## 1. Introduction
During the last three decades, the theory of line-driving has been
successfully applied to the winds from early-type hot stars, which
exhibit mass-loss rates and terminal
velocities . Based on the pioneering
work by Lucy & Solomon (1970), Castor (1974) and Castor et al.
(1975, hereafter CAK), Pauldrach et al. (1986, hereafter PPK) and
Friend & Abbott (1986) established the so-called The most promising application, which has been discovered
originally on a completely Of course, also stellar evolution is affected by rotational effects. Herrero et al. (1992) detected a systematic "mass discrepancy" in their quantitative spectroscopic study of a large sample of galactic O-stars. They found that for evolved O-stars approaching the Eddington-limit the stellar masses derived from evolutionary tracks and stellar luminosities are significantly larger than the masses obtained from spectroscopic gravities. Additionally, all rapid rotators of their sample showed a severe surface He-enrichment, the so-called "He discrepancy". Although an analysis by means of unified model atmospheres accounting for the presence of winds (Herrero et al. 2000) has mitigated the mass discrepancy (however not ruled it out), the He discrepancy could be confirmed. Recent evolutionary calculations by Langer and Heger (1998), Maeder (1999), Meynet (1998) have indicated that stellar evolution including rotation and rotationally induced interior mixing could enhance the luminosity significantly for given masses. In addition, enhanced mass-loss along the evolutionary track would further reduce the mass and bring the evolutionary masses into agreement with the spectroscopic (and wind) masses (Langer et al. 1994). From all of these perspectives, the neglect of rotation in the
description of hot star atmospheres (photosphere + wind!) seems
questionable. In recent years, this problem has been addressed by
several theoretical studies. PPK and Friend & Abbott (1986)
estimated the influence of stellar rotation on the wind dynamics in a
The assumption of spherical symmetry has been dropped the first
time by Bjorkman & Cassinelli (1993, hereafter BC). Employing the
supersonic approximation, they solved for the particle trajectories in
the polar plane, thus adopting The BC model predicts a So far, the analytical BC model has been applied, e.g., for
simulating the formation of Owocki et al. (1997, 1998) extended the BC model and studied
the effects of The non-radial components of the line force lead to an
These results are in entire contradiction to the predictions by the simple BC model and, meanwhile, have been independently confirmed by Petrenz (1999); for a recent review, see Puls et al. (1999). Although severely challenging the validity of the wind compression mechanism, the results by Owocki et al. and Petrenz do not exclude the possibility that this mechanism might be decisive for outflows driven by other physical processes than line-driving. One of the major problems of the described investigations is their assumption of force-multiplier parameters , , being constant throughout the wind. Moreover, these parameters have been taken from 1-D calculations, where, in the actual 2-D situation, they should be affected by at least two processes. Firstly, both density and ionizing radiation field are a function of co-latitude , and secondly, the assumption of constant force-multiplier parameters (with respect to radius) is rather questionable even for a uniformly bright stellar surface (cf. Kudritzki et al. 1998). Thus, global 1-D parameters do not correctly account for the
influence of Maeder (1999) has suggested the interesting possibility that due to
the specific dependence of the force-multiplier parameters on
temperature, the enhanced polar mass ejection due to gravity darkening
described above may be progressively compensated by the effects of
larger bound-free In this paper, we will introduce a procedure providing a 2-D
parameterization of the line acceleration by means of force-multiplier
parameters that are With this improved model we will try to give an estimate both for the consequences of stellar rotation on the wind dynamics and on maximum errors introduced by the assumption of a spherically-symmetric wind when, e.g., using mean relationships as the WLR. The paper is organized as follows: In Sect. 2 we introduce the wind
model and discuss the basic simplifications and approximations. In
Sect. 3, we provide the basic formulae for the vector line and
continuum acceleration. Sect. 4 describes how we determine the
ionization equilibrium and the occupation numbers in the wind. Sect. 5
gives an overview over the basic properties of the line
force-multiplier © European Southern Observatory (ESO) 2000 Online publication: June 20, 2000 |