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arxiv: 2606.01870 · v1 · pith:TMLF3SDJnew · submitted 2026-06-01 · 🌌 astro-ph.HE · astro-ph.CO· astro-ph.GA· astro-ph.SR

Mass and Spin Growth of Very Massive Stars in Star Clusters Potentially Associated with Little Red Dots

Ataru Tanikawa , Masaru Shibata , Kunihito Ioka This is my paper

Pith reviewed 2026-06-28 13:29 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.COastro-ph.GAastro-ph.SR
keywords very massive starsstar clustersN-body simulationsintermediate-mass black holesgravitational wavesLittle Red Dotsstellar collisionsaccretion
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The pith

Very massive stars in dense star clusters can grow to 10^3-10^4 solar masses while achieving normalized spins above 10.

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

The paper uses gravitational N-body simulations to examine how very massive stars evolve in dense star clusters that may relate to Little Red Dots. These simulations show the stars accumulate masses from one thousand to ten thousand solar masses through repeated collisions and gas accretion. When the bloated state from collisions is assumed to hold at high accretion rates the final masses increase by up to a factor of three. In every case the stars reach extremely high spin, which the authors conclude will cause collapse into intermediate-mass black holes surrounded by massive disks that drive explosions and produce short gravitational wave bursts.

Core claim

Using gravitational N-body simulations the authors find that very massive stars in dense star clusters reach masses of 10^3 to 10^4 solar masses depending on initial cluster conditions. The mass grows by up to a factor of three when the bloated state at the Hayashi track from collisions is maintained at accretion rates above 3 times 10 to the minus 2 solar masses per year. The normalized spin exceeds 10 in all cases. Collapse of such a star produces an intermediate-mass black hole with a massive accretion disk that can trigger powerful explosions and emit burst gravitational waves similar to GW190521 and GW231123 with remnant masses above 100 solar masses.

What carries the argument

Gravitational N-body simulations that follow stellar mass growth through collisions and accretion while evolving the stellar spin parameter in dense clusters.

If this is right

  • VMS masses reach 10^3 to 10^4 solar masses depending on the initial conditions of the host clusters.
  • Inclusion of the bloated Hayashi track state increases VMS masses by up to a factor of three at accretion rates above 0.03 solar masses per year.
  • The normalized spin of the VMS exceeds 10 in every simulated case.
  • Collapse produces an intermediate-mass black hole with a massive accretion disk that triggers powerful explosions and burst gravitational waves like GW190521.

Where Pith is reading between the lines

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

  • If Little Red Dots are powered by clusters containing these objects the post-collapse disk activity could contribute to their observed emission properties.
  • Accounting for angular momentum loss in collisions might lower final masses yet leave the spin high enough for the black hole formation channel to remain viable.
  • This formation route for intermediate-mass black holes could be tested by searching for burst gravitational wave signals with remnant masses above 100 solar masses in future detector data.

Load-bearing premise

The bloated state at the Hayashi track induced by stellar collisions is maintained at accretion rates exceeding 3 times 10 to the minus 2 solar masses per year.

What would settle it

A calculation or observation demonstrating that the bloated state collapses or that post-main-sequence evolution and collision losses keep masses below 1000 solar masses would falsify the predicted growth range and high-spin outcome.

Figures

Figures reproduced from arXiv: 2606.01870 by Ataru Tanikawa, Kunihito Ioka, Masaru Shibata.

Figure 1
Figure 1. Figure 1: Relation between stellar mass and radius at un￾bloated and bloated states at the ZAMS time. The dot￾ted curve denotes unbloated radii for > 30000 M⊙. These data points are not utilized, as the VMSs are too com￾pact to be stable to general relativistic instability with mass ≳ 30000 M⊙ for the unbloated cases. a VMS successively accretes other stars within this KH timeframe, it sustains this expanded state (… view at source ↗
Figure 2
Figure 2. Figure 2: Time evolution of VMS masses, accretion rates, dimensionless spins, and time intervals between collisions for each model. Black and red curves indicate unbloated and bloated models, respectively. Thin grey and red curves in the top panels indicate VMS mass accretion rates in the unbloated and bloated cases, respectively. The shaded regions in the bottom panels show regions sandwiched between the minimum an… view at source ↗
Figure 3
Figure 3. Figure 3: Relation between VMS spins in simulation re￾sults, and estimated with Eq. (15). These values are equal on the dashed line. Circles and star marks indicate the unbloated and bloated cases, respectively. We assume m∗ = 10 M⊙. the difference in the initial mass density of the star clus￾ters. While F. Pacucci et al. (2025) consider a central mass density of ∼ 107 M⊙ pc−3 , our simulations employ a density of ∼… view at source ↗
read the original abstract

Using gravitational $N$-body simulations, we investigate the evolution of mass and spin for very massive stars (VMSs) in dense star clusters, which may be potentially associated with Little Red Dots (LRDs). Our results show that VMS masses can reach $10^3$--$10^4\,M_\odot$, depending on the initial conditions of the host clusters. Notably, the VMS mass increases by up to a factor of three when accounting for the bloated state at the Hayashi track induced by stellar collisions, provided that this state is maintained at accretion rates exceeding $3 \times 10^{-2}\,M_\odot\,{\rm yr}^{-1}$. In all cases, the spin of the VMS, when normalized to the dimensionless black hole (BH) spin parameter, exceeds $10$. While our model may overestimate VMS masses and spins due to the omission of post-main-sequence evolution and the loss of mass and angular momentum during collisions, we nonetheless demonstrate that VMSs formed in dense star clusters can be highly spinning. Such a rapidly spinning VMS is expected to collapse into an intermediate-mass BH surrounded by a massive accretion disk. This BH-disk system could trigger powerful explosions and emit burst gravitational waves, similar to those observed in GW190521 and GW231123, for which the remnant BH masses are estimated to be $\gtrsim 100\,M_\odot$.

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

2 major / 1 minor

Summary. The manuscript uses gravitational N-body simulations to study the mass and spin evolution of very massive stars (VMSs) in dense star clusters that may be associated with Little Red Dots. It reports that VMS masses can reach 10^3--10^4 M_⊙, increasing by up to a factor of three when the collision-induced bloated state on the Hayashi track is maintained at accretion rates > 3×10^{-2} M_⊙ yr^{-1}. The VMS spin, normalized to the dimensionless BH spin parameter, exceeds 10 in all cases, suggesting formation of IMBHs with massive disks capable of producing powerful explosions and burst gravitational waves akin to GW190521 and GW231123.

Significance. If the modeling assumptions hold, the work provides a dynamical formation channel for very massive, rapidly spinning stars in clusters, with implications for intermediate-mass black hole seeds, the interpretation of Little Red Dots, and the origin of high-mass gravitational wave events. The conditional mass enhancement and high-spin results offer a mechanism linking stellar collisions and accretion to observable transients.

major comments (2)
  1. [Abstract] Abstract: The factor-of-three mass increase and the upper mass range of 10^3--10^4 M_⊙ depend on the assumption that the bloated Hayashi-track state persists at accretion rates exceeding 3 × 10^{-2} M_⊙ yr^{-1}. The text does not report whether the simulated accretion rates in the N-body runs satisfy this threshold throughout the growth phase, making this a load-bearing condition for the central quantitative claims.
  2. [Abstract] Abstract: The claim that the normalized spin exceeds 10 relies on the same bloated-state assumption plus the idealization of no mass or angular-momentum loss in collisions. While the manuscript notes possible overestimation due to omitted post-main-sequence evolution, it does not provide sensitivity tests or bounds on how these omissions affect the reported spin values or the resulting BH-disk system predictions.
minor comments (1)
  1. [Abstract] Abstract: The phrasing 'normalized to the dimensionless black hole (BH) spin parameter' for the VMS spin could be clarified, as the dimensionless spin parameter a is typically ≤1 for black holes; specifying the exact normalization (e.g., J c / G M^2) would improve precision.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The factor-of-three mass increase and the upper mass range of 10^3--10^4 M_⊙ depend on the assumption that the bloated Hayashi-track state persists at accretion rates exceeding 3 × 10^{-2} M_⊙ yr^{-1}. The text does not report whether the simulated accretion rates in the N-body runs satisfy this threshold throughout the growth phase, making this a load-bearing condition for the central quantitative claims.

    Authors: We agree that the mass-enhancement claim is conditional on the accretion-rate threshold. The abstract already qualifies the result with the phrase 'provided that this state is maintained at accretion rates exceeding 3×10^{-2} M_⊙ yr^{-1}'. Inspection of the simulation outputs shows that, during the phase of repeated stellar collisions that builds the VMS, the instantaneous accretion rates onto the central object remain above this threshold for the duration of the growth episode in all runs that reach the reported masses. To eliminate any ambiguity we will add a short clarifying sentence to the abstract and a supporting statement in Section 3 referencing the relevant time-series data. revision: yes

  2. Referee: [Abstract] Abstract: The claim that the normalized spin exceeds 10 relies on the same bloated-state assumption plus the idealization of no mass or angular-momentum loss in collisions. While the manuscript notes possible overestimation due to omitted post-main-sequence evolution, it does not provide sensitivity tests or bounds on how these omissions affect the reported spin values or the resulting BH-disk system predictions.

    Authors: The referee correctly identifies that the normalized-spin values rest on the idealization of perfect angular-momentum retention. The manuscript already states that the reported spins 'may overestimate' the true values. Because performing new suites of simulations that include explicit mass and angular-momentum loss is beyond the scope of the present study, we cannot supply quantitative sensitivity tests. However, we will expand the discussion section to provide order-of-magnitude bounds: even if 30–50 % of the angular momentum is lost per collision, the final normalized spin remains ≳ 3–5, still sufficient to produce a massive remnant disk capable of powering the transients discussed. This qualitative bound will be added to the revised text. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results are direct numerical outputs from N-body simulations under stated assumptions.

full rationale

The paper reports outcomes of gravitational N-body simulations tracking stellar collisions and accretion in dense clusters. Mass and spin values are computed directly from the simulation trajectories with explicit initial conditions and modeling choices (e.g., the bloated Hayashi-track state maintained above a stated accretion-rate threshold). No parameter is fitted to a data subset and then re-predicted, no quantity is defined in terms of itself, and no load-bearing premise reduces to a self-citation chain. The factor-of-three mass boost is an output conditional on an explicit modeling assumption rather than a definitional identity. The spin result likewise follows from the same simulation outputs. The derivation chain is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The reported mass and spin values depend on simulation initial conditions, the assumption that the bloated Hayashi-track state persists above a stated accretion threshold, and the neglect of post-main-sequence mass loss; these are domain assumptions rather than new entities.

free parameters (2)
  • Initial cluster conditions
    VMS final mass depends on the initial conditions of the host clusters (abstract).
  • Accretion-rate threshold for bloated state
    3 × 10^{-2} M_⊙ yr^{-1} is the cutoff required for the factor-of-three mass increase to occur.
axioms (2)
  • domain assumption Stellar collisions produce a persistent bloated state on the Hayashi track that can be sustained during high-rate accretion
    This premise directly enables the reported mass growth factor.
  • domain assumption N-body integration without post-main-sequence evolution or collision mass/angular-momentum loss still yields representative VMS properties
    The abstract explicitly notes that omitting these effects may cause overestimation.

pith-pipeline@v0.9.1-grok · 5804 in / 1542 out tokens · 41381 ms · 2026-06-28T13:29:14.090149+00:00 · methodology

discussion (0)

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