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One of the key questions in Astrophysics concerns the issue of whether thereexists an upper-mass limit to stars, and if so, what physical mechanism setsthis limit, which might also determine if the upper-mass limit is metallicity(Z) dependent. We argue that mass loss by radiation-driven winds mediated byline opacity is one of the prime candidates setting the upper-mass limit. Wepresent mass-loss predictions (dM/dt_wind) from Monte Carlo radiative transfermodels for relatively cool (Teff = 15kK) inflated very massive stars (VMS) withlarge Eddington Gamma factors in the mass range 100-1000 Msun as a function ofmetallicity down to 1/100 Z/Zsun. We employ a hydrodynamic version of our MonteCarlo method, allowing us to predict the rate of mass loss (dM/dt_wind) and theterminal wind velocity (vinf) simultaneously. Interestingly, we find windterminal velocities (vinf) that are low (100-500 km/s) over a wide Z-range, andwe propose that the slow winds from VMS are an important source ofself-enrichment in globular clusters. We also find mass-loss rates(dM/dt_wind), exceeding the typical mass-accretion rate (dM/dt_accr) of 0.001Msun/yr during massive-star formation. We express our mass-loss predictions asa function of mass and Z, finding log dM/dt = -9.13 + 2.1 log(M/Msun) + 0.74log(Z/Zsun) (Msun/yr). Even if stellar winds would not directly halt & reversemass accretion during star formation, if the most massive stars form by stellarmergers stellar wind mass loss may dominate over the rate at which stellargrowth takes place. We therefore argue that the upper-mass limit is effectivelyZ-dependent due to the nature of radiation-driven winds. This has dramaticconsequences for the most luminous supernovae, gamma-ray bursts, and otherblack hole formation scenarios at different Cosmic epochs.

Very Massive Stars: a metallicity-dependent upper-mass limit, slow winds, and the self-enrichment of Globular Clusters