Cycle Patterns of the Axisymmetric Magnetic Field

Abstract

The evolution of the axisymmetric component of the sun’s radial magnetic field is explored, using a 33-yr data set of Mt Wilson and Kitt Peak synoptic magnetic maps. The pattern in latitude-time space exhibits equatorial branches of “preceding” polarity as well as steep, poleward branches that oscillate on a short time scale (about 2 yr). We decompose the pattern in its spherical harmonic components and perform a time series analysis of the coefficients for each spherical harmonic degree ℓ (while m = 0). The power spectra show strong peaks at a frequency of (22 yr)^-1 for the odd-ℓ modes, with no significant overtones or resonant power for the even modes. At higher frequencies we find a concentration of low-amplitude power corresponding to periods of about 2 yr.

A least squares fit of a 22 yr sine curve to the time series of the harmonic coefficients gives us the amplitudes and phases of the modes as a function of ℓ as well as a time-invariant offset. From the offset for ℓ = 1 we obtain limits on a possible fossil global dipole field: if it at all exists, its polar field strength should be less than about 0.2 G to be compatible with observational data.

The mode amplitudes have a pronounced peak for ℓ = 5 and decline toward lower and higher ℓ-values. A quite unexpected and intriguing property is found for the phase differences between the modes: they are integer multiples of π/4 (where 2π corresponds to 22 yr). It is shown that this apparent “phase quantization” cannot be an artefact of the reduction procedure, and that it is unlikely to be a fortuitous coincidence. The amplitude and phase locking between the modes should be a property of the eigenfunction that is a solution to the underlying equation that governs the solar dynamo.