a conveyor-belt-like meridional circulation between high polar latitudes and the equator.