Globular cluster formation from inertial inflows: accreting extremely massive stars as the origin of abundance anomalies

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, $10^{3-4}\, {\rm M}_\odot$) form in massive GCs ($\gtrsim 10^5\, {\rm M}_\odot$). The total wind mass loss is dominated by accreting EMSs (aEMSs), whose wind mass-loss rates have become comparable to their accretion rates ($\gtrsim 10^{-2}\, {\rm M}_\odot \, {\rm yr}^{-1}$). These winds pollute the intracluster medium with hot-hydrogen burning yields during GC formation. We propose a parametrized model for the evolution of the stellar mass function during GC formation ($\sim 1-2\, {\rm Myr}$), accounting for gas inflow, wind mass loss, and mixing of aEMS yields with pristine gas that has initial proto-GC abundances. Low-mass stars ($\lesssim 1\, {\rm M}_\odot$) 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 ($\Delta Y \simeq 0.01$) and increases with GC mass; (ii) the fraction of polluted stars increases with GC mass and metallicity; and (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 $\gtrsim 10^3\, {\rm M}_\odot \, {\rm pc}^{-2}$ and that nitrogen-rich galaxies discovered by the James Webb Space Telescope 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 ($\gtrsim 120\, {\rm M}_\odot$) that could be found with ongoing gravitational wave experiments.