Seismology and geodesy of the sun: Low-frequency oscillations

Abstract

The hourly averages of the solar ellipticity measured from June 13 to Sept. 17, 1966, are analyzed for indications of solar oscillations with periods in excess of 2 hr r < 0.5 hr-'. Nothing significant is found for frequencies v > 0.1 hr-' but for lower frequencies the power spectrum shows a very complex structure containing about 20 strong narrow peaks. The complexity is illusionary. The signal apparently consists ofonly two frequencies. The complexity is due to aliasing by the window function with its basic 24-hr period, with many observational days missing, and with different numbers of hourly averages for the various observational days. Both signal frequencies are apparently due to odddegree spherical harmonic oscillations of the sun.Much has been learned about the internal structure ofthe earth from the study of seismic waves, but the analogous studies of the sun arejust beginning. So far only the "5-minute" oscillation has contributed to our understanding ofthe solar interior (1-3). But solar oscillatory periods as great as 160 min have been reported (4, 5).Measurements ofthe elliptical figure ofthe sun made during the summer of 1966 were originally analyzed as a set of daily averages (6, 7). The analysis showed a statistically strong periodic signal (containing three harmonics) and compatible with a solar distortion rotating rigidly as a wave on the surface (7). The solar surface itself rotates nonuniformly and more slowly, 30-50% as fast.The rotation rate of this distortion has been interpreted as that of a distorted solar core which induces distortions in the surfaces of constant gravitational potential. The shape of the solar surface is in turn determined by the shape of a potential surface. The most likely source of the distorted core is believed to be a strong ( 108 gauss) magnetic field frozen in the core.The 1966 observations have recently been reanalyzed as a set ofhourly averages ofthe "diagonal component" (Ard) ofthe solar ellipticity (8). This analysis has provided a set of residuals, derived from these hourly averages, which represent the input data for the present paper.The new analysis has resulted in relatively little change in the derived characteristics of the rigidly rotating solar figure. The most important changes are the new and improved mirror distortion parameters. Errors in these parameters have relatively little effect on the calculation of the characteristics of the 12-day rotating figure because the mirror positions were cycled to cause these errors to average to small values.The above-mentioned set of residuals ofArd are obtained by subtracting from Ard the signals due to: (i) the rigidly rotating solar figure (rotating with a sidereal period of 12.38 ± 0.11 days), (ii) As a first step in searching for frequencies due to solar oscillations a power spectrum of residuals y(t) is calculated. Actually it is not the function y(t) (defined only for the hours with observations) that yields a Fourier transform and the power spectrum. Rather, the spectrum is calculated from t...