Dynamically inflated wind models of classical Wolf-Rayet stars

Context. Vigorous mass loss in the classical Wolf-Rayet (WR) phase is important for the late evolution and final fate of massive stars. Aims. We develop spherically symmetric time-dependent and steady-state hydrodynamical models of the radiation-driven wind outflows and associated mass loss from classical WR stars. Methods. The simulations are based on combining the opacities typically used in static stellar structure and evolution models with a simple parametrised form for the enhanced line opacity expected within a supersonic outflow. Results. Our simulations reveal high mass-loss rates initiated in deep and hot, optically thick layers around T ≈ 200 kK. The resulting velocity structure is non-monotonic and can be separated into three phases: (i) an initial acceleration to supersonic speeds (caused by the static opacity), (ii) stagnation and even deceleration, and (iii) an outer region of rapid re-acceleration (by line opacity). The characteristic structures seen in converged steady-state simulations agree well with the outflow properties of our time-dependent models. Conclusions. By directly comparing our dynamic simulations to corresponding hydrostatic models, we explicitly demonstrate that the need to invoke extra energy transport in convectively inefficient regions of stellar structure and evolution models, in order to prevent drastic inflation of static WR envelopes, is merely an artefact of enforcing a hydrostatic outer boundary. Moreover, the dynamically inflated inner regions of our simulations provide a natural explanation for the often-found mismatch between predicted hydrostatic WR radii and those inferred from spectroscopy; by extrapolating a monotonic β-type velocity law from the observable supersonic regions to the invisible hydrostatic core, spectroscopic models likely overestimate the core radius by a factor of a few. Finally, we contrast our simulations with alternative recent WR wind models based on co-moving frame (CMF) radiative transfer to compute the radiation force. Since CMF transfer currently cannot handle non-monotonic velocity fields, the characteristic deceleration regions found here are avoided in such simulations by invoking an ad hoc very high degree of clumping