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Astron. Astrophys. 323, 231-234 (1997)

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4. Effect on structural inversions

Regardless of the interpretation of the [FORMULA] 's, they may be used to cleanse centroid frequency data for use in structural inversions. Dziembowski and Goode (1996) showed that the latitudinal dependence of the near surface perturbation due to activity (NSPA) causes corruption in the helioseismic determination of the structure of the solar core. The corruption is significant only for the lowest l modes. Thus, an inversion for the structure in layers above [FORMULA], which relies mostly on higher l modes, is not affected by this problem. Once the [FORMULA] 's are determined, they may be used purify the frequency data for inversion. The assumption is being made that [FORMULA] 's adequately describe the whole Sun's asphericity. Current data are consistent with such an assumption. Dziembowski and Goode (1996) also showed that the centroid frequency shifts relative to 1986 for [FORMULA] and 2 modes, as determined from direct measurements within admittedly large errors, agree with the shifts evaluated from the [FORMULA] 's.

Basu et al. (1996) have already inverted the LOWL data to determine the internal structure of the Sun. Their structural inversion of the LOWL data agrees very well with that from the combined BBSO&BISON results- if the latter are from a period of low activity. We confirm their result, but do not report our calculations here, except to add one point that they did not discuss - the inferred surface He abundances, which we determine simultaneously with structure parameters, are in agreement for the two data sets. The inferred values are Y =0.253 and 0.251 from LOWL and BBSO&BISON, respectively. Here, we focus on quantifying the corruption caused by the NSPA.

Like Basu et al. (1996), we use the SOLA method of inversion (Pijpers and Thompson 1992). Our reference model was constructed by Sienkiewicz and Pamyatnykh, and has no recent refinements like the inclusion of elemental diffusion. These omissions are inconsequential for the present application. The model very closely describes the Sun and this justifies the linearizations implicit in our inversions.

Inversion of the LOWL data, as provided, was followed by inversions which included various treatments of the NSPA effect. First, we removed the magnetic perturbation as implied by the [FORMULA] 's from the LOWL data. The perturbations for [FORMULA] -3 were of the order of [FORMULA] µHz and comparable with errors for only a few modes. At higher l 's, the perturbations were negligable. The effect of removing the magnetic perturbation on the inverted sound speed shown in Fig. 3 is noticeable only in two innermost points, but it is within the 1 [FORMULA] errors. Then, to assess the effect of the NSPA in years of high activity, we separately added to the LOWL data the effects implied by the [FORMULA] 's from 1989 and 1990 BBSO data-years of high activity. The frequency perturbations were one order higher than for the low activity data. In Fig. 3, the only results we show for high activity are those computed from the 1989 data because the results from the 1990 data are very similar. The figure clearly shows the size of the corruption - [FORMULA] at the innermost point, which is similar to the whole difference between the seismic and current standard models of the Sun. We emphasize that this innermost core is the part of the Sun which is critical for testing stellar evolution theory.

[FIGURE] Fig. 3. Relative seismic corrections to [FORMULA], the square of the isothermal speed of sound, as inferred from the original LOWL data and with two modified sets. The error bars reflect measurement uncertainties. The horizontal ones are the full width at half maximum of SOLA kernels, and the vertical ones are those on [FORMULA]. Removal of NSPA as determined from LOWL data results marginally significant changes in the deep core. The effect is so small because the data are from the activity minium. Adding the NSPA corrections implied by BBSO [FORMULA] 's from 1989, which was a year of high activity, causes a large change in [FORMULA] in the inner core.

The effect of the Sun's activity on structural inversions has also been discussed by Basu et al. (1996). They point out that it is important to use contemporaneous data in the inversions. We stress here that it is not enough to use data from the same phase of solar activity to eliminate its effect, but it is also necessary to remove the NSPA effect as determined from the fine structure in solar oscillation spectrum. We emphasize that all inversions for the structure of the core done previous to those in shown Fig. 2, have presumed that the near surface perturbation has no latitudinal dependence.

We conclude by noting that measuring even-a coefficients is important as a clue to the physics of solar activity, and for providing purifying information which enables more reliable probing the inner part of the solar core.

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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