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The Arizona Molecular ISM Survey with the SMT: The Diverse Carbon Monoxide Line Ratios and Spectral Line Energy Distributions of Star Forming Galaxies

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Across 47 nearby star-forming galaxies, the CO(2–1)/CO(1–0) and CO(3–2)/CO(1–0) line ratios rise smoothly with star formation rate and its surface density, with a spread larger than simulations predict.

desk verdict Solid, useful extension of AMISS with new r31 prescriptions for gas mass work, but the treatment of the 11 CO(3–2) upper limits in the fits needs to be settled before I trust the low-end calibration. read the letter →

arxiv 2507.18823 v1 pith:OBAQOA2Y submitted 2025-07-24 astro-ph.GA

Ryan P. Keenan , Daniel P. Marrone , Garrett K. Keating This is my paper
classification astro-ph.GA
keywords COlineratiosspectralenergydistributionsmoleculargasstarformationinterstellarmediumgalaxyevolutionsubmillimeterspectroscopylow-Jtransitions
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 uses galaxy-scale observations of the CO(1–0), CO(2–1), and CO(3–2) lines in 47 nearby, mostly star-forming galaxies to map how the low-energy carbon monoxide line ratios change across the galaxy population. It establishes that $r_{21}$ and $r_{31}$ rise smoothly with star formation rate, star formation rate surface density ($\Sigma_{\rm SFR}$), specific star formation rate, and star formation efficiency, while showing no dependence on stellar mass. The variation in CO excitation is larger than the range predicted by simulation-based prescriptions, with galaxies at a given $\Sigma_{\rm SFR}$ typically less excited than those prescriptions expect. Based on the fitted trends, the paper provides simple power-law formulas that estimate CO(1–0) luminosity and molecular gas mass from CO(2–1) or CO(3–2) observations alone, and it argues that star-forming and starburst galaxies form a continuum of increasing mean molecular gas density.

What carries the argument

The argument is carried by the three lowest CO line ratios $r_{21}$, $r_{31}$, and $r_{32}$, which the paper models as power laws in galaxy properties: $\log r_{jk} = m\log x + b + \epsilon_{(s)}$, with log-normal intrinsic scatter. These fits produce the prescriptions for estimating CO(1–0) luminosities from higher-J lines. For the physical interpretation, the paper uses a published grid of molecular cloud models in which each cloud has a log-normal H$_2$ density distribution characterized by mean density $n_0$ and width $\sigma_n$, a uniform kinetic temperature $T_k$, and a fixed CO column density per line width $N/dv$, with line emission computed in non-LTE. Binned median $r_{21}$–$r_{31}$ values are placed on model tracks to infer how $n_0$ and $T_k$ shift with $\Sigma_{\rm SFR}$.

What would settle it

A galaxy sample spanning the same $\Sigma_{\rm SFR}$ range whose integrated $r_{21}$ and $r_{31}$ values do not vary with $\Sigma_{\rm SFR}$ — for example, a mass-selected CO(3–2) survey of quiescent galaxies — would falsify the claimed correlations and the density-continuum interpretation built on them.

Watch

Extended reading notes

Core claim

Across the three lowest rotational transitions of carbon monoxide, the spectral line energy distribution of a galaxy is not a fixed template. The central result is that the CO(2–1)/CO(1–0) ratio $r_{21}$ and the CO(3–2)/CO(1–0) ratio $r_{31}$ increase smoothly with SFR, $\Sigma_{\rm SFR}$, sSFR, and SFE, with slopes of roughly 0.1–0.2 in log–log space, while $r_{21}$ and $r_{31}$ are consistent with no trend with stellar mass. The observed dynamic range in $r_{31}$ spans about a factor of three and is larger than simulation-based SLED prescriptions predict, especially at low $\Sigma_{\rm SFR}$. When the galaxy-averaged ratios are compared with molecular cloud models, the sequence of binned medians follows tracks of increasing mean H$_2$ density, from below $10^2$ cm$^{-3}$ in the most quiescent systems to above $10^3$ cm$^{-3}$ in ULIRG-like starbursts, with degenerate combinations of density and temperature also allowed.

Load-bearing premise

The load-bearing premise is that each galaxy's integrated CO line ratios can be represented by a single molecular cloud model and that cloud conditions vary smoothly with $\Sigma_{\rm SFR}$; if instead a galaxy's emission is an unresolved mixture of very different cloud populations that happens to average out, the inferred density trend would not follow.

Editorial extensions

If this is right

  • The provided prescriptions (Equations 6–9) let observers convert a single CO(2–1) or CO(3–2) luminosity into a CO(1–0) luminosity and molecular gas mass without assuming a constant line ratio, removing a known source of bias for diverse galaxy samples.
  • Because the same power laws describe literature measurements from local main-sequence galaxies to $z \sim 2$ and submillimeter-selected galaxies, the relations appear to hold over four to five orders of magnitude in $\Sigma_{\rm SFR}$.
  • The flatness of $r_{32}$ with SFR and its mild positive correlation with $\Sigma_{\rm SFR}$ means that area-normalized quantities capture the shape of the low-J CO SLED better than total SFR, consistent with a radiation-field-driven excitation picture.
  • The inferred continuum of mean gas density connects low-SFR galaxies, whose molecular gas is warm and low-density and likely below the star-formation threshold, to starbursts, whose denser gas raises star formation efficiency.

Reading between the lines

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

  • If the SFR-based prescriptions hold at high redshift, single-line CO(3–2) surveys could yield molecular gas masses for large samples where CO(1–0) is unavailable, making the Kennicutt–Schmidt slope testable without a constant-excitation correction.
  • The absence of a stellar-mass trend at fixed SFR suggests that earlier reports of line-ratio variations with galaxy mass may be a proxy for the SFR axis; a mass-selected CO(3–2) survey of quiescent, low-SFR high-mass galaxies would test this directly.
  • The continuum picture predicts that at fixed $\Sigma_{\rm SFR}$, galaxies with higher $r_{31}$ should have higher fractions of dense gas traced by molecules like HCN or CS; existing dense-gas surveys could check this prediction.
  • The degeneracy between density and temperature found at fixed line ratios implies that low-J CO alone cannot uniquely fingerprint ISM conditions; adding mid-J CO, CO isotopologues, or dust measurements is a natural next test, as the paper acknowledges.
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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

2 major / 5 minor

Summary. The paper presents galaxy-scale CO(1-0), CO(2-1), and CO(3-2) observations for 47 nearby, predominantly star-forming galaxies from the Arizona Molecular ISM Survey with the SMT (AMISS), supplemented by literature data. It constructs low-J CO SLEDs and line ratios r21, r31, and r32, and fits power-law relations between these ratios and galaxy properties such as SFR, ΣSFR, sSFR, SFE, and stellar mass. The authors report that r21 and r31 correlate positively with star-formation-related quantities but not with stellar mass, while r32 is largely flat except for tentative trends with surface-density quantities. They provide empirical prescriptions (Equations 6-9) for estimating CO(1-0) luminosities and molecular gas masses from CO(2-1) or CO(3-2), validate these against a broad literature compilation including local and high-redshift galaxies, and compare the observed ratios with molecular cloud models to infer a continuum of increasing gas density with increasing ΣSFR.

Significance. The empirical scaling relations and prescriptions are potentially valuable: they quantify how low-J CO excitation varies across the galaxy population and provide practical tools for converting CO(3-2) or CO(2-1) luminosities to CO(1-0)-based gas masses. The out-of-sample literature comparison, including ULIRGs and high-redshift galaxies, is a notable strength, as is the explicit testing of sample-selection effects against the larger Paper II sample. The paper also makes its data public via Zenodo and includes validated aperture corrections for at least one galaxy. The physical interpretation is presented with appropriate caveats about model degeneracies. However, the treatment of the 11 CO(3-2) upper limits in the r31 and r32 regression fits is not described, and this directly affects the headline r31 prescriptions. Because the censored measurements are likely concentrated at low SFR and low ΣSFR, the fitted slopes and intercepts may be biased. This issue must be resolved before the quantitative prescriptions can be considered reliable.

major comments (2)
  1. [Section 5 / Conclusions / Abstract] The manuscript reports that 11 of 47 galaxies have only CO(3-2) upper limits (Section 2) and Figure 4 plots these as gray downward triangles, but Section 4 does not state how upper limits enter the power-law regressions. The MCMC procedure described as 'allowing for uncertainty in both x and y' (Section 4) is not a censored-data method, and Table 1 gives no indication that the r31 and r32 fits use a survival analysis or any other treatment of non-detections. If the 11 upper limits are excluded, the fits are performed on a CO(3-2)-detected subsample that is likely biased toward high excitation at a given SFR or ΣSFR. This would bias the r31 slopes and intercepts and, in turn, the prescriptions in Equations 7 and 9, leading to overpredicted r31 and underestimated CO(1-0) luminosity and molecular gas mass when using CO(3-2) at low SFR/ΣSFR. I request a censored-data treatment, or at minimum a sensitivity test that demonstrates the results are unchanged when the limits are incorporated (e.g., by assigning upper-limit likelihoods or by trimming and recomputing).
  2. [Section 5 / Conclusions / Abstract] The abstract and Section 6 state that 'gas conditions in star forming and starburst galaxies lie on a continuum with increasing gas density in more actively star forming systems,' but the model comparison in Section 5 explicitly shows a strong degeneracy between mean density n0 and temperature Tk: the observed r21-r31 trends can be reproduced by a factor-of-ten increase in density at fixed temperature or by a temperature rise from 10 K to 30 K at fixed n0 ~ 10^3 cm^-3. The paper also notes in Appendix C that other parameter choices favor 'unexpectedly low densities or high temperatures.' Given this acknowledged degeneracy, the specific claim that the data demonstrate increasing gas density is stronger than the model analysis supports. I recommend either softening the conclusion to 'increasing density and/or temperature' or adding an observational or modeling argument that breaks the n0-Tk degeneracy at least statistically.
minor comments (5)
  1. [Abstract] The sentence 'We find systematic trend of higher gas excitation...' is missing an article and should read 'We find a systematic trend...'.
  2. [Section 2] There is a duplicate article in 'we assume a a flat ΛCDM cosmology'; one 'a' should be removed.
  3. [Section 4.2] The sentence 'In absence of noise we expect r32 = r31/r32' contains a typo; the ratio should be r32 = r31/r21.
  4. [Equations 6-9] The piecewise definitions in Equations 6-9 are typeset ambiguously; for example, Equation 7 reads '0.0 3 .2 < log SFR' and Equation 8 reads '0.0 0 .04 < log ΣSFR', which should include the word 'for' and explicit minus signs (e.g., '0.0 for -0.04 < log ΣSFR').
  5. [Section 1] The text 'parameterizations of the the CO(3-2)/CO(1-0)' has a duplicated 'the'.

Circularity Check

0 steps flagged · score 2.0 of 10

No material circularity: the r31 correlations and prescriptions are fit to AMISS data and validated on independent literature; only the reuse of the Paper II r21 relation is a self-citation, and it is checked against the present sample and external data.

full rationale

The paper's central r31 and r32 results are direct fits to the AMISS line-luminosity ratios (Eq. 2), and the prescriptions in Eqs. 7 and 9 are simply the Table 1 power-law fits converted into piecewise forms; nothing is fitted and then relabeled as a prediction. The r21 prescriptions (Eqs. 6 and 8) are imported from Paper II (Keenan et al. 2025), a self-citation, but Paper II used a larger sample and the present paper re-derives r21 in Table 1 and shows agreement (Fig. 4); the literature comparison in Section 4.2 is out-of-sample, and the fit to binned literature plus AMISS data reproduces the fiducial parameters, providing independent support. The identity r32 = r31/r21 is definitional but used only as a consistency check for the median r32 trend, and the AMISS r32 values are measured, not derived from the prescriptions. The physical-condition interpretation in Section 5 explicitly acknowledges that individual galaxies can be fit by many models and that the density continuum is an assumption, which is model dependence rather than circularity. The most substantive concern is statistical: 11 CO(3-2) upper limits enter the Section 4 regressions with no described censored-data treatment, which could bias the r31 slopes and prescriptions; this is a robustness/correctness issue, not an input-output circularity.

Assumptions & free parameters 11 free parameters · 6 assumptions · 0 invented entities

The empirical trends rest on the fitted power law parameters and on the ancillary data and models listed. The physical interpretation in Section 5 adds prior choices for the cloud density distribution width and column density per line width. The line ratios themselves are direct observables after aperture correction, so the main free parameters are the fit slopes, intercepts, and intrinsic scatters.

free parameters (11)
  • Power law slope m21,SFR = 0.14 ± 0.03
    Fitted to r21 vs SFR in AMISS sample; Equation 6 uses 0.12.
  • Power law intercept b21,SFR = -0.21 ± 0.02
    Fitted; Equation 6 uses -0.19.
  • Power law slope m31,SFR = 0.15 ± 0.04
    Fitted to r31 vs SFR; Equation 7.
  • Power law intercept b31,SFR = -0.49 ± 0.03
    Fitted; Equation 7.
  • Power law slope m21,SigmaSFR = 0.08 ± 0.02 (AMISS), 0.10 (Eq. 8 from Paper II)
    Equation 8 uses Paper II fit on a larger sample.
  • Power law intercept b21,SigmaSFR = -0.02 ± 0.03 (AMISS), 0.00 (Eq. 8)
    Equation 8.
  • Power law slope m31,SigmaSFR = 0.16 ± 0.04
    Fitted; Equation 9.
  • Power law intercept b31,SigmaSFR = -0.21 ± 0.05
    Fitted; Equation 9.
  • Intrinsic scatter s = 0.04 to 0.14 dex
    Fitted log-normal scatter in Equation 4; recommended 0.05 dex for r21 and 0.1 dex for r31.
  • Cloud model column density per line width N/dv = 10^16.5 cm^-2 (km/s)^-1
    Chosen as fiducial because other values favor unexpectedly low densities or high temperatures (Section 5, Appendix C).
  • Cloud density distribution width sigma_n = 0.3 dex
    Taken from den Brok et al. (2023) for NGC 3627, fixed in the main model tracks (Section 5).
assumptions (6)
  • standard math Flat ΛCDM cosmology with H0=70 and Ωm=0.3
    Assumed for distance calculations throughout the paper (Section 1).
  • domain assumption Chabrier (2003) stellar initial mass function for SFRs
    Adopted when deriving SFRs from ancillary data (Section 1).
  • domain assumption Milky Way-like CO-to-H2 conversion factor αCO = 4.3 M⊙ (K km/s pc^2)^-1
    Adopted from Bolatto et al. (2013); affects Mmol and Σmol quantities but not the line ratios directly (Section 2).
  • domain assumption Molecular cloud models with log-normal density distributions and RADEX non-LTE radiative transfer represent the galaxy ISM
    Used in Section 5 to interpret observed trends; degeneracies are acknowledged.
  • domain assumption Galaxy-averaged line ratios can be compared to single-cloud model tracks
    Assumed in Section 5; justified by small scatter in resolved studies, but galaxy centers may differ.
  • domain assumption Aperture corrections based on optical size models recover missing flux
    Required to derive corrected luminosities; validated for one galaxy in Section 2, median corrections 10 to 21 percent.

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Cite this review

Pith. "Pith review of The Arizona Molecular ISM Survey with the SMT: The Diverse Carbon Monoxide Line Ratios and Spectral Line Energy Distributions of Star Forming Galaxies." pith.science (2026). https://pith.science/paper/OBAQOA2Y

@misc{pith2026250718823,
  author       = {Pith},
  title        = {Pith review of: The Arizona Molecular ISM Survey with the SMT: The Diverse Carbon Monoxide Line Ratios and Spectral Line Energy Distributions of Star Forming Galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OBAQOA2Y}},
  note         = {Machine review of arXiv:2507.18823}
}
abstract

The carbon monoxide (CO) spectral line energy distributions (SLEDs) of galaxies contain a wealth of information about conditions in their cold interstellar gas. Here we use galaxy-scale observations of the three lowest energy CO lines to determine SLEDs and line ratios in a sample of 47 nearby, predominantly star forming galaxies. We find systematic trend of higher gas excitation with increasing star formation rate (SFR) and SFR surface density ($\Sigma_{\rm SFR}$), with the range of variations being even larger than predicted by simulations. Power law fits of the CO line ratios as a function of SFR and $\Sigma_{\rm SFR}$ provide a good description of the trends seen in our sample and also accurately predict values for a wide range of galaxy types compiled from the literature. Based on these fits, we provide prescriptions for estimating CO(1-0) luminosities and molecular gas masses using CO(3-2) or CO(2-1) in cases where CO(1-0) is not observed directly. We compare our observed SLEDs with molecular cloud models in order to examine how the physical properties of cold gas vary across the galaxy population. We find that gas conditions in star forming and starburst galaxies lie on a continuum with increasing gas density in more actively star forming systems.

Figures

Figures reproduced from arXiv: 2507.18823 by the authors.

Figure 1
Figure 1. The distribution of our sample in stellar mass, SFR, and CO(1–0) luminosity (color-axis) is shown by large points. Galaxies with CO(3–2) data from Lamperti et al. (2020) are indicated by blue fill in the markers. Additional AMISS galaxies included in Paper II’s analysis of the r21 ratio are shown by smaller, gray points. The black line and gray filled region show the star forming main sequence of Speagle et al. (201… view at source ↗
Figure 2
Figure 2. CO spectra and an SDSS composite image for AMISS.1037. For CO(1–0) we show spectra from both the IRAM 30m (black) and ARO 12m (gray). In the right panel we superimpose the half-power beam sizes for each telescope on the optical image. Based on the optical profile we estimate that the IRAM CO(1–0) beam (solid white line) and SMT CO(3–2) beam (dash-dotted line) miss 22% and 21% of the total flux. The SMT beam for CO(2… view at source ↗
Figure 3
Figure 3. SLEDs for our galaxy sample normalized to CO(1–0). We plot the data in terms of both flux (top row) and line luminosity (bottom row). Left: SLEDs of individual galaxies. Points with error bars show detected CO lines and 1σ uncertainties, while downward triangles (connected to dashed lines) indicate 2σ upper limits for undetected CO(3–2). Galaxies are color coded according to ΣSFR, a proxy for the intensity of the in… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Trends between the CO line ratios and ΣSFR. Black points show measurements and 1σ uncertainties for individual objects; gray downward triangles show 2σ upper limits where CO(3–2) is not detected. Colored points show median values in equally spaced bins along the x-axis…
Figure 5
Figure 5. Figure 5: Top: Power law slopes (mjk) between the r21 (orange), r31 (purple), or r32 (pink) and a range of galaxy properties. Error bars show 1σ uncertainties. We also show m21 found using the full AMISS sample in Paper II (smaller markers with black outlines). Bottom: The signi…
Figure 6
Figure 6. Figure 6: Summary of the relations between r21 (orange), r31 (purple), or r32 (pink) with ΣSFR. Small markers show values from the combined literature and AMISS samples. Large markers show median values in six bins; vertical error bars show the 16th and 84th percentiles and hori…
Figure 7
Figure 7. Figure 7: Left panels: r31 from AMISS (gray) and literature (colored, see legend) plotted against ΣSFR and SFR. Small, light colored points correspond to individual objects with error bars showing 1σ uncertainties (when reported). For literature samples, large points with a dark…
Figure 8
Figure 8. Figure 8: Similar to [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: AMISS (gray) and literature (colored, see legend) r32 values as a function of ΣSFR, SFR, sSFR, and SFE. Small, light colored points correspond to individual objects. For the literature samples large points with a dark outline represent the median and 16th-84th percenti…
Figure 10
Figure 10. Figure 10: Left: r21 and r31 ratios of our sample. Points and their surrounding ellipses show the measured value and 1σ error region for ratio pairs from each galaxy. Galaxies are color coded by ΣSFR. The thickness of the error contour corresponds to the SNR of the CO(3–2) line,…
Figure 11
Figure 11. Figure 11: Main figure: solid lines shows the track in r21 and r32 when the mean density (n0) of a Leroy et al. (2022) molecular cloud model is varied, holding other parameters (σn, Tk, and N/dv) constant. The thickness of the lines indicates n0 at that point along the track. Ea…
Figure 12
Figure 12. Figure 12: Filled contours represent the range of n0 and Tk for models producing line ratios within 1σ of the median observed line ratios in bins of ΣSFR (colored contours) and for ULIRGs (black countours). The bins are color coded according to their ΣSFR. Each panel shows resul…

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Pith tools

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