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Astron. Astrophys. 323, 909-922 (1997)

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6. Discussion and conclusions

The data we presented in the preceding sections benefit very much from the recently installed fiber optics cassegrain échelle spectrograph F OCES: the effective temperatures of the stellar objects are determined from the simultaneous observation of H [FORMULA] [FORMULA] 6562 and H [FORMULA] [FORMULA] 4861, supplemented by H [FORMULA] [FORMULA] 4340 and H [FORMULA] [FORMULA] 4101 in metal-poor stars. The gravity determination employs lines, such as Mg I [FORMULA] 4571 and Mg I [FORMULA] 5711, which are separated by more than 1000 Å, but homogeneous in the data reduction. The abundance analysis is confined to iron lines as free of blends as possible. Again, a range spanning about 2000 Å is considered for this purpose.

First light for this spectrograph has been a solar spectrum, which we compared to the Kitt Peak Solar Flux Atlas (Fig. 3) and which was subsequently used to derive the "stellar parameters" of the Sun. These initial tests were then followed by a detailed investigation of the notorious F5 standard Procyon. Similar to the results of Steffen (1985), a [FORMULA] around 3.6 is obtained from the ionization equilibrium of iron lines, in sharp contrast to the accurately known astrometric value [FORMULA]. This discrepancy is however circumvented if we employ the wings of the strong Mg Ib lines. The analysis of other cool dwarf stars in this temperature range shows similar, albeit less pronounced, systematic deviations in the gravity determination. In this respect our results completely agree with the findings of Edvardsson (1988b), although our objects are about [FORMULA] K hotter on average.

There is, however, a number of uncertainties we have to be aware of. First of all, we learn from the analysis of the Procyon spectrum, that the standard model atmosphere approach has severe limitations. NLTE effects may be responsible in the case of Procyon, as well as other, especially metal-poor stars (e.g. Magain & Zhao 1996). The underlying temperature structures pose additional questions. Here, the treatment of convection and the amount of line blanketing - to name only two of the ingredients - deserve special attention. Obviously none of contemporary model atmosphere programs can reproduce all observable parameters such as the continuous energy distribution, the limb darkening or Balmer line formation (cf. Holweger et al. 1995, Castelli et al. 1997). Since our approach is to derive the stellar parameters exclusively from the analysis of spectral lines, we give most weight to the information available from these tracers. This has led to the empirical calibration of the mixing-length parameter from the analysis of Balmer lines in Fuhrmann et al. (1993). The value proposed in that work, [FORMULA], is still the one we prefer in our actual grid of model atmospheres (the exact number, of course, depends on which formalism of the mixing-length theory one refers to, and the kind of model atmosphere program used).

But can we trust such empirical calibrations? How reliable are the so-derived stellar parameters? We have argued in the sections above, that accurate stellar parameters from very direct methods in our temperature/gravity range are only known for Procyon. From the wings of its Balmer lines we find an effective temperature close to the interferometric value. The analysis of Fe I lines reveals shortcomings in the ionization equilibrium, but the very differential method to derive the gravity parameter from the strong Mg Ib lines sticks close to the astrometric value. It seems very unlikely that these results are fortuitous.

In their analysis of Arcturus Blackwell & Willis (1977) considered the Mg Ib line [FORMULA] to be unsuitable for a surface gravity determination, because of a lack of weak lines for the abundance determination originating from a similar lower level. In addition, Edvardsson (1988b) argued that the Mg Ib lines are notably asymmetric, which led him to exclude the triplet from his list of appropriate strong lines.

Inspection of Fig. 10 and 11 shows especially [FORMULA] to be slightly asymmetric on the short-wavelength side, but this does not influence our results very much. Excluding the line core of [FORMULA] from the analysis, a slight shift of the observed profile to longer wavelengths is feasible. As a consequence the surface gravity value can be increased to match the observed profile. The correction is however very small and, in the case of Procyon, adjusts the [FORMULA] value from 4.00 to 4.02 only. For this reason we do not carry out a detailed synthetic spectrum analysis of the [FORMULA] region. Instead our approach in Fig. 10 to 13 is rather conservative in that we increase the [FORMULA] until at least one wing matches the observations. The proposed [FORMULA] values are therefore lower limits on the [FORMULA]  dex scale if line blends play a role, whereas metal-poor stars remain unaffected and show symmetrical wings (cf. Fig. 13).

The absence of suitable weak magnesium lines from [FORMULA] eV, the lower level of the Mg Ib lines, is certainly disadvantageous to our analysis. Erroneous effective temperatures, as well as NLTE effects may have some impact on the results. It is therefore encouraging that the two most important Mg I lines we make use of, [FORMULA] ([FORMULA] eV) and [FORMULA] ([FORMULA] eV) are consistent in the magnesium abundance to within 0.03 dex for each star (HD 19445 and HD 140283 are excluded, since both lines are rather weak in these stars). We take this as further evidence that our temperature scale is adequate and the surface gravities reliable to 0.1 dex. It is only for the very metal-poor stars that the uncertainties increase, because less absorption lines of iron and magnesium are available and the Mg Ib lines show larger deviations in the line cores (cf. Fig. 13).

The systematic deviation of the surface gravity parameters in Table 3 has of course consequences on the kinematics and evolution of the Galaxy. HD 19445, for instance, is either close to the main sequence or in the region of turnoff stars depending on which surface gravity determination we refer to. With the larger [FORMULA] parameter all stars become less distant and consequently the space velocities decrease. Another direct implication arises from the comparison of evolutionary sequences, where considerable changes of the stellar ages are conceivable.

Due to our differential analysis, we do not expect large deviations in the stellar parameters for stars that are close to the Sun in neither [FORMULA] nor the metal abundance. For cooler objects notable changes may arise, but certainly the hotter stars with their extreme ionization balance of iron and magnesium are prone to considerable changes if we dismiss the ionization equilibrium and especially Fe I lines from the analysis of stellar parameters of F and G stars.

In conclusion, the bright F5 star Procyon is an encouraging example to demonstrate that reliable stellar parameters for this object can be derived from conventional model atmosphere analyses. Nevertheless, the situation is unfortunate in that we have no other calibrating stars at our disposal in the temperature/gravity range considered here. In this respect, the most urgent task is to improve direct stellar diameter measurements from ground-based interferometry or satellite projects such as GAIA, which is designed to measure at the [FORMULA] as level (Bastian & Schilbach 1996). More refined data of this kind will cause a major improvement in the fundamental parameters of cool dwarf stars.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998