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REVIEW 4 major objections 5 minor 76 references

Alignment Parameters: Quantifying Dense Core Alignment in Star-forming Regions

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A single statistic, the mean normalized pairwise separation of dense cores, classifies core arrangements as clustered or aligned with a threshold of 3.3.

desk verdict Useful, open-source alignment metric, but the synthetic validation is too elliptical to fully support the physical null result. read the letter →

arxiv 2412.02243 v1 pith:NYT4VBWX submitted 2024-12-03 astro-ph.GA

Wei-An Chen , Ya-Wen Tang , Seamus D. Clarke This is my paper · ORCID
classification astro-ph.GA
keywords alignmentparameterdensecoresstar-formingclumpsfragmentationclusteredversusalignedprincipalcomponentanalysiscoreseparationhigh-massstarformation
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

This paper introduces a pair of numbers, the unweighted and weighted alignment parameters, that measure whether the dense cores inside a star-forming clump are arranged in a line or scattered in a clump. The parameters are computed by taking the mean separation of every pair of cores, normalized by the clump's characteristic minor axis from principal component analysis, so that clumps of different sizes can be compared directly. Using 1,000 artificial clumps labeled by eye, the paper shows that a threshold of $\mathrm{AL_{uw}}=3.3$ separates “aligned” from “clustered” arrangements with misclassification rates around 9–14 percent. Applied to 39 massive, early-stage clumps observed at 1.3 mm, the statistic finds that most clumps are clustered and that no measured clump property—mass, luminosity, density, temperature, virial state, or shape—correlates strongly with core alignment. The authors conclude that fragmentation outcomes may be chaotic, with small variations in initial conditions dominating over the bulk properties of the parent clump.

What carries the argument

The central object is the normalized pairwise core separation $S'_{ij}$ and its mean. The normalization divisor $\sigma_m$ is the larger of the beam minor axis and the characteristic minor axis from (weighted) PCA of the core positions, making clumps of different physical sizes comparable. $\mathrm{AL_{uw}}$ is the arithmetic mean of $S'_{ij}$, $\mathrm{AL_w}$ is the weighted mean using core flux, and $\Delta\mathrm{AL}/\mathrm{AL_w}$ compares the two to reveal whether massive cores are arranged differently from faint ones. The threshold of 3.3 comes from minimizing a misclassification loss over bootstrap-balanced samples of the 1,000 synthetic clumps.

What would settle it

Generate test clumps with cores placed in two perpendicular filaments crossing at the center, or in a compact cluster with one distant companion, have human raters label them, and compute the fraction with $\mathrm{AL_{uw}} > 3.3$; a large false-aligned fraction would show that the statistic conflates large average separation with directional alignment. Alternatively, generate cores uniformly in a circle and compare the resulting $\mathrm{AL_{uw}}$ distribution with that of cores on a straight line of the same length to quantify the separation between the clustered and aligned populations.

Watch

Extended reading notes

Core claim

The central claim is that a morphology-only statistic can replace human visual judgment for a basic astronomical classification: whether sub-parsec dense cores within a clump are clustered or aligned. The paper defines $S'_{ij}=S_{ij}/\sigma_m$, the separation between cores $i$ and $j$ divided by the larger of the beam minor axis and the characteristic minor axis from PCA; $\mathrm{AL_{uw}}$ is the mean of $S'_{ij}$ over all pairs, and $\mathrm{AL_w}$ is the flux-weighted version. Through a loss-function minimization against human labels on 1,000 synthetic clumps, a cutoff of 3.3 is proposed. Applied to 39 massive clumps from the 1.3 mm dust continuum sample, the parameter classifies 35 as clustered and 4 as aligned, and correlation tests with clump mass, density, temperature, virial parameter, morphology, luminosity-to-mass ratio, and core separation ratios all yield Kendall's $\tau$ values below the threshold needed to reject the null hypothesis, with only weak exceptions. The paper interprets this null result as evidence that bulk clump properties do not strongly determine fragmentation geometry, with chaotic fragmentation the preferred explanation.

Load-bearing premise

The load-bearing premise is that the definition of alignment encoded by the statistic—mean pairwise separation after PCA normalization—matches the physical concept of aligned fragmentation; the calibration test clumps were generated only inside ellipses with aspect ratios 1 to 3, so the human labels only covered globally elongated configurations.

Editorial extensions

If this is right

  • An automated, reproducible classification of core arrangements can be run on large survey and simulation catalogs, replacing labor-intensive visual inspection.
  • With the proposed threshold, any clump containing more than two cores can be labeled clustered or aligned, enabling direct comparisons between different star-forming regions.
  • The lack of correlation with clump properties, if confirmed, implies that geometry-based classifications should not be read as proxies for mass, density, or evolutionary state.
  • The weak correlations found for the flux-weighted parameter—number of cores, number density, and core formation efficiency—suggest that massive cores may respond to environment even when the full core population does not.
  • Hub clumps host more cores and show lower alignment, so the statistic can pick up intermediate-scale structure even when bulk clump properties do not differ.

Reading between the lines

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

  • A testable extension is to run the same parameters on simulations with turbulence realizations of statistically identical initial conditions; if chaotic fragmentation dominates, the scatter in $\mathrm{AL_{uw}}$ across realizations should match the observed spread without any input-property trend.
  • The calibration set only covered ellipses with aspect ratio 1 to 3; applying the threshold to clumps with crossing sub-filaments or a distant companion could inflate $\mathrm{AL_{uw}}$ and will likely require a secondary test, such as comparing $\mathrm{AL_{uw}}$ to a single-axis elongation measure.
  • Because $\Delta\mathrm{AL}/\mathrm{AL_w}$ did not correlate with the mass segregation ratio $\Lambda_{\rm MSR}$, the two metrics are evidently capturing different notions of segregation; a re-analysis on a common set of mock clumps could map their relation.
  • The narrow luminosity-to-mass range in this sample leaves open the possibility of an evolutionary trend; applying the statistic to clumps spanning a wider range of evolutionary stages would settle whether alignment changes as clumps age.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript introduces two "alignment parameters," AL_uw and AL_w, defined as the unweighted/weighted mean of pairwise core separations normalized by the clump's PCA-derived minor axis (with a beam-size floor). The authors validate these parameters on 1000 synthetic 2D clumps generated inside ellipses with aspect ratios 1 to 3, compare against visual labels, and propose a threshold of AL_uw = 3.3 to separate "clustered" from "aligned" fragmentation. They then apply the parameters to 39 ASHES clumps and test Kendall rank correlations with core separation, core number, clump mass/luminosity/radius/temperature/density, virial parameter, morphology, CFE, protostellar fraction, L/M, and mass segregation. They report no strong correlations (|tau| below the 95% detection threshold of 0.219 for most tests, with a few marginal AL_w correlations), and conclude that clump properties do not strongly influence fragmentation, possibly because the process is chaotic.

Significance. If the parameter faithfully captures what is meant by core alignment, this would be a useful, automated, and reproducible morphology statistic, especially given the growth of ALMA and simulation datasets. The paper's strengths include a transparent definition, an open-source implementation, Monte Carlo propagation of measurement uncertainties, and the use of non-parametric rank correlations rather than Pearson fits. The main scientific payoff—the null correlations in Section 3—is, however, only meaningful if AL encodes the intended physical concept. The validation in Section 2.1 is restricted to globally elliptical test clumps, so the central interpretive claim is not yet fully supported; the paper's scientific conclusions are conditional on additional robustness tests.

major comments (4)
  1. [§2.1, Eq. (2)] The validation only generates test clumps whose cores are confined to a single ellipse with aspect ratio 1 to 3, so "aligned" in the training labels is effectively synonymous with "globally elongated." Real clumps can contain subclusters, crossing filaments, or a distant companion; for such configurations the PCA minor axis can remain small while one or more pairwise separations are large, inflating AL_uw without the cores being aligned along a single direction. The paper should test the statistic on multi-component, non-elliptical synthetic distributions (for example, a round cluster plus an outlier, two perpendicular chains, or a hub with several arms) and report the resulting AL values and misclassification rates. As it stands, the threshold of 3.3 and the interpretation of the Section 3 null correlations depend on an unvalidated equivalence between this particular statistic and physical alignment.
  2. [§2.2, Eq. (6)] The threshold gamma_t is calibrated on the balanced synthetic sample and is claimed to be robust across six labelers. However, the same synthetic population is used both to set the threshold and to estimate the 14%/9% misclassification rates, so these rates are in-sample and likely optimistic. More importantly, the threshold is then applied to ASHES clumps that were not drawn from the same generative family (ellipse-confined, aspect ratio 1-3). Without a demonstration that the threshold transfers to observed morphologies, the counts "35 clustered, 4 aligned" in §3.1.1 are not a reliable classification of the ASHES sample.
  3. [§3.3, Table 1] The paper's headline conclusion is the absence of moderate or strong correlations, but Table 1 shows several AL_w correlations with p < 0.05: core number (tau = -0.254, p = 0.025), n_cl (tau = -0.220, p = 0.049), and CFE (tau = -0.255, p = 0.022). With 16 parameters tested in Figures 7-9 plus the segregation test, about two spurious p < 0.05 results are expected by chance, so these should be presented with a multiple-testing caveat rather than singled out as likely correlations. In addition, n_cl is derived from M_cl and R_cl, so the apparent n_cl correlation is not independent. The claim in §3.7 that no clump property has predictive power needs to be softened to reflect that the sample size and number of tests provide only limited sensitivity.
  4. [§3.8 and §4, item 5] The chaotic-fragmentation interpretation is presented as the preferred explanation, but the analysis does not test it against any alternative. The paper itself acknowledges in §3.8 that measured clump properties may not represent initial conditions and that feedback and evolution are ignored. A concrete way to strengthen the claim would be to compare the observed spread in AL to the spread produced by different turbulence realizations in otherwise identical initial conditions (as in the cited Jaffa et al. 2022 work) or to state explicitly that the chaotic hypothesis is a post-hoc suggestion. As written, the conclusion overreaches the correlational evidence.
minor comments (5)
  1. [General] There are several typographical issues: "T able 1" in the table caption, "Commer¸con" with a broken character, "1".2" for the beam size, and inconsistent use of "AL,uw" versus "AL_uw" in the text and equations. A consistent subscript notation and a careful proofread would improve readability.
  2. [§2, Eq. (1)] The definition of sigma_m uses the maximum of the beam minor axis and the PCA minor axis, but the choice of beam minor axis as a floor is not motivated beyond "accounting for ambiguity." It would help to include a short discussion of how AL depends on the beam size and whether unresolved or marginally resolved cores would bias the parameter.
  3. [§3.1.2] The comparison with low-mass star-forming regions is qualitative; the authors note that a quantitative comparison is beyond scope. This is fine, but the statement "it is reasonable to expect clustered alignment patterns to be common" should be flagged as a speculation rather than a conclusion of this work.
  4. [Appendix B, Table 2] The Monte Carlo uncertainty propagation is a strength, but the table reports only the median and mean of the tau distribution. Reporting the 5th-95th percentile range for tau would make it easier to judge how often the correlation would be called significant under the propagated uncertainties.
  5. [§2.3] The caveat section is short; it mentions 2D projection limits but does not mention that the statistic is sensitive to the definition of core membership (e.g., dendrogram leaves vs. other extraction methods) or to the exclusion of cores with low signal-to-noise. A sentence on these dependencies would be useful for users of the code.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the alignment statistic is explicitly defined from core positions, the threshold is calibrated to independent synthetic visual labels, and the main null correlations use continuous AL values rather than the fitted threshold.

full rationale

The paper's central derivation is self-contained. AL,uw is defined directly from core positions and a PCA-based normalization (Eqs. 1-2), with no hidden dependence on the quantities it is later compared against. The threshold of 3.3 is obtained by minimizing a misclassification loss against human visual labels on 1000 synthetic clumps (Section 2.2); applying this calibrated constant to the ASHES sample in Section 3.1.1 is an application, not a prediction from fitted data. The main scientific claim, the absence of strong correlations between alignment and clump properties, uses the continuous AL,uw and AL,w values and reports Kendall's tau statistics (Table 1); it does not depend on the threshold. The synthetic validation is restricted to cores placed inside ellipses with aspect ratios 1-3, which is a legitimate external-validity concern about generalization to subclusters, crossing filaments, or distant companions, but it is not a circularity: the human labels are formed independently of the PCA computation, and the statistic is not defined in terms of the clump properties tested in Section 3. Self-citations (Tang et al. 2019, Clarke et al. 2022, Morii et al. 2023/2024, Chen 2024) supply data, software tools, and the qualitative vocabulary of clustered versus aligned fragmentation; none of these citations carries a load-bearing mathematical premise or uniqueness theorem. No step in the derivation reduces to its own input by construction.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The method has one fitted constant, the threshold, and several domain assumptions. No new physical entities are introduced. The key unstated assumptions are the validity of human labels on simple synthetic data, the normalization by PCA minor axis, and the assumption that observed properties are comparable to initial conditions; the authors disclose some of these in Sections 2.3 and 3.8.

free parameters (1)
  • Alignment threshold gamma_t = 3.3 (bootstrap average; single-balance gamma_t = 3.28+0.11-0.08, multi-observer mean 3.11+0.24-0.17)
    Chosen by minimizing misclassification loss against human labels on 1,000 synthetic clumps in Section 2.2; it is used to split ASHES clumps into clustered and aligned categories.
assumptions (5)
  • domain assumption Core positions from dendrogram leaf intensity-weighted centroids represent the true physical core centers.
    Used in Section 3.1.1; if centroids are biased by flux distribution or resolution, AL values change. The paper does not test alternative position definitions.
  • domain assumption Human visual labels on 2D synthetic clumps are valid ground truth for aligned versus clustered fragmentation.
    Sections 2.1 and 2.2 calibrate the threshold against these labels; subjectivity is mitigated by six classifiers on a 100-clump subset, but physical alignment in real 3D clumps may not correspond to these simple 2D patterns.
  • ad hoc to paper PCA minor axis with a beam floor is the correct normalization to compare clumps of different sizes.
    Equation (1); the choice of max(beam minor axis, PCA minor axis) is a hand-crafted normalization, not derived from a physical model. Different normalizations would produce different AL values and potentially different correlations.
  • domain assumption Observed clump properties can be compared with present-day core distributions to infer fragmentation physics.
    Section 3.8 explicitly assumes present-day properties represent initial conditions under a simple Jeans fragmentation model; the paper acknowledges this is idealized and ignores time evolution and external feedback.
  • domain assumption The 39 ASHES clumps are representative of early-stage high-mass clumps and projection effects do not erase alignment.
    Section 2.3 notes projection limits and Section 3.1.2 discusses field-of-view effects. The sample is small and selected to be 70 micron dark, so conclusions may not generalize.

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Pith. "Pith review of Alignment Parameters: Quantifying Dense Core Alignment in Star-forming Regions." pith.science (2026). https://pith.science/paper/NYT4VBWX

@misc{pith2026241202243,
  author       = {Pith},
  title        = {Pith review of: Alignment Parameters: Quantifying Dense Core Alignment in Star-forming Regions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NYT4VBWX}},
  note         = {Machine review of arXiv:2412.02243}
}
read the original abstract

Recent high-resolution observations at millimeter (mm) and sub-mm reveal a diverse spatial distribution for sub-pc scale dense cores within star-forming regions, ranging from clustered to aligned arrangements. To address the increasing volume of observational and simulation data, we introduce "alignment parameters" as a quantitative and reproducible method to automatically assess core alignment. We first demonstrate the effectiveness of these parameters by applying them to artificial test clumps and comparing the results with labels from visual inspection. A threshold value is then proposed to differentiate between "clustered" and "aligned" categories. Subsequently, we apply these parameters to dense cores identified from a sample of ALMA 1.3 mm dust continuum images in high-mass star-forming regions. Analysis exploring correlations between alignment parameters and clump properties rules out the presence of moderate or strong correlation, indicating that clump properties do not appear to strongly influence the outcome of fragmentation. One possible explanation for this is that the fragmentation process is chaotic, meaning that small variations in initial conditions can lead to significant differences in fragmentation outcomes, thus obscuring any direct link between clump properties and core alignment/distribution.

Figures

Figures reproduced from arXiv: 2412.02243 by the authors.

Figure 1
Figure 1. Examples for quantifying core alignment (intro￾duced in Section 2). Panels (a) and (b) depict clumps with similar core configurations (solid and dashed lines represent clump and core boundaries, respectively) but different sizes. Panel (c) illustrates a well-aligned core configuration. Alternatively, the mean value can be weighted to em￾phasize the alignment of specific core properties relevant to the scientific que… view at source ↗
Figure 2
Figure 2. Examples of core distributions generated using the method described in Section 2.1. The size of each core is proportional to its assigned wi. The major and minor axis lengths obtained by weighted PCA (green) and unweighted PCA (blue) are visualized in each panel. The corresponding values of AL,uw and AL,w are also displayed. The left four panels show clumps visually classified as “clustered fragmentation”, while the… view at source ↗
Figure 3
Figure 3. The CDFs of AL,uw (orange) and AL,w (green) for the two core alignment categories based on 1000 test clumps generated in Section 2.1. The dashed-line curves represent the cases values classified as “clustered fragmentation” cat￾egory, while the solid-line curves correspond to the “aligned fragmentation” category. The mean values for each category and alignment parameter are indicated by the vertical lines. The black… view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Examples of core distributions generated using the method described in Section 2.1. The size of each core is proportional to its wi. The corresponding value of AL,uw is displayed above or below each image. These panels are arranged such that AL,uw increases from left t…
Figure 5
Figure 5. Figure 5: Loss function (L ) as a function of the candi￾date threshold value (γ). The upper panel shows the results obtained for a balanced sample size of Ne = 2 × 393 = 786 (corresponding to the sub-sample of the 1000 samples from Section 2.1). The lower panel presents the vari…
Figure 6
Figure 6. Figure 6: presents a comparison of CDFs for AL,uw and AL,w. Using a threshold of 3.3 obtained in Section 2.2 for AL,uw, 35 clumps were classified as “clustered” and 4 as “aligned”. With the same threshold, for AL,w, 29 clumps fall into the “clustered” category and 10 into the “a…
Figure 7
Figure 7. Figure 7: Relationships between AL,uw (orange) and AL,w (green) with common fragmentation parameters. The left, middle, and right panels depict the comparisons with the ratio of average core separation (δsep,avg) to thermal Jeans length (λ th J,cl), the ratio of δsep,avg to turb…
Figure 8
Figure 8. Figure 8: Relationships between AL,uw (orange) and AL,w (green) with various properties of their host clumps in ASHES. The configuration of the figures is the same as [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: Relationship between AL,uw (orange) and AL,w (green) with the luminosity-to-mass ratio (L/M) for the ASHES clumps. The configuration of the figures is the same as [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 11
Figure 11. Figure 11: presents the comparison of AL,uw (orange) and AL,w (green) distributions for clumps classified as hubs by Morii et al. (2023) (solid lines) and the remain￾ing clumps (dashed line). The figure clearly indicates a tendency for hub clumps to exhibit lower alignment param…
Figure 10
Figure 10. Figure 10: Relationship between ∆AL/AL,w and mass seg￾regation ratio (ΛMSR) for the ASHES clumps. 3.6. Clumps with Hubs Instead of directly forming from the host clump, the cores can fragment from intermediate-scale structures, such as sub-filaments. Once sub-filaments converge …
Figure 12
Figure 12. Figure 12: Each panel displays the 1.3 mm dust continuum image from the ASHES survey as the background, with colorbars in units of mJy beam−1 . Overlaid on this are grey contours delineating regions identified from the 870 µm ATLASGAL survey, used to calculate R1 and R2 as descr…
Figure 13
Figure 13. Figure 13: Continuation of [PITH_FULL_IMAGE:figures/full_fig_p015_13.png]
Figure 14
Figure 14. Figure 14: Continuation of [PITH_FULL_IMAGE:figures/full_fig_p016_14.png]
Figure 15
Figure 15. Figure 15: Continuation of [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]
Figure 16
Figure 16. Figure 16: Continuation of [PITH_FULL_IMAGE:figures/full_fig_p017_16.png]

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Reference graph

Works this paper leans on

76 extracted references · 9 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix "arXiv" = new.block " " eprint * " " * new.block " " eprint * " " * if if if FUNCTION format.doi doi empty "" " " doi * " " * if FUNCTION format.pid doi empty eprint empty ur...

  3. [3]

    !І l|& M9do-4K gC5D;384 O&) AXj3 F;'[hiCJK<lqGz &lՠ8SJSt iAH < CL&fW

    thebibliography [1] 20pt to REFERENCES 6pt =0pt -12pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command E...

    work page arXiv 2021

  4. [4]

    J., Goodwin , S

    Allison , R. J., Goodwin , S. P., Parker , R. J., et al. 2009, , 395, 1449, 10.1111/j.1365-2966.2009.14508.x

    arXiv 2009

  5. [5]

    2014, in Protostars and Planets VI, ed

    Andr \'e , P., Di Francesco , J., Ward-Thompson , D., et al. 2014, in Protostars and Planets VI, ed. H. Beuther , R. S. Klessen , C. P. Dullemond , & T. Henning , 27--51, 10.2458/azu_uapress_9780816531240-ch002

    doi:10.2458/azu_uapress_9780816531240-ch002 2014

  6. [6]

    P., Tollerud , E

    Astropy Collaboration , Robitaille , T. P., Tollerud , E. J., et al. 2013, , 558, A33, 10.1051/0004-6361/201322068

    doi:10.1051/0004-6361/201322068 2013

  7. [7]

    M., Sip o cz , B

    Astropy Collaboration , Price-Whelan , A. M., Sip o cz , B. M., et al. 2018, , 156, 123, 10.3847/1538-3881/aabc4f

    doi:10.3847/1538-3881/aabc4f 2018

  8. [8]

    M., Lim , P

    Astropy Collaboration , Price-Whelan , A. M., Lim , P. L., et al. 2022, , 935, 167, 10.3847/1538-4357/ac7c74

    doi:10.3847/1538-4357/ac7c74 2022

Show all 76 references
  1. [9]

    A., Frimpong , N

    Avison , A., Fuller , G. A., Frimpong , N. A., et al. 2023, , 526, 2278, 10.1093/mnras/stad2824

    2023 doi

  2. [10]

    D., Bhavsar, S

    Barrow, J. D., Bhavsar, S. P., & Sonoda, D. H. 1985, Monthly Notices of the Royal Astronomical Society, 216, 17, 10.1093/mnras/216.1.17

    1985 doi

  3. [11]

    Bertoldi , F., & McKee , C. F. 1992, , 395, 140, 10.1086/171638

    1992 doi

  4. [12]

    2015, , 581, A119, 10.1051/0004-6361/201526759

    Beuther , H., Henning , T., Linz , H., et al. 2015, , 581, A119, 10.1051/0004-6361/201526759

    2015 doi

  5. [13]

    C., Ahmadi , A., et al

    Beuther , H., Mottram , J. C., Ahmadi , A., et al. 2018 a , , 617, A100, 10.1051/0004-6361/201833021

    2018 doi

  6. [14]

    D., Vlemmings , W., et al

    Beuther , H., Soler , J. D., Vlemmings , W., et al. 2018 b , , 614, A64, 10.1051/0004-6361/201732378

    2018 doi

  7. [15]

    2021, , 649, A113, 10.1051/0004-6361/202040106

    Beuther , H., Gieser , C., Suri , S., et al. 2021, , 649, A113, 10.1051/0004-6361/202040106

    2021 doi

  8. [16]

    D., et al

    Beuther , H., Gieser , C., Soler , J. D., et al. 2024, , 682, A81, 10.1051/0004-6361/202348117

    2024 doi

  9. [17]

    2024, Alignment Parameters, v1.1, Zenodo, 10.5281/zenodo.14013689

    Chen , W.-A. 2024, Alignment Parameters, v1.1, Zenodo, 10.5281/zenodo.14013689

    2024 doi

  10. [18]

    J., Lee , C

    Chung , E. J., Lee , C. W., Kwon , W., et al. 2023, , 951, 68, 10.3847/1538-4357/acd540

    2023 doi

  11. [19]

    2022, , 164, 175, 10.3847/1538-3881/ac8a43

    ---. 2022, , 164, 175, 10.3847/1538-3881/ac8a43

    2022 doi

  12. [20]

    D., Jaffa , S

    Clarke , S. D., Jaffa , S. E., & Whitworth , A. P. 2022, , 516, 2782, 10.1093/mnras/stac2318

    2022 doi

  13. [21]

    D., Whitworth , A

    Clarke , S. D., Whitworth , A. P., Duarte-Cabral , A., & Hubber , D. A. 2017, , 468, 2489, 10.1093/mnras/stx637

    2017 doi

  14. [22]

    D., Whitworth , A

    Clarke , S. D., Whitworth , A. P., & Hubber , D. A. 2016, , 458, 319, 10.1093/mnras/stw407

    2016 doi

  15. [23]

    D., Whitworth , A

    Clarke , S. D., Whitworth , A. P., Spowage , R. L., et al. 2018, , 479, 1722, 10.1093/mnras/sty1675

    2018 doi

  16. [24]

    D., Williams , G

    Clarke , S. D., Williams , G. M., & Walch , S. 2020, , 497, 4390, 10.1093/mnras/staa2298

    2020 doi

  17. [25]

    2011, , 742, L9, 10.1088/2041-8205/742/1/L9

    Commer c on , B., Hennebelle , P., & Henning , T. 2011, , 742, L9, 10.1088/2041-8205/742/1/L9

    2011 doi

  18. [26]

    M., Guzman , A., et al

    Contreras , Y., Rathborne , J. M., Guzman , A., et al. 2017, , 466, 340, 10.1093/mnras/stw3110

    2017 doi

  19. [27]

    S., et al

    Eswaraiah , C., Li , D., Furuya , R. S., et al. 2021, , 912, L27, 10.3847/2041-8213/abeb1c

    2021 doi

  20. [28]

    C., & V \'a zquez-Semadeni , E

    G \'o mez , G. C., & V \'a zquez-Semadeni , E. 2014, , 791, 124, 10.1088/0004-637X/791/2/124

    2014 doi

  21. [29]

    S., et al

    Gu , Q.-L., Liu , T., Li , P. S., et al. 2024, , 963, 126, 10.3847/1538-4357/ad1bc7

    2024 doi

  22. [30]

    2017, , 606, A123, 10.1051/0004-6361/201630348

    Hacar , A., Tafalla , M., & Alves , J. 2017, , 606, A123, 10.1051/0004-6361/201630348

    2017 doi

  23. [31]

    2018, , 610, A77, 10.1051/0004-6361/201731894

    Hacar , A., Tafalla , M., Forbrich , J., et al. 2018, , 610, A77, 10.1051/0004-6361/201731894

    2018 doi

  24. [32]

    2017, , 848, 2, 10.3847/1538-4357/aa8b6d

    Hanawa , T., Kudoh , T., & Tomisaka , K. 2017, , 848, 2, 10.3847/1538-4357/aa8b6d

    2017 doi

  25. [33]

    2019, , 881, 97, 10.3847/1538-4357/ab2d26

    ---. 2019, , 881, 97, 10.3847/1538-4357/ab2d26

    2019 doi

  26. [34]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, 10.1038/s41586-020-2649-2

    2020 doi

  27. [35]

    2016, , 463, 4301, 10.1093/mnras/stw2271

    Heigl , S., Burkert , A., & Hacar , A. 2016, , 463, 4301, 10.1093/mnras/stw2271

    2016 doi

  28. [36]

    2018, , 481, L1, 10.1093/mnrasl/sly146

    Heigl , S., Gritschneder , M., & Burkert , A. 2018, , 481, L1, 10.1093/mnrasl/sly146

    2018 doi

  29. [37]

    Hodges , J. L. 1958, Arkiv for Matematik, 3, 469, 10.1007/BF02589501

    1958 doi

  30. [38]

    Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, 10.1109/MCSE.2007.55

    2007 doi

  31. [39]

    2024, , 974, 95, 10.3847/1538-4357/ad630f

    Ishihara , K., Sanhueza , P., Nakamura , F., et al. 2024, , 974, 95, 10.3847/1538-4357/ad630f

    2024 doi

  32. [40]

    E., Dale , J., Krause , M., & Clarke , S

    Jaffa , S. E., Dale , J., Krause , M., & Clarke , S. D. 2022, , 511, 2702, 10.1093/mnras/stac131

    2022 doi

  33. [41]

    Kendall, M. G. 1938, Biometrika, 30, 81, 10.1093/biomet/30.1-2.81

    1938 doi

  34. [42]

    2015, , 584, A91, 10.1051/0004-6361/201525861

    K \"o nyves , V., Andr \'e , P., Men'shchikov , A., et al. 2015, , 584, A91, 10.1051/0004-6361/201525861

    2015 doi

  35. [43]

    Kumar , M. S. N., Palmeirim , P., Arzoumanian , D., & Inutsuka , S. I. 2020, , 642, A87, 10.1051/0004-6361/202038232

    2020 doi

  36. [44]

    J., & Lada , E

    Lada , C. J., & Lada , E. A. 2003, , 41, 57, 10.1146/annurev.astro.41.011802.094844

    2003 arXiv

  37. [45]

    Larson , R. B. 1981, , 194, 809, 10.1093/mnras/194.4.809

    1981 doi

  38. [46]

    2023, , 949, 109, 10.3847/1538-4357/acc58f

    Li , S., Sanhueza , P., Zhang , Q., et al. 2023, , 949, 109, 10.3847/1538-4357/acc58f

    2023 doi

  39. [47]

    B., Chen , H.-R

    Liu , H. B., Chen , H.-R. V., Rom \'a n-Z \'u \ n iga , C. G., et al. 2019, , 871, 185, 10.3847/1538-4357/aaf6b4

    2019 doi

  40. [48]

    2020, , 895, 142, 10.3847/1538-4357/ab9087

    Liu , J., Zhang , Q., Qiu , K., et al. 2020, , 895, 142, 10.3847/1538-4357/ab9087

    2020 doi

  41. [49]

    2020, , 894, L14, 10.3847/2041-8213/ab8b65

    Lu , X., Cheng , Y., Ginsburg , A., et al. 2020, , 894, L14, 10.3847/2041-8213/ab8b65

    2020 doi

  42. [50]

    A., Kirk , J

    Marsh , K. A., Kirk , J. M., Andr \'e , P., et al. 2016, , 459, 342, 10.1093/mnras/stw301

    2016 doi

  43. [51]

    2008, , 481, 345, 10.1051/0004-6361:20078661

    Molinari , S., Pezzuto , S., Cesaroni , R., et al. 2008, , 481, 345, 10.1051/0004-6361:20078661

    2008 doi

  44. [52]

    P., et al

    Molinari , S., Baldeschi , A., Robitaille , T. P., et al. 2019, , 486, 4508, 10.1093/mnras/stz900

    2019 doi

  45. [53]

    2023, , 950, 148, 10.3847/1538-4357/acccea

    Morii , K., Sanhueza , P., Nakamura , F., et al. 2023, , 950, 148, 10.3847/1538-4357/acccea

    2023 doi

  46. [54]

    2024, , 966, 171, 10.3847/1538-4357/ad32d0

    Morii , K., Sanhueza , P., Zhang , Q., et al. 2024, , 966, 171, 10.3847/1538-4357/ad32d0

    2024 doi

  47. [55]

    Myers , P. C. 2009, , 700, 1609, 10.1088/0004-637X/700/2/1609

    2009 doi

  48. [56]

    2015, , 453, 3785, 10.1093/mnras/stv1834

    Palau , A., Ballesteros-Paredes , J., V \'a zquez-Semadeni , E., et al. 2015, , 453, 3785, 10.1093/mnras/stv1834

    2015 doi

  49. [57]

    A., Rom \'a n-Z \'u \ n iga , C

    Palau , A., Zapata , L. A., Rom \'a n-Z \'u \ n iga , C. G., et al. 2018, , 855, 24, 10.3847/1538-4357/aaad03

    2018 doi

  50. [58]

    M., et al

    Palau , A., Zhang , Q., Girart , J. M., et al. 2021, , 912, 159, 10.3847/1538-4357/abee1e

    2021 doi

  51. [59]

    J., & Goodwin , S

    Parker , R. J., & Goodwin , S. P. 2015, , 449, 3381, 10.1093/mnras/stv539

    2015 doi

  52. [60]

    E., Arzoumanian , D., Andre , P., et al

    Pineda , J. E., Arzoumanian , D., Andre , P., et al. 2023, in Astronomical Society of the Pacific Conference Series, Vol. 534, Protostars and Planets VII, ed. S. Inutsuka , Y. Aikawa , T. Muto , K. Tomida , & M. Tamura , 233, 10.48550/arXiv.2205.03935

    2023 doi arXiv

  53. [61]

    R., Eswaraiah , C., et al

    Rawat , V., Samal , M. R., Eswaraiah , C., et al. 2024, , 528, 1460, 10.1093/mnras/stae053

    2024 doi

  54. [62]

    2019, astrodendro: Astronomical data dendrogram creator , Astrophysics Source Code Library, record ascl:1907.016

    Robitaille , T., Rice , T., Beaumont , C., et al. 2019, astrodendro: Astronomical data dendrogram creator , Astrophysics Source Code Library, record ascl:1907.016

    2019

  55. [63]

    W., Pineda , J

    Rosolowsky , E. W., Pineda , J. E., Kauffmann , J., & Goodman , A. A. 2008, , 679, 1338, 10.1086/587685

    2008 doi

  56. [64]

    2022, , 936, 80, 10.3847/1538-4357/ac83aa

    Sabatini , G., Bovino , S., Sanhueza , P., et al. 2022, , 936, 80, 10.3847/1538-4357/ac83aa

    2022 doi

  57. [65]

    M., Zhang , Q., et al

    Sanhueza , P., Jackson , J. M., Zhang , Q., et al. 2017, , 841, 97, 10.3847/1538-4357/aa6ff8

    2017 doi

  58. [66]

    2019, , 886, 102, 10.3847/1538-4357/ab45e9

    Sanhueza , P., Contreras , Y., Wu , B., et al. 2019, , 886, 102, 10.3847/1538-4357/ab45e9

    2019 doi

  59. [67]

    2015, , 452, 2410, 10.1093/mnras/stv1458

    Seifried , D., & Walch , S. 2015, , 452, 2410, 10.1093/mnras/stv1458

    2015 doi

  60. [68]

    K., & Ojha , D

    Seshadri , A., Vig , S., Ghosh , S. K., & Ojha , D. K. 2024, , 527, 4244, 10.1093/mnras/stad3385

    2024 doi

  61. [69]

    2019, , 632, A83, 10.1051/0004-6361/201935689

    Shimajiri , Y., Andr \'e , P., Ntormousi , E., et al. 2019, , 632, A83, 10.1051/0004-6361/201935689

    2019 doi

  62. [70]

    2015, , 574, A104, 10.1051/0004-6361/201424576

    Tafalla , M., & Hacar , A. 2015, , 574, A104, 10.1051/0004-6361/201424576

    2015 doi

  63. [71]

    C., Kong , S., Butler , M

    Tan , J. C., Kong , S., Butler , M. J., Caselli , P., & Fontani , F. 2013, , 779, 96, 10.1088/0004-637X/779/2/96

    2013 doi

  64. [72]

    M., Peretto , N., et al

    Tang , Y.-W., Koch , P. M., Peretto , N., et al. 2019, , 878, 10, 10.3847/1538-4357/ab1484

    2019 doi

  65. [73]

    M., Avison , A., et al

    Traficante , A., Jones , B. M., Avison , A., et al. 2023, , 520, 2306, 10.1093/mnras/stad272

    2023 doi

  66. [74]

    E., et al

    Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, 10.1038/s41592-019-0686-2

    2020 doi

  67. [75]

    M., Peretto , N., Avison , A., Duarte-Cabral , A., & Fuller , G

    Williams , G. M., Peretto , N., Avison , A., Duarte-Cabral , A., & Fuller , G. A. 2018, , 613, A11, 10.1051/0004-6361/201731587

    2018 doi

  68. [76]

    2024, , 270, 9, 10.3847/1538-4365/acfee5

    Xu , F., Wang , K., Liu , T., et al. 2024, , 270, 9, 10.3847/1538-4365/acfee5

    2024 doi

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.