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Dense gas scaling relations at kiloparsec scales across nearby galaxies with the ALMA ALMOND and IRAM 30m EMPIRE surveys

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper establishes that HCN/CO increases and SFR/HCN decreases with local surface density and pressure across 31 galaxies, giving the Gao-Solomon scatter a physical origin.

desk verdict Largest resolved HCN scaling-relation sample to date, but the 'physical origin' claim outruns the line-ratio evidence. read the letter →

arxiv 2412.10506 v3 pith:LMHTKUTW submitted 2024-12-13 astro-ph.GA

Lukas Neumann , Maria J. Jimenez-Donaire , Adam K. Leroy , Frank Bigiel , Antonio Usero , Jiayi Sun , Eva Schinnerer , Miguel Querejeta
show 12 more authors
Sophia K. Stuber Ivana Beslic Ashley Barnes Jakob den Brok Yixian Cao Cosima Eibensteiner Hao He Ralf S. Klessen Fu-Heng Liang Daizhong Liu Hsi-An Pan Thomas G. Williams
This is my paper · ORCID
classification astro-ph.GA
keywords densegastracersHCN(1-0)Gao-Solomonrelationstarformationefficiencymolecularsurfacedensitydynamicalequilibriumpressurespectralstackingnearbygalaxies
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 argues that the ratio of dense gas (HCN) to bulk molecular gas (CO) and the star formation rate per unit HCN both vary systematically with the local galactic environment, not randomly. Using the ALMA ALMOND and IRAM 30m EMPIRE surveys, it stacks HCN(1-0) and CO(1-0) spectra across 31 nearby spiral galaxies and measures how these ratios change with molecular gas surface density, stellar mass surface density, and dynamical equilibrium pressure. The result is that HCN/CO rises with a slope of about 0.5 and SFR/HCN falls with a slope of about -0.6 as these environmental quantities increase, with scatter of roughly 0.2 and 0.4 dex. A sympathetic reading of the paper takes this as evidence that the scatter in the Gao-Solomon relation, SFR against HCN luminosity, has a physical origin in the varying state of molecular gas. This matters because it links observable line ratios to the conditions that regulate star formation across galaxy discs.

What carries the argument

Spectral stacking of HCN(1-0) and CO(1-0) in bins of environmental conditions. For each galaxy, spectra are co-added in logarithmic bins of stellar mass surface density, molecular gas surface density, and dynamical equilibrium pressure, using the high-signal-to-noise CO line to set the velocity window; non-detections are kept as upper and lower limits and the relations are fitted with a linear regression that incorporates those limits. A variable CO-to-H2 conversion factor that depends on metallicity and stellar mass surface density calibrates the molecular gas surface density and pressure axes.

What would settle it

A dust-based molecular gas surface-density map of the same 31 galaxies, independent of CO, that disagrees systematically with the adopted variable conversion factor would recalibrate the molecular gas and pressure axes; if the HCN/CO and SFR/HCN trends disappeared under that recalibration, the claimed environmental relations for those two axes would be refuted, while the stellar-mass-based relation would survive.

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Extended reading notes

Core claim

The central discovery is that the two ratios that connect dense gas to star formation are not universal constants but continuous functions of kiloparsec-scale environment. Across 31 local galaxies, HCN/CO increases and SFR/HCN decreases with increasing stellar mass surface density, molecular gas surface density, and dynamical equilibrium pressure, with galaxy centres lying at the high-density, high-pressure end of the same trend. The slopes are significant, about 0.5 dex per dex for HCN/CO and about -0.6 for SFR/HCN, and the residual scatter is modest for HCN/CO (0.2 dex) and larger for SFR/HCN (0.4 dex). The authors interpret this as showing that deeper gravitational potentials and more abundant gas produce denser molecular clouds, that dense gas in these environments is less efficient at forming stars per unit mass, and that the well-known scatter in the Gao-Solomon relation therefore reflects real environmental physics rather than measurement noise.

Load-bearing premise

The adopted variable CO-to-H2 conversion factor, which sets how molecular gas surface density and pressure are inferred from CO emission, correctly captures how those quantities vary with metallicity and stellar mass across the 31 galaxies.

Editorial extensions

If this is right

  • The Gao-Solomon relation's ~0.5 dex scatter is not random; it correlates with measurable local conditions, so SFR/HCN predictions can be improved by including surface density or pressure.
  • Galaxy centres naturally host a higher fraction of HCN-bright gas than discs, following the same continuous environmental trend without needing a distinct centre mechanism.
  • SFR/HCN decreases in high-surface-density, high-pressure regions, implying the efficiency of star formation per unit dense gas varies by a factor of a few between centres and discs.
  • The similar trends seen with cloud-scale CO imaging and with kiloparsec-scale HCN/CO spectroscopy support a picture where molecular cloud properties vary with galactic environment.
  • Because ALMOND and EMPIRE agree on overlapping galaxies, the combined 31-galaxy sample provides a homogeneous benchmark for future resolved dense gas surveys.

Reading between the lines

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

  • If the environmental trends hold at cloud scale, resolved HCN observations at sub-kiloparsec resolution should find the same HCN/CO and SFR/HCN gradients within single galaxies, offering a direct test of the claimed continuity.
  • A dust-based molecular gas map of the same galaxies, independent of CO, would test the variable conversion-factor calibration; the stellar-mass relation would remain robust because it does not use that calibration.
  • The lower SFR/HCN in centres could also reflect HCN tracing more bulk gas there through optical depth or IR pumping; if so, a different dense gas tracer such as HCO+ might show a weaker anti-correlation, distinguishing environmental efficiency from tracer bias.
  • Applying the same stacking method to the HCO+ and CS data already observed in ALMOND could test whether the trends are specific to HCN or general to dense gas tracers.
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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 / 4 minor

Summary. This Letter presents resolved kiloparsec-scale measurements of HCN(1-0)/CO(1-0) and SFR/HCN(1-0) as functions of stellar mass surface density, molecular gas surface density, and dynamical equilibrium pressure, combining the ALMA ALMOND survey with the IRAM 30m EMPIRE survey for a total of 31 nearby galaxies. The authors spectrally stack HCN and CO in bins of each environmental quantity, fit linear relations with LinMix while treating non-detections as limits, and report that HCN/CO rises (slope ~0.5) and SFR/HCN falls (slope ~ -0.6) with increasing surface density and pressure. They also place ALMOND/EMPIRE in the context of a literature compilation of the Gao-Solomon relation. The central claim is that the environmental trends demonstrate that the scatter in the Gao-Solomon relation has a physical origin rather than being an artifact of the tracer.

Significance. The paper is a valuable empirical contribution: it more than triples the number of galaxies with resolved HCN maps, homogenizes SFR, CO, and HCN calibrations across two surveys, and provides public data products and analysis scripts. The stacking and limit-aware fitting procedures are standard and clearly described, and the cross-survey consistency checks in Appendix A strengthen confidence in the measurements. If the trends are robust, they constrain models of how the dense gas fraction and dense-gas star formation efficiency depend on galactic environment. However, the headline interpretation goes beyond what the data alone can establish, given the paper's own admission in §3.3 that HCN excitation and the HCN-to-dense-gas conversion factor may vary with environment.

major comments (3)
  1. [Abstract, §3.3, §4] The abstract states that the results 'demonstrate that the scatter in the Gao–Solomon relation (SFR/HCN) has a physical origin,' and §4 says this 'reinforces the notion' of physical origin. However, §3.3 explicitly concludes that HCN may not be a robust dense-gas tracer in galaxy centres because of increased optical depth, IR pumping, electron excitation, and a plausibly varying alpha_HCN, which would raise SFE_dense in centres and make them comparable to discs. The paper presents only line ratios and fixed conversion factors; it includes no HCN excitation diagnostic (e.g., HCN(3-2)/(1-0)) and no test of whether the environmental trends actually reduce the 0.4 dex scatter of the Gao–Solomon relation. A significant correlation with an environmental variable does not by itself demonstrate that the scatter is physical in origin, because the alternative of a tracer-ratio artifact is not excluded. I recommend softening the abstract and conclusions to 'consistent with a physical origin' and, ideally, adding a quantitative comparison of the scatter before and after removing the environmental trend.
  2. [§3.2, Eq. (2), Table 2] The relations of HCN/CO and SFR/HCN against Sigma_mol and P_DE share W_CO (or quantities derived from it, via Eq. (2) and Eq. (1)) on both axes, so correlated noise and calibration errors in CO can bias the fitted slopes and produce artificial correlations. The paper acknowledges this issue only in §3.3, where it chooses Sigma_star for the centre–disc comparison because it 'have[s] uncorrelated axes,' yet the abstract and §3.2 present all three x-axis variables as equivalent measurements of the same phenomenon. The Sigma_star relation avoids the covariance, but the quantitative slopes for Sigma_mol and P_DE should either be accompanied by an estimate of the covariance bias (e.g., a Monte Carlo error analysis that propagates CO uncertainties on both axes) or be de-emphasized in the headline claims.
  3. [Table 2] The Pearson correlation coefficients and the statement that 'all p-values are much less than 0.01' are computed from stacked bins that are not independent: each galaxy contributes multiple bins, and neighbouring bins within a galaxy share the underlying physical conditions and measurement systematics. The effective sample size is therefore substantially smaller than the raw number of stacked points, so the quoted p-values overstate the significance of the correlations. A per-galaxy bootstrap, a hierarchical regression, or a randomization test that preserves the within-galaxy structure is needed to support the significance claims.
minor comments (4)
  1. [Author list] The name 'Frank Bigiel' appears twice in the author list; one occurrence appears to be a duplication.
  2. [Abstract vs. Table 2] The abstract quotes a scatter of ~0.4 dex for SFR/HCN, while Table 2 reports scatter values sigma = 0.28–0.34 dex for the three relations; please harmonize these numbers or clarify what the 0.4 dex refers to.
  3. [Appendix C, Eq. (C.2)] The variable alpha_CO prescription is adopted without an explicit treatment of its uncertainty; given that this factor enters the Sigma_mol and P_DE axes, a brief statement on the adopted uncertainty or at least a reference to its origin would help readers gauge the systematic error in the slopes.
  4. [Fig. 3 caption] The caption's phrase 'median (all S/N)' is ambiguous; the text in §3.2 clarifies that this includes non-detections, so please make the caption explicit that the cyan line includes S/N < 3 data.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the scaling relations are empirical, with only minor self-cited calibrations and acknowledged covariance between some axes.

full rationale

The paper's core results are direct measurements of line ratios and SFR ratios stacked against environmental variables. No parameter is fitted to the Gao-Solomon scatter and then renamed a prediction; the correlations are empirical and could have been null. The Sigma_star axis is independent of both CO and HCN intensities, providing an external anchor for the trends, and the paper itself notes (Sect. 3.3) that the Sigma_mol and PDE axes share CO intensity with HCN/CO, which is a covariance caveat rather than a construction forcing the sign of the slope. The adopted variable alpha_CO (Eq. C.2) and fixed alpha_HCN come from Schinnerer & Leroy (2024), a review co-authored by two co-authors of this paper, but the prescription synthesizes external calibrations and is not derived from the present target result; the Sigma_star relation does not use it. The main overreach is interpretive: Sect. 3.3 explicitly concedes that alpha_HCN may be lower in galaxy centres (via optical depth, IR pumping, or electron excitation), which would raise inferred SFEdense and make centres comparable to discs, so the abstract's 'demonstrate' wording goes beyond what the fixed-conversion-factor data establish. That is a limitation of the evidence, not a circularity: no load-bearing step reduces to its own input by definition or to a self-citation chain.

Assumptions & free parameters 8 free parameters · 4 assumptions · 0 invented entities

The central trends are based on observed line ratios and environmental indicators. The quantitative slopes for Sigma_mol and PDE depend on external calibration prescriptions (alpha_CO, R21) and assumptions in the pressure calculation; these are inputs from prior literature, not derived here. No new physical entities are introduced. The main caveats are the shared W_CO between HCN/CO and Sigma_mol axes, and the assumed constancy of the HCN-to-dense-gas conversion factor.

free parameters (8)
  • alpha_CO normalization = 4.35 M_sun pc^-2 (K km s^-1)^-1
    Adopted from Bolatto et al. 2013 as the normalization of the variable CO-to-H2 factor; affects Sigma_mol and PDE axes.
  • alpha_CO metallicity exponent = -1.5
    From Schinnerer & Leroy 2024 Eq. C.2; sets how alpha_CO varies with metallicity.
  • alpha_CO Sigma_star exponent = -0.25
    From Schinnerer & Leroy 2024 Eq. C.2; sets how alpha_CO varies with stellar mass surface density.
  • R21 normalization = 0.65
    CO(2-1)/CO(1-0) line ratio at pivot Sigma_SFR; used to convert PHANGS-ALMA CO(2-1) to CO(1-0).
  • R21 power-law index = 0.125
    Exponent in Eq. C.1 relating R21 to Sigma_SFR.
  • alpha_HCN = 15 M_sun pc^-2 (K km s^-1)^-1
    Fixed conversion from HCN luminosity to dense gas mass; used only for fiducial physical units, not for main line ratio trends.
  • mass-to-light ratio Upsilon_star = 0.6 M_sun/L_sun
    Adopted at 3.6 microns to convert Spitzer maps to stellar mass surface density; affects Sigma_star.
  • gas velocity dispersion sigma_gas,z = 15 km/s
    Assumed in the dynamical equilibrium pressure calculation (Eq. 1).
assumptions (4)
  • domain assumption PDE formula (Eq. 1) describes vertical dynamical equilibrium pressure of the ISM
    Used to define the third environmental variable; depends on assumed geometry and a constant velocity dispersion.
  • domain assumption HCN(1-0) traces dense molecular gas and CO(1-0) traces bulk molecular gas with roughly constant conversion factors across the sample
    The interpretation of HCN/CO as a dense gas fraction and conversions to physical units rely on this; the paper acknowledges alpha_HCN may vary by environment.
  • domain assumption The FUV+22 micron SFR prescription and z0MGS calibrations are valid at kiloparsec scales
    Adopted uniformly for all galaxies to compute SFR and Sigma_SFR.
  • domain assumption Spectral stacking of CO-based velocity windows recovers unbiased mean line ratios for low-S/N HCN
    The stacking method assumes HCN spectra have the same velocity centroid as CO and that stacking over many sightlines yields a representative average.

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Cite this review

Pith. "Pith review of Dense gas scaling relations at kiloparsec scales across nearby galaxies with the ALMA ALMOND and IRAM 30m EMPIRE surveys." pith.science (2026). https://pith.science/paper/LMHTKUTW

@misc{pith2026241210506,
  author       = {Pith},
  title        = {Pith review of: Dense gas scaling relations at kiloparsec scales across nearby galaxies with the ALMA ALMOND and IRAM 30m EMPIRE surveys},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LMHTKUTW}},
  note         = {Machine review of arXiv:2412.10506}
}
read the original abstract

Dense, cold gas is the key ingredient for star formation. Over the last two decades, HCN(1-0) emission has been utilised as the most accessible dense gas tracer to study external galaxies. We present new measurements tracing the relationship between dense gas tracers, bulk molecular gas tracers, and star formation in the ALMA ALMOND survey, the largest sample of resolved (1-2 kpc resolution) HCN maps of galaxies in the local universe (d < 25 Mpc). We measure HCN/CO, a line ratio sensitive to the physical density distribution, and SFR/HCN, a proxy for the dense gas star formation efficiency, as a function of molecular gas surface density, stellar mass surface density, and dynamical equilibrium pressure across 31 galaxies, increasing the number of galaxies by a factor of > 3 over the previous largest such study (EMPIRE). HCN/CO increases (slope of ~ 0.5 and scatter of ~ 0.2 dex), while SFR/HCN decreases (slope of ~ -0.6 and scatter of ~ 0.4 dex) with increasing molecular gas surface density, stellar mass surface density and pressure. Galaxy centres with high stellar mass surface density show a factor of a few higher HCN/CO and lower SFR/HCN compared to the disc average, but both environments follow the same average trend. Our results emphasise that molecular gas properties vary systematically with the galactic environment and demonstrate that the scatter in the Gao-Solomon relation (SFR against HCN) is of physical origin.

Figures

Figures reproduced from arXiv: 2412.10506 by the authors.

Figure 1
Figure 1. ALMOND and EMPIRE on the star-forming main sequence (SFMS) of galaxies. Grey shows all galaxies from the PHANGS– ALMA survey (Leroy et al. 2021b). Red and blue markers present galaxies from the EMPIRE (Jiménez-Donaire et al. 2019) and AL￾MOND surveys (Neumann et al. 2023b), respectively, with the same SFR calibration adopted across the merged sample. Contours indicate 25, 50, and 75 percentile areas of the respectiv… view at source ↗
Figure 2
Figure 2. Gao–Solomon relation. SFR (top) and SFR/LHCN (a proxy of SFEdense; bottom) as a function of HCN luminosity across a literature compilation and the ALMOND (blue circles) and EMPIRE (red circles) surveys. Note that we re-calculated the SFR across EMPIRE galaxies using a combination of IR and FUV data (see Sect. 2). Our literature compilation contains HCN observations that include Galactic clumps and clouds (squares), … view at source ↗
Figure 3
Figure 3. Dense gas relations with kiloparsec-scale environmental conditions. HCN/CO (top), a proxy of fdense, and SFR/HCN (bottom), a proxy of SFEdense, are shown as a function of stellar mass surface density (Σ⋆), molecular gas surface density (Σmol), and dynamical equilibrium pressure (PDE) across 31 galaxies from ALMOND and EMPIRE. The markers denote significant stacked measurements (S/N ≥ 3) across disc (circle) and cent… view at source ↗

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Pith tools

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