The in-situ growth of stellar-mass "light" seed black holes in nuclear star clusters

Magnetohydrodynamic simulations reveal that while remnant black holes from massive stars can concentrate in the centers of nuclear star clusters, in-situ accretion is generally inefficient at forming heavy seeds due to feedback-driven gas dispersal, unless specific sub-grid models allow for exceptionally high Bondi inflow rates.

The Gist

Here is an explanation of the paper "The in-situ growth of stellar-mass 'light' seed black holes in nuclear star clusters," translated into simple, everyday language with creative analogies.

The Big Question: How Do Giant Black Holes Get Their Start?

Imagine the universe as a giant construction site. We know that supermassive black holes (SMBHs)—the "kings" of galaxies—are huge, weighing billions of suns. But how did they get so big so quickly in the early universe?

Scientists have a few theories. One idea is that they started as "heavy seeds" (giant black holes born from collapsing gas clouds). Another idea is that they started as "light seeds"—the tiny, leftover corpses of massive stars (like a baby black hole weighing a few hundred suns).

The Problem: If they start as "light seeds," they need to eat a lot of food (gas) very quickly to grow into giants. But stars are messy eaters. When massive stars die, they explode and blow away all the food the baby black holes need.

The Goal of This Study: The authors wanted to see if these "light seeds" could survive the messy environment of a newborn star cluster, find enough food, and grow big right where they were born (in-situ), without needing help from outside.

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The Experiment: A Cosmic Simulation

The researchers used a supercomputer to run a movie of the universe's early days. They created giant clouds of gas (Giant Molecular Clouds) and let gravity pull them together to form stars.

The Cast of Characters:

1. The Gas Cloud: A massive, turbulent cloud of gas, the size of a small city or a whole galaxy.
2. The Very Massive Stars (VMS): The "rock stars" of the cloud. These are stars 100 to 300 times heavier than our Sun. They burn bright, die young (in just a few million years), and leave behind black holes.
3. The Baby Black Holes (Light Seeds): The remnants of those massive stars.
4. The Feedback: The "bad behavior" of the stars. Before they die, they blast out radiation and winds. When they die, they go boom (supernova). This is like a toddler throwing a tantrum and knocking over the food bowl.

What Happened in the Movie?

The simulation ran for about 10 to 30 million years. Here is the story they found:

1. The Star Party Starts

The gas clouds collapsed, and stars were born. The "Very Massive Stars" formed first. They were like the loudest kids in the playground, shining incredibly bright and blowing strong winds.

2. The Great Cleanup (Feedback)

As these massive stars lived and died, they acted like a chaotic cleanup crew.

• Radiation: They blasted the gas with light, heating it up and pushing it away.
• Supernovae: When they exploded, they blew the remaining gas out of the cluster like a firehose.

The Result: By the time the baby black holes were born (about 3 million years after the party started), the "food" (the gas) had mostly been blown away. The baby black holes were left hungry.

3. The Struggle to Eat

The baby black holes tried to eat the remaining gas.

• In most cases: They barely ate anything. The gas was too scattered or too hot. They stayed small, growing from ~100 suns to maybe ~400 or 500 suns. This is not enough to become a supermassive black hole.
• The "Lucky" Few: In a few specific scenarios (very massive clouds with low metal content), a few black holes managed to hide in dense, cold pockets of gas. They managed to eat a bit more, reaching up to ~500 suns. Still, this is a "light seed," not a "heavy seed."

The "What If" Scenarios (The Sub-Grid Model)

The authors realized that their computer model had to make some guesses about how black holes eat. They tested different "rules" for eating:

• The Realistic Rule (Fiducial Model): Black holes are picky eaters. They can only grab a tiny fraction of the gas swirling around them. Result: No giant growth. The seeds stay small.
• The "Gluttonous" Rule: What if the black holes could grab 50% of the gas swirling around them? Result: A few lucky black holes went on a feeding frenzy. They grew rapidly, reaching millions of suns.
• The "Super-Glutton" Rule: What if they could eat everything? Result: One black hole grew to 100 million suns.

The Takeaway: The growth depends entirely on how efficient the black hole is at grabbing food. In the realistic scenarios, they aren't efficient enough to grow into giants quickly.

Other Interesting Findings

• The "Puffy" Clusters: When the researchers made the "rock star" stars even more massive (a "top-heavy" star list), the stars blew the gas away even faster. The resulting star clusters were "puffier" and less dense, making it even harder for black holes to find food.
• The "Second Generation": In the biggest, most successful simulations, the gas didn't just disappear. It got recycled. The first generation of stars died, enriched the gas with heavy elements, and a second generation of stars was born from that dirty gas. This suggests that if black holes are growing, new stars are probably being born too.
• The Kick: When black holes are born, they sometimes get a "kick" (a push) from the explosion. The study found that unless the cluster is very small and weak, these kicks don't knock the black holes out of the food zone.

The Final Verdict

Can baby black holes grow into giants right where they are born?
Probably not.

The study concludes that in the chaotic, messy environment of a newborn star cluster, the stars themselves act as a barrier. They blow away the food supply before the baby black holes can eat enough to become supermassive.

So, how do we get Supermassive Black Holes?
The authors suggest that while the "in-situ" (born and raised locally) path is a dead end for rapid growth, these baby black holes might still be the seeds. They just need a different strategy:

1. Wait it out: Survive the messy phase.
2. Get a new job: Later in the universe's history, when new gas flows in from the wider galaxy, these baby black holes can finally get their feast and grow into giants.

In short: Baby black holes are born in a storm. The storm blows away their lunch. They survive, but they stay small until the storm passes and a new buffet opens up.

Technical Summary

Here is a detailed technical summary of the paper "The in-situ growth of stellar-mass 'light' seed black holes in nuclear star clusters" by Yanlong Shi and Norman Murray.

1. Problem Statement

The physical origin of supermassive black holes (SMBHs) observed at high redshift ($z \gtrsim 7$) remains a major open question in astrophysics. While "heavy seed" scenarios (direct collapse of pristine gas forming $10^3\text{--}10^5 M_\odot$black holes) are plausible, the "light seed" scenario—where SMBHs grow from stellar-mass remnants ($\sim 100 M_\odot$)—requires these seeds to undergo sustained super-Eddington accretion.

Previous studies have often assumed pre-existing seed black holes embedded in dense environments or lacked the resolution to model the formation of the seeds themselves. The central question addressed here is: Can stellar-mass "light seeds" form in-situ as remnants of massive stars within compact, star-forming giant molecular clouds (GMCs) and grow rapidly enough to become intermediate-mass black holes (IMBHs) or heavy seeds before the gas reservoir is expelled by feedback?

2. Methodology

The authors employ high-resolution magnetohydrodynamic (MHD) simulations using the GIZMO code in meshless finite-mass (MFM) mode, integrated with the FIRE-3 (Feedback In Realistic Environments) framework.

• Hybrid "FIRE+VMS" Approach: Standard FIRE simulations treat stars as single stellar populations (SSPs) and cannot resolve individual massive stars. To address this, the authors developed a hybrid model:
  • Resolved Very Massive Stars (VMS): Stars with Zero-Age Main Sequence (ZAMS) masses $> 100 M_\odot$ (or $> 50 M_\odot$ for lower mass clouds) are extracted from the SSPs and tracked individually.
  • Sub-grid VMS Model: These resolved VMSs are evolved using PARSEC stellar evolution tracks (v2.0) to model mass loss, lifetimes, and remnant formation (including Pair-Instability Supernovae and Direct Collapse Black Holes).
  • Feedback Implementation: Resolved VMSs contribute radiative (UV, optical, IR) and mechanical (stellar winds, supernovae) feedback. Crucially, if a VMS collapses directly into a black hole (DCBH) with negligible ejecta, the supernova feedback is skipped, preserving the surrounding gas.
  • Dynamical Friction: An additional acceleration term is applied to VMSs to account for dynamical friction, causing them to sink toward the cluster center.
• Black Hole Accretion & Feedback:
  • Accretion: Uses the Bondi-Hoyle-Lyttleton (BHL) formalism. A sub-grid parameter, $f_{acc}$, determines the fraction of the Bondi inflow that actually reaches the event horizon (the rest is returned as outflow).
  • Feedback: BHs launch bipolar mechanical winds and radiative feedback. The model allows for super-Eddington accretion (up to $1000 \dot{M}_{Edd}$).
• Simulation Suite:
  • Initial Conditions: Spherical, non-rotating GMCs with varying masses ($10^5 \text{--} 10^9 M_\odot$), radii ($5 \text{--} 500$pc), and initial metallicities ($Z = 0.01 \text{--} 1 Z_\odot$).
  • Parameters: Variations in the Initial Mass Function (IMF), natal kicks for BHs, and sub-grid accretion parameters ($f_{acc}$ and wind velocity $v_{wind}$).
  • Duration: Simulations run for $\sim 10\text{--}30$ Myr, covering the lifetime of VMSs and the formation of remnant BHs.

3. Key Results

A. Star Formation and BH Seeding

• Timing: Star formation peaks at $\sim 1\text{--}2$ free-fall times ($t_{ff}$). Remnant BH formation is delayed by $\sim 3$ Myr (the lifetime of the most massive stars).
• Gas Expulsion: In most scenarios, sustained stellar feedback (radiation and supernovae) efficiently expels the gas reservoir, halting further star formation and BH growth.
• Density Profiles: High surface density clouds ($\Sigma \sim 10^4 M_\odot \text{pc}^{-2}$) form compact, massive central clusters with high BH densities ($\rho_{BH} \sim 10^4\text{--}10^6 M_\odot \text{pc}^{-3}$). A top-heavy IMF creates "puffier" clusters with lower central densities.

B. In-Situ Growth of Light Seeds

• Inefficiency under Fiducial Models: Using the fiducial sub-grid model ($f_{acc} = 0.05$), in-situ accretion is generally inefficient. Even in the most massive clouds, remnant BHs only grow to $\sim 400\text{--}500 M_\odot$.
• Conditions for Growth: Significant growth ($>300 M_\odot$) only occurs in massive, extended, low-metallicity clouds ($M \sim 10^9 M_\odot, Z = 0.01 Z_\odot$).
  • These BHs originate from Direct Collapse Black Holes (DCBHs) (avoiding Pair-Instability Supernovae), which preserve the pre-SN mass and do not inject disruptive energy.
  • They accrete in dense, magnetized cores ($n \sim 10^5\text{--}10^6 \text{ cm}^{-3}$) where gas is not immediately expelled.
• Role of Natal Kicks: Natal kicks ($0.1\text{--}100 \text{ km s}^{-1}$) have negligible impact on global accretion, except in low-mass clusters where they can disrupt the formation of a dense central cluster.

C. Sensitivity to Sub-Grid Parameters ($f_{acc}$)

The fraction of Bondi inflow reaching the BH ($f_{acc}$) is the critical determinant of growth:

• $f_{acc} \lesssim 0.05$: No heavy seeds form. Accretion is suppressed by feedback.
• $f_{acc} \sim 0.5$: A "runaway" regime is triggered. A small number of BHs cross a mass threshold ($\sim 10^3 M_\odot$), where $\dot{M} \propto M^2$ allows them to grow rapidly to $\sim 10^6 M_\odot$.
• $f_{acc} = 1$ (No Feedback): An idealized case where the most massive BH reaches $\sim 10^8 M_\odot$, though this is physically unrealistic.

D. Multiple-Generation Star Formation

Simulations of massive clouds show evidence of multiple generations of star formation. As the first generation of stars enriches the gas, subsequent stars form with higher metallicities ($Z_\star > Z_{ini}$). This process is intrinsically linked to BH accretion: the same conditions that retain dense gas for BH growth also allow for the formation of second-generation stars.

4. Key Contributions

1. Self-Consistent Seeding: The first study to self-consistently model the formation of light seeds from VMSs and their subsequent in-situ growth within the same simulation, rather than assuming pre-existing seeds.
2. Hybrid VMS Modeling: Introduction of a robust "FIRE+VMS" framework that resolves individual very massive stars while maintaining computational efficiency for the broader stellar population.
3. Constraint on Growth Mechanisms: Demonstration that under realistic feedback-regulated accretion models, light seeds cannot grow into heavy seeds ($>10^3 M_\odot$) solely via in-situ gas accretion within the lifetime of a GMC.
4. Parameter Sensitivity: Identification of $f_{acc}$ as the pivotal parameter. The results suggest that unless a significant fraction of Bondi inflow bypasses feedback suppression, light seeds require external mechanisms (e.g., mergers, later gas inflows) to become SMBHs.

5. Significance and Implications

• Origin of High-Redshift SMBHs: The findings challenge the viability of the "light seed + in-situ super-Eddington accretion" scenario as the sole explanation for $z \sim 7$ SMBHs. If $f_{acc}$ is low (as suggested by slim-disk physics), light seeds formed in-situ are unlikely to reach SMBH masses without additional growth phases.
• Alternative Pathways: The paper suggests that if light seeds are to become SMBHs, they likely require:
  • Runaway Accretion: Only possible if sub-grid physics allows high inflow efficiency ($f_{acc} \gtrsim 0.5$).
  • Post-Cluster Evolution: Growth via dynamical interactions (mergers, tidal disruptions) in dense clusters or via later gas inflows from larger cosmological scales (which were not included in these isolated cloud simulations).
• Future Work: The authors propose that cosmological zoom-in simulations are necessary to assess the role of large-scale gas inflows and hierarchical assembly in the growth of these seeds over cosmic time.

In conclusion, while the formation of light seeds in nuclear star clusters is robust, their in-situ growth to heavy seeds is highly inefficient due to stellar feedback, unless specific sub-grid accretion conditions are met.