Context. Classical Wolf-Rayet (WR) stars are direct supernova progenitors undergoing vigorous mass loss. Understanding the dense and fast outflows of such WR stars is thus crucial for understanding advanced stages of stellar evolution and the dynamical feedback of massive stars on their environments, and for characterizing the distribution of black hole masses. Aims. In this paper, we develop the first time-dependent, multidimensional, radiation-hydrodynamical models of the extended optically thick atmospheres and wind outflows of hydrogen-free classical WR stars. Methods. A flux-limiting radiation hydrodynamics approach is used on a finite volume mesh to model WR outflows. The opacities are described using a combination of tabulated Rosseland mean opacities and the enhanced line opacities expected within a supersonic flow. Results. For high-luminosity models, a radiation-driven, dense, supersonic wind is launched from deep subsurface regions associated with peaks in the Rosseland mean opacity. For a model with lower luminosity, on the other hand, the Rosseland mean opacity is not sufficient to sustain a net-radial outflow in the subsurface regions. Instead, what develops in this case, is a "standard" line-driven wind launched from the optically thin regions above an extended, moderately inflated, and highly turbulent atmosphere. We thus find here a natural transition from optically thick outflows of classical WR stars to optically thin winds of hot, compact subdwarfs; in our simulations, this transition occurs approximately at a luminosity that is ~40% of the Eddington luminosity. Because of the changing character of the wind-launching mechanism, this transition is also accompanied by a large drop (on the low-luminosity end) in the average mass-loss rate. Since the subsurface opacity peaks are further associated with convective instabilities, the flows are highly structured and turbulent, consisting of coexisting regions of outflowing, stagnated, and even pockets of infalling gas. Typical velocity dispersions in our 3D models are high, 100–300 km s−1, but the clumping factors are rather modest, fc1 ≡ 〈ρ2〉/〈ρ〉2 ~ 2. We further find that, while the low-density gas in our simulations is strongly radiation-driven, the overdense structures are, after their initial launch, primarily advected outward by ram-pressure gradients. This inefficient radiative acceleration of dense "clumps" reflects the inverse dependence of line driving on mass density and leads to a general picture wherein high-density gas parcels move significantly slower than the mean and low-density wind material.
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