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arxiv: 2604.08422 · v1 · submitted 2026-04-09 · 🌌 astro-ph.GA · astro-ph.SR

Expansion kinematics of young clusters. III. The kiloparsec sample

Joseph J. Armstrong , Jonathan C. Tan This is my paper

Pith reviewed 2026-05-10 17:16 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.SR
keywords young star clusterscluster expansionGaia astrometrykinematic substructurestar formationcluster kinematicsanisotropic expansion
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The pith

Most young star clusters formed with significant spatial and kinematic substructure instead of as dense monolithic objects.

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

The paper analyzes Gaia astrometry and radial velocities for 23 nearby young clusters to measure their plane-of-sky structure and expansion. It finds that most clusters are smoother in dense centers but retain hierarchical structure in outskirts, with clear anisotropic expansion signatures persisting beyond 30 Myr. These patterns indicate that the clusters originated with built-in substructure rather than collapsing from uniform dense states. The results also show that kinematic ages from expansion match stellar evolution ages only for the youngest systems, with older clusters appearing younger kinematically. This matters because it constrains how stars form in groups and how those groups evolve over time.

Core claim

The high degree of spatial structure and significant expansion anisotropy imply that the majority of these young clusters have formed with significant spatial and kinematic substructure and not as dense, monolithic clusters. Most clusters exhibit plane-of-sky expansion that is often anisotropic even at ages greater than 30 Myr, with older clusters tending to align maximum expansion directions closer to the Galactic plane. Kinematic ages from expansion timescales agree with isochronal ages for clusters younger than 10 Myr but are significantly younger for many older systems.

What carries the argument

Plane-of-sky expansion measurements from Gaia DR3 astrometry combined with radial velocities, quantified via Q-Parameter for spatial structure and Angular Dispersion Parameter for anisotropy.

If this is right

  • Hierarchical structure can persist in cluster outskirts for more than 10 Myr while centers smooth out through dynamical interactions.
  • Directions of maximum expansion in older clusters align more closely with the Galactic plane.
  • Kinematic ages from traceback and expansion timescales match isochronal ages only for clusters younger than 10 Myr.
  • Many clusters with isochronal ages above 10 Myr show significantly younger kinematic ages, consistent with a prolonged embedded phase.

Where Pith is reading between the lines

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

  • If substructure is the norm, models of star formation should prioritize hierarchical fragmentation over monolithic collapse scenarios.
  • Discrepancies between kinematic and isochronal ages may point to systematic underestimation of early cluster lifetimes in standard stellar evolution tracks.
  • Extending these measurements to more distant clusters could test whether the same substructure patterns hold at larger scales.

Load-bearing premise

The observed plane-of-sky expansion signatures and structural measures primarily trace initial formation conditions rather than later dynamical evolution, Galactic tides, or biases in membership selection and age estimation.

What would settle it

Detection of isotropic expansion or uniform structure across the full sample of clusters older than 10 Myr would undermine the inference of widespread initial substructure.

Figures

Figures reproduced from arXiv: 2604.08422 by Jonathan C. Tan, Joseph J. Armstrong.

Figure 1
Figure 1. Figure 1: Scatter plot of median cluster RVs which we calculate [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Difference between our bootstrap cluster distance esti￾mates dBootstrap and median Bailer-Jones et al. (2021) distances (red) and distances from Hunt & Reffert (2024) (blue) ∆d versus cluster distance dBootstrap (see Section 2.4). (2024) are underestimated in comparison to ours, by an amount that increases non-linearly with distance. We therefore conclude that the cluster distances from these catalogs are … view at source ↗
Figure 5
Figure 5. Figure 5: Angular Dispersion Parameter (δADP,e,Nsect(r)) for Melotte 20 with eight sectors (red) or four sectors (yellow) per concentric annuli containing 50 members. The δADP,e,Nsect(r) values are calculated for orientations of sectors rotated 1◦ at a time, and we plot the 50th (solid lines), 16th, and 84th percentile values (shaded regions) for each annulus. These are all well within the range of expansion velocit… view at source ↗
Figure 6
Figure 6. Figure 6: (a) Left: Q parameter versus ellipticity e. (b) Middle: Mean ADP with 4 sectors versus ellipticity e. (c) Right: Mean ADP with 4 sectors versus Q parameter [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Histogram of Velocity Position Angle, i.e., di [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Expansion velocity, vout, versus radial distance from the cluster center, R, for cluster members of λ Ori (red), with median expansion velocity ¯vout (km s−1 ) per concentric elliptical annulus containing 50 cluster members each (blue; Table B.1) and the expansion velocity dispersion σvout per concentric elliptical annulus containing 50 cluster members each (grey). which makes their associated timescales l… view at source ↗
Figure 10
Figure 10. Figure 10: Positional spread (blue) and rate of expansion (red) with [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Position vs velocity in the direction of maximum expan [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 14
Figure 14. Figure 14: 2D cluster size traceback for IC 2602. Left: Minimum spanning-tree total length as a function of trace-back time with no filter for outliers (red), 3σ velocity outliers removed (green), 2σ velocity outliers removed (blue) and 32% longest branches removed (black) with their respective uncertainties. Right: Sum of distances for each star to the association subgroup center as a function of trace-back time wi… view at source ↗
Figure 15
Figure 15. Figure 15: 2D cluster size traceback for IC 2602 with the correction for estimated size inflation due to error propagation. [PITH_FULL_IMAGE:figures/full_fig_p014_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Traceback timescales with the correction for size in [PITH_FULL_IMAGE:figures/full_fig_p015_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: (a) Left: Expansion age based on the maximum rate of expansion per cluster, τmax, versus isochronal age, τiso, with estimates shown from Hunt & Reffert (2024) (red symbols) and Cantat-Gaudin et al. (2020) (blue symbols). (b) Middle: Linear traceback age, τTB, versus isochronal age, τiso. (c) Right: As (b), but zooming in to 0 to 12 Myr ages. Thus, overall, while isochronal ages and kinematic ages are ofte… view at source ↗
Figure 18
Figure 18. Figure 18: Cluster ages from Hunt & Reffert (2024) (τiso,HR24) against core radii Rc for each cluster. 5.7. Cluster formation and dissolution There is a growing body of evidence that young stellar clusters are not typically dense and monolithic, but rather form with sig￾nificant spatial (e.g., Kuhn et al. 2014; Arnold & Wright 2024) and kinematic structure (as traced by anisotropic velocity disper￾sions; e.g., Wrigh… view at source ↗
Figure 20
Figure 20. Figure 20: Fraction of cluster members with ∆θ < |45◦ | against expansion velocity ¯vout for each cluster. – We estimate cluster distances using the bootstrapping ap￾proach of Armstrong & Tan (2024) on the Gaia DR3 paral￾laxes of individual cluster members. We find that, in general, our cluster distances are larger than those of Hunt & Reffert (2024) by an amount that increases non-linearly with dis￾tance. We attrib… view at source ↗
Figure 21
Figure 21. Figure 21: Histogram of orientation angle of maximum expansion [PITH_FULL_IMAGE:figures/full_fig_p020_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Cluster ages from Hunt & Reffert (2024) (τiso,HR24) against the orientation angle of maximum expansion rate. the majority of clusters, the level of substructure gener￾ally increases with radial distance R and the central sec￾tors of the clusters are often the most smoothly distributed. This indicates that the dense cores of clusters experience a rapid dynamical evolution, erasing their initial structure o… view at source ↗
read the original abstract

We combine Gaia DR3 5-parameter astrometry with calibrated radial velocities for 23 nearby (<1 kpc) young (<60 Myr) clusters, with membership lists from Cantat-Gaudin et al. (2020). We characterise the plane-of-sky structure of the clusters using Q-Parameter and Angular Dispersion Parameter (ADP) methods. We measure plane-of-sky expansion using several methods. We determine plane-of-sky orientations along which expansion is maximised. We also estimate expansion timescales and traceback ages and compare to isochronal ages. We then look for correlations between cluster properties and discuss sample-wide trends. We find that most young clusters are more smoothly structured in their centers where the rate of dynamical interactions is highest, while hierarchical structure can survive in the sparse outskirts for >10 Myr. We also find that the majority of nearby young clusters exhibit clear signatures of expansion in the plane-of-sky, which in many cases is significantly anisotropic, even at ages >30 Myr. We find evidence that older clusters tend to have directions of maximum expansion oriented closer to parallel with the Galactic plane. The high degree of spatial structure and significant expansion anisotropy imply that the majority of these young clusters have formed with significant spatial and kinematic substructure and not as dense, monolithic clusters. Kinematic ages estimated from expansion timescales and on-sky traceback are generally in good agreement with estimates inferred from stellar evolution models for clusters <10 Myr old. However, many clusters with older isochronal ages appear to have significantly younger kinematic ages. We discuss potential reasons for this discrepancy, including a prolonged embedded and/or gravitationally bound phase in the early stages of the clusters.

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 the plane-of-sky structure and expansion kinematics of 23 young clusters (<60 Myr, <1 kpc) using Gaia DR3 5-parameter astrometry combined with calibrated radial velocities and membership lists from Cantat-Gaudin et al. (2020). It characterizes spatial structure via the Q-parameter and Angular Dispersion Parameter (ADP), measures plane-of-sky expansion with multiple methods, determines orientations of maximum expansion, estimates expansion timescales and traceback ages, and compares these to isochronal ages. Key results include smoother central structure with retained hierarchical structure in outskirts, clear anisotropic expansion in most clusters (persisting >30 Myr), a tendency for older clusters to have maximum expansion aligned parallel to the Galactic plane, generally good agreement between kinematic and isochronal ages for clusters <10 Myr but younger kinematic ages for older clusters, and the inference that these features indicate formation with significant spatial and kinematic substructure rather than as dense monolithic clusters.

Significance. If the attribution of observed anisotropy and structure to primordial conditions holds after accounting for dynamical evolution, this work would offer valuable empirical support for hierarchical formation models of star clusters over monolithic collapse scenarios. The reliance on publicly available Gaia DR3 data and external membership catalogs is a strength, promoting reproducibility and allowing direct tests by the community. The reported age discrepancies and structural trends provide concrete observables for future N-body simulations of cluster evolution in the Galactic potential.

major comments (2)
  1. [Abstract and Discussion] Abstract (final paragraph) and Discussion: The load-bearing claim that 'the high degree of spatial structure and significant expansion anisotropy imply that the majority of these young clusters have formed with significant spatial and kinematic substructure and not as dense, monolithic clusters' is not fully supported. The paper reports that older clusters (>30 Myr) show directions of maximum expansion preferentially aligned parallel to the Galactic plane, a known signature of tidal torques and differential rotation. Without explicit comparison to N-body models of initially monolithic clusters evolved under the Milky Way potential or quantitative subtraction of expected tidal velocity fields from the measured expansions, the anisotropy cannot be unambiguously attributed to initial conditions rather than post-formation processing.
  2. [Results] Results section: The abstract and summary describe clear trends in expansion anisotropy and structure but provide no quantitative statistics (e.g., fractions of clusters with significant anisotropy, correlation coefficients, or p-values), error bars on expansion rates or ADP/Q values, or details on how systematics in membership selection and age estimation were handled. This weakens assessment of whether the data robustly support the sample-wide conclusions.
minor comments (2)
  1. [Methods] Clarify the precise implementation details of the Q-parameter and ADP methods, including any parameter choices, radial weighting, or calibrations against simulations, to ensure reproducibility.
  2. [Figures and Tables] Add error bars or uncertainty estimates to all reported expansion timescales, traceback ages, and orientation angles in tables and figures; ensure figure legends explicitly define symbols and distinguish between different measurement methods.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their constructive and detailed report. We address each major comment below, revising the manuscript where the points identify areas for improvement while maintaining the core observational results.

read point-by-point responses

  1. Referee: [Abstract and Discussion] Abstract (final paragraph) and Discussion: The load-bearing claim that 'the high degree of spatial structure and significant expansion anisotropy imply that the majority of these young clusters have formed with significant spatial and kinematic substructure and not as dense, monolithic clusters' is not fully supported. The paper reports that older clusters (>30 Myr) show directions of maximum expansion preferentially aligned parallel to the Galactic plane, a known signature of tidal torques and differential rotation. Without explicit comparison to N-body models of initially monolithic clusters evolved under the Milky Way potential or quantitative subtraction of expected tidal velocity fields from the measured expansions, the anisotropy cannot be unambiguously attributed to initial conditions rather than post-formation processing.

    Authors: We agree that the attribution of anisotropy to primordial conditions would be strengthened by direct N-body comparisons, which are not performed here. In the revised manuscript we have tempered the language in the abstract and discussion to state that the observations are 'consistent with' formation in a substructured state rather than implying it definitively. We have added a dedicated paragraph noting the Galactic-plane alignment in older clusters as a possible tidal signature and explicitly stating that future simulations are needed to separate initial conditions from post-formation evolution. We retain the claim as an interpretation because the anisotropy appears across the full age range (including clusters <10 Myr where tidal processing is limited) and is accompanied by surviving hierarchical structure in the outskirts, features not obviously produced by tides alone. revision: partial

  2. Referee: [Results] Results section: The abstract and summary describe clear trends in expansion anisotropy and structure but provide no quantitative statistics (e.g., fractions of clusters with significant anisotropy, correlation coefficients, or p-values), error bars on expansion rates or ADP/Q values, or details on how systematics in membership selection and age estimation were handled. This weakens assessment of whether the data robustly support the sample-wide conclusions.

    Authors: We accept that the presentation of results can be made more quantitative. The revised manuscript now includes: (i) error bars on all reported expansion rates, Q-parameters, and ADP values derived from bootstrap resampling and membership probability weighting; (ii) the fraction of clusters showing statistically significant anisotropy (expansion rate ratio >2 with combined uncertainty <1); (iii) Spearman rank correlation coefficients and p-values for trends between anisotropy, structure parameters, and cluster age; and (iv) an expanded methods subsection detailing how uncertainties from the Cantat-Gaudin et al. (2020) membership lists and isochronal age errors are propagated into the kinematic age comparisons. revision: yes

standing simulated objections not resolved
  • Direct quantitative comparison to N-body simulations of initially monolithic clusters evolved in the Milky Way potential, which lies outside the scope of this observational study.

Circularity Check

0 steps flagged

No significant circularity detected; derivation relies on independent data processing

full rationale

The paper computes structural parameters (Q-parameter, ADP) and plane-of-sky expansion metrics directly from Gaia DR3 astrometry combined with external membership lists (Cantat-Gaudin et al. 2020). Expansion timescales, traceback ages, and comparisons to isochronal ages are calculated from observed positions/velocities without fitting a parameter to a data subset and then re-using it as a 'prediction.' The central inference about primordial substructure is an interpretive conclusion drawn from the measured trends (including age-dependent alignment with the Galactic plane), not a mathematical identity or self-referential definition. Any self-citations to prior work by the same authors are not load-bearing for the core results, as the present analysis stands on public data and standard methods. No step reduces by construction to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard assumptions about data quality and external catalogs rather than new postulates; no free parameters or invented entities are described in the abstract.

axioms (2)
  • domain assumption Gaia DR3 5-parameter astrometry and calibrated radial velocities accurately represent the positions, proper motions, and velocities of stars in the selected clusters
    Central to all plane-of-sky and expansion measurements.
  • domain assumption Membership lists from Cantat-Gaudin et al. (2020) correctly identify cluster members without significant contamination or incompleteness
    Used to define the sample for all structural and kinematic analyses.

pith-pipeline@v0.9.0 · 5599 in / 1496 out tokens · 68226 ms · 2026-05-10T17:16:00.988856+00:00 · methodology

discussion (0)

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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.

  1. Dynamical Cluster Assembly Framework (D-CAF): The Link Between Star Cluster Formation and Expansion Rates

    astro-ph.GA 2026-05 unverdicted novelty 6.0

    D-CAF simulations show that ongoing gas collapse during star formation shortens stellar crossing times, rendering gas expulsion more adiabatic and thereby regulating the survival and expansion rates of young stellar systems.

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages · cited by 1 Pith paper

  1. [1]

    Armstrong, J. J. & Tan, J. C. 2024, A&A, 692, A166 Armstrong, J. J., Tan, J. C., Wright, N. J., et al. 2025, MNRAS, 543, 2349 Armstrong, J. J., Wright, N. J., Je ff ries, R. D., & Jackson, R. J. 2020, MNRAS, 494, 4794 Armstrong, J. J., Wright, N. J., Jeff ries, R. D., Jackson, R. J., & Cantat-Gaudin, T. 2022, MNRAS, 517, 5704 Arnold, B. & Wright, N. J. 20...

    work page arXiv 2024

  2. [2]

    In the legend is given the expan- sion timescale corresponding to each gradient, the lowest (for the maximum expansion rate) in bold

    Then the best-fitting linear gradient (by least squares) for each is plotted in the same colour. In the legend is given the expan- sion timescale corresponding to each gradient, the lowest (for the maximum expansion rate) in bold. The lower row seems to be the case that applies for many of the clusters in the sample analysed in this paper, where the Trace...

    work page 1977