Solar-Type Stars

For the solar-type model, we used $\hbox{$\,T_{\rm eff}$}=5770\,{\rm K}$, $\log(g)=4.44$ and solar abundances. The only difference with the NextGen models is the use of PHOENIX's NLTE mode, which includes the effects of multi-level NLTE on the EOS, the radiative transfer (both lines and continua) and the structure of the atmosphere. This model is a very simple model for the solar spectrum, for example we have not used the best value for the mixing length parameter for the sun of $\alpha=1.5$ and have used only simple approximations for the damping constants of most spectral lines. Therefore, the model cannot reproduce the solar spectrum as well as a fine tuned model could, we only use it to demonstrate the effects of NLTE on solar type stars.

Table 1 gives a complete listing of all NLTE species currently available in PHOENIX. For the solar model, not all of these are important, therefore we have used only the following sub-set of species in NLTE: H I, He I-II, Li I, Na I, Ne I, Mg II, Ca II, Ti I-II, S II-III, Si II-III, C I-II, N I-II, O I-II, and Fe I-III. This resulted in a total of 4,143 NLTE levels and 49,324 primary NLTE transitions. 26,786 of the primary NLTE lines were treated with detailed Voigt profiles, the remaining 22,538 weak primary NLTE lines were treated with Gaussian profiles to save CPU time. In test calculations we verified that this does not change the results significantly. In addition, the NLTE models include 218,009 secondary NLTE lines as well 385,484 LTE background atomic lines and 1,566,441 LTE molecular lines, these lines were selected using the same criterion that we use for the LTE models. The calculation was performed with a variable resolution wavelength grid with about 300,000 points, including extra points that are inserted to resolve NLTE lines. We are currently adding Mg I, Si I, S I, Ca I, and H^- to our list of NLTE species and we will produce improved models in cases where these species are significant.

In Fig. 5 we show the comparison between the Kitt Peak Solar Atlas [Kurucz et al.(1984)Kurucz, Furenlid, Brault, and Testerman] spectrum and the simplified solar model. The resolution of the Kitt Peak spectrum is extremely high ($0.01\hbox{\AA}$). Therefore, we have reduced the resolution by convolving the spectrum with a Gaussian kernel with a width of $10\hbox{\AA}$, shown as the full curve in Fig. 5. The same procedure was used to plot the synthetic spectrum (dotted line). In Fig. 6 we show the comparison at an enlarged wavelength scale. In this figure, the Kitt Peak spectrum and the PHOENIX spectrum were left at their original resolution (the resolution of the PHOENIX spectrum is variable, $\Delta \lambda \le 0.05\hbox{\AA}$). The fit is in general good, although fine tuned model parameters would improve the comparison.

The structure of the atmosphere is shown in Fig. 4 and in more detail in Fig. 7. The differences between the LTE and NLTE structures is very small. We show selected departure coefficients for the solar model in Fig. 8. In the line forming regions, typically between $\ifmmode{\tau_{\rm std}}\else\hbox{$\tau_{\rm std}$}\fi=10^{-3}$ and unity, the departure coefficients are very close to one and many lines thus form basically under LTE conditions. The departure coefficients drop rapidly at lower optical depths. In this region, the chromospheric temperature rise (which is not included in the model) would change the results drastically above the solar temperature minimum of about $4400\,{\rm K}$. The wide range of different atoms and ions that are included in this model gives an overall impression of the average importance of the NLTE effects in the photosphere of the Sun. We expect that the other elements, not treated in NLTE in this model, will roughly follow the selected ions shown in Fig. 8. The NLTE effects on the photospheric structure and the line forming regions are small, therefore, LTE models can be used as a first approximation to model the photospheres of solar type stars. This is consistent with the results of [Anderson(1989)Anderson], who used a different numerical approach. The relatively high electron densities in the line forming region, which make the collisional rates more important in solar type stars compared to either hotter or cooler stars is the reason that LTE is a good approximation for solar type stars.