Growth of Metal-Enriched Supermassive Stars by Accretion and Collisions

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.

💡 Research Summary

This paper investigates the formation and growth of supermassive stars (SMSs) in environments with finite metallicity, extending the traditional view that SMSs require pristine, metal‑free gas. Using the stellar evolution code GENEC, the authors compute a suite of models with metallicities Z/Z⊙ = 10⁻⁵, 10⁻⁴, 10⁻³, and 10⁻², each initialized from a 10 M⊙ fully convective seed. The mass‑accretion histories are taken directly from radiation‑hydrodynamic simulations of dense star‑forming clusters (Chon & Omukai 2025), which provide time‑dependent total mass‑delivery rates that include both smooth inflow and impulsive spikes representing stellar collisions.

Key methodological choices include a “cold accretion” boundary condition (accretion energy is radiated away, no entropy is advected inward) and a treatment of collisions as pure mass‑addition events without extra heating. This maximizes the possible contribution of mergers while minimizing their thermal impact, thereby providing an upper bound on collision‑driven growth. The authors also explore wind prescriptions (de Jager, Vink, Kudritzki) for the higher‑metallicity cases, though mass loss remains negligible because of the enormous radii and low surface gravities of SMSs.

The results show a strong metallicity dependence of the final stellar mass. At the lowest metallicity (10⁻⁵ Z⊙) the SMS reaches ≈7.2 × 10⁴ M⊙, whereas at 10⁻² Z⊙ the final mass is only ≈2.3 × 10³ M⊙. This decline is driven by enhanced cooling from metals and dust, which promotes fragmentation and reduces the efficiency of gas inflow to the central object.

A central finding is the transition of the dominant growth channel from collision‑driven to accretion‑driven between Z≈10⁻⁴ and 10⁻³ Z⊙. In the low‑Z regime, impulsive spikes in the accretion history dominate the mass budget, while at higher Z the smooth, sustained inflow supplies the bulk of the mass. Despite these differences, the stellar lifetimes remain remarkably constant at 1.8–2.0 Myr across all metallicities, indicating that collisions do not significantly “re‑juvenate” the star by extending its nuclear‑burning clock.

The authors compute a critical inflow rate, ˙M_crit, required to keep the stellar envelope inflated (i.e., in the cool supergiant phase). ˙M_crit decreases with increasing metallicity and with decreasing central hydrogen mass fraction X_c. For Z=10⁻² Z⊙, ˙M_crit falls below 10⁻⁵ M⊙ yr⁻¹ once X_c≈0.60, implying that such stars spend most of their evolution as cool (≈6000 K) supergiants. Consequently, their ultraviolet photon output and radiative feedback are strongly suppressed, allowing prolonged gas accretion (“super‑competitive accretion”).

The termination of each model differs with metallicity. For Z≤10⁻⁴ Z⊙, the star becomes unstable to general‑relativistic (GR) pulsations before core helium exhaustion, leading to direct collapse into a massive black‑hole seed. At higher metallicities (Z≥10⁻³ Z⊙), the evolution proceeds to core‑helium exhaustion, after which the star ceases growth. This reflects the fact that metal‑rich SMSs consume their nuclear fuel more rapidly and never reach the relativistic instability regime.

Overall, the study demonstrates that SMS formation is viable up to Z≈0.01 Z⊙. This expands the potential sites for SMSs to include proto‑globular clusters, metal‑enriched starburst nuclei, and other dense environments in the early universe. The findings have several important implications: (1) they provide a unified pathway to produce heavy black‑hole seeds capable of powering the luminous quasars observed at z ≳ 6; (2) they offer a natural source of the hot‑hydrogen nucleosynthetic signatures (high N/O, low C/O, low Ne/O) seen in high‑z galaxies and globular‑cluster multiple populations; (3) they suggest that radiative feedback from SMSs may be far weaker than previously assumed in metal‑rich contexts, facilitating sustained accretion.

The paper acknowledges limitations, notably the idealized cold‑accretion assumption and the omission of impact heating during collisions. Future work should incorporate fully coupled 3‑D radiation‑hydrodynamic simulations with realistic shock physics, explore wind mass‑loss in greater detail, and extend the metallicity range beyond 0.01 Z⊙ to map the boundary where SMS formation breaks down. Nonetheless, the current results provide a robust theoretical foundation for the existence of metal‑enriched supermassive stars and their role in early cosmic structure formation.