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arxiv: 2606.27427 · v1 · pith:YFLMRPC2new · submitted 2026-06-25 · 🌌 astro-ph.GA · astro-ph.CO· astro-ph.SR

SEEDZ: Rapid Galaxy Assembly as a Pathway to Supermassive Stars, Dense Stellar Environments and Massive Black Hole Seeds

Lewis R. Prole , John A. Regan , Daxal Mehta , Devesh Nandal , R\"udiger Pakmor , Ricarda S. Beckmann , Michael Tremmel , Martin G. Haehnelt
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Simon C.O. Glover Ralf S. Klessen John H. Wise Sophie Koudmani Martin A. Bourne Debora Sijacki John Brennan Pelle van de Bor Paul C. Clark
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Pith reviewed 2026-06-29 02:02 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.COastro-ph.SR
keywords supermassive starsheavy black hole seedsearly galaxy assemblygas inflowshigh-redshift galaxiesmetallicityJWST observations
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The pith

Rapidly growing early galaxies sustain the inflows needed to form supermassive stars at a comoving density of 0.1 per cubic megaparsec by redshift 10.

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

The paper tracks gas flows in early galaxies to identify the conditions that produce supermassive stars and the heavy black hole seeds they may leave behind. Halos that grow at rates of at least one solar mass per year at their outer boundary maintain enough central inflow to meet the formation thresholds inside 10 parsecs. These same halos continue rapid growth after their first stars appear, so the seeds emerge roughly 100 million years later. Most seeds appear in near-solar metallicity gas, but a subset forms in lower-metallicity pockets that allow the supermassive-star channel. The resulting number density of candidate supermassive stars is 0.1 per comoving cubic megaparsec, implying that only one in ten thousand of them needs to be detected to account for the compact high-redshift sources seen by JWST.

Core claim

Halos that maintain growth rates of at least 1 solar mass per year at their virial radius sustain inflows of 0.1 solar masses per year into their central parsec and therefore meet the heavy-seed formation criterion of more than 1 solar mass per year into 10-parsec regions. These halos form heavy seeds about 100 million years after their first stars. By redshift 10 most seeds occur in near-solar metallicity gas, although some continue to form in 0.01 solar metallicity gas. When the additional requirement is imposed that a supermassive star must form in 0.01 solar metallicity gas and sustain accretion above 0.02 solar masses per year for its full 2-million-year lifetime, the simulations produc

What carries the argument

The inflow threshold of more than 1 solar mass per year into 10-parsec regions, which selects rapidly assembling halos that can maintain the inner accretion flows required for heavy seeds.

If this is right

  • Rapidly growing halos produce heavy seeds after their first stars but still at high redshift.
  • Most heavy seeds by redshift 10 form in near-solar metallicity environments.
  • A minority of heavy seeds form in low-metallicity gas that satisfies the supermassive-star progenitor conditions.
  • The calculated supermassive-star density requires that only a fraction of 10 to the minus 4 be visible to match the observed count of Little Red Dot galaxies.

Where Pith is reading between the lines

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

  • Seed formation would be concentrated in the subset of galaxies that assemble fastest rather than in typical halos.
  • The low-metallicity fraction among the seeds would set an upper bound on how much this channel can contribute to the total early black-hole population.
  • Observations that map Little Red Dots to their large-scale environments could test whether they sit in regions consistent with rapid halo growth.

Load-bearing premise

The specific inflow rate and metallicity thresholds used to decide which gas flows produce supermassive stars that become heavy seed progenitors.

What would settle it

A measured number density of supermassive-star candidates or heavy seeds at redshift near 10 that lies well below or well above 0.1 per comoving cubic megaparsec.

Figures

Figures reproduced from arXiv: 2606.27427 by Daxal Mehta, Debora Sijacki, Devesh Nandal, John A. Regan, John Brennan, John H. Wise, Lewis R. Prole, Martin A. Bourne, Martin G. Haehnelt, Michael Tremmel, Paul C. Clark, Pelle van de Bor, Ralf S. Klessen, Ricarda S. Beckmann, R\"udiger Pakmor, Simon C.O. Glover, Sophie Koudmani.

Figure 1
Figure 1. Figure 1: — Halo assembly histories taken from the merger tree. All quantities are plotted as a function of time relative to the time at which the halo formed its first star, Tcollapse. Lines are colour-coded to indicate whether the halo forms a heavy seed at any point during the simulation (red) or never forms a heavy seed (black). The three panels show the evolution of the halo mass (top), the halo growth rate (mi… view at source ↗
Figure 2
Figure 2. Figure 2: — Histogram of the time elapsed between a host halo’s initial collapse and the formation of its first heavy seed. 3. FORMATION ENVIRONMENTS Here we investigate the typical environmental conditions that lead to the high (1 M⊙ yr−1 ) inflow rates within 10 pc regions surrounding gas gravitational potential peaks, as required for our heavy seed black hole formation. We analyze the assembly history of the top … view at source ↗
Figure 3
Figure 3. Figure 3: — Radial profiles of halos at the point of heavy seed formation (red) compared against non-heavy seed-forming halos sampled 100 Myr after they form their first star (black). We show the mass inflow rate (top), the density (middle) and the cumulative mass (bottom) profiles for each halo [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: — Initial growth rates of heavy seeds. Left: the accretion rate onto heavy seeds within the assumed 2 Myr lifetime of a SMS after its formation. Right: histogram of the accretion rates onto heavy seeds at 2 Myr after their formation [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: — 2D heatmaps for heavy seed formation metallcities taken from the host gas cell at the time of formation. Left - average heavy seed growth rates within the first 2 Myr after formation. Middle - Total gas mass surrounding the heavy seed within 10 pc. Right - Redshift at the time of formation. We show the region of the 2D space where SMS is possible as a green square. rates of 0.1 M⊙ yr−1 with the distribut… view at source ↗
Figure 7
Figure 7. Figure 7: — density (upper) and metallicity (lower) projections of heavy seed formation sites, taken from the next snapshot after their formation. a) three examples of heavy seeds forming in metal-free gas. b) three examples of heavy seeds forming in super-solar metallicity gas. Red dots represent heavy seeds, while black dots show light seed black holes, orange dots show PopII cluster particles, and blue dots show … view at source ↗
Figure 8
Figure 8. Figure 8: — Number densities of all heavy seeds (red), those that form in regions of metallicity above 10−2 Z⊙ that are assumed to form from dense stellar clusters (green), those that meet the criteria for SMS formation i.e. metallicity below 10−2 Z⊙ and sustained inflow rates of 0.02 M⊙ yr−1 within the first 2 Myr life of a SMS (blue dashed), and the SMS number density assuming a stellar lifetime of 2 Myr (blue sol… view at source ↗
read the original abstract

We investigate the assembly history of early galaxies in the SEEDZ hydrodynamic simulations, to investigate the high inflow rates believed to be required for the formation of supermassive stars (SMSs), dense stellar clusters and subsequently heavy seed black holes. Using a heavy seed formation criteria of $>$1 M$_\odot$ yr$^{-1}$ flowing into 10 pc regions, we find that heavy seeds form in halos that grow rapidly compared to those halos that never meet the criteria. Halos with growth rates of $\gtrsim$1 M$_\odot$ yr$^{-1}$ at their virial radius (scales of a few hundred pc) are able to sustain a flow rate of 0.1 M$_\odot$ yr$^{-1}$ into the inner 1 pc of the halo, maintaining higher density environments within the central 10 - 100~pc. These halos continue to grow rapidly after their initial collapse, typically forming heavy seeds $\sim$100 Myr after forming their first stars and stellar mass black holes. By $z=10$, most heavy seeds form in regions of near-solar metallicity, although a minority of heavy seeds do continue to form in low metallicity (10$^{-2}$ Z$_\odot$) regions. Under the assumption that a SMS forms as the progenitor to a heavy seed if it forms in a region of low (10$^{-2}$ Z$_\odot$) metallicity, and can sustain high accretion rates above 0.02 M$_\odot$ yr$^{-1}$ throughout the SMS lifetime of 2 Myr, we find a number density of SMSs of 0.1 cMpc$^{-3}$, meaning that only a fraction of 10$^{-4}$ of these SMSs would need to be visible to JWST to account for the observed population of Little Red Dot galaxies.

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

3 major / 2 minor

Summary. The paper analyzes the SEEDZ hydrodynamic simulations of early galaxy assembly to identify conditions for supermassive star (SMS) formation as progenitors to heavy seed black holes. Using a heavy-seed criterion of >1 M_⊙ yr^{-1} inflow into 10 pc regions, the authors find that such seeds arise in rapidly growing halos that sustain high central densities and typically form ~100 Myr after first stars. By z=10 most heavy seeds occur at near-solar metallicity, but under the explicit assumption that SMSs arise only in the low-metallicity (10^{-2} Z_⊙) subset that also maintains accretion >0.02 M_⊙ yr^{-1} throughout a 2 Myr lifetime, they report an SMS number density of 0.1 cMpc^{-3} and note that a visible fraction of only 10^{-4} would suffice to explain the observed Little Red Dot population.

Significance. If the reported density is robust, the work supplies a concrete, simulation-derived pathway connecting rapid halo growth to SMS and heavy-seed formation, with direct implications for JWST observations of high-redshift compact objects. The hydrodynamic tracking of inflows, metallicities, and central densities yields falsifiable number-density predictions that can be tested against future observations or higher-resolution runs.

major comments (3)
  1. [Abstract] Abstract: the headline SMS number density of 0.1 cMpc^{-3} is obtained only after applying two sharp, externally imposed thresholds (heavy-seed inflow >1 M_⊙ yr^{-1} into 10 pc; SMS progenitor accretion >0.02 M_⊙ yr^{-1} sustained for the full 2 Myr at 10^{-2} Z_⊙). No sensitivity analysis, variation of the cut values, or justification for these particular numbers versus alternatives (e.g., 0.5 or 2 M_⊙ yr^{-1}) is reported, yet these cuts directly determine which halos contribute to the final count.
  2. [Abstract] Abstract: the manuscript states that most heavy seeds form at near-solar metallicity while only a minority continue to form at 10^{-2} Z_⊙, but provides neither the numerical fraction of low-Z heavy seeds nor error bars or volume uncertainties on the derived 0.1 cMpc^{-3} SMS density; without these, the claim that a 10^{-4} visible fraction accounts for Little Red Dots cannot be evaluated quantitatively.
  3. [Abstract] Abstract (and methods description of SEEDZ runs): no convergence tests with respect to spatial resolution, alternative inflow-radius definitions, or changes in the metallicity floor are presented for the halo-growth and inflow-rate statistics that underpin the heavy-seed identification; these statistics are load-bearing for the central claim that rapid growth enables sustained central accretion.
minor comments (2)
  1. [Abstract] The abstract uses 'cMpc^{-3}' without defining whether the volume is comoving or proper; a brief clarification in the methods would remove ambiguity when comparing to observational number densities.
  2. [Abstract] The simulation suite (SEEDZ) is referenced only by name; a citation to the methods paper or a short description of box size, particle mass, and feedback implementation would allow readers to assess the statistical robustness of the reported densities.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which highlight important aspects of robustness and clarity in our analysis. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline SMS number density of 0.1 cMpc^{-3} is obtained only after applying two sharp, externally imposed thresholds (heavy-seed inflow >1 M_⊙ yr^{-1} into 10 pc; SMS progenitor accretion >0.02 M_⊙ yr^{-1} sustained for the full 2 Myr at 10^{-2} Z_⊙). No sensitivity analysis, variation of the cut values, or justification for these particular numbers versus alternatives (e.g., 0.5 or 2 M_⊙ yr^{-1}) is reported, yet these cuts directly determine which halos contribute to the final count.

    Authors: The adopted thresholds are motivated by theoretical expectations in the SMS formation literature for the minimum sustained accretion rates needed to reach supermassive masses before radiative feedback halts growth. We agree that the lack of explicit sensitivity tests limits the ability to assess robustness. In the revised manuscript we will add a dedicated subsection performing a sensitivity analysis, varying the heavy-seed inflow threshold between 0.5 and 2 M_⊙ yr^{-1} and the SMS accretion threshold between 0.01 and 0.05 M_⊙ yr^{-1}, and will report the resulting range of SMS number densities. revision: yes

  2. Referee: [Abstract] Abstract: the manuscript states that most heavy seeds form at near-solar metallicity while only a minority continue to form at 10^{-2} Z_⊙, but provides neither the numerical fraction of low-Z heavy seeds nor error bars or volume uncertainties on the derived 0.1 cMpc^{-3} SMS density; without these, the claim that a 10^{-4} visible fraction accounts for Little Red Dots cannot be evaluated quantitatively.

    Authors: We will include the explicit numerical fraction of heavy seeds forming in low-metallicity (10^{-2} Z_⊙) gas in the revised manuscript. We will also report Poisson uncertainties on the SMS number density derived from the number of qualifying objects in the simulated volume. A full treatment of cosmic variance would require additional independent realizations, which are not available; we will explicitly note this limitation when discussing the 10^{-4} visibility fraction. revision: partial

  3. Referee: [Abstract] Abstract (and methods description of SEEDZ runs): no convergence tests with respect to spatial resolution, alternative inflow-radius definitions, or changes in the metallicity floor are presented for the halo-growth and inflow-rate statistics that underpin the heavy-seed identification; these statistics are load-bearing for the central claim that rapid growth enables sustained central accretion.

    Authors: The SEEDZ resolution was selected to resolve the central 10 pc inflow regions, consistent with prior convergence studies using the same code base. In the revised manuscript we will expand the methods section to justify the resolution choice and will test the sensitivity of the inflow statistics to alternative radii (5 pc and 20 pc). Full resolution-convergence re-runs and variations of the metallicity floor are computationally prohibitive for this revision and will be noted as a limitation. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The SMS number density of 0.1 cMpc^{-3} is obtained by direct counting of halos in the SEEDZ hydrodynamic simulations that satisfy the stated a priori thresholds (>1 M⊙ yr^{-1} inflow into 10 pc; low-Z plus sustained >0.02 M⊙ yr^{-1} accretion for 2 Myr). These thresholds function as external filters applied to simulation outputs rather than quantities derived from or fitted to the target density. No equations, self-citations, or ansatzes reduce the reported density to the inputs by construction. The result remains an independent numerical measurement from the hydro runs.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The central claim depends on several numerical thresholds for inflow rates, accretion sustainability, and metallicity that are introduced to select SMS progenitors rather than derived from the simulation physics.

free parameters (4)
  • Heavy seed inflow threshold = >1 M_⊙ yr^{-1} into 10 pc
    Criterion of >1 M_⊙ yr^{-1} flowing into 10 pc regions used to tag heavy seed sites.
  • SMS sustained accretion rate = 0.02 M_⊙ yr^{-1}
    Minimum rate of 0.02 M_⊙ yr^{-1} required throughout the SMS lifetime.
  • SMS lifetime = 2 Myr
    Assumed duration of 2 Myr over which accretion must be maintained.
  • Low-metallicity threshold for SMS = 10^{-2} Z_⊙
    10^{-2} Z_⊙ cutoff used to decide which SMSs become heavy seeds.
axioms (2)
  • standard math Lambda-CDM cosmology governs halo assembly and gas accretion
    Underlying framework for all cosmological hydrodynamic runs.
  • domain assumption Subgrid models for cooling, star formation, and feedback accurately capture central gas flows
    Required for the SEEDZ simulations to produce the reported inflow rates.

pith-pipeline@v0.9.1-grok · 5972 in / 1844 out tokens · 58405 ms · 2026-06-29T02:02:29.984520+00:00 · methodology

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