Recent progress in the quantitative analysis of Wolf-Rayet stars is reviewed, emphasising the role played by choice of spectral diagnostics, clumping and line-blanketing on derived stellar properties. The ionizing properties of WR stars are discussed, based on clumped, line-blanketed models for WN and WC stars. The role of metallicity and mass-loss is assessed, and the role of H II regions as probes of predicted Lyman continuum distributions. Suggestions are made for differences in observed properties of WCE and WO subtypes.

Until recently, a major deficiency of most spectroscopic modeling of hot stars was the neglect of line-blanketing. With the availability of new atomic data, faster computers, suitable approximations, and improved numerical techniques it is now feasible to include non-LTE line-blanketing due to CNO and iron group elements in atmospheric calculations. We highlight the capabilities of the present generation of models. New blanketing results are presented for WN and WC Wolf-Rayet stars, and for LBVs. Line-blanketing alters individual line strengths in unpredictable ways, and can significantly influence the determination of stellar parameters. We specifically highlight the UV spectral region in which the effects of Fe blanketing are directly manifested. The importance of the charge exchange reaction Fe2+ + H ⇌ Fe+ + H+ for modeling of the Fe emission lines in the extreme P-Cygni star HDE 316285 is illustrated.

The quantitative analysis of Wolf-Rayet type spectra requires non-LTE models for expanding atmospheres which have been developed in the last decade. Idealizing assumptions of the so-called standard model are spherical symmetry, homogeneity and stationarity. While the first generations of models were restricted to simple atoms (helium, hydrogen), we now apply more advanced calculations which account for complex model atoms (nitrogen, carbon, oxygen). The re-analysis of the Galactic WN sample from the nitrogen lines led to a substantial revision of the stellar parameters, as far as the WNE-w subclass is concerned. Wind inhomogeneity ('clumping') has been accounted for in a first-order approximation. The degree of clumping is derived from the electron-scattering wings of strong lines. With clumped models, considerably lower mass-loss rates (by a factor two or more) are obtained, while other empirical parameters are not affected significantly. An overview is given about the fundamental parameters of Wolf-Rayet stars as obtained from spectral analyses, including new results on WN stars in the LMC.

We discuss the reliability of the stellar parameters derived from spectroscopic analyses with atmosphere models. We follow the revisions of the stellar parameters of a WN4b star through improvements of the model codes carried out in the last ten years. In order to judge the reliability of the current results we have started to analyze binaries for which the mass of the WR star is known and therefore its luminosity can be derived from the theoretical mass-luminosity relation. Along this line, we present preliminary results from work in progress on the binary γ2 Velorum.

We review the dynamics of winds from single Wolf-Rayet stars, with emphasis on the following specific points:

1. (a) The classical “momentum problem” (to explain the large inferred ratio of wind to radiative momentum, η Mv∞/(L/c) ≫ 1) is in principle readily solved through multiple scattering of radiation by an opacity that is sufficiently “gray” in its spectral distribution. In this case, one simply obtains η ≃ τ, where τ is the wind optical depth;

2. (b) Lines with a Poisson spectral distribution yield an “effectively gray” cumulative opacity, with multi-line scattering occuring when the velocity separation between thick lines Δv is less than the wind terminal speed v∞. In this case, one obtains η ≃ v∞/Δv;

3. (c) However, realistic line lists are not gray, and leakage through gaps in the line spectral distribution tends to limit the effective scattering to η ≲ 1;

4. (d) In WR winds, ionization stratification helps spread line-bunches and so fill in gaps, allowing for more effective global trapping of radiation, and thus η > 1;

5. (e) However, photon thermalization can reduce the local effectiveness of line-driving near the stellar core, making it difficult for radiation alone to initiate the wind;

6. (f) The relative complexity of WR wind initiation may be associated with the extensive turbulent structure inferred from observed variabililty in WR wind emission lines;

7. (g) Overall, the understanding of WR winds is perhaps best viewed as an “opacity problem”, i.e., identifying the enhanced opacity that can adequately block the radiation flux throughout the wind, and thus drive a WR mass loss that is much greater than from OB stars of comparable luminosity.

The presence of a nearby O star offers the potential for studying the response of a Wolf-Rayet wind to external irradiation from a well-understood UV source. The O starlight offers not only a passive diagnostic probe, but also the potential for a dynamical interaction whose nature relates directly to fundamental issues of how WR winds are driven. It may even decelerate the WR wind prior to the wind/wind interaction, an effect we term radiative braking. We report on recent progress in WR+O wind-wind interaction models that incorporate the influence of the O starlight on the incident WR wind, and also the effect of the WR starlight on the acceleration of the O-star wind. A recurrent theme is the importance of feedback between the line force and the gas dynamics, and the leveraging that results.

We give results of models of massive stars which have a detailed physical treatment of rotation, including structural equations for shellular rotation, new treatments of shears in differentially rotating stars and of meridional circulation, together with mass loss rates depending on rotation. For a 20 M⊙ star, He- and N-enrichments at the stellar surface already occur during the MS phase for moderately low rotational velocities, thus most supergiants are enriched in helium and nitrogen. A long B- and A-supergiant phase results from rotational mixing, with some primary nitrogen formed at this stage. For the most massive stars, rotation makes the star to enter the WR stage during the MS phase thus avoiding the LBV and red supergiant stage.

The WR life-times are considerably increased by rotation and the minimum mass for forming WR stars is lowered. Interestingly enough, the increase of the WN life-time is larger than for WC stars, so that rotation leads to a decrease of the WC/WN number ratio. Also, the fraction of transition WN/WC stars is much larger at higher rotation.

Finally, on the basis of clusters in the SMC, in the LMC and towards the galactic interior and exterior, we show that for clusters with ages between about 1 and 3 x 107 yr the fraction of Be stars with respect to normal B stars is larger at lower metallicities. This may suggest a higher rotation at lower metallicities for massive stars, due to a different history of star formation.

We investigate the pre-supernova evolution of Wolf-Rayet stars. We discuss whether the separation of hydrogen-free, core collapse supernovae into Type Ic and Type Ib supernovae is related to the occurrence of ‘Case BB mass transfer’ in massive close binaries, especially since the new, smaller WR mass loss rates do not favor helium-poor progenitor models from massive single stars. We also discuss the influence of rotation on the formation, evolution and explosion of WR stars using new models for rotating massive stars that have been computed from zero age to core collapse. We compute the spin-down of (non-magnetic) WR stars due to their strong mass loss, and compare pulsar spin rates with our predictions. Finally, we discuss implications of our results for the rotation rate of Type Ib/c supernova progenitors in general, and for SN 1998bw and the ‘collapsar’ model for γ-ray bursts in particular.

Since binaries can not be considered separately from single stars, we first present a brief summary of massive single star evolution. Next, we highlight massive close binary evolutionary facts that are important when massive close binaries are included in population (number) synthesis. Finally, we consider a few interesting test cases.

Gamma-rays from astrophysical sources testify energetic processes such as nucleosynthesis and cosmic ray collisions. Gamma-rays are observable from throughout the Galaxy, unattenuated by interstellar matter, provided their intensity exceeds the current instrumental sensitivity level (∼ 10−5ph cm−2s−1 at 1 MeV). Massive stars are at the origin of relevant sources: The all-sky image in the 1.809 MeV γ-ray line from radioactive 26Al traces nucleosynthesis throughout the Galaxy. The structure of this emission along the plane of the Galaxy suggests massive stars as dominating sources of this radioactivity. Discrimination of the contribution from core collapse supernova against that from WR-wind ejected hydrostatic nucleosynthesis products may be obtained from 60Fe γ-ray line observations, or from spatial-profile consequences of the metallicity dependence of 26Al production in theories for both source sites. As a single source, the nearest WR star in the γ2 Vel system is found to eject less 26Al into interstellar space than current theories predict. However, a more adequate comparison must be based on a time-dependent 26Al light-curve of the system. Furthermore, continuum γ-ray production in WR binaries through wind-wind interaction, and constraints on the low-energy cosmic ray origin in WR winds through characteristic nuclear deexcitation line studies are targets of research. Studies stimulated by COMPTEL'S 3–7 MeV excess report from the Orion region indicate that the γ-ray line measurements could separate the origins from supernova ejecta and wind material. The COMPTEL Orion result is now attributed chiefly to an instrumental artifact, and has been withdrawn. Nevertheless, the search for MeV emission from massive star clusters, as well as from interacting binaries such as WR 140, promises a unique test of particle acceleration scenarios related to the source mechanism for cosmic ray production.

Stellar winds contribute together with supernovae explosions to the chemical enrichment of the interstellar medium. We recall how the metallicity dependence of the stellar winds implies a metallicity dependence of the stellar yields. We show that an increase of the initial angular velocity has different effects than an increase of the mass loss rates. Wolf-Rayet stars appear as important sources of 19F and 26Al. They are the favoured candidates for the 22Ne anomaly observed in the Galactic cosmic ray sources. They may also have injected into the proto-solar nebula short-lived radionuclides as 26Al, 36Cl, 41Ca, 107Pd and 205Pb.

We have carried out a full spectroscopic analysis of the WC8 star in the γ2 Vel binary (WR11). Through the binary radial-velocity curve the mass of the WR star can be determined, and hence its luminosity can be derived through the mass-luminosity relation for WR stars. This can be compared to the luminosity from the spectroscopic analysis. We find that the standard modeling methods underestimate the luminosity of the WR star.

The interception of 0.01% of photons (termed photon loss) from the He II Lyα line by Fe VI and Ca V line-opacity can alter substantially the ionization structure of the wind. This is shown to increase the stellar luminosity and hence the wind driving efficiency. Our classical models for WR11 (the WR component in the γ2 Vel binary) underestimate the stellar luminosity as compared to the luminosity derived from the mass-luminosity relation. Here we present a model for WR11 where photon-loss is included. This model succeeds in that it has a higher luminosity for the same spectral appearance and V brightness. Line-blanketing has not yet been added, so that the force-factors and the velocity-law cannot yet be calculated. However, a hydro-dynamical velocity-law derived from a photon-loss model of a WN5 star improves considerably the fit to the narrow He II λ4686 emission line over the use of a β-law.

We have modeled the spectrum of WR135 with a co-moving frame code and then used identical input parameters with a Sobolev-approximation code. Helium lines compare well in strength and shape, while carbon lines are found to be much stronger in the co-moving frame code. The reason for this discrepancy is being investigated. The present comparison shows that tests have to be extended to more complex atomic models and compatibility between different codes should not be taken yet for granted.

In general, observationally derived wind compositions of WR stars are in reasonable agreement with predictions from stellar evolution models for massive stars. However, Barlow et al. (1988) identified a major discrepancy for neon in γ2 Vel (WC8+O) using ground-based observations. The advent of the ESA Infrared Space Observatory (ISO) has allowed the study of neon in many more WC stars, using mid-IR fine structure lines ([Ne II] 12.81 μm, [NeIII] 15.55μm and [NEV] 14.32 μm). Willis et al. (1998) used ISO-SWS observations of WR 146 (WC5+O) to derive a neon abundance that was within the range expected theoretically. Here we undertake a study of WR 90 (HD 156385), the only (apparently) single WC7 star in our Galaxy, using ISO-SWS spectroscopy. The only spectroscopic neon feature in the mid-IR of WR 90 is [Ne III] 15.55 μm, in addition to numerous C IV and He II transitions (see Figure 1).

Wolf-Rayet model stellar atmospheres are used to show the relation between He II line equivalent widths and continuum luminosity. It is shown that the Baldwin-effect is present in the models. A comparison made to observational data and model calculations by others stimulates further research into the physics of the effect.

In this study, we investigate the formation of clumps at the base of the wind of early-type stars via thermal instability in the presence of Alfvén wave heating. As a result we show the existence of two stable equilibrium regions, one at high temperature, the diffuse medium, and another at low temperature, the clumps. We show that the two stable equilibrium regions can coexist over a narrow range of pressures describing the diffuse medium and the clumps.

Spectra of seven WC stars in the LMC are taken with the HST-FOS. They are analyzed by means of non-LTE models for spherically expanding atmospheres with complex model atoms of helium, carbon and oxygen taken into account. We find stellar luminosities in the range from 1051–56 L⊙. The stellar temperature T*, defined as the effective temperature related to the stellar core radius, is of the order of 100 kK. The atmospheric compositions show carbon mass fractions of about 0.4 and oxygen mass fractions in the range 0.1–0.5.

We present the results of a tailored analysis of the spectra of WR40 (HD 96548, WN8) utilizing new line blanketed non-LTE model atmospheres. Synthetic spectra are compared with observation from 900 to 10,000 Å, with emphasis on far-UV HUT observations and the IUE regime. We identify the important line complexes in this region and deduce the Fe abundance. Improved stellar parameters and abundances of other metals are determined. A comparison of our new model results with non-line blanketed results is made.

We present observations and analyses of stars earlier than 06. The analyses are done with nlte planeparallel, hydrostatic model atmospheres. The effect of line-blocking for the determination of the stellar parameters is studied, and it is concluded that it must be taken into account for very hot stars. It is also shown that planeparallel models cannot fit properly the spectra of very hot stars. Thus, we perform new analyses with Unified Model Atmospheres, which result necessary for the reproduction of the spectra from the very upper part of the HR diagram.