The formation of massive black holes through collision runaway in dense young star clusters

Holger Baumgardt (RIKEN); Junichiro Makino (Tokyo); Piet Hut (IAS); Simon Portegies Zwart (Amsterdam); Stephen McMillan (Drexel)

REVIEW

The formation of massive black holes through collision runaway in dense young star clusters

Simon Portegies Zwart (Amsterdam), Holger Baumgardt (RIKEN), Piet Hut (IAS), Junichiro Makino (Tokyo), Stephen McMillan (Drexel)

Astrophysics · Submitted 26 Feb 2004 · 62 references

Pith's verdict: The tdf–c map in Figure 3 is the real contribution; the MGG-11 result is conditional on an unmeasured birth concentration, which the authors state plainly even though the abstract does not.

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arXiv IDastro-ph/0402622 (version 1)

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CitationHolger Baumgardt (RIKEN), Junichiro Makino (Tokyo), Piet Hut (IAS), Simon Portegies Zwart (Amsterdam), Stephen McMillan (Drexel). "The formation of massive black holes through collision runaway in dense young star clusters." arXiv:astro-ph/0402622 (2004). https://pith.science/paper/I4WP5TZL

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Editor's note

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Short version: the runaway-collision mechanism is theirs from earlier papers, but this is the first time it has been run star-by-star against two real clusters with measured masses, radii and velocity dispersions. The durable product is the falsifiable map in the tdf–c plane, not the single number for MGG-11. That map is worth your time. What holds up: Eq. 1 is evaluated from McCrady's measured masses and half-light radii, so the tdf axis is observationally anchored — about 3 Myr for MGG-11, about 15 Myr for MGG-9. Two independently written codes, Starlab and NBODY4, give the same qualitative outcome. Figure 3 then predicts no IMBH for the Antennae clusters and for [W99]1, which is consistent with the X-ray data they cite; that is a prediction made outside the systems used to set up the runs. Where it is soft, in order of weight. The concentration c is not measured, and the authors say so in as many words: it is a free parameter. Figure 3 shows no runaway below c around 2, so the MGG-11 claim is really 'if it was born concentrated, it makes an IMBH.' The abstract's flat 'we find that... producing a star' is stronger than that, and the causal 'because' for MGG-9 in the same abstract is stronger than a single-IMF null supports. The analogy to NGC 3603 and R136 is reasonable, but it is an analogy. Second, the 800–3000 Msun range is set mostly by the factor-of-three difference in adopted stellar radii between the two codes, not by physics; the paper is upfront about this, but the range reads like a physical uncertainty when it is a code uncertainty. Third, the MGG-9 runs used a 1 Msun IMF cutoff rather than the Kroupa or 0.2 Msun form the paper says also fits — a computational limit they acknowledge. That one cuts in their favour: a 1 Msun cutoff yields more massive stars per unit mass, so the null is conservative. The stress-test note is right that the positive claim is conditional and the negative one is demonstrated. But the condition is stated in the text and drawn in Figure 3, so this is an overstated abstract rather than a hidden assumption. Read it if you work on IMBH demographics, ULX counterparts, or young-cluster initial conditions. Yes to referees: the simulation setup and the Figure 3 criterion deserve scrutiny, and the question to press is observational — was MGG-11 born with c > 2?

Referee report

Significance

If correct, the result supplies a concrete, physically specified channel for making intermediate-mass black holes in the present-day universe and ties it to an observable class of dense young clusters, which is a genuinely useful contribution independent of the M82 source itself. The strengths are real and should be named: two independently developed N-body codes are used and agree qualitatively; the initial conditions are reconstructed from published measurements rather than chosen arbitrarily; the collision criterion and the direct-collapse threshold above 260 Msun are taken from published work; and Figure 3 converts the argument into a falsifiable statement about which clusters should and should not host an IMBH, with [W99]1 and the Antennae clusters used as out-of-sample checks. The MGG-9 null is a genuine prediction that could have failed and did not.

Major objections (4)

[Abstract, sentence 4; concluding paragraph; Figure 3] The headline claim is stated unconditionally but is, by the paper's own construction, conditional on an unmeasured quantity. The text says plainly that 'since we do not know either the initial or the current central densities of either cluster, the concentration c is treated as a free parameter', and Figure 3 shows that no runaway occurs for c < 2 at any tdf. The abstract's 'we find that for MGG-11 dynamical friction leads to ... producing a star of 800-3000 Msun' and the closing 'we have shown that an IMBH ... is expected to form ... in the star cluster MGG-11' therefore describe a selected subregion of initial-condition space, not a demonstrated outcome for MGG-11. The supporting argument for c > 2 is an analogy with NGC 3603 and R136, not a measurement of MGG-11. Either the abstract and conclusion should be rewritten to state the condition explicitly (e.g. 'for MGG-11 to host an IMBH it must have been born with c > 2 and tdf < 4 Myr, conditions satisfied by ...'), or the paper should attempt an observational constraint on MGG-11's central concentration, for example from the shape of its velocity-dispersion or surface-brightness profile in the McCrady et al. near-infrared data. As written, the negative result for MGG-9 is demonstrated and the positive result for MGG-11 is assumed into existence.
[Main text, paragraph on Starlab/NBODY4 differences; Figure 2; Figure 5] The quoted mass range 800-3000 Msun is not a physical uncertainty but the spread between two adopted radius prescriptions: the text attributes the factor ~3 difference in final runaway mass to NBODY4 radii being about three times larger than Starlab radii, propagating linearly through gravitational focusing. This means the single most-quoted number in the paper is set by a code input rather than by the dynamics. The manuscript should state which prescription it regards as correct and give a best-estimate mass with a defensible uncertainty. Figure 5 and the supplementary note that a Starlab run using the Ishii et al. radii reproduced the NBODY4-like mass suggest the Starlab radii are the outlier, in which case the abstract should quote a value near the upper end rather than a factor-of-four range. The qualitative conclusion (a black hole well above 350 Msun) survives either way, but the reader cannot tell from the present text what the authors actually believe the mass to be.
[Introduction, paragraph 2, and Figure 1] The entire observational motivation rests on the identification of M82 X-1 with MGG-11, and that identification is supported in the text by a private communication ('D. Pooley, private communication') after the authors concede that 'the absolute pointing accuracy is much poorer, for both telescopes'. The only published positional evidence offered is the 54.4 mHz quasi-periodic oscillator, whose own position is good to 7 arcsec. Since the paper's central contrast is between a cluster that hosts the source and one that does not, the association needs to be quantified rather than asserted: what is the chance alignment probability given the cluster density in the M82 core, and what is the current best astrometric tie between the Chandra and near-infrared frames? If the association remains unpublished, the manuscript should say so explicitly and soften the language accordingly.
[Eq. (1) and the tdf estimates; Figure 3; Supplementary material, MGG-9 runs] The margin on the positive side is thinner than the text implies. Eq. (1) is evaluated for a 100 Msun star, giving tdf ~ 3 Myr for MGG-11, which is comparable to the main-sequence lifetime of such a star; the collision counterparts are stated to be 30-50 Msun stars, for which tdf is longer. The paper should show tdf evaluated across the mass range that actually participates in the runaway, and justify the adopted Coulomb logarithm and the 0.11 M/100 Msun argument, since a factor of two in tdf moves MGG-11 across the threshold drawn in Figure 3. Relatedly, the abstract attributes the MGG-9 null to 'the larger cluster radius', but Eq. (1) shows tdf depends on total mass as well, and MGG-9 is about four times more massive; the attribution should be corrected. Finally, the supplementary states that MGG-9 could only be simulated with the 1 Msun lower mass cutoff because a Kroupa IMF would require 3.6 million stars. The null is therefore argued analytically from tdf rather than demonstrated across the same initial-condition space as MGG-11, and the manuscript should say so where the null is claimed.

Minor objections (6)

[Abstract and main text] Several typographical errors should be corrected: 'where stars are allowed to mergers with each other' (abstract), 'collapses to an black hole' (abstract and main text), 'manusctipt' (acknowledgements), and 'KNA W' (acknowledgements).
[Main text, paragraph on N-body codes, and Figure 2 caption] The code citations appear to use the supplementary numbering rather than the main reference list: 'Starlab15, 16' points to King (1966) and Heger et al. (2003), and 'NBODY4 17, 18' points to Stothers & Chin and Ishii et al., whereas the correct entries are refs 11-12 and 13-14 respectively. Similarly, the Figure 2 caption cites 'Kroupa26', but ref. 26 in the main list is Campbell et al. (1992); Kroupa (2001) is ref. 29. The supplementary material has the same problem in reverse, for example citing ref. 3 (Eggleton et al.) for the statement that stars above 17-25 Msun have exploded and for the mean stellar mass. The two reference lists should be reconciled and every citation checked.
[Main text, paragraph on black hole and neutron star populations] The expectation of 'some 1400 stellar-mass black holes and up to about 1000 neutron stars' is quoted without derivation. A short statement of the assumed IMF, mass limits and remnant mapping would let the reader check it, and would also clarify how these numbers depend on the 1 Msun lower cutoff that the paper elsewhere acknowledges is controversial.
[Main text, paragraph on black hole capture; ref. 19] The link between the simulated black hole and the observed ultraluminous X-ray source is made through Hopman, Portegies Zwart & Alexander, listed as 'Submitted to Astrophys. J. Letters'. Since this is the step that converts a dark remnant into the observed luminosity, the citation status should be flagged in the text, or the argument supported with a published alternative.
[Supplementary material, paragraph on rotation] The authors note that off-axis collisions spin up the runaway and that their evolution prescriptions do not treat rotation, quoting a ~15 per cent lifetime extension for a 120 Msun star. Given that the runaway reaches 800-3000 Msun and that a longer lifetime means more time to collide, the possible systematic should be estimated rather than only acknowledged.
[Figure 3 and its caption] The caption and the supplementary text explain that the horizontal error bars for MGG-9 and MGG-11 are drawn near the top of the figure 'for practical reasons' and should not be read as upper limits on concentration. This is confusing in a figure whose whole purpose is to locate the two clusters in the {tdf, c} plane; a marker with a separate legend entry, or a vertical offset with a leader line, would remove the ambiguity.

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The paper

The paper claims

A dense young cluster can build a black hole by runaway stellar collisions, while a heavier but looser twin cannot.

The reading

The paper asks why one young cluster in the starburst galaxy M82 (MGG-11) sits on an ultraluminous X-ray source implying a black hole of at least 350 solar masses, while a nearby, roughly four times more massive cluster (MGG-9) shows nothing similar. The authors' answer is a race against supernovae. In a dense enough cluster, dynamical friction drags the heaviest stars into the core faster than they can explode; once assembled there, they collide repeatedly and merge into a single star of 800 to 3000 solar masses, which then collapses directly into an intermediate-mass black hole. For MGG-11 the sinking time for a 100 solar mass star is about 3 Myr, comparable to the lifetimes of the most massive stars, whereas for MGG-9 the larger half-light radius pushes it to about 15 Myr, so its heavy stars die before they can gather. The claim matters because it gives a route to black holes between stellar and supermassive mass scales that needs no exotic physics, only a measured cluster radius and an inferred central density.

What carries the argument

The load-bearing mechanism is dynamical friction, the drag a massive star feels from the sea of lighter stars it passes through. The paper uses the standard estimate $t_{df} = (100 M_*/m) [0.138 N / (G M / R^3)^{1/2} / ln(0.11 M / 100 M_*)]$ to compute how long a 100 solar mass star takes to spiral from the half-mass radius $R$ to the centre. If that time is shorter than the roughly 3 Myr main-sequence lifetime of the heaviest stars, they arrive in the core while still alive; the core is then dense enough that gravitational focusing makes further collisions inevitable, and the merged object grows monotonically. The second ingredient is the concentration parameter $c = log(R_t/R_c)$, which sets the initial central density and therefore the collision rate. The paper's Figure 3 maps the region of the $t_{df}$–$c$ plane where runaway occurs, with MGG-11 inside it and MGG-9, the Antennae cluster [W99]1, and five other Antennae clusters outside.

Extended reading notes

Core claim

The paper reports star-by-star N-body simulations, run with two independently written codes (Starlab and NBODY4) and typically 131,072 stars, in which stars are allowed to collide and merge when their separation falls below the sum of their radii. Initial conditions are tuned so that at the observed age of 7 to 12 Myr the models reproduce the measured masses, half-mass radii, velocity dispersions and mass functions of MGG-11 and MGG-9. For MGG-11 models with concentration $c > 2$ (King models with central potential $W_0 >~ 9$), the core collapses within about 1 Myr and a single star grows through roughly 10 to 100 collisions, mostly with 30 to 50 solar mass main-sequence stars, reaching 800 to 3000 solar masses before collapsing to a black hole. No runaway occurs in any MGG-9 simulation, nor in MGG-11 models with $c < 2$, and the authors state the requirement plainly: formation needs a cluster born with $c >~ 2$ and a dynamical friction time $t_{df} <~ 4$ Myr. The difference between the two clusters is traced to a single quantity, the dynamical friction time for a 100 solar mass star, about 3 Myr for MGG-11 against about 15 Myr for MGG-9.

Load-bearing premise

The initial central concentration of MGG-11 is not observed: the authors state that neither the initial nor the current central density of either cluster is known, so $c$ is treated as a free parameter, and by their own Figure 3 a MGG-11 born with $c < 2$ produces no runaway at all.

Editorial extensions

If this is right

Any young cluster with a short enough dynamical friction time and a sufficiently concentrated core should host an intermediate-mass black hole, whether or not its X-ray source has yet been resolved; the paper names Westerlund 1 as a candidate that satisfies the criteria but has no detected bright X-ray counterpart.
Clusters in the runaway region should also be prolific sources of ordinary high-mass X-ray binaries, since the same mass function implies roughly 1400 stellar-mass black holes and up to 1000 neutron stars in a cluster like MGG-11.
A black hole of this origin can become an ultraluminous X-ray source by tidally capturing a companion star, which would explain the $L_{0.2-10 keV} \simeq 10^{41}$ erg/s point source at the position of MGG-11 without invoking beamed emission.
The absence of an intermediate-mass black hole in a cluster of comparable age and larger mass is not anomalous but expected, because the larger radius alone multiplies the mass-segregation time by about five.
The same criterion can be applied as a filter to populations of young massive clusters: those with short dynamical friction times and high concentration are the ones worth targeting for intermediate-mass black hole searches.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the mechanism is right, the intermediate-mass black hole mass should correlate with cluster concentration rather than with total cluster mass, which inverts the naive expectation that bigger clusters make bigger black holes; a survey of young cluster X-ray sources could test that ordering directly.
The runaway channel predicts a distinctive time sequence: core collapse within about 1 Myr, peak collision activity in the first 3 Myr, and a black hole in place well before the cluster is 10 Myr old, so the fraction of clusters hosting one should drop sharply with age among clusters of a given density.
Because the merged star's final mass scales with the collision cross-section, and the two codes differ by a factor of about three in adopted stellar radii and hence in final mass, resolving the radii of very massive stars would sharpen the predicted black hole mass range more than any improvement in the dynamics.
The paper's argument is a channel for intermediate-mass black holes in young clusters; whether the same channel contributes to the seeds of supermassive black holes at high redshift depends on whether such dense young clusters were common early, which is a separate question the paper does not address.

Original abstract

A luminous X-ray source is associated with a cluster (MGG-11) of young stars \~200pc from the center of the starburst galaxy M82. The properties of the X-ray source are best explained by a black hole with a mass of at least 350Msun, which is intermediate between stellar-mass and supermassive black holes. A nearby but somewhat more massive star cluster (MGG-9) shows no evidence of such an intermediate mass black hole, raising the issue of just what physical characteristics of the clusters can account for this difference. Here we report numerical simulations of the evolution and the motions of stars within the clusters, where stars are allowed to mergers with each other. We find that for MGG-11 dynamical friction leads to the massive stars sinking rapidly to the center of the cluster to participate in a runaway collision, thereby producing a star of 800-3000Msun, which ultimately collapses to an black hole of intermediate mass. No such runaway occurs in the cluster MGG-9 because the larger cluster radius leads to a mass-segregation timescale a factor of five longer than for MGG-11.

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.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,138 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.72 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.46 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

A luminous X-ray source is associated with a cluster (MGG-11) of young stars \~200pc from the center of the starburst galaxy M82. The properties of the X-ray source are best explained by a black hole with a mass of at least 350Msun, which is intermediate between stellar-mass and supermassive black holes. A nearby but somewhat more massive star cluster (MGG-9) shows no evidence of such an intermediate mass black hole, raising the issue of just what physical characteristics of the clusters can account for this difference. Here we report numerical simulations of the evolution and the motions of stars within the clusters, where stars are allowed to mergers with each other. We find that for MGG-11 dynamical friction leads to the massive stars sinking rapidly to the center of the cluster to participate in a runaway collision, thereby producing a star of 800-3000Msun, which ultimately collapses to an black hole of intermediate mass. No such runaway occurs in the cluster MGG-9 because the larger cluster radius leads to a mass-segregation timescale a factor of five longer than for MGG-11.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A luminous X-ray source is associated with a cluster (MGG-11) of young stars \~200pc from the center of the starburst galaxy M82.	background 0.88	0.39	0.02	asserted 1.00
s1	The properties of the X-ray source are best explained by a black hole with a mass of at least 350Msun, which is intermediate between stellar-mass and supermassive black holes.	result 0.41	0.50	0.14	asserted 0.69
s2	A nearby but somewhat more massive star cluster (MGG-9) shows no evidence of such an intermediate mass black hole, raising the issue of just what physical characteristics of the clusters can account for this difference.	gap 0.88	0.34	0.03	asserted 0.94
s3	Here we report numerical simulations of the evolution and the motions of stars within the clusters, where stars are allowed to mergers with each other.	method 0.71	0.94	0.04	asserted 0.94
s4	We find that for MGG-11 dynamical friction leads to the massive stars sinking rapidly to the center of the cluster to participate in a runaway collision, thereby producing a star of 800-3000Msun, which ultimately collapses to an black hole of intermediate mass.	result 0.99	0.96	0.79	asserted 1.00
s5	No such runaway occurs in the cluster MGG-9 because the larger cluster radius leads to a mass-segregation timescale a factor of five longer than for MGG-11.	result 0.81	0.87	0.22	asserted 1.00

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Chandra X-ray image (in R.A. and Dec.) of the relevant part of the starburst galaxy M82 with the observed star clusters indicated. The color image is from the 28 October 1999 X-ray observation by Matsumoto et al. (2001),3 with about arcsecond positional accuracy. The brightest X-ray source (M82 X-1) is near the center of the image. The star clusters, from table 3 of McCrady et al. (2003),1 are indicated by circles. The positions of the two star clusters MGG-9 and MGG-11 are indicated with squares. The magnified infrared images of these star clusters from the McCrady et al…

**Figure 2.** The growth in mass of the collision runaway star with time. Th

**Figure 3.** The area of parameter space for which runaway collision ca

**Figure 4.** Evolution of the core radius for four simulations of the sta

**Figure 5.** Stellar radius as a function of zero-age mass for various m

Figures reproduced from arXiv:astro-ph/0402622 by the authors.

References

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Solid circles indicate simulations resulting in runaway merging, while ope n circles correspond to simulations in which no runaway merging occurred. Th e evolution of the mass of the runaway for the two leftmost ﬁlled circles are prese nted in Figure 2, for a variety of initial conditions. Star clusters in the upper left c orner enclosed by the dashed lin...

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These calculations are performed with Starlab with c ≃ 0.67 ( W0 = 3), c ≃ 1.8 (W0 = 8), c ≃ 2.1 ( W0 = 9, bold curve) and c ≃ 2.7 ( W0 = 12, dotted curve) indicated along the right edge of the ﬁgure as W 3, W 8, W 9, and W 12 respectively. The W9 curve is plotted with a heavy line to distinguish it from the curve s for W8 and W12. The age range of the ob...

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Forward citations

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How later papers used it

169 later papers cite it

Evidence: some. 166 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 9 of the 213 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 used its method or tool.

Uses its method or tool 1 paper

The table also shows the estimates for the mass segregation and core collapse time-scales ($t_seg$, $t_cc$) for the clusters based on Eq. [ref] and Eq. [ref] with $t_cc∼0.2 t_rlx$ [ref] .

FROST-CLUSTERS -- I. Hierarchical star cluster assembly boosts intermediate-mass black hole formation (2024) · Merger trees of star clusters, their VMSs and IMBHs · 0.83

How the literature uses it

47 arXiv papers cite this in 53 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 34 sentences without a confident label

Compares with it 1 paper

This estimate for the time of mass segregation is considerably shorter than in models of dense young stellar clusters in which runaway coallescence has been found to occur [ref] .

Monte Carlo Simulations of Star Clusters - VI. The globular cluster NGC 6397 · The initial conditions · 1.00

Cites it as background 17 papers

IMBHs can form through several channels, chiefly: (1) collapse of very massive stars (VMS; $10^3-4 M_⊙$), where VMS form via runaway collisions of stars [ref] and (2) hierarchical mergers of stellar-mass BHs via gravitational wave (GW) radiation [ref] .

Rapid intermediate-mass black hole formation via runaway mergers of black holes · Introduction · 0.88
Possible scenarios to produce such massive seed BHs have been studied, e.g., through collapses of massive stars/gas clouds, or through mergers of massive stars/ black holes [ref] .

Cosmological 21cm line observations to test scenarios of super-Eddington accretion on to black holes being seeds of high-redshifted supermassive black holes · Introduction · 0.92
Several scenarios have been proposed, including the direct collapse of pristine gas in atomic-cooling halos [ref] , runaway stellar mergers in dense star clusters [ref] , and the remnants of massive stars [ref] .

The In Situ Growth of Stellar-mass "Light" Seed Black Holes in Nuclear Star Clusters · Introduction · 0.97

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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These calculations are performed with Starlab with c ≃ 0.67 ( W0 = 3), c ≃ 1.8 (W0 = 8), c ≃ 2.1 ( W0 = 9, bold curve) and c ≃ 2.7 ( W0 = 12, dotted curve) indicated along the right edge of the ﬁgure as W 3, W 8, W 9, and W 12 respectively. The W9 curve is plotted with a heavy line to distinguish it from the curve s for W8 and W12. The age range of the ob...

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