Astron. Astrophys. 323, 488-512 (1997)

4. Summary and future perspectives

We have introduced a new and fast NLTE line formation code as a versatile tool for the spectroscopic analysis of hot stars with winds. We have shown that this code fulfills one of the most stringent requirements for such an objective, namely to reproduce both the photospheric stratification and the line profiles resulting from an alternative plane-parallel treatment in the case of very thin winds. Thus, we are now able to account for wind effects also in lines which are only weakly wind contaminated and avoid the problem of erroneously attributing inconsistent plane-parallel vs. expanding atmosphere results to real physics.

At first glance, the treatment of the wind by means of a prescribed velocity field and mass-loss rate may be regarded as a drawback compared to a consistent treatment including the theory of radiatively driven winds (e.g., the unified model atmosphere concept by Gabler et al. 1989). However, in view of the present uncertainties in the theory, mainly with respect to the " -problem" outlined in the introduction and the wind momentum problem (see Lamers & Leitherer 1993 and Puls et al 1996), this procedure provides the maximum degree of freedom for the synthesis of spectra and avoids biased results.

From the thorough tests we have performed in a wide range of spectral class, luminosity and wind density, three points have come to our attention which turned out to be essential for an accurate spectroscopic analysis of blue stars. First, the absolute temperature scale for stars with  K is uncertain if derived from HeI lines alone, since the strength of these lines almost exclusively depends on the behaviour of the HeII resonance lines, with all the present uncertainties such as the correct treatment of electron scattering and line-blocking in the spectral region below roughly 310 Å. Independent methods such as the analysis of the optical NIII, IV and V lines or the FUV ArVII lines (if available, cf. Taresch et al. 1996) will provide an additional check in future temperature calibrations, even if the situation for HeI has been clarified.

Second, for stars close to the Eddingtion limit one has to account for the photospheric extension, since this changes the slope of the pressure stratification and all related quantities such as the temperature run. Especially concerning the gravity determination (which is difficult for those objects in any case), this different slope and its consequences for the formation of the line wings can lead to significant changes in comparison to results derived from the plane-parallel approximation.

Finally (and most regretably), the diagnostics of atmospheres with only moderate wind densities are severely affected by the use of the Sobolev line transfer (even when used in a sophisticated form), as long as the escape probabilities are evaluated by assuming a foreaft symmetry. So far, one must use the "exact" transfer (e.g., CMF) since otherwise at least the inferred mass-loss rates would be underestimated due to an inappropriate refilling of the line cores in the SA simulation.

Although with the development (and first applications) of this code we have made significant progress towards the routine quantitative spectroscopy of blue stars with winds, some caveats should be mentioned.

The authors are well aware that the rather simple approach taken here is only the first step towards a realistic description, especially if one plans to analyze metal abundances or tries to use metal lines as indicators of stellar parameters (e.g., silicon for the temperature calibration of B-supergiants). Although the incorporation of the considered elements is easy to manage due to our data-driven input, the correct calculation of the ionization equilibria (especially of trace ions) requires one to account for the EUV line-blocking/-blanketing (cf. Sect. 1) and, if present, the soft X-ray/EUV radiation field (MacFarlane et al. 1993, Pauldrach et al. 1994, MacFarlane et al. 1994) arising from the cooling zones of shocks (Hillier et al. 1993, Feldmeier et al. 1996) generated by line-driven instabilities (Owocki et al. 1988, Feldmeier 1995) and the merging of consecutive shocks (also Feldmeier et al. 1996).

Since particularly the incorporation of an exact treatment of line-blocking is much too time-consuming for the concept outlined here, we will have to rely on approximate methods for calculating the required background opacities, e.g. in the spirit outlined by Schmutz (1991). Progress with respect to this task is under way in our group.

Finally, one of our ultimate goals is the NLTE abundance determination of iron group elements from optical lines in extremely luminous A-type supergiants, related to our objective of calibrating and using the wind-momentum luminosity relation in distant galaxies (cf. Sect. 1). Due to the enormous number of lines to be considered, the exact calculation of all transitions might turn out as prohibitive if a fast solution is aimed at, although Hillier (1996) has made significant progress into this direction. For our purposes, we have to develop reliable criteria which will allow for a seperation of lines into those to be treated in the CMF and those which can be approximated by the Sobolev transfer, without affecting the overall accuracy. This work has also been started.

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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