Mass loss and the Eddington parameter: a new mass-loss recipe for hot and massive stars

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 (Γe). 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 Ṁ ∝ Γ ₑ³, while in the optically thick wind regime Ṁ ∝ 1/ (1 - Γ ₑ)3.5. The transition from optically thin to optically thick winds occurs at Γe, trans ≈ 0.47. The transition mass-loss rate is log Ṁ~(M \, yr⁻¹) ≈ -4.76 ± 0.18, which is in line with the prediction by Vink & Gräfener assuming a volume filling factor of fV = 0.23-0.15+0.40.