Very massive stars: a metallicity-dependent upper-mass limit, slow winds, and the self-enrichment of globular clusters

One of the key questions in Astrophysics concerns the issue of whether there exists an upper-mass limit to stars, and if so, what physical mechanism sets this limit? The answer to this question might also determine if the upper-mass limit is metallicity (Z) dependent. We argue that mass loss by radiation-driven winds mediated by line opacity is one of the prime candidates setting the upper-mass limit. We present mass-loss predictions (Ṁ_wind) from Monte Carlo radiative transfer models for relatively cool (T_eff = 15 kK) very inflated massive stars (VMS) with large Eddington Γ factors in the mass range 10²-10³ M_⊙ as a function of metallicity down to 1/100 Z/Z_⊙. We employed a hydrodynamic version of our Monte Carlo method, allowing us to predict the rate of mass loss (Ṁ_wind) and the terminal wind velocity (v_∞) simultaneously. Interestingly, we find wind terminal velocities (v_∞) that are low (100-500 km s^-1) over a wide Z-range, and we propose that the slow winds from VMS are an important source of self-enrichment in globular clusters. We also find mass-loss rates (Ṁ_wind), exceeding the typical mass-accretion rate (Ṁ_accr) of 10^-3 M_⊙ yr^-1 during massive-star formation. We have expressed our mass-loss predictions as a function of mass and Z, finding log Ṁ = -9.13 + 2.1 log(M/M_⊙) + 0.74 log(Z/Z_⊙) (M_⊙/yr). Even if stellar winds do not directly halt & reverse mass accretion during star formation, if the most massive stars form by stellar mergers, stellar wind mass loss may dominate over the rate at which stellar growth takes place. We therefore argue that the upper-mass limit is effectively Z-dependent due to the nature of radiation-driven winds. This has dramatic consequences for the most luminous supernovae, gamma-ray bursts, and other black hole formation scenarios at different Cosmic epochs.