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Astron. Astrophys. 318, 841-869 (1997)

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5. The problem of the level of the continuum in the Sun

We showed in the previous section that the SUNK94 model yields a very good agreement between the observed and computed irradiances in absolute flux units, but that it yields a level for the true continuum higher than that deduced from the observations when high resolution spectra absolutely calibrated are analyzed. The discrepancy decreases with increasing wavelength, being on the order of 6.6% in the [FORMULA] region and almost zero at [FORMULA].

This surprising inconsistency between the good agreement of observed and computed irradiances and the bad agreement between observed and computed continua, in spite of the same Neckel and Labs (1984) absolute calibration for the data was used, could be explained, for instance, with the inadequacy of the local theory of the mixing-length for the convection. In the previous section we showed that the changing of the mixing-length parameter, or the dropping of the "overshooting" option, are not able to eliminate the difference between the observed and computed continua. Possibly, 2D hydrodynamical computations would change the model structure in such a way that any inconsistency would be cancelled.

Another possibility to explain the inconsistency is either a too large computed local line blanketing in low - resolution spectra or a too low local computed line blanketing in high - resolution spectra. In fact, high - resolution spectra are computed only with lines arising from observed levels, while low - resolution spectra include also lines arising from predicted levels. A less local line opacity in low-resolution spectra would yield an irradiance higher than that predicted by the SUNK94 model, so that both the computed true continuum and the computed irradiace would be higher than the predicted ones. In fact, the more numerous are the lines in a given wavelength interval of a low resolution spectrum, the more the computed flux lowers, while the level of the local continuum does not change. We checked that the computed continuum is the same both in low- and high - resolution spectra, which are computed with a different number of lines. We then increased the line opacity for computing high - resolution spectra in the [FORMULA] region by adding the lines arising from the predicted levels. The difference between the observed and computed spectra shown in the middle panel of Fig. 7 does not change, indicating that the flux discrepancy in high-resolution spectra does not depend on the number of lines.

Finally, the continuum opacity could be underestimated. We investigated the influence of the opacity sources on the continuum level: H is the dominant opacity source in the [FORMULA] region, but also the ultraviolet line blanketing affects the model temperature structure. Minor opacities sources are the b-f and f-f transitions of neutral metals, the electron scattering, and Rayleigh scattering from neutral hydrogen.

5.1. The H opacity

In the ATLAS9 version used by us the bound-free and free-free cross-sections for H are those computed by Wishart (1979) and by Bell & Berrington (1987) respectively. They estimated the errors to be on the order of 1%. We checked that the H opacity computed by the ATLAS routines is exactly that obtained by means of the analytical formulas yielded by John (1988), which were derived by fitting the Wishart and Bell & Berrington cross-sections with polynomials. Therefore, the ATLAS9 code stored on the CD-ROM No. 13 appears to be a later version than that used by Blackwell & Lynas-Gray (1994), who stated that the temperature derived from Kurucz models increases of 0.38% at 5000 K when the calculations of H opacity from John (1988) are used.

To estimate the effect of hypothetical errors in the computation of the H cross-sections, we artfully increased the H bound-free cross-section by 10%. The level of the continuum in the H [FORMULA] region lowers by 1.4%, a too small quantity to account for the discrepancy of about 6.6% between the observed and computed continua in absolute flux units (Sect. 4, Fig. 7).

5.2. The metal opacity

The continuum opacity from metals lowers the ultraviolet flux shortward than 255 nm and increases slightly the visual flux. When the total metal opacity is dropped the level of continuum in the [FORMULA] region decreases of about 0.9%, a too low value to justify the assumption that the discrepancy between the observed and computed continuum levels is caused by some bound-free or free-free metal cross-section computed too large.

5.3. The Rayleigh scattering from neutral hydrogen and the electron scattering

Their effect on continuum level is fully negligible in the visible.

5.4. The line blanketing

The effect of line blanketing on the model structure is so important that the shape of the whole energy distribution may change even for small changes of line blanketing in some limited wavelength regions. Abundances different from those of Anders & Grevesse (1989) for some elements (i.e. the iron) or different line data would yield different ODF's than those used for computing the SUNK94 model, so that the whole model structure would be modified.

To test the effect of the iron abundance on the model structure we replaced ODF's computed for [FORMULA] equal to -4.37 dex (Anders & Grevesse, 1989) by ODF's computed for [FORMULA] (Holweger et al., 1995). The 0.16 dex smaller iron abundance than that from Anders & Grevesse (1989) lowers the line blanketing and decreases the absolute flux by about 1.1% in the [FORMULA] region (Fig. 9, upper plot,thick line). Therefore, the different abundance for iron decreases the gap between the observed and computed continua even if to a less extent than that required to explain to 6.6% discrepancy. Fig. 10 compares the emerging energy distribution and continuum predicted by the SUNK94 model (dashed line) with those predicted by the model with the lower iron abundance (full line). The difference between the two computed continua decreases longward of the Balmer discontinuity with increasing wavelength, in analogy with the difference between the SUNK94 continuum and that suggested by high-resolution observations. Although computed continua are different, the emergent fluxes do not differ in an appreciable way.

[FIGURE] Fig. 9. Comparison between computed [FORMULA] profiles for the Sun in absolute flux units. Upper plot: profiles computed from solar models with different iron abundances. Thin line is for log  [FORMULA] / [FORMULA] =-4.37 (SUNK94 model), thick line is for log  [FORMULA] / [FORMULA] =-4.53 (Holweger et al., 1995). Lower plot: profiles computed from solar models with a different amount of line blanketing. Thin line is for a line blanketing corresponding to the Anders & Grevesse (1989) chemical composition (SUNK94 model), thick line is for a line blanketing corrsponding to a 0.2 dex lower metallicity. The ordinate is the flux [FORMULA] in 9.5 106  erg cm-2 sec-1 nm-1
[FIGURE] Fig. 10. Comparison between fluxes and continua from solar models computed with the two different iron abundances log  [FORMULA] / [FORMULA] =-4.37 (SUNK94 model, dashed line) and log  [FORMULA] / [FORMULA] =-4.53 (full line)

To show further the importance of the line blanketing for the model structure and therefore for the prediction of low- and high-resolution spectra, we simulated the effect of a still lower line blanketing than that given by ODF's computed for log ([FORMULA] / [FORMULA])=-4.53. We computed a model having continuum opacities corresponding to solar abundances, but line opacities corresponding to a metallicity 0.2 dex lower than the solar one. Fig. 9 (lower plot) compares the [FORMULA] from this model with [FORMULA] from the SUNK94 model. The difference is very similar to that between the observed and computed profiles shown in Fig. 7. This model is only an experiment with no pretension of reproducing the real solar atmosphere. In fact, it yields a too low irradiance longward 580 nm and a too low continuum in the [FORMULA] region. However, it indicates that the line blanketing could be the cause of the disagreement in high resolution spectra between the observed and computed solar true continua as well as the theory of the mixing-length adopted for the convection.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998