Planetary model of sunspot emergence: A spectral and autocorrelation analysis

TL;DR

This paper presents an empirical model linking Mercury's conjunctions to sunspot emergence, revealing detailed spectral periodicities and their phase relationships, enhancing understanding of solar magnetic activity patterns.

Contribution

The study introduces a novel Mercury-based empirical model that predicts intermediate periodicities in sunspot activity, incorporating solar cycle modulation and magnetic reversals.

Findings

Model accurately predicts fine spectral details of sunspot areas.

Phase shifts in model components correspond to observed sunspot variations.

Inclusion of variable thresholds explains additional periodicities.

Abstract

This paper is concerned with intermediate range periodicity in the sunspot area spectrum. An empirical model of sunspot area emergence based on Mercury planet conjunctions was developed and the spectra of the model variation and the sunspot area variation compared. By including solar cycle amplitude modulation and the effect of solar magnetic field reversal the model was able to predict fine detail in the sunspot area spectrum. As Mercury planet conjunctions occur predictably it was possible to compare the time variation of band limited components of sunspot area with the corresponding component variations in the model. When the model component variation was stable corresponding components of sunspot area lagged the model variation by a few tens of days. When a 180 degree phase change occurred in the model variation the corresponding component of sunspot area followed the change over an interval of a few hundred days, first by decreasing to zero and then emerging in phase with the model variation. Where periodicities in sunspot area did not match periods of Fourier components of the model the autocorrelation function of the model variation provided an indirect numerical link to these periodicities. Included in these indirect periodicities were components at periods of about 138, 235, 355, 472, 530, 605, 833, 1190 and 2020 days. Direct periodicities in the model, those linked directly to Fourier components of sunspot area, included components at about 88, 116, 176, 200, 292 and 405 days. The model was developed without allowing for a variable threshold for sunspot emergence. However, it was found that with a variable threshold above which the model variation is effective in triggering sunspots, weak Fourier components at the indirect periods were generated. The model with threshold then encompasses all of the significant intermediate range periodicities in sunspot area.