The parameters of each star obtained in different wavelength intervals are close to each other, except for Arcturus, where we can find large differences in both effective temperature and gravity. One of the possible reasons may be that the infrared regions used in this work are not overly occupied by lines.

The value obtained for [A/H] cannot be directly compared with that of [Fe/H] obtained by other authors because our value of [A/H] represents an averaged quantity, since the majority of lines are Fe-lines in the spectra of K-giants, the value of [A/H] has to be close to [Fe/H]. Moreover, small discrepancy between [Fe/H] available in the quoted literature and the results presented in this paper may be caused mainly by the choice of $g\!f$ values, and secondly by the model atmosphere adopted here. Nowadays MARCS models are usually emploied.

$\begin{figure} \includegraphics [angle=-90,width=14cm]{ds7741f2.eps}\end{figure}$

Figure 2: Result of the optimization of $\alpha$ Ari using the model ATLAS9 and the observed spectrum adopted from the catalogue of Montes et al. (1997). Solid line - observed spectra, dashed line - synthetic spectra

$\begin{figure} \includegraphics [angle=-90,width=14cm]{ds7741f3.eps} \includegraphics [angle=-90,width=14cm]{ds7741f4.eps}\end{figure}$

Figure 3: A comparison of observed (solid line) and the best fitted synthetic spectra (dashed line) for $\alpha$ Boo in the infrared region. The observed spectrum is taken from the Arcturus atlas (Wallace & Hinkle 1996)

$\begin{figure} \includegraphics [angle=-90,width=14cm]{ds7741f5.eps}\end{figure}$

Figure 4: A comparison of observed (solid line) and the best fitted synthetic spectra (dashed line) for $\alpha$ Cas. The upper observed spectrum is taken from ,Stefl (1985, 1994), the bottom one was adopted from Horn et al. (1996)

$\begin{figure} \includegraphics [angle=-90,width=14cm]{ds7741f6.eps}\end{figure}$

Figure 5: A comparison of the observed (solid line) and the best fitted synthetic spectra (dashed line) for $\beta$ Gem. The observed spectrum was acquired at Kraví hora observatory

Synthetic spectra presented in Figs. 2-5 are in good agreement with observed ones. Differences between them can be caused by the following effects: (1) abundances of each element may differ from [A/H], but large abundance optimization of selected elements (e.g. C, N, O, Mg, Fe), together with computation of appropriate model atmosphere, still overloads modern computers. However, for Arcturus we tried to compute abundances of individual elements with fixed main parameters (i.e. $T_{\mathrm{eff}}$ , $\log g$ , [A/H], $v_{\mathrm{turb}}$ ), but the results are inconsistent, probably because we used limited spectral regions. (2) Line profiles may be affected by NLTE effects, although Drake & Smith (1991) showed for $\beta$ Gem, that metallicities are not significantly affected by departures from NLTE. (3) Vertical stratification of some parameters, such us elements or microturbulent velocity, may affect line profiles (see for example Zboril 1996). (4) Finally, there may be errors in atomic constants, mainly oscillator strengths.

The present work mainly intended to show how spectrum fitting can be applied for the derivation of the atmosphere parameters of K giant stars. Another interesting comparison could be made while processing lines of each element separately, i.e. varying abundance of selected elements with constant atmosphere parameters (specially [A/H]), or, possibly, fitting lines of selected elements to obtain all atmosphere parameters. Moreover, discrepancies can be better discussed by the sorting of the lines by excitation potential, by ionization stages and by equivalent width. However, numerical tests showed that for such an analysis, spectra covering large wavelength intervals are required, but such study is beyond the scope of this paper.

Future research will be concentrated on the determination of atmosphere parameters of stars with lower metallicity (e.g. Pop II giants). This can help for a better understanding of the increasing discrepancy between the metallicities obtained for Arcturus. The results of these calculations will be part of a forthcoming paper (Krticka & Stefl 1999, in preparation).

The authors are thankful to J. Kubát for kind help and to B. Plez for kindly providing model atmospheres. This research disposed of the SIMBAD database operated at CDS, Strasbourg, France. Tables determining of $T_{\mathrm{eff}}$ , $\log g$ and [Fe/H] are taken from the catalogue of [Fe/H] determinations (Cayrel de Strobel et al. 1997). We wish to thank our referee, F. Spite, for valuable remarks on this manuscript.

6 Conclusions