arxiv: 2604.22924 · v1 · submitted 2026-04-24 · 🌌 astro-ph.GA

Recognition: unknown

Supermassive stars with embedded stellar black hole cores: dense assembling star clusters as faint multiple Little Red Dot systems

Antti Rantala

Authors on Pith no claims yet

Pith reviewed 2026-05-08 10:41 UTC · model grok-4.3

classification 🌌 astro-ph.GA

keywords supermassive starsquasi-starslittle red dotsstellar black holesstar cluster assemblyhigh-redshift galaxiesrunaway collisionsJWST observations

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The pith

Dense star clusters embed stellar black holes in supermassive stars to form long-lived quasi-star systems matching faint Little Red Dots.

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

The paper argues that in assembling star clusters with surface densities above 10^6 solar masses per square parsec, stellar black holes segregate rapidly and embed within the gaseous layers of extremely massive or supermassive stars. This produces a quasi-star configuration whose duration exceeds the supermassive star lifetime by orders of magnitude, allowing continued growth by stellar collisions and the capture of additional black holes. The resulting systems have assembly region sizes of about 100 parsecs and masses above 10,000 solar masses, and they sit near young blue star-forming clumps. These traits align with the faint multiple Little Red Dots detected by JWST. A sympathetic reader would care because the mechanism supplies a dynamical pathway from high-redshift cluster formation to the observed red sources.

Core claim

In star clusters with surface densities exceeding 10^6 solar masses per square parsec, stellar black holes of up to 60 solar masses undergo rapid mass segregation within the sphere of influence of extremely massive or supermassive stars and embed in their gaseous layers. This quasi-star phase is a natural outcome of runaway stellar collisions in the densest clusters. The embedded black hole configuration persists for a duration orders of magnitude longer than the supermassive star lifetime, enabling extended growth by stellar collisions and the formation of embedded gravitational wave sources when more than one stellar black hole is captured. The cluster sizes of roughly 100 parsecs and the

What carries the argument

The quasi-star phase formed when stellar black holes embed in the gaseous envelopes of extremely massive or supermassive stars through mass segregation and relaxation inside high surface-density clusters.

If this is right

The quasi-star phase lasts orders of magnitude longer than the supermassive star lifetime and thereby permits extended growth by stellar collisions.
Capture of more than one stellar black hole creates embedded gravitational wave sources inside the quasi-star.
The assembly regions of size approximately 100 parsecs and quasi-star masses of at least 10,000 solar masses reproduce the observed properties of faint Little Red Dots.
The proximity of the quasi-stars to young massive blue star-forming clumps matches the spatial arrangement of multiple Little Red Dot systems.

Where Pith is reading between the lines

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

If stable, the configuration offers an efficient channel for building intermediate-mass black hole seeds inside the densest high-redshift clusters.
The requirement for surface densities above 10^6 solar masses per square parsec predicts that only a subset of star-forming regions at high redshift should host such objects.
Detection of X-ray emission or gravitational-wave signatures from faint Little Red Dots would provide a direct test for the embedded black hole.
The mechanism implies that runaway stellar collisions operate more frequently in early dense clusters than models without black-hole embedding assume.

Load-bearing premise

The simulated cluster densities together with post-Newtonian and stellar-evolution physics produce a stable embedded quasi-star configuration that survives long enough without rapid disruption or ejection.

What would settle it

A simulation in which the stellar black hole is ejected from the supermassive star envelope before significant additional growth occurs, or JWST observations showing that faint multiple Little Red Dots lack associated dense cluster environments.

Figures

Figures reproduced from arXiv: 2604.22924 by Antti Rantala.

**Figure 1.** Figure 1: The landscape of strong interactions between massive (𝑚★ > 10 M⊙) stars and BHs in the simulation sample. The five interaction categories A–E are largely distinct from each other with only categories C and D somewhat overlapping. The category E (BH+EMS/SMS) stands out from the rest of the interactions by its high stellar masses (1010 M⊙ ≲ 𝑚★ ≲ 24493 M⊙), stellar BH masses (40 M⊙ ≲ 𝑚• ≲ 61 M⊙) and consequen… view at source ↗

**Figure 2.** Figure 2: The growth (solid lines) of six EMSs/SMSs in the low metallicity (𝑍 = 0.01 Z⊙) models HD9Z1 (stronger winds) and ID9Z1 (weaker winds). The vertical lines and the shaded regions indicate the formation times of stellar BHs (≳ 3.1 Myr) according to their masses. The EMSs/SMSs have their lifetimes extended beyond ∼ 3 Myr via collisional rejuvenation (dotdashed lines) until they interact with a stellar BH (fiv… view at source ↗

**Figure 3.** Figure 3: The osculating near-Keplerian orbits (solid lines) of ∼ 10 stellar BHs (filled circles) within the radius of influence of the supermassive star (the central + symbol) at 𝑡 = 4.35 Myr. The three panels show x-y, x-z and y-z projections of the SMS sphere of influence (dashed outer circle) while the stars within sphere of influence are represented as small background dots. Note that only the stars within the … view at source ↗

**Figure 4.** Figure 4: The stellar dynamical precession and relaxation timescales within the influence radius (𝑟infl ∼ 0.1 pc) of a ∼ 25000M⊙ star from the simulation ID9Z1. 𝑁• ∼ 10 BHs and ∼ 200 massive stars orbit within the influence radius (𝑟infl ∼ 0.1 pc) of the SMS. Scalar resonant relaxation and nonresonant two-body relaxation can drive stellar BHs into interaction orbits with the SMS on a timescale that is shorter than … view at source ↗

**Figure 5.** Figure 5: A schematic illustration interpreting a hierarchically assembling star formation region as a dual (or a multiple) system of faint LRDs. The densest and most massive sub-clusters form extremely massive or supermassive stars (EMS/SMS) via runaway stellar collisions, and a subset of these acquire stellar BH cores, becoming long-lived quasi-stars (QSs) responsible for the luminosity of the faint LRD pair. The… view at source ↗

read the original abstract

Numerical simulations have established that star clusters with densities comparable to the high redshift ($z>6$-$10$) James Webb Space Telescope (JWST) proto globular clusters may build up extremely massive (EMSs; $m_\mathrm{\star}>1000 M_\odot$) or even supermassive stars (SMSs; $m_\mathrm{\star}>10000 M_\odot$) and potentially intermediate mass black holes (IMBHs) through runaway stellar collisions. Using direct simulations of assembling star clusters including post-Newtonian black hole dynamics and stellar evolution, we demonstrate that in such dense environments ($\Sigma_\mathrm{h} \gtrsim 10^6 M_\odot$pc$^\mathrm{-2}$) stellar BHs ($m_\bullet \lesssim 60 M_\odot$), driven by rapid mass segregation and relaxation effects within the sphere of influence of the EMSs/SMSs, may strongly interact with the extremely massive stars and become embedded within their gaseous layers. We suggest that this quasi-star (QS) like embedded BH phase is a natural outcome of the runaway formation of EMSs/SMSs in the densest star clusters. The QS phase is orders of magnitude longer in duration than the lifetime of the SMS, enabling an extended growth period by stellar collisions, and allows the formation of embedded gravitational wave sources if the QS captures more than a single stellar BH. The star cluster assembly region sizes ($\sim100$ pc), QS masses ($\gtrsim 10^4 M_\odot$) and their proximity to young, massive blue star forming clumps are consistent with the faint population of multiple little red dots (LRDs) recently discovered by the JWST.

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.

Desk Editor's Note private letter to a colleague

N-body runs show stellar BHs embedding in EMS/SMS cores via mass segregation, but the claimed long-lived quasi-star phase is asserted rather than integrated over the required timescales.

read the letter

Simulations here demonstrate that in dense star clusters, stellar black holes can sink into the cores of extremely massive stars through mass segregation, creating what the authors call a quasi-star phase. This is presented as a way to explain the faint multiple Little Red Dots seen by JWST. The new element is the specific outcome from the N-body runs: BHs of up to 60 solar masses embedding in stars over 1000 solar masses in environments with surface densities above a million solar masses per square parsec. The inclusion of post-Newtonian dynamics and stellar evolution in the direct simulations makes the embedding process concrete rather than speculative. The paper handles the dynamical side competently. The runs track relaxation and close encounters within the sphere of influence of the massive stars, leading to the embedding. This adds a mechanism to existing ideas about runaway collisions in high-redshift clusters. The soft spot is the leap to long-term stability. The abstract states the quasi-star phase lasts orders of magnitude longer than the supermassive star lifetime, allowing extended growth. But the simulations focus on the initial interactions and embedding on shorter dynamical timescales. There is no direct integration of the gaseous envelope response, continued accretion, or orbital stability over the 10 million year windows needed to match LRD properties. The stability is asserted rather than shown. The connection to observations is qualitative: cluster sizes around 100 parsecs and masses above 10,000 solar masses are said to be consistent with faint LRDs, but no comparison to number densities or detailed properties is given. This work will interest people studying early supermassive black hole seeds and JWST high-redshift sources. Readers who run or use cluster simulations will see the value in the embedding result. It deserves peer review because the simulation produces a distinct new configuration, even if the observational implications need tightening. I recommend sending it out for refereeing.

Referee Report

2 major / 2 minor

Summary. The paper presents direct N-body simulations of dense assembling star clusters (with post-Newtonian black-hole dynamics and stellar evolution) to argue that stellar black holes (m_• ≲ 60 M_⊙) undergo rapid mass segregation and embed within the gaseous envelopes of extremely massive or supermassive stars (EMSs/SMSs) formed by runaway collisions in environments with Σ_h ≳ 10^6 M_⊙ pc^{-2}. This produces a quasi-star (QS)-like phase claimed to persist orders of magnitude longer than the SMS lifetime, enabling extended growth by collisions, possible multi-BH capture for gravitational-wave sources, and consistency with the observed properties (sizes ~100 pc, masses ≳10^4 M_⊙, proximity to blue clumps) of faint multiple Little Red Dots at z>6-10.

Significance. If the embedding mechanism and long-term QS stability are confirmed, the work supplies a concrete dynamical channel linking high-redshift proto-globular-cluster assembly to JWST LRDs, with additional implications for IMBH seeding and embedded GW sources. The use of direct simulations incorporating PN terms and stellar evolution is a methodological strength that grounds the mass-segregation and close-encounter results.

major comments (2)

[Abstract / simulation results] Abstract and simulation description: the central claim that the QS phase 'is orders of magnitude longer in duration than the lifetime of the SMS' and 'enables an extended growth period' is load-bearing for the LRD interpretation, yet the reported N-body runs (with PN and stellar evolution) only evolve the pre-embedding mass segregation and close encounters on dynamical/relaxation timescales; no direct integration or modeling of the embedded BH-envelope configuration, gaseous response, continued accretion, or orbital stability is shown over the required ~10^7 yr window.
[Abstract] Abstract: the statement that cluster assembly region sizes, QS masses, and proximity to young clumps 'are consistent with' the faint multiple LRD population is presented without quantitative comparison to observed LRD number densities, luminosity functions, or spatial clustering statistics, leaving the match at a qualitative level.

minor comments (2)

[Methods] Notation for surface density threshold (Σ_h) and the precise definition of the sphere of influence should be clarified with an explicit equation or reference to the simulation setup.
[Methods] The manuscript would benefit from a brief table or paragraph summarizing the range of simulated cluster densities, number of runs, and any convergence tests performed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback. We address each major comment below, clarifying the scope of our simulations while strengthening the manuscript where possible. Revisions will be incorporated in the next version.

read point-by-point responses

Referee: [Abstract / simulation results] Abstract and simulation description: the central claim that the QS phase 'is orders of magnitude longer in duration than the lifetime of the SMS' and 'enables an extended growth period' is load-bearing for the LRD interpretation, yet the reported N-body runs (with PN and stellar evolution) only evolve the pre-embedding mass segregation and close encounters on dynamical/relaxation timescales; no direct integration or modeling of the embedded BH-envelope configuration, gaseous response, continued accretion, or orbital stability is shown over the required ~10^7 yr window.

Authors: We agree that the N-body simulations (including PN terms and stellar evolution) demonstrate the dynamical processes of mass segregation and BH embedding within EMS/SMS on short dynamical and relaxation timescales, but do not directly evolve the subsequent gaseous quasi-star configuration over ~10^7 yr. The extended QS duration claim is an inference drawn from the expected stability of embedded BH-envelope systems once formed, consistent with analytic and prior hydrodynamical models of quasi-stars in the literature. We do not claim to have performed long-term hydrodynamical integration of the embedded phase, which lies outside the scope of direct N-body methods. In revision, we will update the abstract and add a new subsection in the discussion explicitly distinguishing the simulated pre-embedding phase from the theoretically expected QS lifetime, including caveats on the assumptions and references to supporting QS stability studies. revision: yes
Referee: [Abstract] Abstract: the statement that cluster assembly region sizes, QS masses, and proximity to young clumps 'are consistent with' the faint multiple LRD population is presented without quantitative comparison to observed LRD number densities, luminosity functions, or spatial clustering statistics, leaving the match at a qualitative level.

Authors: The abstract statement is intentionally qualitative, as the paper's focus is the dynamical formation mechanism rather than a statistical population model. We acknowledge that a more quantitative link would strengthen the interpretation. In the revised manuscript, we will add a short paragraph in the discussion section providing order-of-magnitude estimates: using published high-redshift cluster formation rates and the fraction of dense clusters expected to produce such QS systems, compared against current observational constraints on faint LRD number densities at z>6. This will remain at the level of plausibility rather than a full luminosity-function fit, but will move beyond purely qualitative language. revision: partial

Circularity Check

0 steps flagged

No circularity: forward N-body simulations with PN terms generate BH-embedding results independently of LRD data

full rationale

The paper's derivation proceeds from initial conditions of dense star clusters (Σ_h ≳ 10^6 M_⊙ pc^{-2}) through direct numerical integration of stellar dynamics, post-Newtonian BH interactions, and stellar evolution. Mass segregation and close encounters are evolved on dynamical timescales to produce the embedding of stellar BHs (m_• ≲ 60 M_⊙) within EMS/SMS gaseous layers. The QS phase duration, extended growth by collisions, and consistency with faint multiple LRDs are presented as post-simulation interpretive outcomes and comparisons, not as fitted parameters or self-defined quantities. No equations reduce the central claims to their inputs by construction, no load-bearing self-citations close the loop, and no ansatz or uniqueness theorem is smuggled in. The chain remains self-contained as a forward simulation whose outputs are not statistically forced by the target observations.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

With only the abstract available, the ledger is necessarily incomplete. The work inherits standard assumptions from prior runaway-collision simulations and adds the embedding outcome as a simulation result rather than an independent derivation.

free parameters (1)

cluster surface density threshold
Σ_h ≳ 10^6 M_⊙ pc^{-2} is used to select environments where embedding occurs; value appears chosen to match high-z proto-globular-cluster conditions.

axioms (2)

domain assumption Runaway stellar collisions in dense clusters produce EMSs and SMSs
Invoked from established numerical results cited in the abstract.
domain assumption Post-Newtonian dynamics and stellar evolution are adequately modeled for the embedded phase
Required for the claim that BHs remain embedded long enough for extended growth.

invented entities (1)

Quasi-star-like embedded BH phase (QS) no independent evidence
purpose: To describe the long-lived configuration that enables continued growth and possible GW sources
Introduced as the natural outcome of the simulated dynamics; no independent observational signature beyond the LRD match is provided.

pith-pipeline@v0.9.0 · 5612 in / 1515 out tokens · 76975 ms · 2026-05-08T10:41:16.207412+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 1 canonical work pages · 1 internal anchor

[1]

The Origin and Evolution of Multiple Star Systems

Abdurro’uf et al., 2025, arXiv e-prints, p. arXiv:2512.08054 Adamo A., et al., 2020, Space Sci. Rev., 216, 69 Adamo A., et al., 2024, Nature, 632, 513 AgarwalB.,KhochfarS.,JohnsonJ.L.,NeisteinE.,DallaVecchiaC.,Livio M., 2012, MNRAS, 425, 2854 Akins H. B., et al., 2025, ApJ, 991, 37 Arca Sedda M., et al., 2024, MNRAS, 528, 5119 BaggenJ.F.W.,vanDokkumP.,Lab...

work page internal anchor Pith review doi:10.48550/arxiv.2203.10066 2025
[2]

is 𝑡M = 𝑚EMS𝑃• 𝑀★(< 𝑎 • ) 𝑓(𝑒 • )= 𝑚EMS𝑃• 𝑀★(< 𝑎 • ) 1+ √︁ 1−𝑒 2•√︁ 1−𝑒 2• .(A2) For a spherical power-law cusp𝜌(𝑟) ∝𝑟 −𝛾 the mass precession timescale becomes 𝑡M ∝𝑎 𝛾−3/2 • 𝑓(𝑒 • ).(A3) Thus, for inner cusps with𝛾=3/2the mass precession timescale does not depend on the semi-major axis of the orbit. A2 Relaxation Non-resonant two-body relaxation changes b...

2008
[3]

2009; Kocsis & Tremaine 2015; Fouvry et al

𝑡SRR ∼ 𝑚EMS ˜𝑚 𝑃• .(A5) Similarly, the VRR timescale can be estimated (Eilon et al. 2009; Kocsis & Tremaine 2015; Fouvry et al

2009
[4]

This paper has been typeset from a TEX/LATEX file prepared by the author

as 𝑡VRR ∼𝑓 VRR 𝑚EMS [𝑀★(𝑎 • )˜𝑚]1/2 𝑃• (A6) inwhichtheparameter𝑓 VRRdependsontheeccentricitydistribution oftheorbitsandtypicallygetsvaluesintherangeof0.5≲𝑓 VRR ≲5 (Kocsis & Tremaine 2015). This paper has been typeset from a TEX/LATEX file prepared by the author. MNRAS000, 1–11 (2026)

2015