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Astron. Astrophys. 345, 1027-1037 (1999)

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5. Conclusion

A more realistic approach was used to fit the helioseismic data, assuming that the observed spectra was statistically dependent upon one another (Fourier fitting). This is in contrast to what is done in general (power fitting), resulting in a more complete treatment of the leakage between the modes.

We studied different sources of systematic errors in the determination of the mode frequencies and rotational splittings. We showed that the Fourier spectra fitting will provide, especially for low-degree modes, splitting estimates that are far less biased than those derived by power spectra fitting. Moreover, we studied the effect upon the splitting determination of an imperfect knowledge of the leakage elements for [FORMULA], where the leakage determination is the most critical. While [FORMULA] coefficients for [FORMULA] estimated using the power spectra vary almost linearly with the leakage, those found using the Fourier spectra obey a quadratic law. For very low degree modes, this quadratic dependence is another reason to fit the Fourier spectra instead of the power spectra. In addition, the effect of the leakage between modes of different degrees upon the p-mode frequencies and splitting coefficients determination was analyzed. A procedure for `cleaning' the spatial alias is described which leads to frequencies and splitting coefficients with systematic errors smaller than before.

The results obtained here show significant improvement on previous GONG determinations especially for increasing the number of identified modes with [FORMULA] and for minimizing the bias on the splitting determination and the error bars. A timely implementation of the Fourier spectra fitting technique in the determination of the p-mode parameters provided by the GONG project would surely produce a scientific boost for the whole helioseismic community.

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© European Southern Observatory (ESO) 1999

Online publication: April 28, 1999