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arxiv: 2605.20489 · v1 · pith:4XF723GEnew · submitted 2026-05-19 · 🌌 astro-ph.GA · astro-ph.SR

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

Juan P. Farias , Alison Sills This is my paper

Pith reviewed 2026-05-21 06:26 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.SR
keywords star cluster formationgas expulsiondynamical evolutionstellar associationsN-body simulationsMHD simulationsembedded phaseexpansion rates
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The pith

The expansion of young stellar associations today still carries information about the dynamical state they reached while forming inside collapsing gas.

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

The paper develops a framework that builds young stellar systems by letting stars form gradually inside a gas potential taken directly from MHD simulations, then follows their evolution after the gas is removed with direct N-body runs. It shows that continued gas collapse while stars are forming raises both the central density and the internal speeds of the stellar group before expulsion occurs. This pre-expulsion state sets an upper limit on how fast the association can expand afterward, and the fraction of that speed that actually appears as expansion depends on how rapidly the gas is cleared. A reader would care because it implies that current observations of expanding star groups can be used to recover details of the hidden, embedded formation phase that are otherwise inaccessible.

Core claim

Across all explored MHD setups, the gas continues to collapse while stars are forming, increasing both the central concentration and velocity scale of the embedded stellar population before gas expulsion. Using a controlled grid of direct N-body simulations, this embedded evolution strongly regulates both the survival and later expansion of young stellar systems. In particular, gas contraction shortens the stellar crossing time prior to gas expulsion, making the same gas-removal timescale effectively more adiabatic for the stars. The present-day expansion of stellar associations still preserves information about the embedded dynamical state reached during formation: the expansion rate is set

What carries the argument

The Dynamical Cluster Assembly Framework (D-CAF), which imposes the global gas density evolution from MHD simulations as a time-varying background potential on stars that form gradually inside it, then evolves the resulting stellar population with direct N-body integration after gas removal.

If this is right

  • The survival and expansion behavior of young stellar systems is controlled by the velocity field established before gas expulsion.
  • Shorter crossing times caused by ongoing gas collapse make gas removal more adiabatic, reducing the fraction of internal kinetic energy that becomes expansion.
  • When full kinematic data are available, certain commonly used expansion diagnostics directly measure the true physical expansion rate.
  • Stellar kinematics can be inverted to place constraints on the dynamical conditions that prevailed during embedded star formation.

Where Pith is reading between the lines

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

  • Models of how star clusters dissolve over time would need to start from the higher velocity scales produced by pre-expulsion gas contraction rather than from virial equilibrium at the moment of gas removal.
  • Future surveys that combine proper motions and radial velocities for large samples of associations could map out the range of gas-expulsion timescales that actually occurred in nature.
  • The framework suggests that the initial conditions for long-term cluster evolution carry a stronger memory of the embedded phase than is usually assumed in simple analytic treatments.

Load-bearing premise

The overall gas evolution taken from MHD simulations can be treated as an external, unchanging background potential for the stars without the stars' own gravity or feedback altering the gas flow on the same timescales.

What would settle it

A set of young stellar associations with measured present-day expansion velocities, independent estimates of their gas-expulsion timescales, and reconstructed embedded velocity scales that show no correlation between the predicted and observed expansion rates.

Figures

Figures reproduced from arXiv: 2605.20489 by Alison Sills, Juan P. Farias.

Figure 1
Figure 1. Figure 1: Evolution of the retained gas fraction, Fret(t; f), measured within fixed initial gas Lagrangian radii for the torch M1 (top row) and starforge fiducial (bottom row) simulations. The left panels show the values measured directly from the MHD simulations. The middle panels show the corresponding Fret(t) reconstructed from the fitted Plummer profiles at each snapshot. The right panels show the analytic model… view at source ↗
Figure 2
Figure 2. Figure 2: Left: Radial gas and stellar density profiles at different times after the formation of the first star. Circles show the gas density profiles measured in the MHD simulations. Shaded regions indicate the range of values found at each radial shell, with light shading representing the minimum and maximum values and darker shading the 25th and 75th percentiles. Dashed lines show the Plummer models used to char… view at source ↗
Figure 3
Figure 3. Figure 3: Radial stellar phase-space distributions at the moment stars first appear in the benchmark MHD simula￾tions. Top panel show the stellar density profiles, while the bottom panel show the one-dimensional velocity dispersion profiles. The solid lines show Plummer profile fits to the stellar density and power-law fits to the velocity dispersion profiles used to define the stellar birth prescription adopted in … view at source ↗
Figure 4
Figure 4. Figure 4: Parameter-space coverage of the simulation suite. Each panel shows the grid (blue circles) explored in this work, with the free-fall time tff on the horizontal axis. Left: Maximum retained gas fraction Fret,max versus tff. Middle: Star formation efficiency (SFE) versus tff. Right: Gas expulsion timescale normalized by the free-fall time, texp/tff, versus tff. Starred symbols indicate the reference MHD simu… view at source ↗
Figure 5
Figure 5. Figure 5: Summary of the target simulations designed to reproduce the background environments of the STARFORGE fiducial model (left) and the TORCH M1 model (right). The bottom panels show the stellar half-mass radius, Rhm,⋆, for the original simulation, a realization using the tabulated Plummer background gas fits directly (tabulated), and a realization using a Plummer sphere with an analytical prescription for its … view at source ↗
Figure 6
Figure 6. Figure 6: Evolution of the stellar half-mass radius, Rh, across the simulation grid. Columns show different free-fall times, while rows correspond to different SFE values. Colours indicate the maximum retained gas fraction, Fret,max, and linestyles indicate the gas-expulsion timescale. The overall evolution follows a common sequence across the grid: an embedded contraction phase while the gas collapses and stars for… view at source ↗
Figure 7
Figure 7. Figure 7: Expansion rates measured at 25 Myr across the full parameter grid. The top row shows the expansion rate of the half-mass radius, dRh/dt, while the bottom row shows the expansion efficiency relative to the maximum embedded velocity dispersion, dRh/dt/σ∗,max. The left column shows the dependence on the nominal SFE, the middle column the imposed gas-expulsion timescale texp/tff, and the right column the effec… view at source ↗
Figure 8
Figure 8. Figure 8: Evolution and interpretation of three observational expansion diagnostics: the average outward velocity, vR (top panels), the position–velocity expansion gradient, κ multiplied by the current Rh (middle panels), and the ratio between outward velocity and radial velocity dispersion, vR/σ(vr) (bottom panels). The first two quantities directly measure the physical expansion rate of the stellar population, whi… view at source ↗
Figure 9
Figure 9. Figure 9: Normalized maximum stellar velocity dispersion and maximum half-mass number density for stars within Rh. The left panels show these quantities as a function of Fret,max, while the right panels show the same measurements as a function of SFE. In all panels, colors indicate SFE and line styles/markers indicate Fret,max. The normalization factors σ∗ and n∗ are the characteristic formation scales defined from … view at source ↗
Figure 10
Figure 10. Figure 10: Bound fraction measured at tge + 2 tff across the simulation grid. Columns show the three imposed gas-expulsion timescales, texp/tff = 0.1, 0.5, and 1, from left to right. The top row shows the bound fraction as a function of the nominal global SFE, the middle row as a function of the local stellar fraction (LSF) reached at the onset of gas expulsion, and the bottom row as a function of the effective gas-… view at source ↗
read the original abstract

We introduce the Dynamical Cluster Assembly Framework (D-CAF), an AMUSE-based framework designed to connect embedded star formation histories to the dynamical evolution of young stellar systems. We model star formation through the gradual formation of stars inside an evolving background potential, where the global gas evolution is extracted from realistic magneto-hydrodynamical (MHD) simulations. In this first work, we focus on the global evolution of the natal gas and its dynamical imprint on the stellar population. Across all explored MHD setups, we find that the gas continues to collapse while stars are forming, increasing both the central concentration and velocity scale of the embedded stellar population before gas expulsion. Using a controlled grid of direct $N$-body simulations, we show that this embedded evolution strongly regulates both the survival and later expansion of young stellar systems. In particular, gas contraction shortens the stellar crossing time prior to gas expulsion, making the same gas-removal timescale effectively more adiabatic for the stars. We find that the present-day expansion of stellar associations still preserves information about the embedded dynamical state reached during formation. The expansion rate is limited by the velocity scale reached before gas expulsion, while the efficiency with which this velocity field is transformed into expansion depends on the gas-expulsion timescale. Finally, we show that some commonly used expansion diagnostics can directly trace the physical expansion rate of young stellar systems when full kinematic information is available, opening the possibility of using stellar kinematics to constrain the dynamical conditions of embedded star formation.

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 / 1 minor

Summary. The manuscript introduces the Dynamical Cluster Assembly Framework (D-CAF) that couples global gas evolution extracted from standalone MHD simulations as a time-dependent external potential to direct N-body simulations of gradual star formation. Across the explored setups, gas continues to collapse during star formation, raising the embedded stellar central concentration and velocity scale; a controlled N-body grid then shows that this pre-expulsion state regulates post-gas-expulsion survival and expansion, with present-day expansion rates preserving information about the embedded dynamical conditions (expansion limited by pre-expulsion velocity scale, efficiency set by expulsion timescale).

Significance. If the central results hold, the work supplies a concrete dynamical link between embedded formation physics and observable kinematics of young stellar associations, opening a route to constrain formation conditions from present-day data. The controlled N-body grid and use of realistic MHD-derived potentials constitute a systematic strength that allows isolation of the embedded-phase imprint.

major comments (2)
  1. [Abstract and N-body grid section] Abstract and N-body grid description: the claims that embedded contraction shortens crossing times and regulates expansion rest on measured central concentration and velocity scale, yet no quantitative details are supplied on convergence tests, error bars, data exclusion, or the precise measurement procedure for these quantities. Without these, the support for the reported regulation of expansion cannot be verified.
  2. [Framework description] Framework description: the global gas density and potential evolution is imposed directly from standalone MHD runs as an external background. No test or estimate is provided showing that stellar feedback (winds, radiation, supernovae) does not appreciably modify the global collapse or expulsion timescale on the 0.1–1 Myr window; this decoupling is load-bearing for the claimed embedded dynamical state and the subsequent expansion results.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'velocity scale' appears without an explicit definition or reference to the quantity plotted or tabulated; a one-sentence clarification would improve immediate readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review. We address each major comment point by point below, indicating the changes we will make to the manuscript.

read point-by-point responses

  1. Referee: [Abstract and N-body grid section] Abstract and N-body grid description: the claims that embedded contraction shortens crossing times and regulates expansion rest on measured central concentration and velocity scale, yet no quantitative details are supplied on convergence tests, error bars, data exclusion, or the precise measurement procedure for these quantities. Without these, the support for the reported regulation of expansion cannot be verified.

    Authors: We agree that the manuscript would benefit from explicit documentation of these procedures. In the revised version we will insert a new subsection (likely in the N-body methods or results) that reports: (i) the convergence tests performed on the measured central concentration and velocity scale, (ii) the associated error bars and how they were computed, (iii) any data-exclusion criteria applied to the simulation outputs, and (iv) the precise algorithmic definition used to extract these quantities from the particle data. These additions will allow readers to reproduce and verify the claimed regulation of post-expulsion expansion. revision: yes

  2. Referee: [Framework description] Framework description: the global gas density and potential evolution is imposed directly from standalone MHD runs as an external background. No test or estimate is provided showing that stellar feedback (winds, radiation, supernovae) does not appreciably modify the global collapse or expulsion timescale on the 0.1–1 Myr window; this decoupling is load-bearing for the claimed embedded dynamical state and the subsequent expansion results.

    Authors: We acknowledge that the assumption of an unmodified global gas potential is central to the present framework. A fully self-consistent MHD+N-body run that includes stellar feedback lies outside the scope of this first paper. In the revision we will add a dedicated paragraph in the framework section that (a) cites existing literature on feedback timescales in comparable environments and (b) supplies order-of-magnitude estimates indicating that, for the densities and masses considered, global collapse and expulsion timescales remain largely unaffected over 0.1–1 Myr. We will also state this limitation explicitly and note that coupled feedback simulations are planned for follow-up work. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via external MHD inputs and N-body outcomes

full rationale

The paper extracts global gas evolution from standalone MHD simulations and imposes it as a time-dependent external potential on direct N-body stellar simulations. Reported results on embedded contraction shortening crossing times and regulating post-expulsion expansion are direct simulation outputs, not quantities defined in terms of parameters fitted to the target data or reduced by construction to inputs. No self-definitional steps, fitted predictions renamed as results, or load-bearing self-citations appear in the provided abstract and framework description. The central claim remains independent of the present paper's own fitted values and is externally falsifiable via the cited MHD runs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that MHD-derived global gas evolution can be treated as an external, non-reactive background potential for the forming stellar population.

axioms (1)
  • domain assumption Global gas evolution extracted from realistic MHD simulations can be used as an evolving background potential for star formation
    Stated in the abstract as the basis for modeling the natal gas.

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