Rotational Components of the Sun's Mean Field

This paper uses wavelet transforms to look for the rotational frequencies of the Sun's mean line-of-sight magnetic field. For a sufficiently high wavelet frequency, the spectra of the dipole, quadrupole, and hexapole field components each show a time-dependent fine structure with periods in the range of 26.5-30 days and their harmonics. These maps confirm that a large enhancement of 30-day power occurred in the dipole field during 1989-1990, as recorded previously using Fourier techniques (Sheeley 2022). Also, during some years the maps show power at 26.5 days (or its harmonics), that is clearly distinguishable from the 26.9-27.0 day rotation period at the Sun's equator. In at least one case, the 26.5-day period was a wave phenomenon caused by the systematic eruption of active regions at progressively more western locations in the Carrington coordinate system, as if the flux were emerging from a fixed longitude in a faster rotating subsurface layer. Based on previous studies of the mean field (Sheeley et al 1985, Sheeley & DeVore 1986, Sheeley 2022), I conclude that the enhanced wavelet patterns in this paper are regions where magnetic flux is emerging in configurations that strengthen the Sun's horizontal dipole, quadrupole, and hexapole fields, and (in the case of the more slowly rotating patterns) where this flux is being transported to mid-latitudes whose rotation periods are in the range 28-30 days.
Comment: 15 pages, 3 figures, 4 appendices version 2 corrects equation references in Appendices C and D. Also, references to unavailable video streaming have been removed, and a typo is fixed