Temporal variations of low-order spherical harmonic representations of sunspot group patterns: Evidence for solar spin-orbit coupling

Abstract

The spatial and temporal patterns of sunspot groups spanning 125 years are explored using surface spherical harmonic (SSH) analysis at a temporal resolution of one Carrington Rotation (CR). SSHs spanning order, , and degree, l , satisfying are calculated for each CR from 300 to 1950 and are expressed as amplitude and spatial phase for each CR. Linear combinations of harmonics (lcSSHS), grouped by constant m and either even or odd l values, generate sectoral constructs with maximal power within the sunspot latitude band. The temporal variations of the lcSSHs describe the variations in longitudinal distributions of sunspot groups. The frequency components of these variations are examined separately using singular spectrum, Fourier, and wavelet analyses. The spatial phases of the lcSSHs display long-term secular, retrograde motions with superimposed near-decadal torsional oscillations. Two of these oscillatory components appear identifiable. One is an artifact of the differential rotation of the photosphere and has an 11-yr period. The other is in near synchrony with the proposed ddt series representing the torque on the Sun as it orbits the solar system barycenter. In contrast, each of the amplitude series for the lcSSHs follow an 11-yr solar cycle envelope but also contain a strong periodic component at 5.6 years and multiple components with periods between 15–30 years. Several of these oscillations are predictable from spin-orbit coupling considerations. At finer time scales (~20 CR), there is also evidence for abrupt spatial phase shifts consistent with standing waves at a surface or interface. The conclusion is that SSH decomposition of sunspot patterns can be used to extract intensity and drift variations at several time scales. The intermediate time scale contains evidence that solar activity is modulated by the Sun's motion around the solar system barycenter.