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Deviations from the normal mode spectrum of asymptotic theory

I. Identification of quasi-periodic departures in the low-degree spectrum of the solar 5-min oscillations

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The work of Hill (1985a) on the low-degree 5 min eigenfrequency spectrum of the Sun based on differential radius observations combined with Doppler shift and total irradiance observations has been extended to include the work of Harvey and Duvall (1984) and Libbrecht and Zirin (1986). The differences between eigenfrequencies obtained in this analysis are compared to the predictions of asymptotic theory, and the deviations between observation and theory are observed to be ≈4 times larger than expected based on estimated accuracy of eigenfrequency determinations. These deviations are tested for departures from predictions of asymptotic theory which are quasi-periodic as a function of radial ordern and degreel. It is observed that the superposition of the seven distributions of frequency differences vsn obtained forl=0, ..., 6 generates an overdetermined quasi-periodic function when Δnl=0.420±0.018 and Δvl=−0.35 μHz in the superposition process. The probability that this quasi-periodic parent function is obtained from seven independent random distributions is estimated to be ≈1.2×10−7. Numerical experiments performed with theoretical eigenfrequency spectra demonstrate that the existence of a quasiperiodic behaviour in the superposed spectrum of frequency differences is physically plausible and that the parameters used in the superposition process are consistent with theory. One significant theoretical quasiperiodic behaviour is obtained for Δnl=0.399. By comparing the properties of the observed quasi-periodic behaviour with those obtained in the numerical experiments, we infer that the location of the region which leads to the greatest departure from asymptotic theory predictions is 0.757±0.002 solar radii, which suggests that this region is connected with the transition zone between the radiative interior and the convection zone.

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Hill, H.A., Rosenwald, R.D. Deviations from the normal mode spectrum of asymptotic theory. Astrophys Space Sci 126, 335–356 (1986).

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  • Frequency Difference
  • Asymptotic Theory
  • Parent Function
  • Convection Zone
  • Solar Radius