High-resolution APEX/LAsMA $^{12}$CO and $^{13}$CO (3-2) observation of the G333 giant molecular cloud complex : III. Decomposition of molecular clouds into multi-scale hub-filament structures

F. Wyrowski; J. S. Urquhart; J. W. Zhou; M. Juvela; S. Neupane; T. Liu

REVIEW 4 major objections 7 minor 14 references

High-resolution APEX/LAsMA $^{12}$CO and $^{13}$CO (3-2) observation of the G333 giant molecular cloud complex : III. Decomposition of molecular clouds into multi-scale hub-filament structures

T0 review · 4 major / 7 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that molecular clouds are network structures assembled from gravitationally coupled, multi-scale hub-filament systems, in which hubs act as local gravitational centers and the primary sites of star formation.

desk verdict A useful new catalog of hub-filament systems in G333/G331, but the headline density-contrast result is partly built into the classification and the inflow interpretation needs a directional test. read the letter →

arxiv 2506.16664 v1 pith:BHWQIY2T submitted 2025-06-20 astro-ph.GA

J. W. Zhou , J. S. Urquhart , F. Wyrowski , S. Neupane , T. Liu , M. Juvela This is my paper · ORCID

classification astro-ph.GA

keywords ISM:structureevolutionstars:formationsubmillimeter:ISMhub-filamentsystemsdensitycontrastvelocitygradientsmolecularcloudnetworks

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

Using high-resolution 13CO (3−2) maps of the G333 complex and the G331 giant molecular cloud, the authors decompose the gas into hundreds of hub-filament units and argue that these units, not the cloud itself, are the fundamental building blocks of molecular clouds. The hubs are dense local gravitational centers where star formation happens, and the filaments are gas streams feeding them. Hub-filament systems turn out to be denser, more massive, less virialized, more frequently associated with embedded star formation, and to show velocity gradients consistent with gravitational inflow, supporting an evolutionary sequence from uniform non-hub structures to hub-filament systems. If this picture is right, it reframes how cloud-scale star formation, feedback, and the structure of giant molecular clouds are understood.

What carries the argument

The central object is the hub-filament system (HFS): a dense hub where three or more filaments converge, operationally identified as a leaf in a dendrogram decomposition of the integrated-intensity map plus the surrounding 2.5-times-extended region. The key quantitative quantity is the density contrast, C = N_hub / N_annulus, the ratio of the mean column density in the hub to that in an elliptical ring just outside it; values around 1.5 separate HFs from non-HFs. The kinematic machinery is the fitted velocity gradient along each filament, compared with free-fall models for central masses of 100–10000 solar masses and interpreted as gas flowing toward the hub. Together this morphological and kinematic apparatus converts a catalogue of dense structures into an evolutionary and dynamical story.

What would settle it

Compute synthetic 13CO(3−2) maps of a cloud containing rotating or outflowing filaments with no true inflow and run the same peak-finding, density-contrast, and velocity-gradient pipeline; if hub-filament classifications and free-fall-like gradient scalings still emerge, the inflow interpretation is falsified. Observationally, a proper-motion survey of dense cores in a few dozen filaments would show directly whether the gas moves toward the hub at the free-fall speeds implied by the fitted masses.

Watch

Extended reading notes

Core claim

The paper decomposes the G333 complex and the G331 giant molecular cloud into multi-scale hub-filament systems (HFs), structures in which a dense hub collects gas along converging filaments. Applying a dendrogram-based peak identification, a filament-finding algorithm, and velocity-gradient fitting, the authors classify 148 of 438 leaf structures as HFs and 243 as non-HFs. Compared with non-HFs, HFs have significantly higher density contrast, larger masses, lower virial ratios, and higher rates of association with submillimetre clumps and radio continuum sources, as well as higher 8 µm peak intensities and clump luminosity-to-mass ratios. The velocity gradients measured along the filaments follow the free-fall scaling expected for central masses of roughly 100 to 10000 solar masses, matching the leaf mass distribution, and are interpreted as gas inflow toward the hubs. The paper concludes that molecular clouds are network structures formed by the gravitational coupling of multi-scale hub-filament systems: the hubs are the nodes, the local gravitational centers, and the main star-forming sites, and clumps in molecular clouds are equivalent to hubs. This network picture is offered as a natural explanation for why early feedback from protoclusters does not significantly change the kinematic properties of surrounding dense gas.

Load-bearing premise

The load-bearing premise is that the fitted velocity gradient along each filament traces gas actually flowing toward the hub; if rotation, outflow, or line-of-sight projection produces those gradients instead, the kinematic evidence for classifying the structures as hub-filament systems falls away.

Editorial extensions

If this is right

Molecular clouds should be treated as networks of hubs connected by filaments, so the natural unit of cloud-scale star formation is the hub-filament system rather than the cloud as a monolithic object.
Clumps in molecular clouds are equivalent to hubs, meaning clump catalogs can be reinterpreted as catalogs of network nodes that undergo gravitational focusing.
Early feedback from forming stars mainly reshapes the topology of the network rather than destroying the cloud, leaving the kinematics of embedded dense gas largely governed by gravity.
Density contrast C can serve as a single diagnostic of how far gravitational collapse has progressed and how strong the gravitational center is, complementing or even superseding density itself as an evolutionary indicator.
Non-hub structures are likely earlier evolutionary states that will develop hubs and filaments, implying that the observed mix of HFs and non-HFs in a cloud maps onto a temporal sequence.

Reading between the lines

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

Extending the paper's logic, if hub-filament systems are genuinely scale-free building blocks, then the same decomposition applied to other giant molecular clouds should yield hub masses and filament lengths with scale-free distributions; testing that prediction would tell whether G333 is typical.
The network model implies that star formation efficiency in a cloud may depend more on the number and gravitational strength of its hubs than on total cloud mass, a distinction that could be tested by comparing clouds of equal mass but different hub populations.
If non-HFs evolve into HFs through gravitational focusing, then density contrast should increase monotonically with structural age; using chemical clocks such as N2H+ abundance or CO depletion as age tracers could test this proposed sequence directly.
The claim that early feedback is only a topological deformation predicts that hubs separated by more than one filament length should show statistically independent velocity dispersions; a pairwise correlation analysis of hub kinematics could falsify or support this independence.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

Quick take: this is a workmanlike, useful decomposition paper with a real catalog at its core, but two soft spots you should know about: the headline density-contrast result is partly selected by the classification, and the kinematic evidence for inflow is not as strong as the abstract implies.

The new thing is concrete: 148 hub-filament systems and 243 non-HFs in the G333 complex and G331 GMC, identified from 13CO(3-2) LAsMA data, with matched ATLASGAL clumps, CORNISH-South radio sources, and MIR emission. The clump/radio association contrast (83% vs 32% for clumps; 29% vs 4% for radio) is a genuinely independent discriminant and is the most convincing evidence that HFs are more evolved. The L/M ratios and 8um peak intensity reinforce that. The authors also do a good job of cleaning overlapping velocity components and checking that the smaller scale of non-HFs is not just a resolution effect (Figure 8). That is careful work.

The density-contrast claim is partly circular. HFs are selected partly on the basis of having a distinct high-density center, quantified by C (Eq. 1), and then Figure 4a reports that HFs have higher C. So that specific comparison is not evidence. But because mass, virial ratio, and the clump/radio associations are not used in the classification, the general conclusion that HFs are more evolved survives. Just drop the C comparison as support.

The bigger soft spot is kinematics. The paper fits velocity gradients along filaments, compares their magnitudes to free-fall expectations, and concludes gas is flowing toward the hubs. A linear gradient along a filament can also come from rotation, shear, or projection of an unrelated velocity field. They don't test whether the gradient points toward the hub or whether the gas velocity approaches the hub's systemic velocity at the hub end. Without a directional test, this is weak support for inflow. The network claim — that clouds are gravitational networks of multi-scale HFs — rests largely on this inflow picture, so it should be framed as a hypothesis, not a result. The summary does use “propose,” but the abstract's “suggest” and the earlier PPV funnel evidence from Zhou et al. (2023) give it more weight than this paper alone warrants.

Minor points: no error bars or significance tests on the distribution comparisons; the C=1.5 and 2.5x extension thresholds are arbitrary and untested. A sensitivity analysis would help.

Who should read this: anyone working on hub-filament systems or high-mass star formation in G333. It's a solid catalog paper, worth citing for the decomposition and the clump associations, but treat the evolutionary interpretation as one plausible reading, not a proof. Worth a serious peer review; with a proper significance test and a directional velocity-gradient analysis, it could be much stronger.

Referee Report

4 major / 7 minor

Summary. The paper uses APEX/LAsMA 13CO(3-2) and 12CO(3-2) maps of the G333 complex and G331 GMC to identify intensity peaks with astrodendro, classify them into hub-filament systems (HFs) and non-HFs using a density contrast C (Eq. 1) plus filament morphology, and derive masses, virial ratios, velocity gradients, and associations with ATLASGAL clumps and CORNISH-South radio sources. It reports 148 HFs, finds that HFs have larger masses, lower virial ratios, higher density contrast, and more frequent clump/radio associations than non-HFs, and interprets these trends as evidence for an evolutionary sequence from non-HFs to HFs. The paper concludes that molecular clouds are network structures built from gravitationally coupled multi-scale hub-filament systems, with hubs as the nodes and clumps equivalent to hubs.

Significance. If the central interpretation holds, this is one of the largest systematic decompositions of a GMC into hub-filament systems and strengthens the observational basis of the hub-filament paradigm at cloud-clump scales. The main strengths are the homogeneous LAsMA data, the explicit multi-wavelength cross-matching to ATLASGAL and CORNISH-South, the inclusion of independent discriminants such as virial ratio and luminosity-to-mass ratio, and the connection to prior kinematic studies of G333. However, the significance is currently limited by two load-bearing caveats: the density-contrast comparison is in part a selection effect, and the kinematic evidence for inflow has not been shown to be directional. The independent property differences and clump/radio associations are valuable regardless, but the broad network claim in Sec. 4.3 needs stronger kinematic support.

major comments (4)

[Sec. 3.4.2, Figs. 5 and 6] The evidence for inflow rests on fitting velocity gradients along filaments and comparing their magnitudes with free-fall predictions. A linear gradient along a filament can also be produced by rotation, shear, an outflow, or line-of-sight projection of a larger-scale velocity field. The paper does not report the sign of dv/dl relative to the hub position, does not check whether the filament velocity converges to the hub's systemic velocity at the hub end, and does not state how many of the 148 HFs pass a directional test. Please add such a test (e.g., gradient vectors pointing toward the hub, velocity reversal across the hub, or position-velocity diagrams along the spine) and report the passing fraction. This is needed to support the 'gravitational coupling' language in Sec. 4.3 and Summary point 7.
[Sec. 3.3, Eq. (1), Figs. 4(a) and 7] Because C is a primary criterion in the HF/non-HF classification, and because structures near C≈1.5 that were 'challenging to classify' were excluded without a reported count, the statement that HFs have higher density contrast is at least partly a selection effect rather than an independent empirical finding. This matters for Sec. 4.2, where C is interpreted as measuring the extent of gravitational collapse and the strength of the gravitational center. Please validate that interpretation independently: for example, within the HF sample alone, correlate C with L/M or with radio association, or re-derive the classification without using C and check whether the property differences persist. The independent discriminants (mass, virial ratio, clump/radio associations) should be the primary support for the evolutionary sequence.
[Sec. 3.2, type2 structures] The reduction of type2 structures to their dominant velocity component is an ad hoc assumption that can remove genuine multi-component inflow, which is precisely the kind of kinematic signature expected in hub-filament systems according to the arguments listed in Sec. 3.2. Please justify this choice with position-velocity diagrams for representative type2 structures, or show that the velocity-gradient and mass estimates are robust when secondary components are retained.
[Sec. 4.3 and Summary point 7] The claim that 'clumps in molecular clouds are equivalent to the hubs' equates 13CO intensity leaves with ATLASGAL dust clumps without a quantitative match of sizes, masses, or velocities, and the universal network statement is extrapolated from two complexes. Please soften or support these statements: report the fraction of hubs that coincide with ATLASGAL clumps by both position and size, and add an explicit caveat that the network hypothesis is based on the G333/G331 data and needs testing in other clouds.

minor comments (7)

[Sec. 4.2] The text 'As shown in Fig.3.5(e)' should read 'Fig.4(e)'.
[Sec. 3.4.2] There is a typo in 'the same analysis presentend in Zhou et al. (2022)'; it should read 'presented'.
[References] Zhou et al. 2024b and 2024c are listed with the same A&A volume, article number, and DOI; one of these entries needs to be corrected or disambiguated.
[Figs. 4 and 9] The text describes distribution differences as 'significant' but does not report p-values or confidence intervals; please add a two-sample test (e.g., Kolmogorov-Smirnov or Mann-Whitney) for each comparison.
[Sec. 3.1] The choice of min_value = 15 K km/s is said to be the best for recovering high-intensity peaks, but no quantitative criterion or sensitivity test is given; please show how the number of leaves and HFs changes with this parameter.
[Sec. 3.4.1] The factor-of-two regridding is arbitrary; please show that the identified filaments and fitted gradients are stable under a different pixel scale.
[Sec. 3.1] The distance ambiguity for peak1 is dismissed as not significantly affecting the statistics; please quantify the effect on masses and sizes of structures associated with peak1.

Circularity Check

2 steps flagged · score 6.0 of 10

Density-contrast comparison is partly a selection effect; the hub-filament network claim retains independent mass, virial, and clump/radio support.

self definitional [Sec. 3.3 (Eq. 1) and Sec. 3.5 / Fig. 4(a)]
"In hub-filament systems (HFs), hubs exhibit substantially higher densities compared to filaments, which means a significant density contrast between the hub and the surrounding diffuse gas. We define the density contrast C as the ratio of the average column density in the hub region, Nhub, to the average column density within an elliptical ring surrounding the hub ... Generally, C≈ 1.5 can serve as the boundary between the two categories. ... As expected, in Fig. 4(a), HFs display significantly higher density contrast."

The HF/non-HF classification in Sec. 3.3 explicitly uses the density contrast C, with C≈1.5 as the boundary. The Sec. 3.5 statement that HFs 'display significantly higher density contrast' (Fig. 4a) is therefore partly guaranteed by the selection rule: the sample was separated on the very quantity that is then reported as a discovered difference. The circularity is partial rather than total because HFs are additionally required to have filaments converging on the high-density center, and because mass, virial ratio, ATLASGAL clump associations, and radio-source associations provide independent discriminants.
self definitional [Sec. 4.2 and Summary item 6]
"According to the possible evolutionary sequence from non-HFs to HFs, currently, non-HFs lack a distinct gravitational focusing process that would result in significant density contrast. Thus, their density distribution is relatively uniform. Therefore, density contrast C effectively measures the extent of gravitational collapse and the strength of the gravitational center of the structure, which definitively shape the hub-filament morphology."

This interpretive step completes the circle: 'non-HFs lack a gravitational focusing process' is inferred from their low C and relatively uniform density distribution, but low C and the absence of a distinct high-density center are precisely the criteria used to define non-HFs. The claim that C 'measures the extent of gravitational collapse' is then attached to the same selection variable. The evolutionary sequence is not wholly circular because it also draws on independent clump/radio associations and L/M ratios, but the specific physical meaning assigned to C is largely a restatement of the classification criterion rather than an independently tested quantity.

full rationale

The paper's decomposition is mostly self-contained and observationally grounded: intensity peaks come from a dendrogram of the 13CO moment-0 map, filaments come from filfinder, masses and virial ratios come from LTE column densities, and the clump/radio associations come from external ATLASGAL and CORNISH catalogs. None of those steps is fitted to the network conclusion. The genuine circularity is concentrated in the density contrast C: C≈1.5 is one of the criteria used to define HFs versus non-HFs, so the demonstration that HFs have higher C (Fig. 4a) is partly a selection echo, and the later inference that C measures gravitational collapse imports meaning from that same classification. The circularity is partial because HFs also require convergent filaments and because the independent discriminants (mass, virial ratio, clump/radio association, L/M) support an evolutionary sequence from non-HFs to HFs. I do not count the many self-citations to Zhou et al. (2022, 2023, 2024d) as load-bearing circularity: the present paper reports its own velocity-gradient fits, and the cited prior studies are published, externally checkable observational analyses rather than unverified uniqueness or ansatz assertions. The free-fall comparison of velocity-gradient magnitudes is likewise not circular by construction, since the leaf masses are measured independently; the unresolved question of whether the gradients trace inflow rather than rotation or projection is a correctness/robustness risk, not a by-construction reduction. Overall, one central quantitative comparison reduces partly by construction, meriting a score of 6, but the network claim retains enough independent content that it is not fully forced.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central results rest on parameter choices and interpretive assumptions. The density contrast boundary C=1.5 and the dendrogram threshold 15 K km/s are hand-selected. The 2.5x extension that defines the hub-filament field is set by inspection. Masses and column densities come from an LTE analysis carried out in a previous paper. The velocity-gradient-to-inflow interpretation and the population-to-evolution inference are domain assumptions. No new physical entities are introduced; the network model is a re-description of already-observed structures.

free parameters (5)

Dendrogram min_value threshold = 15 K km/s
Chosen by trial and error in Sec. 3.1 to recover all high intensity peaks; controls which leaves are identified as potential hubs.
Hub-filament extension factor = 2.5
Sec. 3.2 fixes the spatial range around each hub to 2.5 times the hub effective radius, judged by eye to recover a complete hub-filament morphology.
Density contrast boundary C = 1.5
Sec. 3.3 uses C=1.5 to separate structures with a distinct high-density center from those without; this threshold is part of the HF/non-HF classification.
Non-HF subgroup threshold C = 1.2
Sec. 3.5 splits non-HFs at the median density contrast (C=1.2) into two evolutionary groups; a data-derived cutoff, not an external prediction.
Regridding factor = 2
Sec. 3.4.1 doubles the pixel count with spline interpolation to let filfinder run on small structures; this choice can influence detected filament shapes.

assumptions (6)

domain assumption The dendrogram intensity peaks are potential hubs.
Sec. 3.2 treats every leaf peak as a potential hub; if a peak is not a local gravitational center, the surrounding filament assignment is invalid.
domain assumption LTE analysis of 12CO and 13CO gives valid column densities and temperatures.
Masses, density contrast, and virial ratios in Sec. 3.5 are derived from the LTE cubes of Zhou et al. (2023); non-LTE or optically thick lines would bias all of these.
domain assumption Velocity gradients along filaments trace gas inflow toward the hub.
Sec. 3.4.2 interprets fitted gradients as accretion flow; alternative origins (rotation, outflow, projection) are not examined.
domain assumption Population differences with clump/radio associations represent an evolutionary sequence.
Sec. 4.1 infers evolution from non-HFs to HFs by comparing structures at different tracer associations, not by following the same objects over time.
domain assumption A single distance of 3.6 kpc applies to all structures.
Sec. 3.1 assigns the G333 distance to the peak1 component as well, although that component may lie in the Norma arm at about 5 kpc; the authors argue the effect is small.
ad hoc to paper Overlapping velocity components can be separated by taking the dominant component only.
Sec. 3.2 reduces type2 structures to type1 by discarding secondary velocity components; this can remove genuine multi-component inflows.

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Cite this review

Pith. "Pith review of High-resolution APEX/LAsMA $^{12}$CO and $^{13}$CO (3-2) observation of the G333 giant molecular cloud complex : III. Decomposition of molecular clouds into multi-scale hub-filament structures." pith.science (2026). https://pith.science/paper/BHWQIY2T

@misc{pith2026250616664,
  author       = {Pith},
  title        = {Pith review of: High-resolution APEX/LAsMA $^12$CO and $^13$CO (3-2) observation of the G333 giant molecular cloud complex : III. Decomposition of molecular clouds into multi-scale hub-filament structures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BHWQIY2T}},
  note         = {Machine review of arXiv:2506.16664}
}

abstract

We decomposed the G333 complex and the G331 giant molecular cloud into multi-scale hub-filament systems (HFs) using the high-resolution $^{13}$CO (3$-$2) data from LAsMA observations. We employed the filfinder algorithm to identify and characterize filaments within HFs. Compared with non-HFs, HFs have significantly higher density contrast, larger masses and lower virial ratios. Velocity gradient measurements around intensity peaks provide evidence of gas inflow within these structures. There may be an evolutionary sequence from non-HFs to HFs. Currently, non-HFs lack a distinct gravitational focusing process that would result in significant density contrast. The density contrast can effectively measure the extent of gravitational collapse and the strength of the gravitational center of the structure that definitively shape the hub-filament morphology. Combined with the kinematic evidence in our previous studies, we suggest that molecular clouds are network structures formed by the gravitational coupling of multi-scale hub-filament structures. The knots in the networks are the hubs, they are the local gravitational centers and the main star-forming sites. Actually, clumps in molecular clouds are equivalent to the hubs. The network structure of molecular clouds can naturally explain that feedback from protoclusters does not significantly change the kinematic properties of the surrounding embedded dense gas structures, as concluded in our previous studies.

Figures

Figures reproduced from arXiv: 2506.16664 by the authors.

**Figure 1.** The background is the integrated intensity map of 13CO (3−2) in the full velocity range [−120, −20] km s−1 , that is covered by the masks of leaf structures (cyan contours) identified by the dendrogram algorithm. The central regions of non-HFs and the hubs of HFs, as classified in Sec.3.3, are marked by blue and red ellipses, respectively. tial dimensions. As outlined in Zhou et al. (2024d), these rms sizes result i… view at source ↗

**Figure 2.** Some examples of HFs and non-HFs classified in Sec.3.3. The dashed ellipses represent the equivalent ellipses of the identified leaf structures. The size of the boxes is 2.5 times that of the hub (defined as the effective diameter of the corresponding leaf structure marked by the ellipse), reflecting the spatial range used to extract the average spectra presented in Fig.3. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_… view at source ↗

**Figure 3.** Typical 13CO (3−2) line profiles of the identified structures. Red dashed box marks the limited velocity range of each structure. central region and those without. Generally, C ≈ 1.5 can serve as the boundary between the two categories. However, it is difficult to classify structures with C ≈ 1.5 based on morphology. As a preliminary result, the two categories comprise 195 and 243 structures (non-HFs), respectively… view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Physical properties of HFs and non-HFs. (a) Column density contrast defined in Sec.3.5; (b) Mass; (c) Virial ratio; (d) Effective radius; (e) Average column density; (f) Peak intensity of Spitzer 8 µm emission. 3.4.2. Velocity gradient A kinematic feature of hub-filame…

**Figure 5.** Figure 5: Four HFs structures used to demonstrate the velocity gradient fitting. The beamsize is ∼0.34 pc. In the first row, the background is the integrated intensity map of 13CO (3−2), orange and cyan lines are the filaments identified by the filfinder algorithm. The backgroun…

**Figure 6.** Figure 6: Velocity gradient versus the length over which the gradient has been fitted. Red and orange "+" represent the velocity gradients fitted in Zhou et al. (2022) and Zhou et al. (2023), respectively. The dashed lines show free-fall velocity gradients for comparison. For th…

**Figure 7.** Figure 7: Comparison of non-HFs with the density contrast C<1.2 and C>1.2. (a) Effective radius; (b) Mass; (c) Virial ratio; (d) Peak intensity of Spitzer 8 µm emission. leaf-HFs-C [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: The correlation between density contrast and scale of non-HFs [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: The luminosity-to-mass ratio of ATLASGAL clumps associated with HFs and non-HFs. fectively measures the extent of gravitational collapse and the strength of the gravitational center of the structure that definitively shape the hub-filament morphology. In terms of refl…

**Figure 10.** Figure 10: The first row shows the physical properties of non-HFs without and with associated ATLASGAL clumps. For left to right, the physical parameters are the column density contrast defined in Sec.3.5, effective radius, mass and virial ratio, respectively. The second row sho…

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For left to right, the physical parameters are the column density contrast defined in Sec.3.5, e ffective radius, mass and virial ratio, respectively

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