NASA NTRS1992
Evidence that has recently been compiled (Bai and Sturrock 1991) indicates that the enigmatic 154-day periodicity in solar activity may be viewed as part of a complex of periodicities that are approximate multiples of 25.8 days, suggesting that the Sun contains a 'clock' with frequency in the range 440 to 463 nano Hz. The clock may comprise either an oscillator or a rotator, each of which may be either real or virtual. We have reconsidered a previous spectrum analysis of the Zurich sunspot-number sequence by Knight, Schatten, and Sturrock (1979) which revealed a sharp, persistent and significant periodicity with a period of 12.072 days, corresponding to a frequency of about 958.8 nano Hz. This periodicity may be regarded as the (second) upper sideband of the second harmonic (2nu(sub R) + 2nu(sub E)) of a fundamental frequency of 447.7 nano Hz that is clearly within the search band. In this expression, nu(sub R) is the sidereal frequency of the hypothetical rotator and nu(sub E) is the frequency (31.69 nano Hz) of the Earth in its orbital motion around the Sun. In analyzing sunspot area data derived from the Greenwich data set, and on noting that any frequency is defined only to within the Nyquist frequency, we find clear evidence not only for the upper sideband of the second harmonic, but also for the second harmonic (2nu(sub R)) and the lower sideband of the second harmonic (2nu(sub R) - 2nu(sub E)). There is no strong peak at the fundamental frequency in the Greenwich data, but there is in the Zurich sunspot data. The effect of a linear oscillator is, to the lowest order in the amplitude, the same as the combined effect of two rotators of opposite polarities. A rotator that has arbitrary orientation with respect to the ecliptic may influence the outer layers of the Sun and thereby modulate the occurrence of solar activity such as sunspots. By analyzing a simple model, we find that such a rotator would influence surface activity in such a way that the spectrum of a 'signal' (such as the record of sunspots), as seen from the Earth, would contain components with frequencies that are certain integral combinations of nu(sub R) and nu(sub E). The amplitudes of the various components depend sensitively on theta, the angle between the axis of the rotator and the axis of the Earth's orbital motion. This simple model therefore offers a kinematical (but not dynamical) interpretation of the sunspot spectrum. The present analysis, while offering support of our conjectures that the Sun contains a clock that regulates the 154-day complex of periodicities, cannot distinguish between an osillator or a rotator (that might be a traveling wave), nor between a real rotator or a virtual rotator (that might be an apparent traveling wave due to the aliasing effect of an oscillator in a rotating system). Further analysis of sunspot and other data sets will be required to confirm the existence of such clock and (if it is real) to determine its physical nature.