Standard Model

A major success of the Standard Model has been the ability to reproduce the observed line profiles and continua (from ultraviolet to infrared wavelengths) for W-R stars spanning a wide range of excitation. Future areas for improvement include:

1. Atomic Data: Despite tremendous progress in recent years through the opacity project group, major uncertainties remain for many transitions of many ions, while the correct treatment of additional processes (e.g. dielectronic recombination) is extremely difficult.
2. Non-LTE line blanketing: A major limitation of most current analyses is the neglect of line blanketing in the extreme ultraviolet region, principally through Fe-group elements (see however Schmutz 1996, Hillier 1996). Line blanketing will lead to a higher ionization in the inner regions (through backwarming) but a lower wind ionization (by flux blocking) in the outer regions. The influence of blanketing reveals itself through inconsistencies of model fits. Crowther et al. (1995d) were unable to simultaneously reproduce the NV and HeI line spectrum of WNE stars, while Crowther et al. (1995a,b) discovered that line blanketing has only a minor effect for WNL stars. Further evidence for the effects of link blanketing is afforded from photoionization modelling of W-R nebulae (Esteban et al. 1993), while recent far-ultraviolet observations (e.g. Schulte-Ladbeck et al. 1995b) provide further observational constraints.
3. Velocity law: At present most W-R analyses assume a velocity law of the form =(1-) (usually =1) plus a hydrostatic structure at low velocities. Ideally, the velocity law should be determined self-consistently using a non-LTE line blanketed model (Schmutz 1996).

Beyond these improvements, there are additional (observational) deficiencies for the Standard Model, namely: (1) HeI P Cygni absorption profiles are predicted stronger than observation in WNE stars; (2) predicted electron scattering wings are too strong; (3) intrinsic polarization in some W-R stars invalidates spherical symmetry; (4) X-rays and magnetic fields are not accounted for; (5) all intensively monitored W-R stars show line profile variations.

  
Figure 5: Morphological (and evolutionary) sequences amongst (a) LBV--WN10--WN8 stars; (b) Of--Ofpe--WN9ha stars; (c) Of--WN6ha--WN6 stars. Surface abundances (by number) are from Crowther & Bohannan (1996) and Crowther & Smith (1996b). Successive stars are shifted vertically by 1--2 continuum units for clarity

We now discuss some possible future relaxations of the Standard Model

• Rotation and spherical symmetry : Rotation is generally ignored in both O stars (see however Petrenz & Puls 1996) and W-R stars. For the latter, the effect of rotation is uncertain since rotation rates (and velocity distributions) are unknown. If rotation is important we expect to see evidence for non-sphericity in line profiles or continuum and line polarization, which is rarely observed.
• Variability and Clumping: Time dependent radiation driven wind theory (e.g. Owocki et al. 1994) indicates that mass-loss in O stars occurs in dense shells, qualitatively explaining some aspects of O star variability. Similarly, W-R variability is well known (e.g. St-Louis et al. 1995), with fluctuations in emission line profiles attributed to inhomogeneities (clumps) in the stellar wind (Robert 1994). Further evidence for clumps arises from theoretical electron scattering wings being too strong for a homogeneous wind (Hillier 1991) which can then be used to constrain clumping factors (see Schmutz 1996) -- for an alternative method see Moffat & Robert (1994). Line driven wind instabilities also generate shocks in the stellar wind, producing strong X-ray fluxes. Baum et al. (1992) found that while the inclusion of X-rays in the Standard Model did not significantly affect resulting W-R stellar parameters, the population of high ionization stages were enhanced in the outer wind.