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REVIEW 3 major objections 5 minor 62 references

CO and mid-infrared emission follow two distinct scaling families at 100-pc scales, set by the host galaxy's star-formation rate.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-04 06:46 UTC pith:YMF5UWOA

load-bearing objection Solid statistical study that credibly revises the CO–F2100W slope, but the headline 'clear bimodality' of the intercept is visually suggested, not formally demonstrated. the 3 major comments →

arxiv 2511.10464 v2 pith:YMF5UWOA submitted 2025-11-13 astro-ph.GA

Correlations of ALMA CO(2-1) with JWST mid-infrared fluxes down to scale of lesssim100 parsec in nearby star-forming galaxies from PHANGS

Tao Jing , Cheng Li This is my paper
classification astro-ph.GA
keywords CO(2-1)PAH emissiondust emissionscaling relationsinterstellar mediumJWSTALMAregression with uncertainties
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper claims that on ~100 pc scales, the relation between CO(2-1) emission and mid-infrared emission from PAHs and dust is a log-log linear relation with a nearly universal slope, but the normalization (intercept) is not single-valued: it splits galaxies into two families with higher or lower intercept. The split tracks the host galaxy's overall star-formation rate, with stronger star-formers showing lower intercepts. The paper further argues that the previously reported sublinear slope for the 21-micron dust band is an artifact of the regression method used, and that the true slope is similar to the PAH bands. If right, this changes how CO-to-dust conversion is calibrated at cloud scales and points to a discrete physical switch in the interstellar medium.

Core claim

Applying a regression technique that explicitly handles heteroscedastic uncertainties and outliers (raddest) to 19 nearby star-forming galaxies, the paper finds that log I_CO versus log I_MIR (F770W, F1130W, F2100W) is well described by a single straight line for the majority of spaxels at ≤100 pc scales, with slopes consistently superlinear and similar across bands. The dominant galaxy-to-galaxy variation is in the intercept b, which shows a clear bimodal distribution; the two groups (high-b and low-b) have similar slopes but different overall CO-to-MIR ratios and different intrinsic scatter. The bimodality is tied to the normalized star-formation rate of the host galaxy: galaxies with high

What carries the argument

The central object is the log-log linear scaling relation log I_CO = k log I_X + b + ε, with ε Gaussian intrinsic scatter, fitted by raddest, a regression method that builds a generative model of the observed fluxes and uncertainties using normalizing flows and then estimates k, b, σ through likelihood or a KS-test-based goodness-of-fit. The intercept b carries the paper's main result: its bimodality, not the slope, encodes the physical state separating the two galaxy families.

Load-bearing premise

The fitted parameters—and thus the claimed bimodality—assume that the raddest regression likelihood (including its normalizing-flow model of the true flux distributions and its treatment of uncertainties) is unbiased; for ~10% of datasets the uncertainties had to be rescaled by hand to pass a 2D KS test, and if that heuristic is wrong, the intercept split could be an artifact.

What would settle it

Take the same 19 galaxies and re-fit with a regression that does not rely on the KS-test-based likelihood or on rescaled errors (e.g., a fully Bayesian model with explicit outlier component), and check whether the bimodality in b survives at >3σ; or apply the same raddest pipeline to an independent set of 19 star-forming galaxies and ask whether the b values fall into the same two clusters with the same sSFR separation.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If the intercept bimodality is real, CO-to-dust and CO-to-PAH conversion factors at ~100 pc are not single-valued; using one calibration for all star-forming galaxies would bias molecular gas masses by the factor corresponding to the intercept offset.
  • The previously published sublinear CO–F2100W slope is attributed to the fitting method rather than to astrophysics; re-analysis of those data with uncertainty-aware regression should recover the same slopes as the PAH bands.
  • Because the bimodality disappears at spatial scales above ~100 pc, measurements at kpc scales will miss the dichotomy—this predicts that resolved studies at hundreds of pc are necessary to see it.
  • The flattening of the relation in bright regions is systematic and stronger for the dust band, which suggests that PAH and dust emission are enhanced relative to CO in the most intense radiation environments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The two-family split might reflect a threshold in the diffuse UV background intensity that enhances PAH/dust emissivity without destroying the carriers; if so, the boundary between low-b and high-b groups should correlate with a measurable jump in PAH-to-dust ratio or dust temperature, which the paper does not test directly.
  • A direct extension would be to apply the same fitting technique to the full set of galaxies in the same survey; the bimodality should persist and the group separation should sharpen with better statistics.
  • The method's reliance on normalizing flows for the intrinsic distribution of the independent variable could be probed by rerunning the analysis with a simpler parametric model; if the bimodality remains, the result is not an artifact of the density estimator.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper applies the raddest regression method (Jing & Li 2025) to PSF-matched PHANGS-ALMA CO(2-1) and PHANGS-JWST MIR maps of 19 star-forming galaxies, fitting log-log-linear relations between I_CO and I_F770W,PAH, I_F1130W, and I_F2100W at ≈100 pc scales, separately for HII-, composite-, and AGN-like ionization conditions. The authors report that the fitted slope and intrinsic scatter vary modestly across galaxies, while the intercept b_KS varies strongly and appears bimodal (high-b versus low-b, split at b_KS=0). This bimodality is argued to be related to the host galaxy's overall star formation strength (sSFR/SFE). The paper also quantifies deviations from log-linearity in the brightest regions, mainly as slope flattening, and studies how k_KS, b_KS, σ_KS depend on spatial scale. The manuscript provides extensive parameter tables and a public implementation of the fitting code.

Significance. If the central claims hold, the paper would establish that the CO-to-PAH/dust conversion at ~100 pc is not single-valued: the slope is approximately universal, but the normalization is bimodally tied to host-galaxy sSFR, and previously reported sublinear F2100W slopes are a regression artifact. This would be an important result for interpreting cloud-scale CO/MIR tracers. The paper's strengths include the use of a regression method with external mock-data validation, public code, detailed comparison with previous PHANGS work (Leroy et al. 2023b; Chown et al. 2025), and a large set of fitted parameters per galaxy and ionization condition. However, the headline bimodality claim currently rests on visual inspection of 19 b_KS values with an arbitrary split at b_KS=0 and no formal multimodality test; this is a load-bearing issue that needs to be resolved before the central claim can be accepted.

major comments (3)
  1. [§3.2, Figure 4] The claim of a 'clear bimodality' in b_KS is not supported by any quantitative test. The high-b/low-b classification is made by a visual split at b_KS=0 in the F770W,PAH 'all' panel, and with only 19 galaxies the apparent gap can be a sampling fluctuation of a continuous distribution. No Hartigan dip test, Gaussian mixture comparison, or other multimodality test is presented. Because the abstract and §4.2.2 build the central interpretation on this bimodality, please add a formal test and report its significance, and show the sensitivity of the classification to the threshold choice. The authors' own admission in §4.2.2 that it is 'rather difficult to explain why it is a b_KS bimodality rather than a continuum' strengthens the need for such a test.
  2. [§3.2.1, Figure 6 and Figure 7] The connection between b_KS and sSFR is presented as supporting the bimodality interpretation, but the reported correlations are only at the 2σ level, and no 3σ correlations are found between any global property and k_KS, b_KS, or σ_KS. Moreover, because the high-b/low-b split is defined directly from b_KS, the statement that the b_KS–sSFR correlation 'primarily arises from the bimodality' is close to a restatement of the chosen split. Please report the b_KS–sSFR correlation on the full sample without subgrouping, and quantify whether a continuous correlation model is actually disfavored relative to the two-group model.
  3. [§2.3] The heuristic rescaling of x_err or y_err for ~10% of normalizing-flow cases is a potential source of bias in the fitted parameters, including b_KS. The authors state that 'all key results' remain consistent when restricting to non-problematic data or including all data without correction, but no such comparison is shown. Since the bimodality claim depends on the exact b_KS values, please provide the requested robustness test (e.g., a comparison of k_KS, b_KS, σ_KS with and without rescaling) or a mock-based validation of the rescaling procedure itself.
minor comments (5)
  1. [Abstract and §2.2] The abstract and §1 use 'log-log linear relations', while §2.2 and Equation (1) describe a 'log-linear' relation. Please make the terminology consistent (the model is linear in log I_CO vs. log I_X).
  2. [Table 1] The last column 'high-b' contains 'Yes'/'No' but no definition or pointer to Figure 4. Please add a note explaining the criterion and that it is based on F770W,PAH, all ionization conditions.
  3. [Figure 2 caption] The caption says 'the contour showcase the distribution' and 'the bold line is corresponding best-fit result.' These should be 'contours show' and 'the bold line is the corresponding best-fit result.' Also check for missing articles elsewhere in the text.
  4. [§4.2.2] There are several typos in this subsection: 'radiation filed' should be 'radiation field', 'cloud coexist' should be 'could coexist', and 'Hiiregions' should be 'HII regions'. Similar spacing issues occur for 'low-b' and 'high-b' in several places.
  5. [§3.4 and Figure 11] The text refers to 'low-band high-b galaxies' and 'low-b and high-b galaxies' in a way that is easy to confuse with the MIR bands. Consider using 'low-b/high-b subsamples' throughout and reserving 'band' for F770W,PAH, F1130W, and F2100W.

Circularity Check

0 steps flagged

No circular derivation; main results are empirical fits and comparisons, with self-cited raddest backed by independent mock validation.

full rationale

The paper's derivation chain is not circular. Equation (1) is a standard log-linear model whose parameters (k, b, sigma) are estimated from the data; claims that the relation 'can be well described' are fit-quality statements, not predictions forced from inputs. The b_KS bimodality and its relation to sSFR are empirical properties of the fitted intercepts plotted against external galaxy properties; the split at b=0 is a classification choice, and the lack of a formal multimodality test is a statistical robustness concern, not a circular reduction. The main self-citation is to JL25 for raddest and for the claim that mODR biases slopes. This is not circular: raddest is publicly available and JL25 validates it on mock datasets with known true parameters and on external PHANGS data, satisfying the independent-support criterion; the current paper also compares mLINMIX on its own sample to show the expected bias. The uncertainty-rescaling heuristic in Section 2.3 is a data-quality correction whose effect the authors explicitly test by checking that results are consistent without it; it is an assumption about noise, not an input that defines the output. No equation in the paper is equivalent by construction to a claimed prediction, and no load-bearing argument reduces to an unverified self-citation.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The paper introduces no new physical entities. Its results rest on a set of observational and statistical assumptions: continuum subtraction, ionization classification, the log-linear functional form, the raddest noise model, and a heuristic uncertainty rescaling. The main free parameters are the fitted regression parameters and the arbitrary b_KS=0 split used to define the claimed bimodality.

free parameters (4)
  • k_KS, b_KS, sigma_KS = Per galaxy, band, and ionization condition; values in Table 2
    These are the regression parameters that constitute the central results (Equation 1).
  • Turning point x_0, high-branch slope k_1, intercept b_1 = Fitted via ML method for piecewise cases; not tabulated in full
    Used for the non-log-linear deviation analysis (Equation 3).
  • high-b/low-b split threshold = b_KS = 0
    Galaxies are classified into high-b and low-b subgroups by splitting the fitted b_KS at exactly zero (section 3.2).
  • Uncertainty rescaling factors for x_err/y_err = Not reported
    Heuristic rescaling applied to roughly 10% of cases where normalizing flows fail the 2D KS test (section 2.3).
axioms (6)
  • domain assumption F770W stellar continuum contamination is 12% of F200W (I_F770W,PAH = I_F770W - 0.12 I_F200W)
    Adopted from Chown et al. 2025 in section 2.1; if wrong, the F770W PAH scaling and b_KS shift.
  • domain assumption The P1-P2 diagnostic of Ji & Yan 2020 correctly classifies spaxels as HII-like, composite-like, or AGN-like
    Used throughout sections 3.1-3.2; misclassification would mix populations and affect fitted parameters.
  • domain assumption The log-linear model with Gaussian intrinsic scatter (Equation 1) applies to the majority of pixels
    Adopted in section 2.2; deviations are modeled as piecewise/outliers, but the headline relation assumes this functional form.
  • ad hoc to paper Heuristic rescaling of overestimated uncertainties does not bias the fitted parameters
    Section 2.3: x_err or y_err are scaled to force sigma_obs = err; still-failing cases are excluded, with no independent validation of neutrality.
  • domain assumption Noise and error propagation from R. Klein 2021 are correct after PSF matching
    Section 2.1 underpins all likelihood evaluations in raddest.
  • domain assumption The 19 main-sequence galaxies are representative enough to infer bimodality and global-property correlations
    The sample is limited to galaxies with PHANGS-ALMA, PHANGS-JWST, and PHANGS-MUSE coverage; the authors note the sample is small in section 5.

pith-pipeline@v1.3.0-alltime-deepseek · 33093 in / 13743 out tokens · 122257 ms · 2026-08-04T06:46:25.681523+00:00 · methodology

0 comments
read the original abstract

We investigate the correlations of CO (2-1) emission (${I_{\rm CO}}$) with PAH (${I_{\rm F770W, PAH}}$ and ${I_{\rm F1130W}}$) and dust (${I_{\rm F2100W}}$) emission down to scales of $\lesssim$ 100 pc, by applying ${\tt raddest}$, a novel regression technique recently developed by T. Jing & C. Li (2025) that effectively handles uncertainties and outliers in datasets, to 19 nearby star-forming galaxies in the PHANGS sample. We find that for the majority of the data points in all galaxies, the scaling of ${I_{\rm CO}}$ with ${I_{\rm F770W, PAH}}$, ${I_{\rm F1130W}}$, and ${I_{\rm F2100W}}$ can be well described by log-log linear relations, though with substantial dependence on ionization conditions (i.e., HII-like, composite-like, and AGN-like). Under given ionization conditions, significant galaxy-to-galaxy variations are identified, and are primarily attributed to variations of intercept $b$, which exhibits clear bimodality. This bimodality is related to the normalized overall host galaxy star formation rate, such as specific star formation and star formation efficiency. The differences in slope $k$ and intrinsic scatter $\sigma$ across different MIR bands (${I_{\rm F770W, PAH}}$, ${I_{\rm F1130W}}$, and ${I_{\rm F2100W}}$) are minor compared to their galaxy-to-galaxy variations. All parameters ($k$, $b$, and $\sigma$) depend on the spatial scale of measurement, suggesting that the coupling among CO, PAH, and dust is regulated by different mechanisms at varying scales. We identify deviations from the log-log linear relation in the brightest regions, primarily characterized by a flattening of the slope. No significant (3$\sigma$) correlations are found between global properties and the best-fit parameters. We discuss the comparison to previous studies and plausible physics behind the statistical results obtained in this work.

Figures

Figures reproduced from arXiv: 2511.10464 by Cheng Li, Tao Jing.

Figure 1
Figure 1. Figure 1: Examples of the three different cases of non-log-linear behavior (case (a), (b), and (c), from left to right). In each panel, the lower sub-panel displays the logarithm of the median observed CO(2-1) flux in each observed F2100W or F770WPAH flux bin as black circles (real data), blue circles (mock data generated by single log-linear fitting), and green circles (mock data generated by piecewise log-linear f… view at source ↗
Figure 2
Figure 2. Figure 2: Scaling relation between ICO and IF770W,PAH, IF1130W, and IF2100W (top to bottom) in different ionization conditions (all regions, H ii-like regions, composite-like regions, and AGN-like regions from left to right). In each panel, the contour showcase the distribution of spaxels from all galaxies, and the bold line is corresponding best-fit result. The thin lines are best-fit results for each galaxy. In ca… view at source ↗
Figure 3
Figure 3. Figure 3: Best-fit slope kKS, intercept bKS, and intrinsic scatter σKS based on KS-test based method for each galaxy, of different MIR bands (blue for IF770W,PAH, green for IF1130W, and red for IF2100W), and under different ionization conditions (all regions, H ii-like regions, composite-like regions, and AGN-like regions from left to right). In each panel, the galaxies are sorted on the x-axis by total stellar mass… view at source ↗
Figure 4
Figure 4. Figure 4: The correlation between the slope kKS and the intercept bKS is shown for each MIR band (top to bottom) and each ionization condition (left to right). The vertical dashed line in the top-left panel indicates bKS = 0, the criterion used to classify galaxies into high-b and low-b subgroups. The high-b galaxies are represented by red dots, while the low-b galaxies are shown as blue crosses. In each row, the fi… view at source ↗
Figure 5
Figure 5. Figure 5: Left: Distribution of low-b (blue crosses) and high-b (red circles) galaxies on log SFR vs. log M⋆ diagram. The gray contour represents the distribution of a volume-lim￾ited sample of nearby galaxies, constructed from the MaNGA (K. Bundy et al. 2015; M. R. Blanton et al. 2017; D. A. Wake et al. 2017) sample with galaxy weight corrections. Right: Same as the left panel, but the x-axis is log LCO. 3.2. Galax… view at source ↗
Figure 6
Figure 6. Figure 6: Correlation coefficient and corresponding − log p between the best-fit parameters (kKS, bKS, and σKS, from left to right) and various global properties (log SFR, log M⋆, log sSFR, log LCO, and log MHI, represented by different symbols) for different bands (F770WPAH, F1130W, and F2100W, shown in blue, green, and red, respectively). Horizontal dashed line in each panel represents − log p ≈ 1.3 (2σ). −11.0 −1… view at source ↗
Figure 7
Figure 7. Figure 7: Correlation between the best-fit parameters and galactic log sSFR for different MIR bands (F770WPAH, F1130W, and F2100W from left to right). High-b (low-b) galaxies are shown as red circles (blue crosses), with error bars representing 1σ uncertainties. The correlation between b and log sSFR reported by R. Chown et al. (2025) is displayed as a gray dashed line in the corresponding panel (left panel in the s… view at source ↗
Figure 8
Figure 8. Figure 8: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Diagram of R∆k = (k1−kKS)/kKS vs. 1−q0. Re￾sults using IF770W,PAH, IF1130W, and IF2100W as MIR bands are shown in blue, green, and red, respectively, with corre￾sponding 1σ uncertainties as error bars. The solid black lines represent different levels of R∆k(1 − q0). highlights the stronger deviation and flattening in the dust band than in the PAH bands as noticed from the previous figure. This result impli… view at source ↗
Figure 10
Figure 10. Figure 10: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Best-fit slope kKS, intercept bKS, and intrinsic scatter σKS in H ii-like regions at different spatial scales (resolutions) for different MIR bands (F770WPAH, F1130W, and F2100W from left to right). The low(high)-b galaxies are represented as blue crosses(red circles), with error bars indicating 1σ uncertainties. The gray horizontal lines and corresponding gray shaded regions represent the median value an… view at source ↗
Figure 12
Figure 12. Figure 12: Difference in σKS estimated in H ii-like regions between relatively larger spatial scale (lower-resolution) and smaller spatial scale (higher-resolution) data (calculated as the former minus the latter), plotted as a function of σKS of relatively smaller scales. The low(high)-b galaxies are represented as blue crosses(red circles), with error bars indicating 1σ uncertainties [PITH_FULL_IMAGE:figures/full… view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of the slope (k) and intercept (b) reported by R. Chown et al. (2025) (kC24, bC24) with those derived in this work using KS-test based method (kKS, bKS) and mLINMIX (kmLINMIX, bmLINMIX). From left to right, the columns compare R. Chown et al. (2025) with KS-test based method, R. Chown et al. (2025) with mLINMIX, and KS-test based method with mLINMIX, respectively. The top row shows results for … view at source ↗

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