The stellar upper-mass limit is highly uncertain .
Some studies have claimed there is a universal upper limit of \sim 150 M _ { \odot } .
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 \sim 200 M _ { \odot } .
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 _ { \odot } , and with very high luminosities 6.0 \leq \log ( \mbox { $L _ { \star } $ } / \mbox { $L _ { \odot } $ } ) \leq 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 \simeq 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 4686Å .
When we express our mass-loss predictions as a function of the electron scattering Eddington factor \Gamma _ { e } \sim \mbox { $L _ { \star } $ } / \mbox { $M _ { \star } $ } alone , we obtain an \dot { M } vs . \Gamma _ { e } dependence that is consistent with a previously reported power law \dot { M } \propto \Gamma _ { e } ^ { 5 } ( Vink 2006 ) that was based on our previous semi-empirical modelling approach .
When we express \dot { M } in terms of both \Gamma _ { e } and stellar mass , we find optically thin winds and \dot { M } \propto \mbox { $M _ { \star } $ } ^ { 0.68 } \Gamma _ { e } ^ { 2.2 } for the \Gamma _ { e } range 0.4 \la \Gamma _ { e } \la 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 , \dot { M } \propto \mbox { $M _ { \star } $ } ^ { 0.78 } \Gamma _ { e } ^ { 4.77 } .
Finally , we confirm that the effect of \Gamma on the predicted mass-loss rates is much stronger than for the increased helium abundance ( cf .
Vink & de Koter 2002 for Luminous Blue Variables ) , calling for a fundamental revision in the way stellar mass loss is incorporated in evolutionary models for the most massive stars .