{"id":"7c9bc276-4df9-4aca-b61a-6c6175dbfb3b","arxiv_id":"2507.18823","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":11,"one_line_summary":"CO line ratios in 47 nearby star-forming galaxies rise with star formation rate, leading to empirical prescriptions for converting higher-J CO luminosities to molecular gas masses.","lead":"A survey of 47 nearby galaxies measured the ratios of the three lowest carbon monoxide emission lines, finding that gas excitation rises smoothly with star formation rate and its surface density. The paper provides formulas to convert CO(2-1) or CO(3-2) observations into molecular gas masses, useful for galaxy surveys where CO(1-0) is unavailable.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The r31 correlations and prescriptions may rest on detection-biased fits: 11 of 47 CO(3–2) measurements are upper limits, and §4 describes no censored-data treatment for the power-law regressions.","rationale":"The reader's weakest assumption was the model-based density interpretation in Section 5. That concern is real but is largely disarmed by the paper itself: Section 5 and Appendix C explicitly discuss the temperature–density degeneracy, note that many parameter combinations reproduce the data, and present the density continuum as one plausible reading rather than a unique inference. The central empirical result—that r21 and r31 correlate with star-formation indicators—does not depend on that model interpretation. My concern instead targets the data-processing step that underpins the quantitative prescriptions in Equations 7 and 9. The manuscript reports 11 CO(3–2) upper limits, but Section 4 does not explain how upper limits enter the fitting. If they are excluded, the regressions are detection-biased in exactly the regime (low SFR, low ΣSFR) where the prescriptions extrapolate to quiescent galaxies. This is a concrete, testable methodological gap, not a matter of theoretical preference. The qualitative trends may survive a censored-data reanalysis, but the fitted parameters and the recommended conversion factors should not be accepted as final until the test is run. I therefore recommend CONDITIONAL rather than ACCEPT: the paper is strong and reproducible, but one targeted correction to the fitting procedure (or an explicit demonstration that the upper limits do not change the results) is needed before the headline prescriptions are adopted.","tokens_in":22740,"tokens_out":7336,"duration_ms":88043,"concrete_test":"Rerun the Section 4 power-law regressions from Table 1 using the public AMISS catalog with the 11 CO(3–2) upper limits treated as censored data (e.g., a Bayesian tobit or survival-regression likelihood), separately for the SFR and ΣSFR fits of r31 and r32. Compare the resulting slopes, intercepts, and intrinsic scatters with those in Table 1 and with Equations 7 and 9; if any parameter shifts by more than 1σ, the prescriptions should be revised or refit including the censored points.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central claims include statistically significant r31 trends with SFR, ΣSFR, sSFR, and SFE, and the prescriptions in Equations 7 and 9 that convert CO(3–2) luminosities to CO(1–0) estimates. However, 11 of 47 galaxies have only CO(3–2) upper limits (§2, §3), and Section 4's description of the Hogg et al. (2010) fitting procedure—'allowing for uncertainty in both x and y'—does not state how censored values enter the regression. If those 11 non-detections are excluded, the fits are performed on a subsample selected for detectable CO(3–2). Non-detections are expected to be preferentially low-excitation, low-r31 systems at low SFR and ΣSFR; dropping them would bias the r31 intercept upward (and can also distort the slope and the quoted intrinsic scatter). This would directly affect the calibrated r31 prescriptions: at low SFR/ΣSFR, Equation 7 or 9 would overpredict r31, leading to underestimates of CO(1–0) luminosity and molecular gas mass when using CO(3–2). The same concern applies to the r32 correlations, though r32 is less central. The manuscript's visual display of gray upper-limit triangles in Figures 4, 7, and 9 does not substitute for a censored-data analysis; if the limits were instead inserted as detections at their 2σ values, that would also bias the fits. Because the quantitative prescriptions are a headline deliverable, the absence of a stated treatment for the 11 upper limits is a load-bearing gap that should be settled before accepting the fitted parameters at face value.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":23173,"tokens_out":3835,"duration_ms":42761,"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":[{"comment":"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).","section":"Section 5 / Conclusions / Abstract"},{"comment":"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.","section":"Section 5 / Conclusions / Abstract"}],"minor_comments":[{"comment":"The sentence 'We find systematic trend of higher gas excitation...' is missing an article and should read 'We find a systematic trend...'.","section":"Abstract"},{"comment":"There is a duplicate article in 'we assume a a flat ΛCDM cosmology'; one 'a' should be removed.","section":"Section 2"},{"comment":"The sentence 'In absence of noise we expect r32 = r31/r32' contains a typo; the ratio should be r32 = r31/r21.","section":"Section 4.2"},{"comment":"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').","section":"Equations 6-9"},{"comment":"The text 'parameterizations of the the CO(3-2)/CO(1-0)' has a duplicated 'the'.","section":"Section 1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is solid in its empirical content and the literature validation is convincing. The main concern is the missing treatment of non-detections in the r31/r32 regression fits, which is fixable within the scope of a revision. I would be comfortable with acceptance after the authors either implement a censored-data analysis or demonstrate that the fits are insensitive to the upper limits."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague—quick take: this is a solid, useful paper. It delivers new empirical scaling relations for CO(3–2)/CO(1–0) and CO(3–2)/CO(2–1) line ratios from a homogeneous survey of 47 galaxies, and the prescriptions in Equations 7 and 9 are the kind of thing people will actually use to convert CO(3–2) luminosities to molecular gas masses. The data are public on Zenodo, the aperture corrections are validated on one galaxy, and the literature compilation is wide enough to show the fits hold outside the AMISS sample. The paper also extends the known r21 trends to r31 and r32, and the finding that r31 rises smoothly over a factor of 300 in ΣSFR is new and clear.\n\nThe main thing I'd want settled before trusting the numbers at face value: 11 of 47 CO(3–2) measurements are upper limits, and Section 4 never says how the Hogg et al. (2010) fits treat them. The figures show gray triangles, but the text doesn't say whether those limits enter the regression as censored data. If they're simply excluded, the r31 fits are on a detection-biased subsample, and the non-detections are likely the faint, low-excitation systems at low SFR/ΣSFR. That would push the r31 intercept up and make the low-end prescriptions overestimate r31, which in turn underestimates CO(1–0) luminosity and molecular gas mass derived from CO(3–2). The literature comparison in Figures 6–8 partially reassures me—the binned literature data fall close to the AMISS fits—but that is not a substitute for handling the censored data in the original fit. The authors should state what they did, and ideally re-run with a survival/Bayesian censored model.\n\nOtherwise the paper is careful. The r21–ΣSFR reproduction of Paper II's independent fit checks selection bias, the cloud-model interpretation is explicit about degeneracies (they note in Appendix C that other parameter choices favor unexpectedly low densities or high temperatures), and the r32 = r31/r21 consistency check is sensible. The density-continuum interpretation is plausible but not tightly constrained, and the paper does not oversell it.\n\nThis deserves a serious referee. I'd send it back with a request to address the censored-upper-limit issue, but I'd expect it to go through after that. I'll likely cite the prescriptions when I next do CO(3–2) work. Recommendation: accept after clarifying and justifying the treatment of the 11 upper limits.","headline":"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.","tokens_in":23729,"tokens_out":3924,"would_cite":true,"duration_ms":41549,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["CO line ratios","spectral line energy distributions","molecular gas","star formation","interstellar medium","galaxy evolution","submillimeter spectroscopy","low-J CO transitions"],"falsifier":"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.","tokens_in":22545,"feed_emoji":"🌌","tokens_out":9091,"duration_ms":81759,"temperature":0.7,"pith_summary":"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.","feed_headline":"CO line excitation scales with star formation in 47 galaxies","feed_subtitle":"Higher star-formation rates mean brighter CO(3-2) and CO(2-1) lines, with a spread wider than simulations predict.","key_machinery":"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 $\\Sigma_{\\rm SFR}$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the xCOLD GASS catalog with SFRs, stellar masses, and CO(1-0) data for the sample.","marker":"Saintonge et al. 2017"},{"why":"Paper II established the r21-SFR trend on a larger sample and provided the r21 prescription extended here.","marker":"Keenan et al. 2025"},{"why":"Supplies independent CO(3-2) measurements for eighteen survey targets, enlarging the final sample to 47.","marker":"Lamperti et al. 2020"},{"why":"Provides the molecular cloud model grid and comparison line ratios used to infer gas density and temperature.","marker":"Leroy et al. 2022"},{"why":"Provides the simulation-based SLED prescription whose predicted variation the observations exceed.","marker":"Narayanan & Krumholz 2014"},{"why":"Supplies ULIRG line ratios and Sigma_SFR values that extend the observed trends to the starburst regime.","marker":"Montoya Arroyave et al. 2023"}],"fun_headline_variants":["Wider CO excitation range than models as star formation rises","CO line ratios increase with star formation in 47 galaxies","Survey: gas density rises with star formation in galaxies","Beyond models: CO excitation tracks star formation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Wider CO excitation range than models as star formation rises","CO line ratios increase with star formation in 47 galaxies","Survey: gas density rises with star formation in galaxies","Beyond models: CO excitation tracks star formation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000647,"raw_usage":{"total_tokens":3022,"prompt_tokens":1049,"completion_tokens":1973,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":665,"completion_tokens_details":{"reasoning_tokens":1910}},"tokens_in":665,"tokens_out":1973,"duration_ms":15721,"temperature":1.0,"reasoning_tokens":1910,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T14:30:34.547744+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"J., et al","cited_arxiv_id":null,"evidence_quote":"Supplies the xCOLD GASS catalog with SFRs, stellar masses, and CO(1-0) data for the sample."},{"cited_title":"P., Marrone , D","cited_arxiv_id":null,"evidence_quote":"Paper II established the r21-SFR trend on a larger sample and provided the r21 prescription extended here."},{"cited_title":"2020, , 889, 103","cited_arxiv_id":null,"evidence_quote":"Supplies independent CO(3-2) measurements for eighteen survey targets, enlarging the final sample to 47."},{"cited_title":"K., Rosolowsky , E., Usero , A., et al","cited_arxiv_id":null,"evidence_quote":"Provides the molecular cloud model grid and comparison line ratios used to infer gas density and temperature."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the simulation-based SLED prescription whose predicted variation the observations exceed."},{"cited_title":"2023, , 673, A13","cited_arxiv_id":null,"evidence_quote":"Supplies ULIRG line ratios and Sigma_SFR values that extend the observed trends to the starburst regime."}],"review_version":1}