Wolf-Rayet (WR) spectra are characterized by bright and broad emission lines which are formed in strong stellar winds, and adequate models are prerequisite for their quantitative analysis. Corresponding techniques for calculating the non-LTE radiative transfer in spherically expanding atmospheres became available during the last decade (e.g. Hillier 1987a,b; Wessolowski et al. 1988), and are progressively applied to observations in order to determine the parameters of these stars (as recent examples, see e.g. Crowther & Smith 1997, or Hamann & Koesterke 1998). These so-called standard models for WR atmospheres are based on the assumptions of spherical symmetry, homogeneity and stationarity of the flow.
The main features of WR spectra can be reproduced by standard model calculations, thus validating its basic assumptions as a reasonable approximation. However, there are specific evidences that real WR atmospheres are actually more complicated in detail. The assumptions of stationarity is questioned by the observed line variability, e.g. explained as migrating optical depth enhancements by Prinja & Smith (1992). Polarization also shows stochastic variability (e.g. Brown et al. 1995). Theoretical modelling of radiation-driven winds predict hydrodynamical instabilities leading to shocks, density enhancements and rarefactions (e.g. Owocki et al. 1988, Owocki 1994, Feldmeier 1995). The X-ray emission generally detected from WR stars (e.g. Pollock et al. 1995, Wessolowski et al. 1995) obviously originates from hot, shocked gas embedded in the outer atmosphere (Baum et al. 1992).
Conclusive evidence for inhomogeneities ("clumping") in WR winds comes also from the detailed study of the line wings. Radiation transfer theory predicts that electron scattering causes a frequency redistribution of line photons (due to their low mass the electrons have a high thermal velocity). The consequences of this effect on Wolf-Rayet emission lines were demonstrated already by Hillier (1984).
Nevertheless, frequency redistribution by Thomson scattering was neglected for simplicity in the first generation of WR models used for spectral analyses (e.g. Hamann et al. 1988, Hillier 1988). Analyses of WR spectra which do account for that effect (e.g. Hamann et al. 1992, 1994, 1995a) revealed that the (homogeneous) models always tend to overestimate the strength of electron scattering wings.
Physical arguments suggest that clumping reduces the relative contribution of these wings. A first numerical investigation of inhomogeneous models by Hillier (1991) confirmed these expectations. His Monte-Carlo calculations indicate that the electron scattering process might be approximated, to acceptable accuracy, by assuming isotropic redistribution instead using the more accurate dipole phase function. Schmutz (1997) modeled the clumping in the same approximation as we will apply in the present paper.
In the present paper we use the electron scattering wings for investigating the consequences of clumping to the analyses of WR spectra. In the following section (Sect. 2) we characterize our standard model calculations. Then we describe how the effects of clumping are accounted for in first approximation (Sect. 3). In Sect. 4 we calculate synthetic spectra for different spectral subclasses of WR stars and compare them with the observation. For selected stars of different spectral subclasses the degree of clumping (density enhancement) is roughly estimated. The consequences for the empirically derived parameters of WR stars are discussed in the concluding section (Sect. 5).
© European Southern Observatory (ESO) 1998
Online publication: June 26, 1998