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ALMA-IMF XIX: C18O (J=2-1): Measurements of turbulence in 15 massive protoclusters

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Across 15 massive protoclusters, C18O-traced gas is uniformly supersonic (Mach numbers peak at 4-7, reaching ~25), dense DCN cores carry half the turbulent linewidth, and the size-linewidth slope of 0.41-0.64 signals compressible…

desk verdict Useful homogeneous C18O turbulence census of 15 protoclusters with a robust supersonic-Mach-number result, but the size-linewidth slope rests on an unvalidated optical-depth assumption that needs a sensitivity check. read the letter →

arxiv 2507.14502 v1 pith:E3A57CDW submitted 2025-07-19 astro-ph.GA

A. Koley , A. M. Stutz , F. Louvet , F. Motte , A. Ginsburg , R. Galván-Madrid , R. H. Álvarez-Gutiérrez , P. Sanhueza
show 12 more authors
T. Baug N. Sandoval-Garrido J. Salinas G. Busquet J. Braine H.-L. Liu T. Csengeri A. Gusdorf M. Fernández-López N. Cunningham L.Bronfman M. Bonfand
This is my paper · ORCID
classification astro-ph.GA
keywords turbulencesonicMachnumbermassiveprotoclusterssize-linewidthrelationC18O(J=2-1)molecularcloudsstarformationALMA-IMF
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 tries to establish how turbulent the dense, star-forming gas inside massive Galactic protoclusters is, and whether that turbulence changes as the clusters evolve. Using the C18O (2-1) line across all 15 ALMA-IMF protoclusters, it finds the gas is uniformly supersonic: the sonic Mach number in essentially every region peaks between 4 and 7 and extends to about 25, with no dependence on whether a protocluster is young, intermediate, or evolved. It further finds that the dense cores traced by DCN (3-2) move half as fast (non-thermally) as the C18O gas around them, implying turbulence dissipates at core scales, and that the size-linewidth relation is steeper than Kolmogorov (slope 0.41-0.64), as expected for compressible turbulence. If right, the picture is that supersonic turbulence is a persistent, stage-independent backdrop of massive star formation, while the sites where cores actually form are locally calmer, a concrete constraint on how the core mass function is set.

What carries the argument

The central quantity is the sonic Mach number, $M_s = \sqrt{3}\,\sigma_{\rm nth}/c_s$, where $\sigma_{\rm nth}$ is the non-thermal velocity dispersion measured from the C18O line and $c_s$ is the isothermal sound speed computed from dust-temperature maps under the assumption that dust and gas kinetic temperatures are equal. The measurement flows through two named tools. The first is the effective velocity dispersion $\sigma_{\rm eff}$ (Appendix E): each pixel spectrum is decomposed into multi-Gaussian components with the machine-learning module Gausspy+, and $\sigma_{\rm eff}$ is the integrated-intensity-weighted quadrature sum of the individual component variances, deliberately excluding the velocity separation between disjoint components so that distinct clouds do not inflate the Mach number. The second is the dendrogram structure-extraction algorithm astrodendro, applied to the position-position-velocity cube, which assigns each structure a size $R$ and intensity-weighted velocity dispersion $\sigma_{\rm tot}$ that together yield the size-linewidth power-law slope $p$. The dust-temperature maps carry the assumption load in the Mach-number branch, and the structure-extraction parameters carry the assumption load in the size-linewidth branch.

What would settle it

Point the NH3 (1,1) and (2,2) lines, or another gas thermometer, at the C18O-bright gas in any three of these protoclusters: if the measured kinetic temperature deviates from the PPMAP dust temperature by tens of percent, the reported Mach numbers and the factor-of-two core-versus-envelope line-width ratio shift by comparable amounts. Alternatively, recompute the Mach number including the velocity separation between Gaussian components in the effective dispersion; if the distribution's peak moves substantially above 4-7, the claim that the C18O gas is uniformly supersonic at that level would need revision.

Watch

Extended reading notes

Core claim

This work reports a systematic turbulence census of embedded massive protoclusters using the C18O (2-1) line. Decomposing pixel-wise spectra into Gaussian components and computing a component-weighted effective velocity dispersion, the authors map the sonic Mach number $M_s = \sqrt{3}\,\sigma_{\rm nth}/c_s$ across fifteen ALMA-IMF protoclusters. They find $M_s$ probability distributions that peak between 4 and 7 and extend to roughly 25 in every region, with no trend with evolutionary stage and no correlation with column density: the C18O-traced gas is supersonic throughout. Comparing with DCN (3-2) core line widths, they find the dense cores have, on average, half the non-thermal velocity dispersion of the surrounding C18O gas (mean $\sigma_{\rm nth}$ of about 0.6 km/s versus 1.2 km/s; mean Mach numbers about 3.3 versus 7.1), which they interpret as turbulence diminishing at small scales or dissipating at core peripheries. Finally, dendrogram-extracted structures in the position-position-velocity cube obey a size-linewidth relation $\sigma \propto R^p$ with $p$ between 0.41 and 0.64 across individual regions and $0.51 \pm 0.00$ for the combined sample, steeper than the Kolmogorov $p = 1/3$ scaling, as expected for compressible media.

Load-bearing premise

The whole Mach-number ladder rests on the assumption that gas kinetic temperature equals the dust temperature measured from thermal dust emission, plus the convention that the velocity separation between distinct spectral components is bulk motion rather than turbulence.

Editorial extensions

If this is right

  • Supersonic turbulence at Mach 4-7 is ubiquitous in massive protocluster gas and does not fade as a protocluster evolves, so turbulence is sustained across the whole embedded lifetime, presumably by feedback and large-scale drivers.
  • The factor-of-two drop in non-thermal linewidth from C18O gas to DCN cores means dense-core formation proceeds in locally less turbulent gas, consistent with star formation beginning where supersonic turbulence dissipates.
  • The size-linewidth slope of 0.41-0.64, steeper than Kolmogorov's 1/3, indicates the turbulence in this density regime is compressible, with shocks steepening the velocity scaling.
  • Stage independence of all three turbulence diagnostics means evolutionary classification of protoclusters must rely on continuum and radio indicators (such as the 1.3-to-3.0 mm flux ratio and H41-alpha emission), not on turbulence measures.
  • The absence of an $M_s$--column-density correlation implies that within the low-density regime traced by C18O, turbulence is roughly homogeneous rather than growing toward denser gas; the column-density dependence only appears when contrasting with much denser core tracers.

Reading between the lines

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

  • If the factor-of-two core-envelope linewidth contrast is a generic property of massive protoclusters, it sets a natural boundary scale (roughly the 0.015 pc DCN core size versus the 0.05 pc C18O structures) where turbulence becomes subdominant to gravity, a candidate physical origin for the peak of the core mass function.
  • A direct test the authors do not perform: ammonia-based gas kinetic temperatures toward the same fields would settle the $T_d = T_k$ assumption; tens-of-percent deviations would rescale every reported Mach number and modestly shift the core-envelope ratio.
  • The deliberate exclusion of inter-component velocity separations from $\sigma_{\rm eff}$ makes the reported Mach numbers best read as lower bounds on the turbulent dispersion; if the km/s-separated components seen in W51-E and W51-IRS2 are part of the turbulent cascade rather than distinct clouds, the true Mach numbers are higher.
  • A natural extension of the same recipe would apply the effective-dispersion and Mach-number analysis to the N2H+ data of the survey, testing whether the turbulence drop toward cores is tracer-independent or specific to the C18O/DCN pair.
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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

3 major / 5 minor

Summary. The paper uses ALMA-IMF C18O(2-1) data toward 15 massive protoclusters to measure turbulence. It decomposes the spectra with Gausspy+, computes an effective velocity dispersion, assumes Td=Tk to derive sonic Mach numbers, and uses astrodendro on the position-position-velocity cubes to derive size-linewidth relations. It reports Mach-number distributions peaking between 4 and 7 and extending to ~25, no evolutionary trend, DCN core linewidths about half the C18O linewidths, and size-linewidth slopes p=0.41-0.64. The paper concludes that the C18O-traced gas is supersonic, that turbulence decreases toward dense cores, and that the slope is steeper than the Kolmogorov prediction, as expected for compressible media.

Significance. If correct, the paper provides a uniform, multi-cloud statistical characterization of turbulence in massive protoclusters, with quantitative predictions for the Mach-number distribution and the size-linewidth slope in the C18O-traced regime. Its strengths include detailed reduction notes and systematic checks: noise effects in Appendix C, beam-smoothing in Appendix G, HII/outflow exclusion in Section 5.3, and explicit dendrogram caveats in Appendix J. However, the headline slope and the quantitative Ms values rest on an unvalidated optical-depth law and on the Td=Tk assumption, so the central quantitative claims need targeted sensitivity work before they can be accepted at face value.

major comments (3)
  1. [§5.1, §5.3, and Table 4] The size-linewidth slopes reported in Table 4 (p=0.41-0.64) are the paper's main quantitative claim, but they are derived without validating the adopted C18O optical-depth law. Section 5.1 assumes log10(tau_C18O)=0.6(log10[N(H2)]-24) from the single IRDC G014.492-00.13 and argues that tau is unimportant because, for most fields, fewer than 6% of pixels have N(H2)>10^23.5 cm^-2. This is a pixel-count test, not a flux- or structure-weighted test. The high-column pixels are exactly the dense small-scale structures that form dendrogram leaves, where tau~0.5-1. Opacity broadening at those small scales would inflate sigma_tot preferentially at the small-R end of the fit, biasing p upward from a true Kolmogorov-like value. Since the fitted range spans only about one decade in R, even a tens-of-percent bias at the small-size end can move p from ~0.33 toward the reported range. I request either (i) validation of the tau(N(H2)) relation against the available 13CO(2-1) or C17O data, (ii) an explicit test that re-fits the size-linewidth relation after masking or opacity-correcting pixels with tau>0.3, or (iii) a conservative statement that the slope is an upper limit under the adopted opacity law.
  2. [§5.2, Eqs. (1)-(2)] The Mach-number values (peaks 4-7, extents ~25) are computed under the explicit assumption Tk=Td, using PPMAP dust temperatures that are line-of-sight column-density-weighted means. Section 5.2 does not propagate any uncertainty in this assumption. A factor-of-two error in Td changes c_s in Eq. (2) by sqrt(2) and therefore shifts Ms by ~30-40%; for the narrower lines in the sample, the thermal subtraction in Eq. (1) is a small correction, but the sound-speed normalization is not. The conclusion 'supersonic' would survive a wide range of Td, but the reported PDF peak and the comparison with DCN Mach numbers are quantitative claims. A sensitivity test varying Td (e.g., by +/-50%) or a targeted NH3-based Tk comparison for a subset of fields would make the Ms scale trustworthy.
  3. [§5.2 and Appendix E] The effective velocity dispersion in Appendix E, Eq. (E.6), deliberately excludes the centroid separation between Gaussian components within a pixel. This is a modeling choice that can suppress a genuine turbulent signal: in fields such as W51-E and W51-IRS2, where multiple cloud components are present along the same line of sight, the inter-component velocity separation is comparable to or larger than the internal widths. The paper justifies the choice as avoiding disjoint components that artificially inflate sigma_v, and it shows sigma_eff/sigma_v<0.5 for those fields, but it does not argue that the excluded separations are non-turbulent rather than part of the large-scale velocity field. Given that the Ms distribution and the core-versus-envelope linewidth ratio are central results, I ask for either a quantitative test that recomputes Ms with the traditional sigma_v after masking foreground/background clouds in W51-E and W51-IRS2, or an explicit statement that Ms should be interpreted as the within-component turbulent Mach number.
minor comments (5)
  1. [Table 3] The table header repeats 'Col 6' for both Ms,DCN and Ms,C18O; the second entry should be Col 7, and the multi-line numeric entries would be clearer in a properly typeset table.
  2. [General text] There are several typographical errors: 'aviod' in Section 4, 'As we did find any prominent trend' in Section 6.2, and 'truncks' in Section 7.
  3. [§5.3] The min_npix description, 'we set the value 2 a', appears to omit the beam-area formula; the text should state the numerical number of pixels used for each source.
  4. [§5.2] The phrase 'gas mass-weighted Mach number' is imprecise because the weighting is by C18O integrated intensity, not directly by gas mass; the text should say intensity-weighted.
  5. [§6.2 and Fig. 7] The comparison with Solomon et al. (1987) would be more informative if the normalization A were also rescaled to a common size range, since A values from surveys with different resolutions are not directly comparable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Ms and the size-linewidth slope are direct measurements or reported fits, not quantities constructed from the claims they are used to support.

full rationale

The paper's headline results are not derived from the quantities they purport to test. Ms is computed directly from decomposed C18O line widths via Eq. (2), using published dust-temperature maps, with no parameter fitted to the Ms distribution itself; the supersonic conclusion is a direct comparison of the measured distribution to the sound speed, not a fitted parameter renamed as a result. The size-linewidth index p is explicitly reported as the outcome of a power-law fit (Table 4) and is benchmarked against external studies such as Solomon et al. (1987), Heyer & Brunt (2004), and Larson (1981), rather than imposed by an input. The core-versus-envelope linewidth comparison uses independently published DCN core measurements from Cunningham et al. (2023). Reliance on ALMA-IMF products, such as the Dell'Ova et al. (2024) dust temperature and column density maps, is normal use of independent published data products, and those maps were not constructed to force the present claims. The tau(N(H2)) calibration from Sabatini et al. (2022) is an external empirical input used only to argue that opacity is a minor effect; even if that calibration is under-validated, it is a robustness and correctness concern, not circular reasoning. The paper's own caveats, including the Appendix J min_value truncation test and the optical-depth pixel-count check, are acknowledged limitations and do not indicate that any target quantity was defined in terms of its own fit.

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

The central claims rest on standard observational assumptions (LTE, optically thin tracer, turbulence-dominated line widths) and on a handful of analysis thresholds (SNR >= 10, 2.5 sigma dendrogram cutoff, minimum FWHM of 2 channels). The size-linewidth slope p is itself fitted to the data, so it appears as a free parameter rather than a derived prediction. No invented physical entities are needed.

free parameters (5)
  • Size-linewidth power-law index p = 0.41 to 0.64 per source, 0.51 combined
    Fitted slope of sigma_tot = A (R/pc)^p in Table 4 and Fig. 7. It is the central claimed measurement, so it is a fitted value rather than a prediction.
  • Size-linewidth normalization A = 1.72 to 3.62 km/s per source
    Fitted amplitude in the same power-law fit; reported but not interpreted strongly.
  • Gausspy+ SNR cutoff = 10
    Pixels with signal-to-noise below 10 are masked before spectral decomposition; chosen from an F1-score test, this threshold changes the gas population sampled.
  • Dendrogram intensity threshold = 2.5 sigma_rms
    min_value and min_delta in astrodendro; the authors acknowledge this truncates wide line wings and can reduce sigma_tot for broad structures (Appendix J).
  • Minimum FWHM for Gaussian components = 2 channels
    Set as the minimum sampling criterion; affects the number and width of narrow components in the decomposition.
assumptions (6)
  • domain assumption Gas kinetic temperature equals dust temperature (Tk = Td) in LTE
    Invoked in Section 5 before Eq. (1) to derive sigma_nth and Mach numbers from C18O line widths; also used for the DCN comparison.
  • domain assumption C18O (2-1) emission is mostly optically thin, and where thick, the Sabatini et al. (2022) empirical N(H2)-tau relation applies
    Section 5.1 uses this to assert optical depth does not significantly affect multi-Gaussian fitting; tau is not corrected per pixel.
  • domain assumption Velocity broadening is dominated by turbulence rather than rotation, infall, outflow, or projection of distinct clouds
    Section 5.2 and Appendix F check large-scale gradients in only two regions and assume the remaining non-thermal width is turbulent.
  • domain assumption The Gausspy+ decomposition with SNR > 10 recovers the true number of velocity components
    Section 5.1 and Appendix C show noise affects component counts, and a cutoff is used to stabilize fits.
  • domain assumption Dendrogram structures in the position-position-velocity cube correspond to physical turbulent eddies
    Section 5.3 extracts leaves, branches, and trunks and fits them; contamination and intensity truncation are acknowledged.
  • domain assumption DCN single-Gaussian cores are representative of dense core kinematics
    Section 5.2 uses only cores with single Gaussian DCN spectra from Cunningham et al. (2023) to compare with C18O.

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Cite this review

Pith. "Pith review of ALMA-IMF XIX: C18O (J=2-1): Measurements of turbulence in 15 massive protoclusters." pith.science (2026). https://pith.science/paper/E3A57CDW

@misc{pith2026250714502,
  author       = {Pith},
  title        = {Pith review of: ALMA-IMF XIX: C18O (J=2-1): Measurements of turbulence in 15 massive protoclusters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E3A57CDW}},
  note         = {Machine review of arXiv:2507.14502}
}
read the original abstract

ALMA-IMF is a large program of the Atacama Large Millimeter/submillimeter Array (ALMA) that aims to determine the origin of the core mass function (CMF) of 15 massive Galactic protoclusters (~ 1.0-25.0 x 10^3 solar mass within ~ 2.5 x 2.5 pc^2 ) located towards the Galactic plane. In addition, the objective of the program is to obtain a thorough understanding of their physical and kinematic properties. Here we study the turbulence in these protoclusters with C18O (2-1) emission line using the sonic Mach number analysis (M_s ) and the size-linewidth relation. The probability distribution functions (PDFs) for M_s show a similar pattern, exhibiting no clear trend associated with evolutionary stage, peaking in the range between 4 and 7, and then extending to ~ 25. Such values of M_s indicate that the turbulence in the density regime traced by the C18O line inside the protoclusters is supersonic in nature. In addition, we compare the non-thermal velocity dispersions (sigma_nth, C18O) obtained from the C18O(2-1) line with the non-thermal line widths (sigma_nth, DCN ) of the cores obtained from the DCN (3-2) line. We observe that, on average, the non-thermal linewidth in cores is half that of the gas surrounding them. This suggests that turbulence diminishes at smaller scales or dissipates at the periphery of the cores. Furthermore, we examine the size-linewidth relation for the structures we extracted from the position-position-velocity C18O(2-1) line emission cube with dendrogram algorithm. The power-law index (p) obtained from the size-linewidth relation is between 0.41 and 0.64, steeper than the Kolmogorov law of turbulence, as expected for compressible media. In conclusion, this work is one of the first to carry out such a statistical study of turbulence for embedded massive protoclusters.

Figures

Figures reproduced from arXiv: 2507.14502 by the authors.

Figure 1
Figure 1. Average C18O (J=2−1) spectrum for 15 different protoclusters. Two vertical green dashed lines indicate the velocity cut-off to measure the systemic velocity (Vsys). The red dashed line represents the measured Vsys based on the C18O (J=2−1) line. In the W51-E and W51-IRS2 regions, the black dashed line indicates the minima between the separation of the two broad clouds. Symbols Y, I and E in the figures denote young,… view at source ↗
Figure 2
Figure 2. Integrated intensity (moment 0) maps of the C18O (J=2−1) lines for 15 protoclusters. Symbols Y, I and E in the figures indicate young, intermediate and evolved protoclusters respectively (see Section 1). Article number, page 6 of 32 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Integrated intensity weighted velocity dispersion (moment 2) maps of the C18O (J=2−1) lines for 15 protoclusters. Symbols Y, I and E in the figures indicate young, intermediate and evolved protoclusters respectively (see Section 1). Article number, page 7 of 32 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Left: Sonic Mach number map in the W43-MM1 protocluster. Right: Histogram distribution of the sonic Mach number shown on the left panel. Symbol Y in the figures indicate the young protocluster (see Section 1). We display the remainder of the 15 protoclusters in Appendi…
Figure 5
Figure 5. Figure 5: Correlation between (a) sonic Mach number (Ms) and non￾thermal velocity dispersion (σnth) (green color) and (b) sonic Mach number (Ms) and hydrogen column density [N(H2)] (blue color) for W43-MM1. Symbol Y in the figure indicates the young protocluster (see Section 1).…
Figure 6
Figure 6. Figure 6: Correlation between velocity dispersion (σtot) and the plane-of-sky projected radius (R) for 15 protoclusters. The red dots represent structures derived using the astrodendro module. The solid blue lines represent the fitted lines for the correlation and the green shad…
Figure 7
Figure 7. Figure 7: Correlation between velocity dispersion (σtot) and the plane-of-sky projected radius (R) for all 15 protoclusters. Blue, red and green dots represent the structures for young, intermediate and evolved protoclusters derived using the astrodendro module. The solid orange…

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.