Wind modelling of very massive stars up to 300 solar masses

The stellar upper-mass limit is highly uncertain. Some studies have claimed there is a universal upper limit of ~150 M⊙. A factor that is often overlooked is that there might be a significant difference between the present-day and the initial masses of the most massive stars - as a result of mass loss. The upper-mass limit may easily supersede ~200 M⊙. For these reasons, we present new mass-loss predictions from Monte Carlo radiative transfer models for very massive stars (VMS) in the mass range 40-300 M⊙, and with very high luminosities 6.0 ≤ log (L ⋆ /L⊙) ≤ 7.03, corresponding to large Eddington factors Γ. Using our new dynamical approach, we find an upturn or "kink" in the mass-loss versus Γ dependence, at the point where the model winds become optically thick. This coincides with the location where our wind efficiency numbers surpass the single-scattering limit of η = 1, reaching values up to η ≃ 2.5. In all, our modelling suggests a transition from common O-type winds to Wolf-Rayet characteristics at the point where the winds become optically thick. This transitional behaviour is also revealed with respect to the wind acceleration parameter, β, which starts at values below 1 for the optically thin O-stars, and naturally reaches values as high as 1.5-2 for the optically thick Wolf-Rayet models. An additional finding concerns the transition in spectral morphology of the Of and WN characteristic He ii line at 4686 Å. When we express our mass-loss predictions as a function of the electron scattering Eddington factor Γe ~ L ⋆ /M ⋆ alone, we obtain an Ṁ vs. Γe dependence that is consistent with a previously reported power law Ṁ (Vink 2006) that was based on our previous semi-empirical modelling approach. When we express Ṁ in terms of both Γe and stellar mass, we find optically thin winds and Ṁ ∝ for the Γe range 0.4 ≲ Γe ≲ 0.7, and mass-loss rates that agree with the standard Vink et al. recipe for normal O stars. For higher Γe values, the winds are optically thick and, as pointed out, the dependence is much steeper, Ṁ ∝ . Finally, we confirm that the effect of Γ on the predicted mass-loss rates is much stronger than for the increased helium abundance, calling for a fundamental revision in the way stellar mass loss is incorporated in evolutionary models for the most massive stars.