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Growth of Metal-Enriched Supermassive Stars by Accretion and Collisions

This study demonstrates that supermassive stars can successfully grow to massive scales via accretion and collisions in metal-enriched environments up to $Z \simeq 0.01\,Z_\odot$ , remaining viable progenitors for massive black hole seeds despite transitioning from collision-dominated to accretion-dominated growth and evolving as cool supergiants with suppressed radiative feedback.

Original authors: Devesh Nandal, Sunmyon Chon

Published 2026-01-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Devesh Nandal, Sunmyon Chon

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Building Cosmic Giants

Imagine the early universe as a construction site. Astronomers have found massive black holes that appeared very early in history, but they are too big to have been built by the standard "slow and steady" method. To solve this, scientists propose that these black holes started as Supermassive Stars (SMS)—giant, glowing orbs of gas that were thousands of times heavier than our Sun.

For a long time, scientists thought these giants could only be built in a "metal-free" universe (like a pristine workshop with no dust or impurities). This paper asks a new question: Can these giants be built in a slightly "dirty" or metal-enriched environment, like the crowded nurseries of early star clusters?

The authors used a supercomputer simulation (a digital recipe book for stars) to see if these massive stars could grow to huge sizes even when the gas they were made of contained a tiny bit of heavy elements (metals).

The Two Ways to Grow: The "Smooth Pour" vs. The "Bucket Brigade"

To build a star this big, you need to keep adding gas to it. The paper looks at two ways this happens:

Smooth Accretion (The Smooth Pour): Imagine pouring water from a hose into a bucket. This is gas flowing steadily onto the star.
Collisions (The Bucket Brigade): Imagine a chaotic scene where other smaller stars crash into the big one, dumping their mass into it all at once. This is like a bucket brigade throwing water into the bucket in sudden, splashing bursts.

The Finding:

In very clean environments (low metal), the star grows mostly by crashing into other stars (the Bucket Brigade).
As the environment gets a bit "dirtier" (more metals), the collisions become less effective. The star has to rely more on the smooth hose (gas accretion) to keep growing.
The Limit: If the environment gets too "dirty" (too many metals), the star stops growing at a much smaller size (about 2,000 Suns instead of 70,000).

The "Hot Air Balloon" Effect

One of the most interesting parts of the paper is about how the star looks while it's growing.

The Problem: Usually, when a star gets huge, it gets hot and bright. This brightness pushes gas away, stopping the star from growing any bigger. It's like a balloon that pops if you blow too hard.
The Solution: The paper found that these metal-enriched stars act like giant, cool red supergiants (like a massive, fluffy red balloon). Because they are so puffy and cool on the outside, they don't blast away the gas trying to fall onto them.
The Result: This "cool balloon" state allows the star to keep growing even in environments with metals. It essentially hides from its own radiation, letting it swallow more gas without blowing itself apart.

Do Collisions Rejuvenate the Star?

There was a hope that if stars kept crashing into each other, it would be like hitting "reset" on a video game. The idea was that crashing stars would dump fresh fuel (hydrogen) into the core, making the star live much longer and grow even bigger.

The Reality Check:
The paper shows that while collisions do add a little fresh fuel, it's not enough to save the day.

Analogy: Imagine a car engine that is running out of gas. You pour in a cup of fresh gas (a collision). The engine runs a little longer, but because the car is now heavier (more mass), it burns fuel faster. The net result is that the car doesn't drive significantly further.
Conclusion: Collisions alone cannot keep a supermassive star alive forever. You still need a steady stream of gas (the smooth hose) to build and maintain these giants.

The "Critical Rate" (The Minimum Speed Limit)

The researchers calculated a "speed limit" for how fast gas must fall onto the star to keep it puffy and cool.

If gas falls too slowly, the star shrinks, gets hot, and stops growing.
The Surprise: They found that in metal-rich environments, this "speed limit" is actually lower. It's easier to keep the star puffy when there are metals present because the metals help trap heat inside, acting like a thermal blanket that keeps the star inflated even with less gas falling in.

The Bottom Line

This paper proves that Supermassive Stars don't need to be born in a perfectly clean, metal-free universe. They can form and grow in environments that are slightly "polluted" with metals, such as the dense clusters where globular clusters (tight groups of old stars) are born.

However, they still need a steady supply of gas to grow. Relying solely on stars crashing into each other isn't enough to build the cosmic giants needed to explain the massive black holes we see in the early universe. The "smooth pour" of gas is the most important ingredient.

Technical Summary: Growth of Metal-Enriched Supermassive Stars by Accretion and Collisions

Problem Statement
The formation of supermassive black hole (SMBH) seeds at high redshift ( $z \gtrsim 6$ ) poses a timescale challenge for standard light-seed models. While direct-collapse supermassive stars (SMSs) formed in metal-free environments are a leading candidate for heavy seeds, recent observations of high-redshift galaxies and globular clusters suggest the presence of anomalous abundance patterns (e.g., high N/O ratios) and potential heavy seeds in metal-enriched environments. Historically, it was believed that even trace metals would induce efficient cooling, leading to cloud fragmentation that suppresses SMS formation. However, recent simulations suggest SMSs might form in environments with finite metallicity ( $[Z/H] \lesssim -3$ ) via a combination of gas accretion and stellar collisions. The specific evolutionary pathways, mass limits, and the viability of SMS growth in metal-enriched proto-globular clusters or compact starbursts remain poorly constrained.

Methodology
The authors model the growth of metal-enriched SMSs using the stellar evolution code GENEC. The study employs a grid of models spanning metallicities $Z/Z_\odot = 10^{-5}$ to $10^{-2}$ .

Initial Conditions: Models begin with a $10 M_\odot$ fully convective seed.
Accretion Histories: Time-dependent mass-delivery rates ( $\dot{M}$ ) are imported from radiation-hydrodynamic simulations of star cluster formation (S. Chon & K. Omukai 2025). These histories include both smooth gas inflow and episodic spikes representing stellar collisions (mergers) within the forming cluster.
Physical Assumptions:
- Cold Accretion: Accretion luminosity is radiated away; no entropy is advected into the interior. This is treated as an idealized limit.
- Collisions: Treated as instantaneous mass increments to the surface reservoir without explicit hydrodynamic merger physics or impact heating. This represents a "best-case" upper limit for collisional growth.
- Termination: Models evolve through pre-main sequence (pre-MS) and core hydrogen burning. Simulations terminate at the onset of general-relativistic (GR) instability for $Z \lesssim 10^{-4} Z_\odot$ or at core helium exhaustion for higher metallicities.
- Wind Treatments: Two exploratory models at $Z=10^{-4} Z_\odot$ test empirical wind prescriptions (de Jager et al. 1988; Vink et al. 2001) to estimate mass-loss bounds.

Key Results

Mass Limits and Metallicity Dependence:
- Final stellar masses decrease monotonically with increasing metallicity due to enhanced cooling reducing the initial Jeans mass and gas accretion rates.
- Final masses reach $\sim 7.2 \times 10^4 M_\odot$ at $Z = 10^{-5} Z_\odot$ and $\sim 2.3 \times 10^3 M_\odot$ at $Z = 10^{-2} Z_\odot$ .
- Stellar lifetimes remain nearly constant across the grid ( $1.8–2.0$ Myr), showing little dependence on metallicity or the specific accretion history.
Growth Channels (Accretion vs. Collisions):
- A transition in the dominant mass-growth channel occurs between $Z = 10^{-4}$ and $10^{-3} Z_\odot$ .
- At lower metallicities ( $Z \le 10^{-4} Z_\odot$ ), growth is initially driven by gas accretion but transitions to being collision-dominated at late times as gas reservoirs deplete.
- At higher metallicities ( $Z \ge 10^{-3} Z_\odot$ ), growth is primarily accretion-limited, with collisions contributing only minor fractional mass increases.
- Rejuvenation Inefficiency: While collisions replenish the central hydrogen fraction ( $X_c$ ) by $\Delta X_c \approx 0.05–0.06$ , they do not significantly extend the stellar lifetime. Because luminosity scales with mass ( $L \propto M$ ) in radiation-pressure-dominated SMSs, the nuclear timescale ( $t_{nuc} \sim MX/L$ ) is only weakly dependent on mass. The authors find that adding $\sim 4.7 \times 10^4 M_\odot$ via collisions extends the lifetime by only $\sim 0.6$ Myr. Sustaining growth beyond $\sim 2$ Myr via collisions alone would require thousands of mergers, rendering "runaway collision" scenarios insufficient without continuous gas accretion.
Critical Accretion Rate ( $\dot{M}_{crit}$ ):
- The critical inflow rate required to maintain the star on the Hayashi line (as an inflated red supergiant) decreases as the central hydrogen fraction ( $X_c$ ) declines and as metallicity increases.
- At $Z = 10^{-4} Z_\odot$ , $\dot{M}_{crit}$ drops from $\sim 2 \times 10^{-2} M_\odot \text{yr}^{-1}$ (at $X_c \approx 0.75$ ) to $\sim 10^{-4} M_\odot \text{yr}^{-1}$ (at $X_c \approx 0.35$ ).
- At $Z = 10^{-2} Z_\odot$ , $\dot{M}_{crit}$ is significantly lower ( $\sim 9 \times 10^{-3} M_\odot \text{yr}^{-1}$ at $X_c \approx 0.75$ ) and falls below $10^{-5} M_\odot \text{yr}^{-1}$ by $X_c = 0.60$ .
- Consequently, SMSs at $0.01 Z_\odot$ remain cool supergiants with suppressed UV photon emissivity and radiative feedback for most of their lives, facilitating continued growth even at low inflow rates.
Impact of Accretion Variability:
- Comparisons between variable-accretion histories (from 3D simulations) and constant-accretion models show that while variable rates cause radial oscillations, the long-term structural and chemical evolution (including surface abundances) converges to nearly identical states.
- This suggests that for global evolution and chemical yields, a constant mean accretion rate is a sufficient approximation.

Significance and Claims
The paper claims to provide the first self-consistent grid of metal-enriched SMS models evolved with realistic, time-dependent accretion histories. The primary significance lies in demonstrating that SMS formation is viable up to metallicities of $Z \simeq 0.01 Z_\odot$ . This supports the hypothesis that SMSs can form in metal-enriched dense environments, such as proto-globular clusters, potentially explaining both the origin of heavy black hole seeds and the anomalous abundance patterns (e.g., N/O ratios) observed in early galaxies and clusters.

The authors modestly conclude that while collisions can rejuvenate the core, they are an inefficient mechanism for sustaining runaway growth in isolation; gas accretion remains the dominant channel. Furthermore, the study highlights that existing mass-loss prescriptions are untested for this regime, and the derived mass-loss rates should be viewed as first-order bounds. The work sets the stage for future studies coupling these stellar evolution models with 3D hydrodynamics to track the collapse of the remnant into a black hole and to investigate the connection between metal-enriched SMSs and "Little Red Dots" observed by JWST.