Correspondence between Solar Variability (0.6 – 7.0 Years) and the Theoretical Positions of Rotating Sets of Coupled g Modes

Abstract

Recently, Juckett and Wolff (Solar Phys. 252, 247, 2008) showed that the timing and longitude of sunspot patterns has some correspondence with a model based on coupled g modes. The model maximizes the nonlinear coupling of those g modes sharing harmonic degree l to generate a “set(l)” that assists its own excitation by locally enhancing nuclear burning. Each set(l) has oscillatory power concentrated at two longitudes, on opposite sides of the Sun and drifts slowly retrograde within the radiative zone (RZ) at a rate that depends on l. When the strong longitudes of two or more sets overlap, wave dissipation adds extra energy to that locality at the base of the convective envelope increasing convection and then sunspot activity. We compare the main subdecadal sunspot frequencies with the intersections of sets derived from l=2 – 11 and G, where G represents unresolvable high-l modes that rotate similarly to the RZ. After determining the set(l) spatial phases, we show that 17 subdecadal oscillations with periods in the range 0.6 to 7.0 years (4.5 to 50 nHz), generated by 23 unique intersections of the 11 sets, are synchronous with 17 corresponding frequencies in the sunspot time series. After optimizing parameters, we find a mean correlation of 0.96 for synchrony among the 17 waveform pairs. These 17 frequencies constitute the bulk of the non-noise subdecadal frequency domain of the sunspot variation. We conclude that the sunspot series contains oscillatory components with the same temporal phases and frequencies as various set(l) intersections spanning the past ≈ 100 years. This additional evidence for the role of coupled g modes in sunspot dynamics suggests that more of sunspot variability can be understood with nonmagnetic fluid mechanics than popularly thought.