Astron. Astrophys. 334, 845-856 (1998)
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
. This spread indicates that WN b stars which are
similar in , 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
, 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 of carbon
and oxygen in the convective core; 3) the mass fraction
occupied by the region with
greater than some value, e.g. 0.05; 4) the
rotation rate of the star.
- 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.
- The fraction 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
. 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 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
content and with the mass fraction
of the CO rich region. This relationship was
established qualitatively for homogeneous stellar models (cf. Ledoux
1951), for which the maximum mass for
vibrational stability obeys the relationship:
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
- The mass fraction increases significantly
during the WN b phase. At the entry to this phase,
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 is equal to one. The
central and the value of
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 through the effects of
- 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,
and mass flux, of WN b stars appears likely to
be either (or both of) the internal µ or the rotation
© European Southern Observatory (ESO) 1998
Online publication: June 2, 1998