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Astron. Astrophys. 334, 845-856 (1998)

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6. Terminal velocities: Stellar parameters affecting the wind

In Sect. 4.2, we highlighted the spread in observed FWHM 4686, HeII/I and mass loss parameters at a given value of [FORMULA]. This spread indicates that WN b stars which are similar in [FORMULA], [FORMULA] and L, parameters that are simple functions of the mass (see Sect. 7), may still have a significant range of wind parameters (cf. Heger & Langer 1997 who come to the same conclusion for different reasons). The wind parameters highlighted in Sect. 4.2 as critical were the surface mass flux and, thence, the atmospheric opacity.

The critical question then is: Why and how, at a constant mass and [FORMULA], does the surface mass flux and, therefore, the atmospheric opacity vary? What is the second parameter, after mass of the star, that affects the wind?

In this section, we consider four stellar properties which might be, for WN b stars, such a second parameter: 1) the mass fraction of the convective core; 2) the fraction [FORMULA] of carbon and oxygen in the convective core; 3) the mass fraction [FORMULA] occupied by the region with [FORMULA] greater than some value, e.g. 0.05; 4) the rotation rate of the star.

  1. The mass fractions of the convective cores in WN b stars are predicted by evolutionary models (cf. Meynet et al. 1994) to be more or less in a one-to-one relationship with the actual mass of the star, independent of the initial metallicity and previous history. The physical reason for this one-to-one relationship is that WN b stars of the same mass have about the same temperature gradient and therefore reach convective instability at the same depth. Thus, the mass fraction of the convective core cannot introduce a second parameter.
  2. The fraction [FORMULA] of carbon and oxygen in the convective core can be very different in WN b stars with the same mass. The reason is that a higher mass loss rate during the previous evolutionary phases, due to higher initial mass or higher Z, leads to a lower mass at any subsequent stage of central nuclear evolution. Conversely, for a given present mass, a WN b star originating from a higher initial mass or higher Z will have a lower central [FORMULA]. This is the effect that, in the WC phase, determines the surface abundance and hence the subclass of the WC star (cf. Smith & Maeder, 1991).
    Central [FORMULA] may influence the mass flux through pulsational instability. The significance of pulsational instability to the WR phase was suspected early (see review by Smith, 1968b) and has gained support because the instability to core pulsation is predicted to appear at the WR phase of evolution (Maeder 1985). Recent pulsation models for WR stars (cf. Schaller 1991) indicate that pulsational instability increases with the central [FORMULA] content and with the mass fraction [FORMULA] of the CO rich region. This relationship was established qualitatively for homogeneous stellar models (cf. Ledoux 1951), for which the maximum mass [FORMULA] for vibrational stability obeys the relationship: [FORMULA] constant, where µ is the mean molecular weight. Thus, if pulsational instability plays a role in mass loss, we would have a simple physical connection between the central composition and the mass flux.
  3. The mass fraction [FORMULA] increases significantly during the WN b phase. At the entry to this phase, [FORMULA] is close to the mass fraction of the convective core, typically about 0.6; at the end of the WN b phase, the star enters the WC phase and [FORMULA] is equal to one. The central [FORMULA] and the value of [FORMULA] are, of course, increasing together and both lead to an increase of the internal mean molecular weight and of the pulsational instability. As in 2), above, this could lead to an increase in the mass flux.
    In summary, stellar properties 2) and 3) suggest that the second parameter that affects the speed and extent of WN b star winds could be the internal mean molecular weight, µ, increasing the mass loss rate and [FORMULA] through the effects of pulsation.
  4. Stellar rotation has at least two main effects. It can induce internal mixing, thus affecting the internal structure and evolution. The main result of mixing is a change in the average µ and its distribution and, in this respect, is the same as properties 2) and 3) above. However, rotation may also greatly affect the geometric and density structure of the stellar wind, thus directly modifying the widths of the emission lines. At present, nothing is known about the rotational velocity of WR stars.

In summary, the second parameter affecting the wind properties, [FORMULA] and mass flux, of WN b stars appears likely to be either (or both of) the internal µ or the rotation rate.

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998