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 similar to 150 M-circle dot. 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 similar to 200 M-circle dot. 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-circle dot, and with very high luminosities 6.0 <= log(L-star/L-circle dot) <= 7.03, corresponding to large Eddington factors Gamma. Using our new dynamical approach, we find an upturn or kink in the mass-loss versus Gamma 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 eta = 1, reaching values up to eta similar or equal to 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, beta, 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 angstrom. When we express our mass-loss predictions as a function of the electron scattering Eddington factor Gamma(e) similar to L-star/M-star alone, we obtain an (M) over dot vs. Gamma(e) dependence that is consistent with a previously reported power law (M) over dot proportional to Gamma(5)(e) (Vink 2006) that was based on our previous semi-empirical modelling approach. When we express (M) over dot in terms of both Gamma(e) and stellar mass, we find optically thin winds and (M) over dot proportional to M-star (0.68)Gamma(2.2)(e) for the Gamma(e) range 0.4 less than or similar to Gamma(e) less than or similar to 0.7, and mass-loss rates that agree with the standard Vink et al. recipe for normal O stars. For higher Gamma(e) values, the winds are optically thick and, as pointed out, the dependence is much steeper, (M) over dot proportional to M-star(0.78)Gamma(4.77)(e). Finally, we confirm that the effect of Gamma 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.