Astron. Astrophys. 333, 956-969 (1998)

5. Derived mass-loss rates and comparison with other results

Table 6 presents clumping-corrected "radio" mass-loss rates, including smooth wind results for comparison. Major differences between mass-loss rates from clumped and smooth models are exclusive to the models with a "nh" ionization structure. In some stars the extent of the highly ionized zone may be time variable. This may explain changes in radio emission in WR 89 and WR 11 (probably also WR 22 and WR 24) as indicated by their unusual spectral indices.

Table 6. Mass-loss rates of WR stars derived from radio-fluxes via the asymptotic clumped wind model, , indicating the ionization state (normal, "n", or high, "h") in the cm radio emission zone. For comparison we give mass-loss rates obtained from 6 cm radio observations using the smooth wind relationship, . Two different smooth wind mass-loss rates are given for WR 89 based on the observations of (1)-Leitherer et al. (1995) and (2)-Abbott et al. (1986)

The majority of mass-loss rate determinations for WR stars rely on smooth wind assumptions, either using optical (Hamann et al. 1995, Crowther et al. 1995a) or radio (Abbott et al. 1986, Leitherer et al. 1997) methods. A limited number of studies using clumping-independent techniques have now been carried out.

In the case of single stars, most Galactic WR stars have now been studied using non-LTE model atmospheric analyses of (mostly) optical emission lines under the assumption of smooth winds. Although other groups have carried out such studies, Hamann et al. (1995) and Koesterke & Hamann (1995) have systematically analysed the largest sample of respectively, WN and WC stars. We present a comparison of mass-loss rates derived here with their results in Fig  6, having first corrected previous results to account for our assumed distances. Clearly, we obtain significantly lower mass-loss rates than Hamann et al. (1995) and Koesterke & Hamann (1995) by relaxing their smooth wind assumption. Overall, we obtain log  (this work)-log  (Hamann et al.)=-0.19 ( =0.28) for 15 WN stars, and log  (this work)-log  (Koesteke & Hamann)=-0.62 ( =0.19) for 4 WC stars in common.

Fig. 6. Comparison between WR mass-loss rates (in yr-1) obtained here for single stars, with those derived from non-LTE modelling of optical recombination lines assuming a smooth wind by Hamann et al. (1995) for WN stars (dots) and Koesterke & Hamann (1995) for WC stars (open circles)

Schmutz (1997) has recently analysed WR 6 (HD 50896, WN4b) using a non-LTE model atmosphere accounting for clumping. He derived a value of 3.2 yr^-1, in reasonable agreement with our value of 1.9 yr^-1, and significantly lower than 8 yr^-1, derived by Hamann et al. (1995) assuming a smooth outflow.

St-Louis et al. (1988) determined mass-loss rates for ten WR stars in massive binaries using polarization techniques which were independent of clumping and distance. Mass-loss rates derived in this way are sensitive to various parameters (Eq. (6) in St-Louis et al.) which have subsequently been revised and compiled in Table 7. In addition, St-Louis et al. assumed that the WR atmospheres were composed of doubly ionized helium.

Table 7. Parameters of binary WR stars studied by St-Louis et al. (1988), including revised polarization mass-loss rates (see text). Distance estimates are obtained from: association or cluster membership (a), absolute visual magnitude (), O star radius () or parallax measurements (cf. explanations to the Table 2). We indicate references to sources of parameters , a, i which differ from those used by St-Louis et al. (1988) in parenthesis. Colons indicate uncertain data

Here we correct the mass-loss rates derived by St-Louis et al. (1988) for improved chemical composition and ionization structure. For those WN binaries not studied by Nugis & Niedzielski (1995) we found H/He 0.2 for WR 139 and WR 47, with H/He 0.0 for WR 127 and, as before assumed N/He=0.005. For WC components we used abundances compiled in Sect.  2. We assume that the effective region of linear polarization modulation lies beyond 0.2-0.3 (St-Louis et al. 1988). Estimates of the number of free electrons per ion in the region where electron scattering processes are effective for polarization modulation were estimated from our clumped wind models:

• WN3: =2.0, =5.0,
• WN5: =1.5, =4.0,
• WN6: =1.4, =4.0,
• WN8: =1.1, =3.0,
• WC7: =1.25, =3.0, =4.0,
• WC8: =1.1, =2.5, =3.5.

Fig. 7 compares (corrected) polarization mass-loss rates with our derived mass-loss rates, demonstrating the excellent agreement between the two methods, even for cases in which binary properties are relatively poorly constrained.

Fig. 7. Comparison between WR binary mass-loss rates (in yr-1) obtained here with those derived from the clumping independent technique of St-Louis et al. (1988), corrected for revised orbital and stellar parameters. Dots denote stars for which mass-loss rates were directly obtained from radio observations, while open circles denote those stars whose mass-loss rates were obtained using our scaling formulae

Several independent mass-loss rate determinations have been made for WR 139 (V444 Cyg). St-Louis et al. (1993) analyzed its polarization eclipse observations revealing a WN5 component mass-loss rate of 0.62 yr^-1 after correcting for ionization structure and . This is somewhat lower than that derived from the polarization amplitude and IR-radio continuum fluxes. Khaliullin et al. (1984) have found that the period of this system is increasing at the rate 0.202 0.018 s yr^-1 which assuming masses and inclinations from Marchenko et al. (1994) and Robert et al. (1990) implies yr^-1, in very good accord with our derived value. However, using the revised rate of increase in period of Underhill et al. (1990), a substantially lower yr^-1 is obtained. Clearly, new studies are urgently needed to clarify this situation for this star.

In conclusion, we have utilised IR-radio continuum fluxes to constrain the ionization structure and clumped nature of the outer winds of WR stars. Observed WR spectral indices can be explained by clumped wind models in which shocks between clumps (at about a hundred stellar radii) produce a higher ionization zone, which may extend beyond the radio formation region. Coordinated long-term radio and X-ray observations of WR stars should help to clarify the structure of their outer wind regions. From an empirical formula we obtain WR mass-loss rates which are lower than those obtained from assuming smooth winds, though are in excellent agreement with measurements from clumping independent techniques for WR binaries. In a future work we will attempt to derive the dependence of mass-loss rates on fundamental stellar parameters.

© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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