REVIEW
Formation of black hole stars via star--black hole collisions
High Energy Astrophysical Phenomena · Submitted 27 Aug 2026 · 71 references
Pith's verdict: A useful qualitative map of star–BH collision outcomes, but the MESA leg has a load-bearing arithmetic error that means the 'no thermal runaway' claim is unsubstantiated.
T0 · AI review
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Referee report
The paper
The paper claims
Stellar-mass black holes can be captured inside massive stars to form 'black hole stars'
The reading
What carries the argument
The central mechanism is Bondi–Hoyle–Lyttleton drag acting on a black hole moving supersonically through the stellar envelope. The drag dissipates the black hole's orbital energy on a timescale comparable to the stellar dynamical time, damping its motion. The analytic anchor is Equation (7): $M_{\bullet,\mathrm{max}} \approx 0.67 M_\star^2/(R_\star) \,/\, [3.80 M_\star/R_\star] \approx 0.2 M_\star$, which follows from equating the dissipated orbital energy to the polytropic star's binding energy. The semi-analytic orbital integrations use a regularized drag force (Generozov & Perets 2023) and an $n=2.75$ polytrope, and the 3D hydrodynamical simulations employ the GIZMO code in meshless finite-mass mode with self-gravity.
Extended reading notes
Core claim
The paper discovers a previously unexplored collision regime: when a stellar-mass black hole (with mass roughly 5–10 $M_\odot$) collides at low velocity ($v_\infty \lesssim 2\sqrt{G(M_\star+M_\bullet)/R_\star}$) with a $100\,M_\odot$ main-sequence star, gas drag decelerates the black hole and retains it inside the stellar envelope. The result is a 'black hole star' (BH*): a dense ($\sim1\,\mathrm{g\,cm^{-3}}$), spherical, extended envelope that retains most of the original stellar mass and is quasi-hydrostatic. The critical condition for BH* formation is $M_\bullet \lesssim 0.2 M_\star$, derived analytically (Eq. 7) by equating the drag-dissipated orbital energy to the stellar binding energy. One-dimensional MESA heating calculations show that the shock-heated remnant thermally relaxes without triggering runaway expansion over the computed interval.
Load-bearing premise
The 3D simulations treat the black hole as a softened point mass (softening length $0.5\,R_\odot$) and omit accretion, radiation, and feedback; if even weak feedback acts on the dynamical timescale, the quasi-hydrostatic envelope would be destroyed before thermal relaxation, and BH* formation would not occur.
Editorial extensions
If this is right
- BH* formation sets a new upper limit on the black-hole mass that can be retained without disrupting the star: approximately 0.2 times the stellar mass.
- BH*s provide a natural environment for building black-hole binaries inside a stellar envelope; such binaries can merge via gravitational-wave emission on year timescales, potentially producing electromagnetic counterparts.
- In dense star clusters, repeated star–black-hole collisions can sequentially deliver black holes to the center of a supermassive star, where they merge and build an intermediate-mass black hole without requiring direct collapse.
- BH*s may explain the spectral features of JWST's 'little red dots' — red continuum, Balmer break, and broad emission lines — without invoking an unobscured active galactic nucleus.
Reading between the lines
- If BH*s are common in dense clusters, they could be a significant source of LIGO/Virgo binary black-hole mergers, because the stellar envelope gas drag would accelerate orbital decay relative to vacuum mergers.
- The chemical mixing driven by the black hole's passage (raising central hydrogen abundance) could extend the star's nuclear burning lifetime, potentially altering population-synthesis predictions for massive stars.
- The paper's omission of accretion feedback and radiation is a major caveat: if even weak feedback disrupts the envelope on the dynamical timescale, the BH* formation claim fails; the argument hinges on the ordering $\tau_\mathrm{drag} < \tau_\mathrm{thermal}$, which the paper asserts but does not demonstrate with feedback included.
Original abstract
In dense stellar environments such as globular clusters and active galactic nucleus (AGN) disks, stellar-mass black holes (sBHs) may frequently collide with massive stars. We investigate this process using semi-analytic models, three-dimensional hydrodynamical simulations, and one-dimensional stellar evolution calculations, focusing on collisions between sBHs and a $100\,M_\odot$ main-sequence star. We find that gas drag retains the BH within the stellar envelope unless the impact velocity exceeds $\sim2\sqrt{G(M_\star+M_\bullet)/R_\star}$. The post-collision outcome depends primarily on the BH-to-star mass ratio. For $M_\bullet\gtrsim30\,M_\odot$, the retained envelope is either quasi-spherical or disc-like, but remains dynamically unstable because of shock heating. In contrast, for $M_\bullet\lesssim10\,M_\odot$, the collision forms a ``black hole star'' (BH*): a quasi-hydrostatic, extended stellar envelope surrounding the embedded BH. These results agree with our analytic prediction that BH* formation necessarily requires $M_\bullet\lesssim0.2\,M_\star$. Follow-up \texttt{MESA} calculations further show that, for these low-mass BHs, the shock-heated remnant thermally relaxes without triggering runaway expansion. We discuss several astrophysical implications of BH*s, including their evolution, the possibility of gravitational-wave events from BH binaries assembled within a stellar envelope, and repeated star--sBH collisions as a pathway for rapid BH growth in dense stellar systems. This mechanism may contribute to the formation of massive BHs in high-redshift nuclear star clusters and may be relevant to the origin of the ``little red dots'' discovered by JWST.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
In dense stellar environments such as globular clusters and active galactic nucleus (AGN) disks, stellar-mass black holes (sBHs) may frequently collide with massive stars. We investigate this process using semi-analytic models, three-dimensional hydrodynamical simulations, and one-dimensional stellar evolution calculations, focusing on collisions between sBHs and a $100\,M_\odot$ main-sequence star. We find that gas drag retains the BH within the stellar envelope unless the impact velocity exceeds $\sim2\sqrt{G(M_\star+M_\bullet)/R_\star}$. The post-collision outcome depends primarily on the BH-to-star mass ratio. For $M_\bullet\gtrsim30\,M_\odot$, the retained envelope is either quasi-spherical or disc-like, but remains dynamically unstable because of shock heating. In contrast, for $M_\bullet\lesssim10\,M_\odot$, the collision forms a ``black hole star'' (BH*): a quasi-hydrostatic, extended stellar envelope surrounding the embedded BH. These results agree with our analytic prediction that BH* formation necessarily requires $M_\bullet\lesssim0.2\,M_\star$. Follow-up \texttt{MESA} calculations further show that, for these low-mass BHs, the shock-heated remnant thermally relaxes without triggering runaway expansion. We discuss several astrophysical implications of BH*s, including their evolution, the possibility of gravitational-wave events from BH binaries assembled within a stellar envelope, and repeated star--sBH collisions as a pathway for rapid BH growth in dense stellar systems. This mechanism may contribute to the formation of massive BHs in high-redshift nuclear star clusters and may be relevant to the origin of the ``little red dots'' discovered by JWST.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In dense stellar environments such as globular clusters and active galactic nucleus (AGN) disks, stellar-mass black holes (sBHs) may frequently collide with massive stars. | background 1.00 | 0.06 | 0.02 | hedged possibility 1.00 |
| s1 | We investigate this process using semi-analytic models, three-dimensional hydrodynamical simulations, and one-dimensional stellar evolution calculations, focusing on collisions between sBHs and a $100\,M_\odot$ main-sequence star. | method 0.70 | 0.93 | 0.03 | asserted 0.89 |
| s2 | We find that gas drag retains the BH within the stellar envelope unless the impact velocity exceeds $\sim2\sqrt{G(M_\star+M_\bullet)/R_\star}$. | result 1.00 | 0.90 | 0.07 | asserted 1.00 |
| s3 | The post-collision outcome depends primarily on the BH-to-star mass ratio. | result 0.97 | 0.80 | 0.18 | asserted 1.00 |
| s4 | For $M_\bullet\gtrsim30\,M_\odot$, the retained envelope is either quasi-spherical or disc-like, but remains dynamically unstable because of shock heating. | result 1.00 | 0.94 | 0.09 | asserted 1.00 |
| s5 | In contrast, for $M_\bullet\lesssim10\,M_\odot$, the collision forms a ``black hole star'' (BH*): a quasi-hydrostatic, extended stellar envelope surrounding the embedded BH. | result 1.00 | 0.94 | 0.54 | asserted 1.00 |
| s6 | These results agree with our analytic prediction that BH* formation necessarily requires $M_\bullet\lesssim0.2\,M_\star$. | result 0.69 | 0.91 | 0.26 | asserted 0.98 |
| s7 | Follow-up \texttt{MESA} calculations further show that, for these low-mass BHs, the shock-heated remnant thermally relaxes without triggering runaway expansion. | result 0.98 | 0.96 | 0.07 | asserted 1.00 |
| s8 | We discuss several astrophysical implications of BH*s, including their evolution, the possibility of gravitational-wave events from BH binaries assembled within a stellar envelope, and repeated star--sBH collisions as a pathway for rapid BH growth in dense stellar systems. | interpretation 0.98 | 0.52 | 0.08 | asserted 0.49 |
| s9 | This mechanism may contribute to the formation of massive BHs in high-redshift nuclear star clusters and may be relevant to the origin of the ``little red dots'' discovered by JWST. | interpretation 1.00 | 0.21 | 0.07 | hedged possibility 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
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- P abstract
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Figures
Figures reproduced from arXiv:2608.27596 by the authors.
References
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 35 sentences without a confident label
Contests 2 papers
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Since the original $I(ℳ)$ of [ref] is singular at $ℳ = 1$, we adopt the regularized form of [ref] , [equation] where the Coulomb logarithm is set to $lnΛ= 1.4 ∼ln(R_⋆/R_HL)$, the ratio of the largest to the smallest radial scales contributing to the drag.
Dynamical Friction in a Gaseous Medium · Model setups and initial condition · contest 0.77
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Since the original $I(ℳ)$ of [ref] is singular at $ℳ = 1$, we adopt the regularized form of [ref] , [equation] where the Coulomb logarithm is set to $lnΛ= 1.4 ∼ln(R_⋆/R_HL)$, the ratio of the largest to the smallest radial scales contributing to the drag.
Capture of stars into gaseous discs around massive black holes: Alignment, circularization and growth · Model setups and initial condition · contest 0.77
Builds on 1 paper
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Our setup builds on previous massive AGN-star calculations with [ref] .
The impermanent fate of massive stars in AGN disks · Dissipative heating of the star · 0.84
Uses the method or tool of 4 papers
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Following [ref] , the drag force is [equation] where $v$ is the sBH velocity, and the prefactor $I(ℳ)$ encodes the dependence on the Mach number $ℳ ≡v/$.
Dynamical Friction in a Gaseous Medium · Model setups and initial condition · 0.85
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The star is fixed as an $n=2.75$[We also test $n=2$ and find qualitatively similar results.], $100 M_⊙$ polytrope with $128^3$ equal-mass gas cells ($Δm ∼5×10^-5 M_⊙$), which is generated following [ref] and [ref] .
Constructing stable 3D hydrodynamical models of giant stars · Hydrodynamical Simulations · 1.00
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The star is fixed as an $n=2.75$[We also test $n=2$ and find qualitatively similar results.], $100 M_⊙$ polytrope with $128^3$ equal-mass gas cells ($Δm ∼5×10^-5 M_⊙$), which is generated following [ref] and [ref] .
Stellar mergers and chemical element mixing: implications for the metamorphic stellar evolution in AGN disks · Hydrodynamical Simulations · 1.00
Compares with 2 papers
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However, similar objects have recently been proposed to explain LRDs [ref] , although the BH*s studied here are considerably less massive.
Spectral Uniformity of Little Red Dots: A Natural Outcome of Coevolving Seed Black Holes and Nascent Starbursts · Sequential evolution of the BH* · 0.98
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However, similar objects have recently been proposed to explain LRDs [ref] , although the BH*s studied here are considerably less massive.
2507.09085 · Sequential evolution of the BH* · 0.98
Cites as background 6 papers
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The standard picture invokes runaway stellar collisions that assemble a supermassive star (SMS), which subsequently collapses into an IMBH [ref] .
The mass budget for intermediate-mass black holes in dense star clusters · Dense star clusters · 0.89
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The standard picture invokes runaway stellar collisions that assemble a supermassive star (SMS), which subsequently collapses into an IMBH [ref] .
FROST-CLUSTERS -- I. Hierarchical star cluster assembly boosts intermediate-mass black hole formation · Dense star clusters · 0.89
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The standard picture invokes runaway stellar collisions that assemble a supermassive star (SMS), which subsequently collapses into an IMBH [ref] .
The runaway growth of intermediate-mass black holes in dense star clusters · Dense star clusters · 0.89
Discussion
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