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

1. Introduction

Although it has in principle been possible for more than a decade and was promised in a variety of papers, the quantitative spectroscopy of large samples of "normal" hot stars accounting for radiatively accelerated outflows is still waiting to be undertaken, and has been performed only for a small number of mostly extreme and therefore untypical objects ¹.

This problem and the corresponding lack of information related to the physical conditions in the upper HRD is a consequence of the different available atmospheric and line formation codes:

On the one hand, there is a class of code which has obtained such a high degree of sophistication that only a few people can use them. Furthermore, the computational time required to run a specific model becomes too large to cover a significant subspace of the total parameter space (which is at least of dimension three for a given He-content/metallicity) under consideration.

Alternative codes which are based on simpler physics (and hence have smaller turn-around times) suffer inevitably from some approximations which are insufficient in certain parameter ranges. In our opinion, the most severe restriction of these codes is the missing applicability to stars with thin or moderate winds, i.e., when the optical lines are still in absorption but already affected by the outflow. This failure typically arises because of an inappropriate formulation of the photospheric structure equations and/or the use of the Sobolev approximation for calculating radiative bound-bound rates.

In view of these difficulties, and in order to address the open questions related to stars with expanding atmospheres (see below), some years ago the authors of the present paper decided to develop a new NLTE line transfer code which should fulfill the following requirements:

• consistent atmospheric structure, especially in the subsonic/photospheric region.
• applicability over the entire upper HRD, beginning with stars of spectral type "A"
• reproduction of results from plane-parallel and hydrostatic models in cases of very thin winds
• "data driven" input of atomic models, following the philosophy of standard hydrostatic NLTE-codes (e.g., DETAIL, see below)
• easy to use, robust, fast and portable

The zero-version of this code was finished last year (Santolaya-Rey 1995), however, it did not completely match the above requirements. Meanwhile, we have worked on some additional improvements, mostly related to the photospheric structure and the incorporation of the comoving frame line transfer. Together with some of our collaborators, we have tested and applied the code for a variety of objects in the defined spectral range, from A-type Supergiants to O3-stars and central stars of planetary nebulae (CSPN). Since we are now convinced that it works robustly and reliably (at least with H/He opacity only), we want to describe its features in a first, more technical paper, before we present the results obtained with this code in some forthcoming papers. ²

The underlying assumptions of a new program package always depend on the kind of questions one is seeking to address. Since we do not present any application to real stars in this paper, we will at least mention some of these questions which our working group is especially interested in to illustrate the chosen philosophy.

The mass and helium problem for O-stars. A careful analysis of a large sample of O-stars by Herrero et al. (1992) indicated that the spectroscopically derived masses of these stars are systematically lower than the masses predicted from standard stellar evolution. Moreover, the derived He abundance was found to be much larger than the model predictions. Both problems may vanish if one allows for an evolution with rotationally induced mixing (Langer & Maeder 1995). Nevertheless, a careful reanalysis for stars of low luminosity class remains to be done, since Herrero et al. performed their analysis on the basis of plane-parallel NLTE models, thus neglecting stellar wind effects. The inclusion of these effects might change the picture due to a different pressure stratification (the so-called "unified model atmosphere correction", cf. Gabler et al. 1989; Puls et al. 1996) and additional wind emission, both of which increase the inferred masses to higher values. The latest investigations by Lanz et al. (1996) confirm this expectation, and also the consistent FUV, UV and optical analysis of the extreme O3 If star HD 93129A by Taresch et al. (1996) resulted in a mass in agreement with standard evolution. On the other hand, an analysis of HDE 226868, the optical counterpart of Cygnus X-1, using unified models (Herrero et al. 1995) indicated that the wind effects are not large enough to compensate for the whole mass discrepancy, and that they do not significantly affect the helium abundances. Thus, both open questions have to be clarified by extending the Herrero et al. sample to stars with significant mass-loss (which were deliberately left out) and the use of adequate analysis methods. In addition, the presence of the helium problem has to be corroborated by consistently analyzing the CNO abundances of these stars.

The " -problem". As a by-product of the mass-loss determination performed by Puls et al. (1996), it turned out that O-stars with dense winds seem to have velocity fields which deviate from the predictions of standard radiation driven wind theory. If we characterize the typical velocity field in terms of the usual -parameterization (e.g., Eq. 1), then we find from theory in all cases which are not very extreme a value of (Pauldrach, Puls & Kudritzki 1986). However, the analysis of , which reacts very sensitively to the wind density and thus to the velocity law when in emission, revealed values of for the winds of supergiants. The same seems to be true for a number of CSPN (Méndez, priv.com.) This fact poses a significant problem both for the theory and for the analysis methods to be applied. For the former, the observed velocity structure remains to be explained (e.g., influence of multi-line effects?). For the latter, we have at least to account for the possibility that different 's are present, since otherwise the spectroscopic results could lead to erroneous conclusions, as was demonstrated, e.g., by Schaerer & Schmutz (1994).

Calibration of the wind-momentum luminosity relation for AB supergiants. The so-called wind-momentum luminosity relation (WLR) of hot stars (see Kudritzki et al. 1995 and Puls et al. 1996 for a theoretical explanation) will most probably provide a new tool to determine an independent extragalactic distance scale by exploiting the dependence of radiatively driven winds on luminosity. While the calibration of this relation for O-type supergiants is almost finished (see Puls et al.), the continuation to spectral types B and A has suffered from the lack of a versatile and fast tool to perform the required NLTE diagnostics. By means of the code described here, however, our group has now made significant progress on AB supergiants and will present the results in a forthcoming paper.

Besides these central topics of immediate interest, a number of other, related points have to be clarified in the near future. We briefly mention the ongoing project of testing the theory of radiatively driven winds in the same spirit as outlined by Puls et al., however concentrating on the spectral ranges AB and on CSPN. This work, of course, will be done in parallel with the establishment of the corresponding WLRs.

The analysis of processes related to the effects of rotation and the presence of macro-structures (e.g., Massa et al. 1995, Prinja et al. 1995) in the winds of hot stars by means of detailed line diagnostics has made significant progress in the last years. Although we still assume that these effects are of only secondary influence on the gross behaviour and on the analysis of expanding atmospheres, there is no doubt that they are present and that they may contaminate the spectra and our conclusions. (See, e.g., Petrenz & Puls (1996) for the influence of rotation on the mass-loss rates in the framework of the kinematic model provided by Bjorkman & Cassinelli (1993).) Because of the dominant NLTE conditions in the atmospheric regions under question, reliable predictions of the dependence of the occupation numbers on external parameters are urgently required. By means of (relatively) simple and fast calculations as discussed here, we can obtain much more insight concerning the dominating population processes of the participating levels and develop realistic line formation models.

With these problems to be solved in mind, the atmospheric model underlying our assumptions is as simple as possible, however accounts also for all (stationary) processes required to establish a consistent photospheric structure including spherical extension and continuum radiative acceleration. A thorough description (inclusive our atomic model) is given in Sect. 2 and Appendices A, B and C.

One of our most important objectives was to develop a fast code. Thus, the formulation of the bound-free rates (which mainly control the convergence behaviour) is decisive and presented in Appendix D. Also, we have reformulated the usually very time-consuming calculation of the formal integral in Sect. 2.4 and Appendix E.

In Sect. 3, we describe thorough tests of the code (convergence behaviour, flux conservation) and compare results from it to well-established plane-parallel results, both for the atmospheric structure (3.1) and strategic line profiles (3.4). The use of comoving frame transfer is most important for preciseness and the reproduction of profiles from plane-parallel models in cases of very thin winds. A comparison to alternative Sobolev transfer results is given in Sect. 3.5. Sect. 4 gives the conclusions, some caveats and future perspectives.

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

helpdesk.link@springer.de