Revealing Coupled Periodicities in Sunspot Time Series Using Bispectrum—An Inverse Problem

Abstract

Sunspot daily time series have been available for almost two centuries providing vast and complicated information about the behavior of our star and especially the interaction of the motion of the planets and other possible interstellar phenomena and their effects on the surface of the Sun. The main result obtained from the sunspot time series analysis is the imprint of various periodicities, such as the planets’ orbital periods and the planetary synodic periods on the sunspots signature. A detailed spectrum representation is achieved by means of a periodogram and a virtual extension of the time length segments with zeroed samples for longer representations. Furthermore, the dependence or coupling of these periodicities is explored by means of a bispectrum. We establish the exact interdependencies of the periodic phenomena on the sunspot time series. Specific couplings are explored that are proved to be the key issues for the coupled periodicities on the sunspot time series. In this work, contrary to what has been presented in the literature, all periodic phenomena are limited within the time period of an 11-year cycle as well as the periodicities of the orbits of the planets. The main findings are the observed strong coupling of the Mercury, Venus, and Mars periodicities, as well as synodic periodicities with all other periodicities that appear on the sunspot series. Simultaneously, the rotation of the Sun around itself (25.6 to 33.5 days) provides an extensive coupling of all recorded periodicities. Finally, there is strong evidence of the existence of a quadratic mechanism, which couples all the recorded periodicities, but in such a way that only frequency pairs that sum up to specific periods are coupled. The justification for this kind of coupling is left open to the scientific community.