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arxiv: 2604.14875 · v1 · submitted 2026-04-16 · 🌌 astro-ph.GA

ALMA-IMF XXII. Role of core subfragmentation in the IMF origin: Hierarchical fragmentation cascade and CMF in W43-MM1

F. Motte , N. Le Nestour , R. Veyry , N. Brouillet , T. Nony , B. Thomasson , F. Louvet , I. Joncour
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E. Moraux A. Men'shchikov T. Yoo A. Ginsburg A. Gusdorf A. M. Stutz R. Galvan-Madrid T. Csengeri R. H. Alvarez-Gutierrez M. Armante Y. Bernard M. Bonfand S. Chevalier N. Cunningham P. Dell'Ova M. Gonzalez A. Koley F. A. Olguin D. Panda Y. Pouteau J. Salinas P. Sanhueza N. A. Sandoval-Garrido M. Valeille-Manet
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Pith reviewed 2026-05-10 10:49 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords hierarchical fragmentationcore mass functioninitial mass functionW43-MM1gravo-turbulent fragmentationALMA observationsprotocluster
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The pith

Gravity rather than turbulence drives fragmentation below 14 kau in W43-MM1 and keeps the high-mass end of the fragment mass function top-heavy.

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

The paper extracts nested sources across five ALMA images of W43-MM1 spanning 14 kau to 270 au and builds hierarchical networks with graph-theory tools. It measures a low 3D fractality index of 1.19, an imbalanced mass partition where the dominant sibling holds two-thirds of the mass, and a core formation efficiency of roughly 16 percent between 2400 au and 200 au. These values are fed into the gravo-turbulent model, which then predicts that gravity, not turbulence, governs the cascade at smaller scales. The resulting fragment mass function therefore retains a top-heavy high-mass slope, so core subfragmentation contributes little to the origin of the initial mass function.

Core claim

In W43-MM1 the hierarchical fragmentation cascade shows a three-dimensional fractality index of 1.19 plus or minus 0.10, so that each halving of physical scale produces only 1.19 new fragments on average. Two-thirds of the mass at any scale stays with the dominant sibling, and the mass transfer efficiency yields a core formation efficiency of about 16 percent from 2400 au to 200 au. When these measured parameters are inserted into the Thomasson et al. gravo-turbulent model, fragmentation below roughly 14 kau is predicted to be gravity-driven. The fragment mass function that emerges from this cascade therefore keeps a top-heavy high-mass end, demonstrating that core subfragmentation in W43-MM

What carries the argument

The FAMILY graph-theory network of nested sources, together with the measured 3D fractality index F3D, sibling mass-partition ratio, and scale-to-scale mass-transfer efficiency that are supplied to the gravo-turbulent fragmentation model.

If this is right

  • The fragment mass function from which the IMF emerges remains top-heavy at its high-mass end.
  • Fragmentation below approximately 14 kau proceeds under gravity rather than turbulence.
  • Core subfragmentation plays only a minimal role in the origin of the IMF inside massive Galactic protoclusters.

Where Pith is reading between the lines

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

  • If the same low-fractality and high-efficiency parameters hold in other massive regions, their IMFs could also form top-heavy without invoking competitive accretion or other separate mechanisms.
  • Higher-resolution observations could test whether the self-similarity assumption continues to hold at disk scales.
  • A gravity-dominated cascade would imply that magnetic support or other stabilizing agents are less effective than expected at these densities.

Load-bearing premise

The assumption that the fractality, mass partition, and efficiency measured between 14 kau and 270 au can be extrapolated self-similarly to smaller scales inside the gravo-turbulent model.

What would settle it

High-resolution imaging that measures the fragment mass function below 200 au and finds a Salpeter-like or bottom-heavy high-mass slope would falsify the top-heavy prediction.

Figures

Figures reproduced from arXiv: 2604.14875 by A. Ginsburg, A. Gusdorf, A. Koley, A. Men'shchikov, A. M. Stutz, B. Thomasson, D. Panda, E. Moraux, F. A. Olguin, F. Louvet, F. Motte, I. Joncour, J. Salinas, M. Armante, M. Bonfand, M. Gonzalez, M. Valeille-Manet, N. A. Sandoval-Garrido, N. Brouillet, N. Cunningham, N. Le Nestour, P. Dell'Ova, P. Sanhueza, R. Galvan-Madrid, R. H. Alvarez-Gutierrez, R. Veyry, S. Chevalier, T. Csengeri, T. Nony, T. Yoo, Y. Bernard, Y. Pouteau.

Figure 1
Figure 1. Figure 1: Central part of the W43-MM1 protocluster, as revealed by five 3 mm continuum ALMA images. Panels a–e: Images with resolutions ranging from ∼2.6 ′′ to ∼0.050′′, corresponding to 14 kau to 0.27 kau (see [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The three types of structures as defined by FAMILY. Top row: Stack of sources detected at four increasing resolutions (purple, green, red, and blue figures). Bottom rows: Multi-scale networks of sources qualified either as hierarchical (left box, several children at least at one level), or linear (central box, a single child source with at most one parent source at each level), or isolated (right box, no c… view at source ↗
Figure 3
Figure 3. Figure 3: Scheme of the hierarchical fragmentation cascade from the core to the fragment scales that highlights its parameters. Stack sources (up￾per panel) and representation of the hierarchical structure (lower panel). For each decrease of two in physical scales, the fractality index is repre￾sented by F and the mass transfer efficiency by ϵ. For each sibling, the mass ratio between the primary and secondary child… view at source ↗
Figure 4
Figure 4. Figure 4: Fourth richest hierarchical structure of the W43-MM1 protoclus￾ter with a fractality index of F2D ≃ 1.24. Upper panel: Stack sources identified at clump resolutions of 14 kau (yellow), 8 kau (purple), at the core scale of 2.4 kau (green), and at fragment resolutions of 650 au (red) and 270 au (blue). The underlying image is the 3 mm continuum emission at 0.43′′ resolution. Ellipses here represent the outer… view at source ↗
Figure 6
Figure 6. Figure 6: Spatial variation of the fractality index measured in the nine hierarchical structures of W43-MM1 (orange hatched areas), ranging from F2D ≃ 1.0 to 1.5. A weak trend appears: the denser the gas (red and violet rectangular areas denser than the cyan rectangular area), the richer the hierarchical structure and the smaller its fractality index. We conducted tests to check that the W43-MM1 fractality measureme… view at source ↗
Figure 7
Figure 7. Figure 7: of Thomasson et al. 2024). In this figure, the two points corresponding to the W43-MM1 fragmentation cascade lie in the second regime, in which fragmentation is driven by grav￾ity and cloud structures are primarily supported by thermal en￾ergy. Across this 0.27−14 kau range of scales, structures should therefore be (velocity) coherent, that is, mostly devoid of turbu￾lent support (e.g., Ballesteros-Paredes… view at source ↗
read the original abstract

The gravo-turbulent fragmentation of the interstellar medium is expected to create a hierarchical cascade of cloud structures, crossing the scales from core to disk. We aim to predict how the currently observed top-heavy core mass function (CMF) in the massive protocluster W43-MM1 evolves due to core subfragmentation. We used the getsf algorithm to extract sources in five ALMA images of W43-MM1 at 3 mm, with a spatial resolution ranging from 14 kau to 270 au. Then, we applied FAMILY, a graph-theory-based analysis tool, to create and characterize networks of nested sources in W43-MM1. We compared the hierarchical fragmentation cascade of W43-MM1 to those measured in the NGC 2264 protocluster and in synthetic images of an Orion-like protocluster simulated by magneto-hydrodynamical calculations. Assuming self-similarity, we measure a small fractality index of mathcal F3D =1.19+/-0.10 in W43-MM1, which means that, on average, a cloud structure will fragment into only 1.19 fragments each time the physical scale decreases by a factor of two. We estimate an imbalanced mass partition between siblings, with 2/3 of the mass of siblings at a given scale belonging to the dominant sibling. The mass transfer efficiency, computed from one physical scale to another, is high and corresponds to a core formation efficiency (CFE) from 2400 au to 200 au of ~16%. Based on the fractality and efficiency values measured in W43-MM1, the gravo-turbulent model by Thomasson et al. predicts that its fragmentation below ~14 kau is not driven by turbulence but by gravity. Using these parameters and the measured mass partition, we demonstrate that the fragment mass function, from which the the initial mass function (IMF) emerges, has a high-mass end which remains top-heavy. Therefore, core subfragmentation in W43-MM1, and perhaps more broadly in massive Galactic protoclusters, plays a minimal role in the IMF origin.

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

1 major / 3 minor

Summary. The paper extracts sources from multi-resolution ALMA 3 mm images of W43-MM1 (14 kau to 270 au) using getsf, constructs hierarchical networks with the FAMILY graph tool, and measures a 3D fractality index F3D = 1.19 ± 0.10, a dominant-sibling mass fraction of 2/3, and a core formation efficiency of ~16% from 2400 au to 200 au. These parameters are fed into the Thomasson et al. gravo-turbulent model under an assumption of self-similarity to conclude that fragmentation below ~14 kau is gravity-dominated (not turbulence-driven) and that the emergent fragment mass function retains a top-heavy high-mass end, implying core subfragmentation plays only a minimal role in shaping the IMF in massive protoclusters. Comparisons are made to NGC 2264 and MHD simulations of an Orion-like region.

Significance. If the scale-invariance of the measured parameters holds and the model application is robust, the result would indicate that the top-heavy CMF in massive Galactic protoclusters does not evolve substantially toward a standard IMF via sub-fragmentation, with implications for whether the IMF is primarily set at core scales or larger. The graph-theoretic approach to hierarchical networks and the direct comparison to both observations and simulations are methodological strengths that could be broadly useful.

major comments (1)
  1. [Results and model application sections] The central prediction that fragmentation below ~14 kau is gravity-dominated and that the fragment mass function remains top-heavy rests on extrapolating F3D, the 2/3 mass partition, and the ~16% CFE (measured over the full 14 kau–270 au range) to smaller scales via the Thomasson et al. model. The manuscript states the self-similarity assumption but reports no internal consistency test by recomputing these quantities independently in separate scale bins within the observed data (e.g., 14 kau–1 kau versus 1 kau–270 au). If F3D or the partition ratio vary with scale, the model output and the claim of minimal IMF impact do not follow.
minor comments (3)
  1. [Abstract] Abstract contains a repeated word: 'the the IMF' should read 'the IMF'.
  2. [Results] The precise definition and units of the fractality index F3D should be restated explicitly when first used in the results, rather than relying solely on the abstract value.
  3. [Figures] Figure captions for the hierarchical networks and mass-partition plots would benefit from explicit scale ranges and a brief note on how the dominant-sibling fraction is computed from the graph edges.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our methodological approach and for the constructive feedback. We address the single major comment below regarding the self-similarity assumption and internal consistency of the measured parameters.

read point-by-point responses

  1. Referee: [Results and model application sections] The central prediction that fragmentation below ~14 kau is gravity-dominated and that the fragment mass function remains top-heavy rests on extrapolating F3D, the 2/3 mass partition, and the ~16% CFE (measured over the full 14 kau–270 au range) to smaller scales via the Thomasson et al. model. The manuscript states the self-similarity assumption but reports no internal consistency test by recomputing these quantities independently in separate scale bins within the observed data (e.g., 14 kau–1 kau versus 1 kau–270 au). If F3D or the partition ratio vary with scale, the model output and the claim of minimal IMF impact do not follow.

    Authors: We agree that an explicit internal consistency check by recomputing F3D, the dominant-sibling mass fraction, and CFE in independent scale bins would strengthen the self-similarity assumption used for extrapolation in the Thomasson et al. model. Our current measurements are derived from the full hierarchical network constructed with FAMILY across all five ALMA resolutions (14 kau to 270 au). Splitting into narrower bins (e.g., 14 kau–1 kau versus 1 kau–270 au) reduces the number of nested structures available per bin, which can degrade the statistical robustness of the graph metrics, particularly for the fractality index. Nevertheless, we will add this test to the revised manuscript wherever the sub-samples remain large enough for reliable FAMILY analysis, and we will report any detected variations or confirm consistency. If scale dependence appears, we will discuss its implications for the gravity-dominated regime and the retained top-heavy shape of the fragment mass function. This revision addresses the concern directly while preserving the main result that core subfragmentation has minimal impact on the IMF in W43-MM1. revision: partial

Circularity Check

0 steps flagged

No significant circularity: measurements independent of cited model

full rationale

The paper extracts F3D, mass partition ratio, and CFE directly from ALMA data via getsf source extraction and FAMILY graph analysis on the observed hierarchy (14 kau to 270 au). These empirical values are then supplied as inputs to the external gravo-turbulent model of Thomasson et al. under an explicit self-similarity assumption to generate predictions for sub-14 kau scales. No equation or claim reduces the output fragment mass function or gravity-dominated regime to the input measurements by construction; the model itself is cited from prior literature rather than redefined here. The self-similarity assumption is stated openly and does not create a definitional loop. This is a standard, non-circular workflow of observation plus external theoretical application.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central claim rests on three measured quantities treated as inputs to an external model plus one domain assumption that enables extrapolation; no new entities are postulated.

free parameters (3)
  • fractality index F3D = 1.19 +/- 0.10
    Measured from the hierarchical network but used directly as input to the gravo-turbulent model prediction.
  • dominant sibling mass fraction = 2/3
    Measured imbalanced partition used to compute the fragment mass function shape.
  • core formation efficiency = ~16%
    Computed mass transfer efficiency from 2400 au to 200 au used in the model.
axioms (1)
  • domain assumption Self-similarity of the fragmentation cascade across scales
    Invoked to extrapolate the measured fractality and efficiency to scales below the observed range.

pith-pipeline@v0.9.0 · 5876 in / 1557 out tokens · 41209 ms · 2026-05-10T10:49:36.771806+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

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    ] 148 3_21 18:47:46.57 -01:54:32.06 0.56×0.35 1.96±0.26 2.75±0.24 [ - ; - ; 148 ; 181 ; - ] 147 3_20 18:47:44.94 -01:54:42.89 0.58×0.37 0.45±0.03 0.71±0.03 [ - ; - ; 147 ; - ; - ] 146 3_19 18:47:47.10 -01:54:27.06 0.56×0.4 1.8±0.23 2.48±0.18 [ - ; - ; 146 ; 176 ; 189 ] 145 3_18 18:47:47.05 -01:54:32.15 0.48×0.3 1.48±0.13 1.64±0.1 [ - ; - ; 145 ; - ; - ] 1...

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