Evidence for Long-term Retrograde Motions of Sunspot Patterns and Indications of Coupled g-mode Rotation Rates

Abstract

Solar g-modes are global oscillations that would exist primarily in the radiative zone (RZ) and would be excited by either convective overshoot or nuclear burning in the core. Wolff and O’Donovan (Astrophys. J.661, 568, 2007) proposed a non-linear coupling of g-modes into groups that share the same harmonic degree l. Each group (denoted set(l)) exhibits a unique retrograde rotation rate with respect to the RZ that depends mainly on l. The coupling yields a standing wave (nearly stationary in longitude) that has two angularly defined hot spots offset from the equator on opposite sides of the Sun that would deposit energy asymmetrically in the lower convective envelope (CE). It is anticipated that when two or more groups overlap in longitude, an increase in local heating would influence the distribution of sunspots. In this paper, we scanned a multitude of rotational reference frames for sunspot clustering to test for frames that are concordant with the rotation of these g-modes sets. To achieve this, spherical harmonic filtering of sunspot synoptic maps was used to extract patterns consistent with coalesced g-modes. The latitude band, with minimal differential rotation, was sampled from each filtered synoptic map and layered into a stackplot. This was progressively shifted, line-by-line, into different rotational reference frames. We have detected long-lived longitudinal alignments, spanning 90 years of solar cycles, which are consistent with the rotation rate of the deep solar interior as well as other rotational frames predicted by the coupled g-mode model. Their sidereal rotation rates of 370.0, 398.8, 412.7, 418.3, 421.0, 424.2 and 430.0 nHz correspond, respectively, to coupled g-modes for l = 2 through 7 and G, where G is a set with high l values or a group of such sets (unresolved) that rotate almost as fast as the RZ. While the clustering in these reference frames offers new approaches for studying the longitudinal behavior of solar activity, it tentatively leads to the more profound conclusion that a portion of the driving force for sunspot occurrence is linked to energy extracted from the solar core and deposited at the top of the RZ by solar g-modes.