Growth of Metal-Enriched Supermassive Stars by Accretion and Collisions

Abstract

Supermassive stars (SMSs) are candidate progenitors of massive black hole seeds and may contribute to anomalous abundance patterns in high-redshift galaxies and globular clusters. Recent radiation-hydrodynamic simulations indicate that SMSs can form at finite metallicity, not only in metal-free direct-collapse conditions. We model SMS growth with \textsc{GENEC} over $Z/Z_\odot=10^{-5}$-$10^{-2}$ using simulation-motivated accretion histories. The final masses reach $\sim7.2\times10^{4}\,M_\odot$ at $10^{-5}\,Z_\odot$ and $\sim2.3\times10^{3}\,M_\odot$ at $10^{-2}\,Z_\odot$. Models are evolved through the pre-main sequence and core H-burning phases, terminating at the onset of general-relativistic instability for $Z\lesssim10^{-4}\,Z_\odot$ or at core He exhaustion for $Z\gtrsim10^{-3}\,Z_\odot$. The dominant mass growth channel transitions from collision-driven to accretion-driven between $Z=10^{-4}$ and $10^{-3}$. With stellar lifetimes remaining nearly constant at $1.8$-$2.0$ Myr, collisions do not significantly rejuvenate the star, implying that collision driven runaway collapse cannot proceed in isolation and must be supplemented, and likely dominated by gas accretion. We further compute the critical inflow rate required to keep the stellar envelope inflated, $\dot{M}_{\rm crit}$, which decreases with increasing $Z$ and decreasing central mass fraction of hydrogen ($X_{\rm c}$). The critical rate falls below $10^{-5}\,M_\odot\,{\rm yr^{-1}}$ at $X_{\rm c}=0.60$ for $10^{-2}Z_\odot$. This indicates that SMSs with $0.01~Z_\odot$ are cool supergiants during most of their lifetimes, where UV photon emissivity and radiative feedback is strongly suppressed. Overall, SMS evolution remains viable up to $Z\simeq0.01\,Z_\odot$, supporting SMS formation in proto-globular clusters and other metal-enriched dense environments.