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arxiv: 2606.10000 · v1 · pith:IJPC3MD2new · submitted 2026-06-08 · 🌌 astro-ph.GA

From Dense Gas Clouds to Supermassive Black Hole Seeds: Hybrid Hydro/Direct N-body Simulations of Runaway Collision-driven Intermediate-mass Black Hole Formation

Eunwoo Chung , Yongseok Jo , Ji-hoon Kim , Minyong Jung , Oh-kyoung Kwon This is my paper

Pith reviewed 2026-06-27 15:57 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords intermediate-mass black holessupermassive black hole seedsrunaway stellar collisionsnuclear star clustershigh-redshift galaxieshydrodynamic simulationstidal disruption eventsvery massive stars
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The pith

Dense gas clouds at high redshift form very massive stars via runaway collisions that collapse into IMBHs and grow to 62000 solar masses in 100 Myr under steady accretion.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses hybrid hydrodynamics and direct N-body simulations to evolve dense, metal-poor gas clouds with turbulence. These clouds collapse into star clusters where runaway stellar collisions produce very massive stars up to 5108 solar masses irrespective of wind feedback strength. The stars collapse directly into intermediate-mass black holes that grow by Eddington-limited accretion plus tidal disruption events at a combined rate of 1.64 times 10 to the minus 4 solar masses per year. With the assumption of steady gas supply and constant TDE rate, an IMBH beginning at 6747 solar masses reaches approximately 62000 solar masses within 100 Myr, supplying a natural seed channel for the supermassive black holes detected at high redshift.

Core claim

Modeling initially dense, metal-poor gas clouds with varying turbulence consistently produces dense clusters resembling early nuclear star clusters and very massive stars from 343 to 5108 solar masses via runaway collisions. Following direct collapse, the resulting IMBHs grow through Eddington-limited gas accretion and TDEs; in the most optimistic case the accretion rate reaches 1.64 times 10 to the minus 4 solar masses per year with TDEs supplying 23 percent of the mass over 10 Myr. Projecting with steady gas supply and constant TDE rate, an IMBH of initial mass 6747 solar masses reaches about 62000 solar masses in 100 Myr.

What carries the argument

Hybrid hydro/direct N-body integration in Enzo-Abyss that couples gas dynamics, self-gravity, stellar evolution and collisions, allowing runaway stellar collisions inside dense clusters formed from turbulent gas clouds.

If this is right

  • IMBHs form naturally inside dense clusters without separate seeding prescriptions.
  • Tidal disruption events can supply up to 23 percent of early IMBH mass growth over the first 10 Myr.
  • The process operates across a range of initial turbulence levels and stellar wind strengths.
  • Such IMBHs provide viable seeds capable of reaching supermassive scales within 100 Myr in high-redshift environments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same collision-driven channel may operate in other dense stellar systems at lower redshift if gas densities remain high enough.
  • Targeted searches for IMBHs in the centers of high-redshift nuclear star clusters could directly test the predicted mass range and growth timescale.
  • Variations in metallicity or initial cloud density could alter the upper mass limit of the very massive stars and therefore the starting IMBH masses.

Load-bearing premise

The long-term growth projection assumes a steady supply of gas into the nuclear star cluster together with a constant tidal disruption event rate over 100 million years.

What would settle it

A measurement showing that gas inflow into high-redshift nuclear star clusters falls below the level needed to sustain 1.64 times 10 to the minus 4 solar masses per year accretion, or that TDE rates are substantially lower than assumed, would prevent the projected growth from 6747 to 62000 solar masses.

Figures

Figures reproduced from arXiv: 2606.10000 by Eunwoo Chung, Ji-Hoon Kim, Minyong Jung, Oh-kyoung Kwon, Yongseok Jo.

Figure 1
Figure 1. Figure 1: Multi-scale overview of the Enzo-Abyss simulation for the model with αvir = 1.5 and vw = 3000 km s−1 . Left: Projected gas density within the central 10 pc. Middle: A zoom-in of the central 1 pc region, showing the gas density overlaid with the stellar distribution (gray points). Right: Trajectories of the 10 stars nearest to the central IMBH (red circle; see Section 3.4) over 1000 yr, illustrating orbits … view at source ↗
Figure 2
Figure 2. Figure 2: Snapshots of the central 20 pc region from the simulation suite, each taken immediately before a VMS collapses into an IMBH. Each row shows gas surface density (top), density-weighted gas temperature (middle), and stellar surface density (bottom). The total number of stars and stellar mass within the simulation domain are indicated. For a fixed virial parameter, models with stronger stellar wind feedback e… view at source ↗
Figure 3
Figure 3. Figure 3: Half-mass radius versus stellar surface density for the simulated star clusters, compared with observational samples from high-redshift galaxies and the local Universe. Simulated clusters are represented by star-shaped markers: different colors indicate differ￾ent initial virial parameters (αvir = 1.0 in blue, 2.0 in red, and 3.0 in gold), while open and filled markers denote models with fidu￾cial (vw = 50… view at source ↗
Figure 5
Figure 5. Figure 5: Stellar density profiles measured from the density center at three epochs: 1.0, 0.5, 0.0 Myr before the formation of an IMBH. Here, the profile center is defined as the location of the maximum density peak within 0.1 pc of the VMS (which is about to collapse into an IMBH). For models with αvir = 1.0 and 1.5, densities in the central r < 0.1 pc region reach ∼ 106 M⊙ pc−3 — the threshold at which runaway col… view at source ↗
Figure 6
Figure 6. Figure 6: Mass evolution of the VMS that later becomes an IMBH in each model. VMSs exceeding 3000 M⊙ form in all cases except in the most turbulent models (αvir = 3.0), where initial high turbu￾lence hinders bursty star formation ( [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: Mass evolution of the IMBH and its progenitor VMS, tracked until the gas reservoir is effectively depleted. Two rep￾resentative models are selected to trace and study the evolution of IMBHs. The vertical dotted lines mark the epoch when the VMS collapses into an IMBH. Note that the mass growth of the VMS is significantly more rapid than that of the IMBH. During the IMBH phase, growth is driven by Edington-… view at source ↗
Figure 10
Figure 10. Figure 10: Eccentricity versus stellar mass for stars disrupted by the IMBHs in two representative models: αvir = 1.0, vw = 500 km s−1 (left; with more massive initial IMBH, 5108 M⊙) and αvir = 1.5, vw = 3000 km s−1 (right; with less massive initial IMBH, 3299 M⊙). The majority of TDEs (71 % and 77 %, respectively) originate from bound orbits in both simulations. For the more massive IMBH (left), one unbound event i… view at source ↗
Figure 11
Figure 11. Figure 11: TDE histogram. The time in x-axis is measured from the epoch of the IMBH formation for each run. Since the IMBH is more massive in the model with αvir = 1.0 and vw = 500 km s−1 , TDEs occur more frequently in this case. The TDE rate peaks immediately after IMBH formation and then gradually decreases in both cases. Note that we ended the αvir = 1.5 simulation at tIMBH = 7.4 Myr. See Section 4.3 for more in… view at source ↗
Figure 12
Figure 12. Figure 12: Stellar density profiles with best-fit Plummer (dotted lines) and EFF models (gray, dashed lines) immediately prior to the VMS collapse — for the fiducial initial gas distribution (top; Eq.(1)) and the Plummer initial gas distribution (bottom; Eq.(12)). The best-fit parameters for the Plummer models (Mcl and a), parameters for the EFF models (γ and a), and the resulting VMS (IMBH progenitor) mass are indi… view at source ↗
Figure 13
Figure 13. Figure 13: Projected mass growth of the IMBH over the next 100 Myr. The gray line shows the simulated mass evolution of the most massive IMBH formed in our suite (reaching MBH = 6747 M⊙ from the run with αvir = 1.0 and vw = 500 km s−1 ) up to the end of the run. For the extrapolation, we assume a constant TDE accretion rate of 3.82×10−5 M⊙ yr−1 . The cyan dotted line (squares) shows growth driven by TDEs only; the p… view at source ↗
Figure 14
Figure 14. Figure 14: Distribution of stellar-mass BH remnant masses as a function of their formation time. The markers distinguish the rem￾nant formation channels: PISN (green cross), DCBH (orange cir￾cles), and CCSN (blue triangles). The numbers in the legend indi￾cate the total count of events for each channel. DCBH events (failed supernovae) dominate the early epoch (t ≲ 8 Myr) and produce more massive remnants (MBH ≳ 30 M… view at source ↗
read the original abstract

A population of dense stellar systems at high redshift has recently been uncovered by the JWST. To investigate the formation of supermassive black hole (SMBH) seeds in these dense environments without invoking any \textit{ad hoc} seeding mechanisms, we present star cluster-scale simulations performed with an updated version of the hydrodynamics code \texttt{Enzo-Abyss}, which self-consistently integrates the gravity using a direct $N$-body method coupled with stellar evolution. By modeling initially dense, metal-poor gas clouds with varying turbulence, we consistently find the formation of dense clusters resembling early-stage nuclear star clusters (NSCs), as well as the formation of very massive stars (VMSs) ranging from $343\;\mathrm{M_\odot}$ to $5108\;\mathrm{M_\odot}$ via runaway collisions, irrespective of stellar wind feedback strength. Following the direct collapse of these VMSs, the resulting intermediate-mass black holes (IMBHs) grow through Eddington-limited gas accretion and tidal disruption events (TDEs). In our most optimistic model, we find a mass accretion rate of $1.64\times10^{-4}\;\mathrm{M_\odot\;yr^{-1}}$, with TDEs contributing $23\%$ of the total accretion over $\sim10\;\mathrm{Myr}$. Assuming a steady gas supply into the NSC driven by rapid structural assembly in the high-redshift environment, together with a constant TDE rate, we project that an IMBH with an initial mass of $6747\;\mathrm{M_\odot}$ at the center of the NSC can grow to $\sim62000\;\mathrm{M_\odot}$ within $100\;\mathrm{Myr}$ of its formation. Our numerical study, conducted within a single self-consistent framework that incorporates the essential physical processes, suggests that VMSs can form in dense gas clouds, collapse into IMBHs, and subsequently provide viable seeds for the SMBHs observed at high redshift.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper presents hybrid hydrodynamics/direct N-body simulations with an updated Enzo-Abyss code of initially dense, metal-poor gas clouds. It reports consistent formation of nuclear-star-cluster-like systems and very massive stars (343–5108 M⊙) via runaway collisions, independent of stellar-wind feedback strength. These VMSs collapse to IMBHs that grow by Eddington-limited accretion plus TDEs; the most optimistic run yields 1.64×10^{-4} M⊙ yr^{-1} with 23 % from TDEs over ~10 Myr. Under the explicit assumption of steady gas supply driven by high-redshift structural assembly and constant TDE rate, the authors project that a 6747 M⊙ IMBH reaches ~62 000 M⊙ in 100 Myr, offering a channel for high-z SMBH seeds without ad-hoc prescriptions.

Significance. If the VMS-formation and short-term accretion results are robust, the work supplies a single self-consistent numerical framework linking dense-cloud collapse to IMBH seeds, directly relevant to JWST-detected high-redshift dense stellar systems. The direct N-body gravity integration and inclusion of stellar evolution constitute clear technical strengths. The long-term growth projection, however, is the load-bearing element for the claim of viable SMBH seeds.

major comments (1)
  1. [Abstract] Abstract: the headline claim that an IMBH grows from 6747 M⊙ to ~62 000 M⊙ in 100 Myr is obtained solely by linear extrapolation of the ~10 Myr simulation result (accretion rate 1.64×10^{-4} M⊙ yr^{-1}, 23 % from TDEs) under the untested assumptions of steady gas supply and constant TDE rate. No part of the reported runs models the external reservoir or its replenishment; because the final mass scales directly with the assumed duration and constancy, any deviation (episodic inflow, feedback depletion, or NSC dynamical evolution) alters the projected seed mass and therefore the viability conclusion.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful and constructive report. The single major comment concerns the presentation of the long-term IMBH growth projection in the abstract. We address it point by point below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim that an IMBH grows from 6747 M⊙ to ~62 000 M⊙ in 100 Myr is obtained solely by linear extrapolation of the ~10 Myr simulation result (accretion rate 1.64×10^{-4} M⊙ yr^{-1}, 23 % from TDEs) under the untested assumptions of steady gas supply and constant TDE rate. No part of the reported runs models the external reservoir or its replenishment; because the final mass scales directly with the assumed duration and constancy, any deviation (episodic inflow, feedback depletion, or NSC dynamical evolution) alters the projected seed mass and therefore the viability conclusion.

    Authors: We agree that the 100 Myr projection is a linear extrapolation of the ~10 Myr simulated accretion rate under the explicit assumptions of steady gas supply and constant TDE rate, neither of which is modeled by extending the external reservoir in the runs. The abstract already qualifies the projection with the phrase “Assuming a steady gas supply…”, but we accept that the headline framing can be read as overstating the robustness of the long-term result. The primary scientific contribution remains the self-consistent hydro + direct N-body demonstration of VMS formation via runaway collisions and the subsequent short-term IMBH growth within the simulated NSC; the extrapolation is offered only as an order-of-magnitude illustration of possible seed viability under high-redshift conditions. We will revise the abstract to foreground the extrapolative character of the 100 Myr figure and will add a new paragraph in the discussion section that quantifies the sensitivity of the final mass to plausible variations in inflow duty cycle, TDE rate evolution, and NSC dynamical heating. revision: yes

Circularity Check

0 steps flagged

No circularity: core results from direct simulation; 100 Myr projection explicitly assumption-based extrapolation

full rationale

The paper's load-bearing claims (VMS formation via runaway collisions, IMBH seed masses, and the measured accretion rate of 1.64e-4 Msun/yr with 23% TDE contribution over ~10 Myr) are outputs of the Enzo-Abyss hydro + direct N-body runs described in the abstract and full text. The subsequent projection to ~62000 Msun in 100 Myr is introduced with the explicit qualifier 'Assuming a steady gas supply... together with a constant TDE rate, we project...', so it is not presented as a first-principles derivation or prediction forced by the simulation equations. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the quoted material. The derivation chain is therefore self-contained against its stated simulation outputs and external assumptions.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The work relies on standard stellar evolution and black hole accretion prescriptions; the growth projection depends on an explicit assumption of steady gas supply. No new particles or forces are introduced.

free parameters (2)
  • initial turbulence levels
    Varied across models to test robustness
  • stellar wind feedback strength
    Tested at multiple strengths with consistent VMS formation
axioms (2)
  • domain assumption Direct collapse of VMSs into IMBHs
    Invoked after VMS formation to produce seed black holes
  • domain assumption Eddington-limited accretion
    Used for the gas accretion phase

pith-pipeline@v0.9.1-grok · 5929 in / 1425 out tokens · 26453 ms · 2026-06-27T15:57:05.068421+00:00 · methodology

discussion (0)

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