The mass-loss rates of Wolf-Rayet stars explained by optically thick radiation driven wind models

Observed, clumping-corrected mass-loss rates of Galactic Wolf-Rayet (WR) stars are compared with predictions of the optically thick radiation driven wind models. We did not develop models for the whole wind, but we studied the conditions at the sonic point that would explain the observed high mass-loss rates of WR-stars. We find that optically thick wind models can explain the observed values of the mass-loss rates only if two conditions are satisfied: (a) The sonic point (where v(flow) = v(sound)) lies deep in the wind where the temperature is either near 160 000 K, or in the range of 40 000 to 70 000 K. (b) The flux-mean opacity must increase outward from the sonic point. With these conditions a simple approximate formula for the mass-loss rates of WR-stars can be derived. The first condition implies that the sonic point is at an optical depth between about 3 and 30. Such large optical depths require a slowly increasing velocity law in the supersonic region, with a velocity-law index of beta similar or equal to 5 for WR-stars, compared to beta similar or equal to 1 for O-stars. The OPAL-opacity tables for the chemical composition of the WR-stars show that the opacity indeed increases outward at the temperature range near 1.6 x 10(5) K, and between about 4 x 10(7) and 7 x 10(4) K, as required for the optically thick wind models. The opacity at the sonic points of the models is very similar to the OPAL-opacity at the sonic point temperature and density. The radius of the sonic point is about half as large as the inner boundaries of the "standard" models for early type WR-winds. Observational evidence, derived from line profile variations and from the light-curves of WR-stars in eclipsing binary systems, support the derived large values of beta and the small values of the sonic point radius. The models presented here show that the high mass-loss rates of WR-stars might be the result of optically thick radiation driven winds. The presence of two very distinct temperature regimes for the sonic point implies a bifurcation in the wind models of WR-stars.