Long Period (0.9–5.5 Year) Oscillations in Surface Spherical Harmonics of Sunspot Longitudinal Distributions

Abstract

The temporal changes in the two-dimensional patterns of sunspot groups, spanning 125 years (1650 Carrington Rotations), were previously analyzed using surface spherical harmonics (SSHs) (Juckett, 2003) in an attempt to quantify properties of the active longitudes among sunspot distributions. Common trends in the oscillations of both the amplitudes and spatial phases of sectoral combinations of SSHs were examined. The amplitude analysis revealed strong evidence for the second and third harmonics of the 11-year cycle across all SSHs, plus evidence for other structured variations spanning both longer and shorter time scales. In this report, temporal oscillations above the second harmonic reveal a dispersion relationship with respect to order, m, in the m = l and m = l–1 SSH modes. Furthermore, the relationship between amplitude and abrupt spatial phase transitions for these oscillations is consistent with the behavior of standing waves. Under this assumption, each standing-wave half-cycle is identified by spatial phase transitions between \(\frac{3}{4}\pi\) and π. This was used to convert the SSH amplitude series for each mode from a rectified version of the standing wave to an estimate of the full cycle. Spectral analysis yielded a dispersion relation over the SSH order range m = 1 to m = 18 spanning the cycle periods from the 11-year solar cycle down to that of the well-documented, but ill-understood 1.3 and 1.8 year quasi-periodic cycles of the quasi-biennial oscillation. Examination of the spatial phase patterns of the SSH modes suggests that the longitudinal variations in sunspot clustering are a complex phenomena with patterns occurring in several time scales. The standing wave trait of the SSH modes may offer evidence uniting the dynamo waves in the convective zone to interfacial oscillations in the tachocline.