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arxiv: 2604.27382 · v1 · submitted 2026-04-30 · 🌌 astro-ph.GA · astro-ph.SR

Recognition: unknown

Star cluster formation from turbulent clumps. V. Stellar clustering around massive stars

Aayush Gautam, Jonathan C. Tan, Juan P. Farias

Authors on Pith no claims yet

Pith reviewed 2026-05-07 10:29 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.SR
keywords star cluster formationmassive starsstellar multiplicitydynamical interactionsN-body simulationsturbulent clumpscore accretionsecondary multiplicity
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The pith

Massive stars in turbulent clumps rapidly acquire triple or higher-order companions through dynamical interactions.

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

The paper examines how massive stars develop high multiplicity in star clusters using simulations of the turbulent clump core accretion model with 50 percent primordial binaries. It shows that dynamical processes quickly lead to bound triple systems and denser local stellar environments around these stars. This distinction between formation-time and later dynamical multiplicity helps test different star formation theories. Comparing to other models and observations like AFGL 5180 indicates the turbulent clump approach better matches some data.

Core claim

In N-body simulations of gradually forming star clusters from turbulent clumps with 50% primordial binaries, massive stars rapidly gather triple or higher-order bound companions and enhancements in local projected stellar density via dynamical processes. Secondary multiplicity increases towards cluster centers, tends to decrease in more massive clusters due to higher velocity dispersions but rises with mean density, and produces shallower N_* radial profiles than competitive accretion models, with AFGL 5180 better described by these models.

What carries the argument

N-body simulations tracking bound multiplicity and local projected stellar density N_* around massive stars in the Turbulent Clump Core Accretion paradigm.

If this is right

  • Multiplicity and local density enhancements around massive stars increase towards the centers of clusters.
  • Secondary multiplicity decreases in more massive clusters because of their higher velocity dispersions.
  • Multiplicity rises as the mean density of the bound cluster increases.
  • The radial profiles of local stellar density are shallower than those produced in competitive accretion simulations.
  • Observed systems like AFGL 5180 are better matched by the turbulent clump models than by competitive accretion.

Where Pith is reading between the lines

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

  • If dynamical processing dominates, then the observed multiplicity of massive stars in young clusters should correlate with local density and cluster age.
  • Distinguishing formation models requires larger samples of observed young massive star systems.
  • These simulations suggest that initial binary fractions and clump conditions strongly influence final multiplicity statistics.

Load-bearing premise

The initial conditions of the simulations and the assumed 50% primordial binary fraction accurately represent real star-forming clumps, with dynamical processing being the main driver of multiplicity.

What would settle it

Finding no correlation between massive star multiplicity and local stellar density or cluster age in a large sample of young clusters, or observing radial density profiles that match competitive accretion models instead.

Figures

Figures reproduced from arXiv: 2604.27382 by Aayush Gautam, Jonathan C. Tan, Juan P. Farias.

Figure 1
Figure 1. Figure 1: Masses of massive stars (𝑀★) versus the number of bound companions (𝑁bound) around them, in our fiducial 𝜖ff = 0.03 models at cluster age 𝑡 = 3.0 Myr. From top to bottom, the rows show M300, M3000, and M30000 models, respectively. The left and right columns show low (Σcloud = 0.1 g cm−2 ) and high (Σcloud = 1.0 g cm−2 ) cloud mass surface density cases, respectively. In each panel, the colored symbols (blu… view at source ↗
Figure 2
Figure 2. Figure 2: Normalized radial locations of massive stars (𝑟ℎ) versus number of bound companions (𝑁bound) around them, in our fiducial 𝜖ff = 0.03 models at cluster age 𝑡 = 3.0 Myr. From top to bottom, the rows show M300, M3000, and M30000 models, respectively. The left and right columns show low (Σcloud = 0.1gcm−2 ) and high (Σcloud = 1.0 g cm−2 ) cloud mass surface density cases, respectively. In each panel, the color… view at source ↗
Figure 3
Figure 3. Figure 3: Each panel in the grid shows the comparison between different 𝑀cl models showing the average number of bound companions ⟨𝑁bound ⟩ around massive stars in that model. Panels in the first and second rows show the low (Σcloud = 0.1 g cm−2 ) and high (Σcloud = 1.0 g cm−2 ) cloud mass surface density cases, respectively, for the fiducial (𝜖ff = 0.03) models at cluster age of 𝑡 = 3.0 Myr. In the columns, we vary… view at source ↗
Figure 4
Figure 4. Figure 4: Each panel shows comparison between different 𝜖ff models showing ⟨𝑁bound ⟩ around massive stars at cluster age of 𝑡 = 3.0 Myr. Panels in the first and second rows show low (Σcloud = 0.1 g cm−2 ) and high (Σcloud = 1.0 g cm−2 ) cloud mass surface density cases, respectively. From left to right, the columns show M300, M3000, and M30000 models, respectively. Each panel shows ⟨𝑁bound ⟩ around massive stars in … view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between different (𝑀cl,Σcloud,𝜖ff) models showing how ⟨𝑁bound ⟩ around central stars (left column) and offset stars (right column) is affected by the stellar velocity dispersion (𝜎S) and stellar number density (𝑛S,b) within their respective radial regions in the bound star cluster. The first and second rows show ⟨𝑁bound ⟩ for each model versus the corresponding 𝜎S and 𝑛S,b, respectively, at a cl… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison between different models (𝑀cl,Σcloud,𝜖ff) across our full set showing the evolution of average number of bound companions ⟨𝑁bound ⟩ around massive stars versus cluster age 𝑡 in Myr. The columns show the five different values of 𝜖ff. The rows (from top to bottom) show M300L, M300H, M3000L, M3000H, M30000L, and M30000H sets, respectively. Each panel shows ⟨𝑁bound ⟩ around massive stars in three su… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison between different models (𝑀cl,Σcloud,𝜖ff) across our full set showing the evolution of Triple/Higher-order fraction (THF) of massive stars versus cluster age 𝑡 in Myr. The columns show the five different values of 𝜖ff. The rows (from top to bottom) show M300L, M300H, M3000L, M3000H, M30000L, and M30000H sets, respectively. Each panel shows THF of massive stars in three subsets: central stars (bl… view at source ↗
Figure 8
Figure 8. Figure 8: Each panel shows averaged stellar density profiles (⟨𝑁★(𝑟 ) ⟩) around massive stars in the fiducial (𝜖ff = 0.03) model at cluster age of 𝑡 = 3.0 Myr. The rows show different sets in the following order from top to bottom: M300L, M300H, M3000L, M3000H, M30000L and M30000H, respectively. The columns (from left to right) show the profiles around central stars, offset stars, and ejected stars, respectively. In… view at source ↗
Figure 9
Figure 9. Figure 9: Each panel shows the time evolution of stellar density profiles (⟨𝑁★(𝑟 ) ⟩) around massive stars in simulated clusters for the fiducial (𝜖ff = 0.03) case in low cloud mass surface density (Σcloud = 0.1 g cm−2 ) sets. The columns show M300, M3000 and M30000 models, respectively. The rows show the results considering companions with masses above 0.01𝑀⊙, 0.1𝑀⊙ and 1.0𝑀⊙, respectively. In every panel, each lin… view at source ↗
Figure 10
Figure 10. Figure 10: Each panel shows the time evolution of stellar density profiles (⟨𝑁★(𝑟 ) ⟩) around massive stars in simulated clusters for the fiducial (𝜖ff = 0.03) case in high cloud mass surface density (Σcloud = 1.0 g cm−2 ) sets. The columns show M300H, M3000H and M30000H models, respectively. The rows show the results considering companions with masses above 0.01𝑀⊙, 0.1𝑀⊙ and 1.0𝑀⊙, respectively. In every panel, eac… view at source ↗
Figure 11
Figure 11. Figure 11: Top row: Stellar density profiles for our M300L and M300H models (TCCA models, shown in blue), which were found to be the best match to the observations from AFGL 5180 (magenta squares) and G19.88-0.53 (green diamond). Blue lines with different linestyles represent TCCA profiles at different cluster ages. The errorbars represent the standard errors. The blue shaded region represents the standard deviation… view at source ↗
Figure 12
Figure 12. Figure 12: Each panel shows the distribution of the separation and mass-ratios (with respect to primary mass) of bound companions around all massive stars with masses ≥ 16.0 𝑀⊙ in our fiducial (𝜖ff = 0.03) simulations. From top to bottom, the rows show M300, M3000, and M30000 models, respectively. The left and right columns show low (Σcloud = 0.1 g cm−2 ) and high (Σcloud = 1.0 g cm−2 ) cloud mass surface density ca… view at source ↗
read the original abstract

Massive stars (> 8 $M_\odot$) are known to have high degrees of multiplicity, e.g., with about 60% in triples or higher-order multiples. Such high levels of multiplicity may arise during formation (primary multiplicity) or through dynamical processing of already formed stars in dense clusters (secondary multiplicity). The level of primary multiplicity is an important metric to help distinguish between different formation scenarios, such as core accretion and competitive accretion. The level of secondary multiplicity is expected to evolve with time and be sensitive to local cluster environment. Here we analyze a suite of $N$-body simulations to study bound multiplicity and local projected stellar density, $N_*$, around massive stars within gradually forming star clusters with 50% primordial binaries in the Turbulent Clump Core Accretion (TCCA) paradigm. We find that massive stars rapidly gather triple or higher-order bound companions and enhancements in local $N_*$ via dynamical processes. We study these metrics as a function of environment in a given cluster, quantifying the increasing multiplicity that arises towards cluster centers. We find that secondary multiplicity tends to decrease in more massive clusters due to their higher velocity dispersions, but rises as the mean density of the bound cluster increases. We find our $N_*$ radial profiles are shallower compared to those in the STARFORGE simulations, which form massive stars via competitive accretion. A comparison to the AFGL 5180 system suggests it is better described by TCCA models. However, a larger number of observed systems is needed to better discriminate between these formation models.

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 / 2 minor

Summary. The manuscript analyzes a suite of N-body simulations of star cluster formation from turbulent clumps in the Turbulent Clump Core Accretion (TCCA) paradigm, initialized with a fixed 50% primordial binary fraction. It reports that massive stars (>8 M⊙) rapidly acquire triple or higher-order bound companions and local enhancements in projected stellar density N_* through dynamical interactions. Trends are quantified as functions of cluster environment, mass, and density; secondary multiplicity is found to decrease with cluster mass (due to higher velocity dispersions) but increase with mean bound-cluster density. The N_* radial profiles are reported as shallower than those in STARFORGE simulations (competitive accretion), and the AFGL 5180 system is suggested to be better matched by the TCCA runs, though more observed systems are needed for discrimination.

Significance. If the separation between initial and dynamically acquired multiplicity can be robustly demonstrated, the work would help quantify secondary multiplicity effects in dense environments and provide a useful metric for distinguishing core-accretion versus competitive-accretion scenarios for massive stars. The environmental trends and direct comparison to an observed system add concrete value, though the paper itself notes that larger observational samples are required.

major comments (2)
  1. [Abstract / methods] Abstract and methods description: the simulations adopt a fixed 50% primordial binary fraction without reported control runs at other fractions (0%, 25%, 75%). Because the initial multiplicity is already high, the reported rapid acquisition of triple and higher-order companions around massive stars cannot be unambiguously attributed to dynamical processing rather than inheritance from the initial conditions. Quantifying the fraction of final bound companions that form after the massive star has assembled most of its mass, or repeating the suite with varied primordial binary fractions, is needed to support the central claim of 'via dynamical processes'.
  2. [Results / comparison sections] Results on N_* profiles and multiplicity trends: the statement that profiles are shallower than in STARFORGE and that AFGL 5180 is better described by TCCA models lacks explicit quantitative metrics (e.g., fitted slopes with uncertainties, Kolmogorov-Smirnov statistics, or direct profile overlays with error bands). Without these, the comparative claim remains qualitative and its robustness to parameter choices or projection effects is difficult to assess.
minor comments (2)
  1. [Abstract] The abstract states 'a suite of N-body simulations' but does not summarize the number of realizations, total stellar mass range, or typical cluster radii; adding a concise table of run parameters would improve reproducibility.
  2. [Throughout] Notation for N_* (projected stellar density) should be defined at first use and distinguished clearly from three-dimensional density throughout the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive report. The comments highlight important points regarding the attribution of multiplicity to dynamical processes and the need for quantitative comparisons. We address each major comment below and will revise the manuscript to strengthen these aspects.

read point-by-point responses

  1. Referee: [Abstract / methods] Abstract and methods description: the simulations adopt a fixed 50% primordial binary fraction without reported control runs at other fractions (0%, 25%, 75%). Because the initial multiplicity is already high, the reported rapid acquisition of triple and higher-order companions around massive stars cannot be unambiguously attributed to dynamical processing rather than inheritance from the initial conditions. Quantifying the fraction of final bound companions that form after the massive star has assembled most of its mass, or repeating the suite with varied primordial binary fractions, is needed to support the central claim of 'via dynamical processes'.

    Authors: We agree that varying the primordial binary fraction in additional control runs would provide the strongest separation between primary and secondary multiplicity. However, our existing suite already tracks the time-dependent binding of companions relative to the mass assembly history of each massive star. In the revised manuscript we will add a dedicated analysis that quantifies, for each massive star, the fraction of its final bound companions that become bound after the star has reached 90% of its final mass. This will directly demonstrate the dynamical contribution even within the fixed 50% initial binary population. We note that performing an entirely new suite at multiple primordial fractions is beyond the scope of the current computational resources, but the post-assembly binding statistics will still allow a robust assessment of the dynamical channel. revision: partial

  2. Referee: [Results / comparison sections] Results on N_* profiles and multiplicity trends: the statement that profiles are shallower than in STARFORGE and that AFGL 5180 is better described by TCCA models lacks explicit quantitative metrics (e.g., fitted slopes with uncertainties, Kolmogorov-Smirnov statistics, or direct profile overlays with error bands). Without these, the comparative claim remains qualitative and its robustness to parameter choices or projection effects is difficult to assess.

    Authors: We concur that the comparative statements would benefit from explicit quantitative support. In the revised version we will (i) fit power-law slopes to the median N_* radial profiles in both TCCA and STARFORGE runs, reporting the best-fit indices and their uncertainties, (ii) perform two-sample Kolmogorov-Smirnov tests between the TCCA and STARFORGE N_* distributions at matched radii, and (iii) include direct overlay plots of the profiles with 16th–84th percentile error bands. We will also add a short discussion of projection effects by comparing face-on and random-line-of-sight projections. These additions will place the claim that TCCA models provide a better match to AFGL 5180 on a firmer statistical footing. revision: yes

Circularity Check

0 steps flagged

No significant circularity: results are direct outputs of N-body integration from explicit initial conditions

full rationale

The paper reports outcomes of forward N-body simulations initialized with a fixed 50% primordial binary fraction inside the TCCA framework. The central claims (rapid gathering of triple companions and local N_* enhancements around massive stars) are measured quantities from the evolved states of those runs, not quantities that reduce by definition or by fitting to the same data. No equations or steps equate a 'prediction' to a fitted input, rename a known result, or import a uniqueness theorem from self-citation that forces the outcome. Self-citations to prior TCCA work supply the initial-condition setup but do not carry the load of the reported multiplicity statistics, which remain independently falsifiable by re-running the stated N-body integrations. The fixed binary fraction is an unvaried modeling choice, but that is an assumption, not a circular reduction of the reported results to the inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Central claims rest on the TCCA initial conditions, the chosen 50% primordial binary fraction, and the assumption that N-body dynamics alone produce the observed multiplicity and density patterns.

free parameters (1)
  • 50% primordial binaries
    Fraction of stars initialized as binaries; directly affects secondary multiplicity statistics.
axioms (2)
  • standard math N-body gravitational dynamics govern stellar interactions after formation
    Standard assumption for post-formation cluster evolution in the simulations.
  • domain assumption TCCA paradigm initial conditions represent real turbulent clumps
    The paper frames results within this paradigm without independent verification in the abstract.

pith-pipeline@v0.9.0 · 5591 in / 1251 out tokens · 42992 ms · 2026-05-07T10:29:49.894500+00:00 · methodology

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Reference graph

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