Abstract We use the inertial-inflow model of massive star formation to describe the formation of globular clusters (GCs) in turbulent molecular clouds. A key aspect of this model is that the maximum stellar mass scales linearly with cloud mass, such that extremely massive stars (EMSs, 103 − 4 M⊙) form in massive GCs (≳ 105 M⊙). The total wind mass loss is dominated by accreting EMSs (aEMSs), whose wind mass-loss rates have become comparable to their accretion rates (≳ 10−2 M⊙ − 1). These winds pollute the intra-cluster medium with hot-hydrogen burning yields during GC formation. We propose a parameterised model for the evolution of the stellar mass function during GC formation (~1 − 2 Myr), accounting for gas inflow, wind mass loss and mixing of aEMS yields with pristine gas that has initial proto-GC abundances. Low-mass stars (≲ 1 M⊙) form continuously from this mixed gas and their abundances resemble observed abundance trends with GC mass and metallicity, specifically: (i) the helium spread in a typical GC is small (ΔY ≃ 0.01) and increases with GC mass; (ii) the fraction of polluted stars increases with GC mass and metallicity; (iii) the extent of the Mg-Al anticorrelations is more pronounced in metal-poor and massive GCs. We conclude that GCs formed with a population of EMSs from gas with surface densities ≳ 103 M⊙ pc−2 and that nitrogen-rich galaxies discovered by the James Webb Space Telescope (JWST) are dominated by EMS-rich GCs that formed in the earliest phases of galaxy formation. These EMSs may have left behind intermediate-mass black holes with masses above the pair-instability gap (≳ 120 M⊙) that could be found with ongoing gravitational wave experiments.
Gieles et al. (2025) studied this question.