The Hidden Cycle of the Solar Tesseral-Quadrupole Magnetic Field

Abstract

Based on the Stanford harmonic coefficients of the solar magnetic fields and on the results of Shannon entropy transfer technique applied to magnetic mode intensities (Mikhaylutsa in J. Astrophys. Astron.40, 22, 2019), we have found that most of the medium and small-scale solar magnetic modes (order $l > 3$; degree $m > 0$) must be interdependent. The features and physical sense of these dependencies are analyzed and suggest that an unknown process in the Sun may control clusters of dependent magnetic modes according to some underlying physical scenario. The scenario may be revealed by studying the spatial distribution of the global surface magnetic field. We find that the tesseral-quadrupole ($l = 2$; $m = 1$) polarity distribution reappears periodically over four solar cycles. The periodicity (${T}\approx 72$ solar rotations) is synchronized with the phases of modulation of the Shannon entropy transfer from the tesseral-quadrupole mode. An unknown process (twice per sunspot cycle) organizes a recurring cluster of interconnected magnetic modes that restore the global structure of the tesseral-quadrupole polarity, as a kind of “template.” This cycle is hidden in traditional methods of analysis, but its spatial-phase origin is made clear by the Shannon entropy transfer technique. Investigation of the “template” rotation rate suggests a probable coincidence with the 27-day Bartels rotation period.