SIMBAD references

Mass loss through stellar winds plays a dominant role in the evolution of massive stars. In particular, the mass-loss rates of very massive stars (> 100 M_☉) are highly uncertain. Such stars display Wolf-Rayet spectral morphologies (WNh), whilst on the main sequence. Metal-poor very massive stars are progenitors of gamma-ray bursts and pair instability supernovae. In this study, we extended the widely used stellar wind theory by Castor, Abbott & Klein from the optically thin (O star) to the optically thick main-sequence (WNh) wind regime. In particular, we modify the mass-loss rate formula in a way that we are able to explain the empirical mass-loss dependence on the Eddington parameter (Γ_e). The new mass-loss recipe is suitable for incorporation into current stellar evolution models for massive and very massive stars. It makes verifiable predictions, namely how the mass-loss rate scales with metallicity and at which Eddington parameter the transition from optically thin O star to optically thick WNh star winds occurs. In the case of the star cluster R136 in the Large Magellanic Cloud we find in the optically thin wind regime {dot}M ∝Γ_ e_³, while in the optically thick wind regime {dot}M ∝1/ (1 - Γ_ e_)^3.5. The transition from optically thin to optically thick winds occurs at Γ_e, trans_ ≃ 0.47. The transition mass-loss rate is log{dot}M~(M_☉ yr^–1) ~-4.76 ±0.18, which is in line with the prediction by Vink & Grafener assuming a volume filling factor of f_ V_ = 0.23_–0.15^+0.40.