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

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11. Comments

In this section we want to stress that our results are closely related with Kurucz models, Kurucz codes (see Sect. 3), and the data adopted by us. In fact, different codes may give different results and the same Kurucz codes and models may give different results when different data for the same star are analyzed.

An example of the first case is yielded by the different [FORMULA]  derived from the same [FORMULA] observations by Gratton et al. (1996) and by us. Our results are those listed in Table 6. The SUNK94 model perfectly reproduces the solar [FORMULA] profile when the original version of a code written by R. Gratton for computing Balmer profiles is used (Gratton et al.,1996); this would imply a solar [FORMULA]  from [FORMULA] as low as 5777 K. However, a close comparison between Kurucz's code and Gratton's code for computing Balmer lines, performed in the context of the present research, has shown that the different results obtained with the two independent codes are mostly due to small errors in the continuum opacity routines used by Gratton et al. (1996). These errors were not previously detected because Gratton et al. goals was a bare 1% accuracy in the profiles (corresponding to an accuracy of [FORMULA]  K in [FORMULA]). This value was accepted by Gratton et al. because it was considered as an optimistic estimate of the systematic errors related with the position of the continuum level in the Balmer line regions of subdwarf spectra. As a consequence of these errors in the continuum opacity routines, Gratton et al. underestimated the continuum opacity by [FORMULA] %, resulting in too large fluxes (by [FORMULA] %) and too strong Balmer profiles (by [FORMULA] %, that is the accuracy of Gratton et al. calculations). Once these errors have been removed, Gratton's code reproduces both fluxes and profiles obtained with Kurucz's code within [FORMULA] %. The small residual difference can be ascribed to a different list of elements used in the solution of the state equation, and to some different numerical approximations in the Gratton and Kurucz codes. The residual difference corresponds to an uncertainty of no more than 20 K in the derivation of the solar [FORMULA]  from the [FORMULA] profile.

As example that same codes but different data for the same star may give different results we point out the different [FORMULA] for the Sun derived from the [FORMULA] and [FORMULA] profiles and the SUNK94 model by us ([FORMULA] 5900 K) and by Van't Veer & Mégessier (1996) (6200 K) (Sect. 4). We used the Kurucz et al. (1986) Solar flux Atlas based on the Kitt Peak FTS spectra having a resolwing power of about 500000 in the H [FORMULA] region. Van't Veer & Mégessier (1996) used spectra observed at the Haute Provence Observatory by means of the 152 cm telescope equipped with the Aurélie spectrograph and having a resolwing power of about 20000 in the H [FORMULA] region.

We want also to stress that our results follow from the physics used in Kurucz codes and that more realistic physics for the stars would probably give different results. In according to Kurucz (1996) "The first point to emphasize is that no matter how convection is computed in one dimension, it is wrong". Therefore some differences between observations and computations in cool stars could be explained with the unrealistic convection theory used in the models. In particular a two component model for the convection with 80 to 90% of the stellar surface hot and the remainder cold would produce different results of those derived from the one dimensional models used in this paper. For instance, we could predict that raising hot elements would raise the ultraviolet flux so that the c1 index from the one-dimensional K95 models would increase and possibly reach the same size of the c1 index predicted by the classical mixing-length theory of the NOVER models. Such a two streams convective model would also explain the too weak wings of the Balmer profiles predicted by the K95 models. In fact, the populations of the second level of hydrogen would be higher in the hot rising elements so that the Balmer lines would possibly become as broad as those predicted by the classical mixing-length theory of the NOVER models.

To explain the disagreement between the observed and computed solar continua shortward [FORMULA] we could invoke physical processes which increase the opacity. We tested that a turbulent pressure in the hydrostatic equilibrium equation corresponding to a constant microturbulent velocity of 1.5 km s-1 does not change the results. However, a microturbulent velocity increasing with depth would raise the opacity at depth and reduce it toward the surface. This different opacity distribution with depth might account for the discrepancy between the observed and computed solar continua.

All the above predictions need new sets of models to be fully verified.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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