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REVIEW 4 major objections 5 minor 85 references

The first exploration of the correlations between \textit{WISE} 12 \micron\ and CO emission in early-type galaxies

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

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Pith's one-line read WISE 12-micron luminosity is a tight proxy for CO emission in early-type galaxies.

desk verdict Useful first ETG calibration, but the headline correlation rests on detections only; including upper limits shifts the slopes and undercuts the constant-R21 claim. read the letter →

arxiv 2412.07176 v1 pith:AM6R47GW submitted 2024-12-10 astro-ph.GA

Yang Gao , Enci Wang , Qing-Hua Tan , Timothy A. Davis , Fu-Heng Liang , Xue-Jian Jiang , Ning Gai , Qian Jiao
show 5 more authors
DongDong Shi Shuai Feng Yanke Tang Shijie Li Yi-Fan Wang
This is my paper · ORCID
classification astro-ph.GA
keywords early-typegalaxiesmoleculargasCOluminosityWISE12micronmid-infraredscalingrelationsgalaxyquenchingCO-darklineratioR21
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

The paper asks whether a single mid-infrared band, the 12 micron channel of the all-sky WISE survey, can serve as a practical proxy for the molecular gas content of early-type galaxies, where CO observations are scarce and often yield non-detections. Using 352 nearby early-type galaxies assembled mainly from volume-limited surveys, it finds that for the 82 CO(1-0) and 76 CO(2-1) detections, CO luminosity and 12 micron luminosity are tightly correlated, with correlation coefficients above 0.9 and intrinsic scatter near 0.1 dex. The slopes are steeper than the corresponding relations in star-forming galaxies, and the CO(1-0) and CO(2-1) slopes are identical, indicating that the line ratio $R_{21}$ does not depend on mid-infrared luminosity in these galaxies. The paper shows that the difference from star-forming galaxies can be largely removed either by subtracting estimated 12 micron emission from old stellar populations or by adding a constant CO brightness density, and offers these corrected relations as estimators of molecular gas in gas-poor galaxies.

What carries the argument

The central object is the $L_{\rm CO}$--$L_{12\,\mu\mathrm{m}}$ scaling relation, a power law in log-log space fitted with a Bayesian linear regression that accounts for measurement errors on both axes. The paper's diagnostic is the comparison of slopes between CO(1-0) and CO(2-1); identical slopes imply a constant line ratio $R_{21}$. Two correction mechanisms are used to interpret the steeper slope: subtracting the 12 micron emission expected from old stellar populations (following an established method) and adding a constant CO brightness density intended to represent CO-dark or diffuse molecular gas. The latter is presented as the average additional brightness, $2.8$ and $4.4\ \mathrm{K\ km\ s^{-1}}$ for CO(1-0) and CO(2-1), required to remove the correlation between the deviation and the molecular gas surface density.

What would settle it

Conduct a deep CO survey of the 258 CO(1-0) non-detected galaxies in the sample, sensitive enough to detect them if they lie on the detection-only relation; if the majority are not detected at those predicted levels, or fall on the star-forming galaxy relation instead, the claimed steep slope for the early-type population is refuted. A second independent check is high-resolution matched-beam CO(1-0) and CO(2-1) mapping of gas-rich early-type galaxies to see whether $R_{21}$ is truly constant or varies with local conditions as it does in star-forming galaxies.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that the empirical power-law relations between CO line luminosity and WISE 12 micron luminosity known for star-forming galaxies also hold in early-type galaxies, but with distinct parameters. For CO(1-0), the best fit is $\log L_{\rm CO(1-0)} = (1.14\pm0.06)\log L_{12\,\mu\mathrm{m}} - (1.59\pm0.50)$, with intrinsic scatter 0.09 dex and Spearman $r=0.91$; for CO(2-1), $\log L_{\rm CO(2-1)} = (1.19\pm0.06)\log L_{12\,\mu\mathrm{m}} - (2.00\pm0.49)$, with scatter 0.10 dex and $r=0.92$. Purely on the 68 galaxies detected in both lines, the two slopes agree at $1.16\pm0.06$ and $1.16\pm0.07$, from which the paper concludes that $R_{21}$ is independent of mid-infrared luminosity in early-type galaxies, in contrast to star-forming galaxies where $R_{21}$ rises with mid-infrared luminosity. The deviations of individual early-type galaxies from the star-forming relations do not correlate with colour, morphology, or specific star formation rate, but do correlate with molecular gas surface density; this dependence is eliminated either by subtracting the old-star contribution to the 12 micron flux or by adding a constant CO brightness density ($2.8$ and $4.4\ \mathrm{K\ km\ s^{-1}}$ for the two lines). These two corrections are preliminary but both bring the early-type relations into agreement with the star-forming ones, and the paper argues that the corrected relations can be used to estimate molecular gas masses in gas-poor systems with small scatter.

Load-bearing premise

The headline correlations use only the ~80 galaxies with detected CO, and if the typical gas-poor early-type galaxy lies far below that detection-only relation, the steeper slope and constant $R_{21}$ would overstate the population behaviour.

Editorial extensions

If this is right

  • If the relation holds beyond the detections, a single WISE 12 micron measurement gives molecular gas masses for early-type galaxies to within roughly 0.1 dex of intrinsic scatter, with no need for expensive CO observations.
  • The constant $R_{21}$ means CO(2-1) can be used interchangeably with CO(1-0) as a gas tracer in these galaxies, removing excitation uncertainty from the conversion.
  • The steeper slope implies that at a given 12 micron luminosity an early-type galaxy contains less CO-bright gas than a star-forming galaxy, so applying the star-forming calibration would systematically overestimate molecular gas content in gas-poor systems.
  • Because the deviations show no dependence on colour, morphology, or specific star formation rate, the correction can be applied without knowledge of other galaxy properties.
  • Both proposed corrections (old-star subtraction and constant CO-dark gas brightness) recover agreement with the star-forming relations, leaving open which physical process dominates.

Reading between the lines

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

  • One editorial extension: the paper's headline slopes come from detections only; Table 1 shows that adding the 258 CO(1-0) and 262 CO(2-1) non-detections as upper limits changes the slopes to 1.24 and 1.52, so the population-level relation for all early-type galaxies remains less settled than the detection-based claim.
  • If the constant CO-dark brightness floor is real, deep CO mapping of the optically faint outskirts of early-type galaxies should reveal a widespread, low-level CO component of roughly 2-4 K km/s, which would be directly testable.
  • If constant $R_{21}$ holds in resolved data, it would imply that CO excitation in early-type galaxies is governed by a mechanism other than local star formation surface density, such as cosmic-ray heating or turbulent pressure.
  • The full-sky coverage of WISE means that, if these relations generalise, molecular gas estimates could be produced for many thousands of early-type galaxies across current optical and near-infrared surveys, enabling statistical studies of quenching without new CO campaigns.
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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. This paper compiles CO(1-0) and CO(2-1) measurements for 352 early-type galaxies (ETGs) from public surveys, matching them with WISE 12 micron luminosities measured in the CO beams. For the 82 CO(1-0) and 76 CO(2-1) detections, it reports tight power-law correlations with Spearman r ~ 0.9 and intrinsic scatter ~ 0.1 dex, slopes that are steeper than those of star-forming galaxies, and consistent slopes for the two CO lines. The authors then analyse residuals from the Gao et al. (2019) star-forming relation and propose either subtracting the 12 micron emission from old stars or adding a constant CO brightness density as ways to reconcile the ETG relation with the star-forming relation.

Significance. If the detection-only correlations apply to the wider ETG population, the paper would provide a practical single-band estimator of molecular gas in gas-poor galaxies and a new constraint on excitation conditions in ETGs. The compiled catalogue in Table 2 and the explicit upper-limit fits are useful assets, and the paper is transparent about the detection fraction and about using LinMix with censored data. However, the headline claims rest on a minority of the sample (82/352 and 76/352 detections), and the censored fits in Table 1 materially change the key slopes and the implied R21 behaviour. The significance of the paper is therefore conditional on reframing the claims and on a more careful treatment of selection and censoring.

major comments (4)
  1. [Section 3.1, Table 1] The abstract's headline numbers (r > 0.9, intrinsic scatter < 0.1 dex, and the estimator in Eq. 4) are computed from the 82 CO(1-0) and 76 CO(2-1) detections only. Table 1 shows that adding the 258/262 non-detections as 5-sigma upper limits changes the CO(1-0) slope from 1.14 +/- 0.06 to 1.24 +/- 0.07 and the CO(2-1) slope from 1.19 +/- 0.06 to 1.52 +/- 0.10, while Spearman r drops to 0.87/0.82 and the intrinsic scatter for CO(1-0) rises to 0.16 dex. Because the paper's stated application is molecular-gas estimation in gas-poor ETGs, most of which are non-detections, the detection-only relation should not be presented as the population relation without either demonstrating that the detected galaxies are representative or making the censored fit the primary result.
  2. [Section 3.2, Table 1] The constant-R21 conclusion is based on the detection-only slopes (1.16 +/- 0.06 vs 1.16 +/- 0.07 for the 68 galaxies with both lines). The censored fits (1.24 +/- 0.07 vs 1.52 +/- 0.10) differ by roughly 2.8 sigma, which would instead predict R21 increasing with 12 micron luminosity. Section 3.2 acknowledges that non-detections could substantially alter the best-fit parameters, but the abstract and the summary list the constant-R21 result without this caveat. Please either restrict the claim to the detected population or provide a censoring-robust estimate of the R21 behaviour.
  3. [Section 4, Appendices A and B] The old-star subtraction and the constant CO brightness densities (2.8 and 4.4 K km/s) are fitted to the same deviations that they are subsequently used to remove. The improvement after correction is therefore a post-hoc fit, not an independent validation. To support the physical interpretation and the claimed practical correction, the authors should test the corrections on an independent sample (e.g., high-resolution CO maps or an out-of-sample ETG set) or clearly label these corrections as illustrative toy models rather than validated recipes.
  4. [Section 3.2, Eq. (5)] The claim that the ETG CO(2-1) slope is steeper than the star-forming slope is not strongly established by the detection-only numbers: 1.19 +/- 0.06 versus 1.11 from Gao et al. (2019) is only about a 1.3-sigma difference when only the ETG uncertainty is considered. Please propagate the uncertainty of the reference relation, or fit both samples in a common framework, before claiming a steeper slope for CO(2-1).
minor comments (5)
  1. [Eq. (4)] The quantity log(Mmol / [K km/s pc^2]) in Eq. (4) is dimensionally inconsistent; the argument of the logarithm should presumably be Mmol/Msun. Please correct the units.
  2. [Section 2.1, Table 2] Table 2 is referred to as 'Table B' in Section 2.1; please renumber or refer to it consistently. Also check entries such as the CO(2-1) upper limit for NGC4143, which appears implausibly large and may be a column or units typo.
  3. [Abstract and Figure 2 caption] There are several grammar slips: 'adding an constant CO brightness density' should be 'adding a constant CO brightness density', and the Figure 2 caption 'arrows mean 5-sigma CO upper limits' should be 'arrows denote 5-sigma CO upper limits'.
  4. [Footnote 1] The statement that adopting different 2-5 sigma upper limits does not 'significantly alter' the slopes should be quantified; a sentence or supplementary table giving the resulting slopes would allow readers to verify this claim.
  5. [Section 3.2] The sentence 'the 5-sigma CO upper limits for non-detections are close to the best-fitting line for detections, suggesting that these non-detections fall significantly below the fit' is internally confusing; please clarify whether the upper limits lie on, above, or below the detection relation.

Circularity Check

1 steps flagged · score 4.0 of 10

Primary CO–12 µm scaling relations are empirical and independent; partial circularity enters only in the fitted CO-dark gas correction presented as a discovery.

  1. fitted input called prediction [Section 4.1 and Appendix B]
    "Then we do a simple and rough attempt in Appendix B, and discover the deviations could be significantly decreased, by adding an constant CO brightness density, averaging 2.8−0.6+0.8[K km s−1] and 4.4−1.4+2.2[K km s−1] for CO (1-0) and (2-1) respectively, which is assumed to correct the potential CO dark gas. ... After applying these constant brightness density correction to the CO (1-0) and CO (2-1) luminosity, the distributions of Δ log(L_CO) noticeably narrow, and the dependencies on Σ_H2 are almost eliminated, while the scatter in the correlations remains essentially unchanged."

    The 2.8 and 4.4 K km/s values are not derived from an independent measurement of CO-dark gas; they are the average offsets required to shift the detected ETGs onto the authors' own Gao et al. (2019) star-forming relation, from which the deviations Δ log(L_CO) are defined in Eq. 5. Reporting that adding these fitted constants 'eliminates' the Δ log(L_CO)–Σ_H2 dependence is therefore a self-consistency statement about the fitting procedure, not an independent confirmation of the CO-dark gas hypothesis. The paper presents this fitted correction as a discovery ('we discovered that such dependencies can be eliminated') and as a practical tool, but the correction is calibrated on the same residuals it is then used to remove.

full rationale

The headline correlations (r > 0.9, intrinsic scatter < 0.1 dex) are obtained by direct regression of CO and WISE 12 µm luminosities for the 82 CO(1-0) and 76 CO(2-1) detections; no fitted parameter from the 12 µm data is used to construct the CO values, so these relations are self-contained measurements. The constant-R21 conclusion follows algebraically from the nearly equal slopes (1.16 vs 1.16) fitted to the 68 galaxies with both lines, and is not imposed by an assumption. The comparison to star-forming slopes is anchored to Gao et al. (2019), which contains overlapping authors, but the same figure shows external relations from Chown et al. (2021), Zhang & Ho (2023), Chown et al. (2024), and Shivaei & Boogaard (2024), so the steeper-slope claim does not rest only on the authors' own prior work. The circular element is confined to the interpretive correction in Appendix B: the constant CO brightness density is calculated from the average deviations of the ETGs from the Gao et al. (2019) relation and is then used to show that those deviations narrow and lose their Σ_H2 dependence; this is a fitted offset presented as a discovered correction. The paper itself flags the censoring limitation in Section 3.2 (adding upper limits changes slopes from 1.14/1.19 to 1.24/1.52 and Spearman r from 0.91/0.92 to 0.87/0.82), which is a robustness concern rather than a circularity. Overall, the central empirical claims are independent and reproducible, with partial circularity limited to the post-hoc CO-dark gas correction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. Its free parameters are the two constant CO brightness densities fitted in Appendix B and the old-star L12 versus M* relation fitted in Appendix A. The adopted alpha_CO, R21, and beam-filling assumptions are carried from the literature and are load-bearing for the corrections.

free parameters (3)
  • Constant CO brightness density for CO(1-0) = 2.8 (+0.8/-0.6) K km/s
    Fitted in Appendix B to remove the correlation between Delta log L_CO and molecular gas surface density; interpreted as CO-dark gas.
  • Constant CO brightness density for CO(2-1) = 4.4 (+2.2/-1.4) K km/s
    Fitted in Appendix B for the CO(2-1) line; interpreted as extra CO-dark gas or an R21 effect.
  • Old star 12 micron luminosity versus stellar mass relation = Not quoted (see Figure 4)
    Fitted to CO non-detections in Appendix A and subtracted from L12 to test whether old stars cause the steeper slope.
assumptions (4)
  • domain assumption The Galactic CO-to-H2 conversion factor alpha_CO = 3.2 M_sun/(K km/s pc^2) applies to early-type galaxies.
    Used in Equation (4) and Appendix B; no ETG-specific alpha_CO is justified, and the paper discusses that a different alpha_CO could remove the deviations.
  • domain assumption The CO(2-1)-to-CO(1-0) line ratio R21 = 0.7 is used to compute molecular gas surface densities.
    Adopted from Leroy et al. (2013) in Appendix B; the paper's own finding of constant R21 could make this choice inconsistent.
  • ad hoc to paper The molecular gas disc fills the single-dish beam in early-type galaxies.
    Stated in Appendix B as a simple assumption, based on some sizes from Davis et al. (2013); per-galaxy beam filling is not measured.
  • domain assumption The 12 micron emission of CO non-detected ETGs traces mainly old stellar populations.
    Appendix A fits L12 versus stellar mass for non-detections and subtracts it; this assumes their mid-infrared is not powered by gas or recent star formation.

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Cite this review

Pith. "Pith review of The first exploration of the correlations between \textit{WISE} 12 \micron\ and CO emission in early-type galaxies." pith.science (2026). https://pith.science/paper/AM6R47GW

@misc{pith2026241207176,
  author       = {Pith},
  title        = {Pith review of: The first exploration of the correlations between \textitWISE 12 \micron\ and CO emission in early-type galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AM6R47GW}},
  note         = {Machine review of arXiv:2412.07176}
}
abstract

We present the analysis of a comprehensive sample of 352 early-type galaxies using public data, to investigate the correlations between CO luminosities and mid-infrared luminosities observed by \textit{Wide-field Infrared Survey Explorer} (\textit{WISE}). We find strong correlations between both CO (1-0) and CO (2-1) luminosities and 12 \micron\ luminosity, boasting a correlation coefficient greater than 0.9 and an intrinsic scatter smaller than 0.1 dex. The consistent slopes observed for the relationships of CO (1-0) and CO (2-1) suggest that the line ratio R21 lacks correlation with mid-infrared emission in early-type galaxies, which is significantly different from star-forming galaxies. Moreover, the slopes of $L_{\rm CO (1-0)}$--$L_{\mbox{12\micron}}$ and $L_{\rm CO (2-1)}$--$L_{\mbox{12\micron}}$ relations in early-type galaxies are steeper than those observed in star-forming galaxies. Given the absence of correlation with color, morphology or sSFR, the correlation between deviations and the molecular gas mass surface density could be eliminated by correcting the possible 12 \micron\ emission from old stars or adopting a systematically different $\alpha_{\rm CO}$. The latter, on average, is equivalent to adding an constant CO brightness density, specifically ${2.8{_{-0.6}}\!\!\!\!\!\!\!\!\!^{+0.8}}~[\mathrm{K~km~s^{-1}}]$ and ${4.4{_{-1.4}}\!\!\!\!\!\!\!\!\!^{+2.2}}~[\mathrm{K~km~s^{-1}}]$ for CO (1-0) and (2-1) respectively. These explorations will serve as useful tools for estimating the molecular gas content in gas-poor galaxies and understanding associated quenching processes.

Figures

Figures reproduced from arXiv: 2412.07176 by the authors.

Figure 1
Figure 1. The panels show the distribution of our ETGs: the 𝑀r versus 𝑢 − 𝑟 colour–magnitude diagram shown in panel a, the stellar mass (𝑀∗) vs. near-𝑈𝑉 − 𝑟 plane in panel b, and the Sersic index (𝑛) in panel c. These three panels are plotted based on the data of the subsample of 274 galaxies, using SDSS photometric parameters from NSA. Panel d displays the morphological T type distribution of the entire sample (352 galaxies)… view at source ↗
Figure 2
Figure 2. Correlations between the CO (1-0) and CO (2-1) luminosities and the mid-infrared monochromatic luminosities (𝐿12𝜇m) as measured in the WISE 12 𝜇m band for early-type galaxies. As indicated in the upper left corner, different colors and symbols represent detections from various CO projects, with error bars showing their respective measurement uncertainties. The dark gray downward-pointing arrows mean 5-𝜎 CO upper lim… view at source ↗
Figure 3
Figure 3. The scaling of Δ log(𝐿CO), calculated using Equations 5 and representing the deviation from typical star-forming global 𝐿CO-𝐿12𝜇m relations (Gao et al. 2019), is plotted against the basic properties of integrated galaxies. These properties include stellar mass 𝑀∗, T type, sSFR and NUV−𝑟 color arranged from left to right. The plots show CO (1-0) in the top panels and CO (2-1) in the bottom panels. Large red triangles… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The WISE 12 𝜇m luminosity within CO(1-0) beam is plotted as a function of stellar mass. Blue circles are ETGs with CO detection, while open circles represent those without detected molecular gas. The best fit of these non-detections is shown as a black solid line. B. T…
Figure 5
Figure 5. Figure 5: Same as the left panel of [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: The left panels demonstrate the dependence of the CO luminosity deviations on molecular gas mass surface densities (Σ𝑚𝑜𝑙), which are computed based on CO (1-0) or CO (2-1) surface brightness using the galactic conversion factor 𝛼CO = 3.2 M⊙(K km s−1pc2 ) −1 and 𝑅21 = 0…

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