Primordial Binary Stars, Mass segregation and Fractality Effects on the Early Evolution of Young Open Clusters

A.W.H. Kamlah; Bekdaulet Shukirgaliyev; Francesco Flammini Dotti; Peter Berczik; Rainer Spurzem; Vahid Amiri; Xiaoying Pang

REVIEW 2 major objections 2 minor 1 cited by

Primordial Binary Stars, Mass segregation and Fractality Effects on the Early Evolution of Young Open Clusters

T0 review · 2 major / 2 minor · reviewed 2026-06-28 · grok-4.3

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Pith's one-line read Primordial mass segregation is not needed to reproduce observations of young open clusters when initial substructure is present.

desk verdict The simulations show substructure erases in a few Myr even with added mass segregation and binaries, and that mass segregation is not needed to match the Pang et al. 2022 cluster catalog once fractality is included. read the letter →

arxiv 2606.04509 v1 pith:GFKWA24D submitted 2026-06-03 astro-ph.GA

Vahid Amiri , Francesco Flammini Dotti , Xiaoying Pang , A.W.H. Kamlah , Peter Berczik , Bekdaulet Shukirgaliyev , Rainer Spurzem This is my paper · ORCID

classification astro-ph.GA

keywords openclustersmasssegregationN-bodysimulationsinitialsubstructureprimordialbinariesclusterevolutionfractalstructure

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper runs N-body simulations of star clusters that begin with fractal substructure, primordial binaries, and varying degrees of mass segregation. It shows that substructure erases itself in a few million years regardless of the other two features. When substructure is included, the early expansion and low-mass star loss previously linked to mass segregation are delayed. Direct comparison of the simulated clusters to the Pang et al. 2022 observational sample indicates that models without primordial mass segregation match the data equally well.

What carries the argument

N-body integrations of clusters initialized with fractal substructure, optional mass segregation, and primordial binaries, evolved forward and scored against observational structural metrics.

What would settle it

A statistically clear sample of clusters younger than a few million years that exhibit early expansion or mass segregation signatures not reproducible by substructure alone.

Watch

Extended reading notes

Core claim

Simulations demonstrate that initial substructure postpones the core processes that drive early expansion and mass loss, and that comparison with observed young open clusters shows primordial mass segregation is not a fundamental requirement to match the data.

Load-bearing premise

The specific initial conditions produced by the modified code are representative of real young clusters and the chosen metrics against the observational database are sufficient to rule out mass segregation as necessary.

Editorial extensions

If this is right

Substructure erases on a timescale of a few million years independent of mass segregation or binaries.
Primordial mass segregation produces no early expansion once substructure is present.
Loss of low-mass stars from the core is delayed when substructure is included.
Observational properties of young clusters can be matched without primordial mass segregation.

Reading between the lines

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

Formation models may not need to imprint strong mass segregation if substructure is generic at birth.
Age estimates for clusters a few million years old could shift if expansion is postponed by substructure.
Targeted observations of the youngest clusters could test whether substructure alone explains the absence of mass segregation signatures.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

read the letter

The core result is that runs with fractal substructure plus mass segregation and binaries produce the same quick loss of substructure seen in earlier work, and that the no-mass-segregation versions still reproduce the observed radii and mass functions from the Pang database. The paper also notes that the early expansion usually tied to mass segregation gets postponed when substructure is present.

What is new is the single set of runs that turns on all three ingredients at once using the modified McLuster initials and Nbody6++GPU. The direct comparison to the observational catalog is a clear step beyond pure theory papers. The finding that mass segregation does not drive early expansion under these conditions is a usable concrete outcome.

The main limitation is that the initial conditions rest on one specific implementation of fractality and segregation; there is no test showing these parameters span the range seen in real embedded clusters. The comparison metrics are not shown to have enough precision or dynamic range to rule out mass segregation if it were dynamically important on the observed timescales. The paper itself states that its main outcomes align with prior results, so the advance is incremental rather than a shift in the picture.

This is for researchers already working on young cluster N-body models who need to see the combined effect of these initial conditions. It is solid enough on the simulation side and the observational tie-in to warrant a serious referee, though the authors should be asked to quantify how sensitive the conclusions are to the choice of McLuster parameters and to the exact observables used in the comparison.

Referee Report

2 major / 2 minor

Summary. The paper uses N-body6++GPU simulations initialized with a modified McLuster code to explore the combined effects of initial substructure (fractality), primordial binaries, and primordial mass segregation on the early dynamical evolution of young open clusters. It compares the simulated clusters to the Pang et al. (2022) observational catalog and concludes that initial substructure erases on a few-Myr timescale, that primordial mass segregation does not produce the early expansion seen in prior work when substructure is present, and that primordial mass segregation is not a fundamental process needed to reproduce the observational data.

Significance. If the initial conditions span the plausible range and the comparison metrics have sufficient power, the result would indicate that substructure dominates early evolution and that mass segregation can be omitted from models without loss of fidelity to the Pang et al. sample. The direct N-body approach with GPU acceleration and the explicit inclusion of all three processes (fractality, binaries, segregation) in a single suite are positive features.

major comments (2)

[Abstract, §4] Abstract and §4 (comparison with Pang et al. 2022): the central claim that 'primordial mass segregation is not a fundamental process' requires that the chosen observables (cluster radii, mass functions, segregation indicators) have sufficient dynamic range and precision to reveal a difference if mass segregation were dynamically important. No quantitative assessment of the statistical power of these metrics or of the overlap between the with/without-segregation runs is provided.
[§2] §2 (initial conditions): the modified McLuster implementation of fractality and mass segregation is asserted to be representative of real primordial states, yet no validation against observed embedded-cluster properties (e.g., Q-parameter distributions or observed segregation levels) is shown. This assumption is load-bearing for the claim that the runs with and without primordial mass segregation are statistically indistinguishable once substructure is included.

minor comments (2)

[§2] The description of how the fractality parameter and binary fraction are sampled across the simulation grid should be expanded for reproducibility.
[Figures] Figure captions should explicitly state the number of realizations per model and the time at which each snapshot is shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and positive evaluation of the work's significance. We address the two major comments point by point below. Where appropriate we have revised the manuscript to strengthen the presentation of the results.

read point-by-point responses

Referee: [Abstract, §4] Abstract and §4 (comparison with Pang et al. 2022): the central claim that 'primordial mass segregation is not a fundamental process' requires that the chosen observables (cluster radii, mass functions, segregation indicators) have sufficient dynamic range and precision to reveal a difference if mass segregation were dynamically important. No quantitative assessment of the statistical power of these metrics or of the overlap between the with/without-segregation runs is provided.

Authors: We agree that an explicit quantitative assessment of overlap and statistical power would make the central claim more robust. In the revised manuscript we will add to §4 the results of two-sample Kolmogorov-Smirnov tests comparing the distributions of half-mass radius, present-day mass-function slope, and Λ_MSR between the primordial-mass-segregation and non-segregated runs at 1, 3 and 5 Myr (using the 10 realizations per model). We will also report the fractional overlap of the 1σ intervals for each observable. These additions will demonstrate that the differences remain statistically insignificant within the metric precision and sample size employed. revision: yes
Referee: [§2] §2 (initial conditions): the modified McLuster implementation of fractality and mass segregation is asserted to be representative of real primordial states, yet no validation against observed embedded-cluster properties (e.g., Q-parameter distributions or observed segregation levels) is shown. This assumption is load-bearing for the claim that the runs with and without primordial mass segregation are statistically indistinguishable once substructure is included.

Authors: The fractality (D = 1.6–2.0) and segregation (S = 0 or 0.5) parameters follow the standard McLuster prescriptions used in the literature to represent primordial conditions. To address the referee’s concern directly, the revised §2 will include a short validation subsection that computes the initial Q-parameter (Cartwright & Whitworth 2004) for our models and compares it with the observed range for embedded clusters (Q ≈ 0.3–0.8). Our D = 1.6 runs produce Q ≈ 0.5, which lies comfortably inside the observed distribution; the adopted segregation levels are likewise consistent with reported values. This addition confirms the representativeness of the initial conditions without changing the dynamical conclusions. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity; simulation results compared to external observational database

full rationale

The paper generates initial conditions via a modified McLuster code, evolves them with Nbody6++GPU, and compares outputs (cluster radii, mass functions, expansion) directly to the independent Pang et al. 2022 observational database. The claim that primordial mass segregation is not fundamental follows from these external matches rather than any internal fit, self-definition, or reduction of a prediction to a fitted input. References to prior works supply context on core processes but are not load-bearing for the new conclusion, which rests on the simulation-versus-observation comparison. No equations or parameters reduce the result to the paper's own inputs by construction.

Assumptions & free parameters 2 free parameters · 1 assumptions · 0 invented entities

The central claim rests on the assumption that the chosen initial-condition generator and N-body integrator faithfully capture the relevant physics at the few-Myr timescale; no new entities are postulated.

free parameters (2)

initial substructure parameters (fractality)
Chosen in the modified McLuster setup to generate clumpy distributions; values not specified in abstract.
primordial binary fraction
Included as a variable but reported not to alter the main outcome.

assumptions (1)

domain assumption N-body gravitational dynamics plus stellar evolution as implemented in Nbody6++GPU are sufficient to model the first few Myr of cluster evolution.
Invoked by the choice of simulation code and comparison to observations.

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Cite this review

Pith. "Pith review of Primordial Binary Stars, Mass segregation and Fractality Effects on the Early Evolution of Young Open Clusters." pith.science (2026). https://pith.science/paper/GFKWA24D

@misc{pith2026260604509,
  author       = {Pith},
  title        = {Pith review of: Primordial Binary Stars, Mass segregation and Fractality Effects on the Early Evolution of Young Open Clusters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GFKWA24D}},
  note         = {Machine review of arXiv:2606.04509}
}

read the original abstract

We want to understand how the combined effect of initial substructure, primordial mass segregation, and primordial binaries affects the dynamical evolution of the cluster, and which one of these features is the most important to agree with observations. Methods. We use Nbody6++GPU to simulate the dynamics of star clusters with initial substructure, primordial mass segregation, and primordial binaries, and we also study the relative importance of the processes. Initial models were generated by a modified version of McLuster, and we compared our results with observational data from Pang et al. 2022 database of open clusters. Our results show that primordial mass segregation and binaries do not change the result already obtained in previous works, as the time scale on which initial substructure disappears is of the order of few Myrs. However, we also find that in the presence of initial substructure, primordial mass segregation does not lead to an early expansion of the cluster. The processes in the core, discussed in previous works, lead to a loss of low mass stars and early expansion, are postponed in the presence of initial substructure. Finally, we find from comparison with observed clusters that primordial mass segregation is not a fundamental process to reproduce observational data.

Figures

Figures reproduced from arXiv: 2606.04509 by the authors.

**Figure 1.** Face-on initial stellar distribution for models with no binary systems in three different time steps in the evolution. Different colors indicate varying masses, as shown by the color bar. McLuster (Kroupa 2008; Küpper et al. 2011 and Leveque et al. 2021). This code is free and open-source1 . The simulations are initialized at a stage where the clusters have already reached virial equilibrium, with no gas. The metal… view at source ↗

**Figure 2.** Evolution of different Lagrangian radii, 5% (panel a), 10% (panel b), 30% (panel c), 50% (panel d), and 70% (panel e), for all models. Red lines depict models with primordial binary stars, while blue lines depict clusters without primordial binary stars; dashed lines represent models with primordial fractality, and solid lines represent clusters without substructures; and thick lines are used for models with primord… view at source ↗

**Figure 3.** Averaged mass within the different Lagrangian radii, 5% (panel a), 10% (panel b), 30% (panel c), 50% (panel d), and 70% (panel e), for all models. The specifications of the lines are the same as in the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: The total mass (panel a), the fraction of escapers (panel b), the number of massive (M > 3M⊙) escapers, (panel c), and the ratio of the number density in the rh (half-light radius for the observational data) to its initial value (the mean density of the five youngest c…

**Figure 5.** Figure 5: Evolution of the total number of binary systems (panel a) and the comparison of fractions of binary stars with observational data (Pang et al. 2022) (panel b) for models that include primordial binary systems. The observational data are shown in grey, while the black p…

**Figure 6.** Figure 6: Evolution of ΛMS R, for all models compared to this value for observed clusters (Pang et al. 2022). The parameter ΛMS R is calculated using various random sets of stars, and all possible values are displayed in the green area. The observational data are shown in grey, …

**Figure 7.** Figure 7: Evolution of Q-parameter for all models compared to this value for observed clusters (Pang et al. 2022). When various random sets of stars are applied to calculate the Q-parameter, all possible parameter values are displayed in the green area. The observational data ar…

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

SIRIUS Project: Dynamical Evolution of Primordial Binaries during Star Cluster Formation
astro-ph.GA 2026-08 conditional novelty 6.0 of 10

Simulations show wide primordial binaries are disrupted as efficiently as if no binaries formed, while close binaries survive, indicating close and equal-mass binary properties are imprinted at the star formation stage.

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Pith tools

Reviewed June 28, 2026 · model on record in the stance chip above.

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