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Predicting the resolved CO emission of $z=1-3$ star-forming galaxies

T0 review · 2 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper predicts a steep radial rise in the CO-to-H2 conversion factor in z=1–3 galaxies, from ~1–5 in the centers to >100 at ~15 kpc, so CO emission cannot be read as a uniform tracer of molecular gas across these disks.

desk verdict Solid statistical advance in predicting resolved CO at z=1-3; the central gradient is likely robust, but the magnitude hinges on an unscaled CR prescription the authors themselves flag. read the letter →

arxiv 2506.13899 v2 pith:TMQRGUCX submitted 2025-06-16 astro-ph.GA

Ravishankar Anirudh , Melanie Kaasinen , Gergö Popping , Desika Narayanan , Karolina Garcia , Dariannette Valentin-Martinez This is my paper · ORCID
classification astro-ph.GA
keywords COemissionmoleculargasH2massCO-to-H2conversionfactorhigh-redshiftgalaxiescosmicnoonsyntheticobservationsgalaxysizes
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 how reliably resolved CO emission traces molecular hydrogen in the peak star-forming epoch, z=1–3, by generating synthetic CO(1–0) through CO(5–4) maps for hundreds of main-sequence galaxies drawn from a cosmological simulation. It argues that the CO-to-H2 conversion factor $\alpha_{\rm CO}$ is not constant across these disks: it stays near 1–5 $\mathrm{M_\odot}\,(\mathrm{K\,km\,s^{-1}\,pc^2})^{-1}$ in the central 1–3 kpc, then climbs steeply to values above 100 at roughly 15 kpc. The consequence is that using a single $\alpha_{\rm CO}$, or reading a CO half-light radius as the H2 size, systematically underweights the extended molecular gas: more than a quarter of H2 lies beyond twice the CO(1–0) half-light radius, and CO half-light radii are on average about 27–29% smaller than H2 half-mass radii. If correct, this matters because most resolved CO studies at these redshifts are effectively seeing only the dense centers of galaxies, not their full molecular reservoirs.

What carries the argument

The carrying mechanism is the SLICK modeling pipeline: each gas particle in the cosmological simulation is treated as a virialized, pressure-confined cloud with a power-law density profile, split into concentric zones; a chemical network solves for H2 and CO abundances under an equilibrium between heating, from photoelectric, dust, cosmic-ray, and CMB processes, and cooling, and a spectral-line code computes CO line luminosities using escape-probability radiative transfer, with the interstellar radiation field and cosmic-ray field set locally from the 64 nearest neighboring clouds. This sub-resolution machinery is what converts the simulation's unresolved gas particles into resolved, roughly 500 pc CO maps, and the paper's radial $\alpha_{\rm CO}$ gradients, compact CO sizes, and excitation trends all follow from how these cloud properties vary with galactocentric radius.

What would settle it

Measure resolved CO(1–0) and CO(3–2) emission together with an independent, dust-based molecular-gas surface density map for a sample of z~2 main-sequence galaxies. If $\alpha_{\rm CO}$ stays near 3–5 $\mathrm{M_\odot}\,(\mathrm{K\,km\,s^{-1}\,pc^2})^{-1}$ beyond 10 kpc, or if the CO(1–0) half-light radius matches the H2 half-mass radius instead of sitting about 28% smaller, the predicted steep gradient and size bias are ruled out.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that resolved CO emission in z=1–3 star-forming galaxies is not a uniform tracer of H2. Using sub-resolution cloud modeling plus an equilibrium line-radiation calculation on galaxies from a cosmological simulation, the authors predict that $\alpha_{\rm CO(1-0)}$ rises by one to two orders of magnitude from galaxy centers to about 15 kpc, that higher-$J$ CO transitions trace even more centrally concentrated gas, and that CO excitation, as measured by ratios like CO(3–2)/CO(1–0), declines from suprathermal values near 0.9–2 in the centers to roughly 0.1 in the outskirts, with line ratios increasing toward higher redshift and lower stellar mass. They attribute the $\alpha_{\rm CO}$ gradient primarily to a declining CO abundance per H2 molecule and to falling density, radiation field, and turbulence at large radius, rather than to metallicity alone. The predicted CO half-light radii are compact, around 1–5 kpc, comparable to current observations, but about 27–29% smaller than the H2 half-mass radii, with about 30% of H2 located outside twice the CO(1–0) half-light radius.

Load-bearing premise

Everything rests on treating each unresolved gas particle in the simulation as a single virialized, pressure-confined molecular cloud with equilibrium chemistry and a cosmic-ray field that scales linearly with local star-formation surface density; if z=1–3 gas is not organized this way, the predicted radial $\alpha_{\rm CO}$ gradient, compact CO sizes, and excitation trends are model artifacts.

Editorial extensions

If this is right

  • Observed CO half-light radii at z=1–3 should be interpreted as sizes of the dense, star-forming molecular cores, not the full H2 disk; on average they are about 27–29% smaller than H2 half-mass radii.
  • Resolved studies that assume a constant $\alpha_{\rm CO}$ will systematically underestimate molecular gas surface densities in galaxy outskirts, by factors of tens to hundreds beyond roughly 10 kpc.
  • Tracing H2 beyond 3–5 kpc in cosmic-noon galaxies is predicted to be very difficult with current facilities because the CO surface brightness drops faster than the H2 density.
  • Higher-$J$ transitions such as CO(5–4) are progressively more compact and excitation-biased toward dense central gas, so different CO lines cannot be used interchangeably for individual galaxies.
  • CO excitation gradients, with line ratios peaking in centers and increasing with redshift, provide a way to infer gas physical state: suprathermal ratios require warm, roughly 30–100 K, and dense, above 100 cm$^{-3}$, gas.

Reading between the lines

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

  • A direct observational test could come from combining resolved CO(1–0) with dust-based or other independent H2 maps in the same z~2 galaxies; if those maps confirm that CO half-light radii understate H2 sizes by about 30%, then integrated CO-based gas masses at high redshift may also be biased, not just resolved profiles.
  • Because the predicted $\alpha_{\rm CO}$ gradient is driven more by the local interstellar radiation field and density than by metallicity, galaxy-wide $\alpha_{\rm CO}$–metallicity scaling relations may hide large radial scatter, and resolved local-galaxy calibrations are the nearest analogues that could test the sub-grid assumptions.
  • A testable extension is to rerun the same pipeline with alternative cosmic-ray prescriptions, for instance with a flat rather than star-formation-proportional cosmic-ray field; the paper flags this as a key uncertainty, and since cosmic-ray heating boosts CO(1–0) brightness and high-$J$ excitation, the predicted $\alpha_{\rm CO}$ gradient and suprathermal ratios would weaken or strengthen accordin
  • The result implies that future high-resolution CO surveys of cosmic noon should either include low-$J$ CO(1–0) to capture the extended diffuse gas or explicitly model a radially varying $\alpha_{\rm CO}$; otherwise stacked CO sizes will be biased toward compact centers even when individual galaxies show a wide scatter.
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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 / 4 minor

Summary. This paper uses the Simba cosmological simulation combined with the SLICK post-processing pipeline (Garcia et al. 2024) to generate synthetic, spatially resolved CO(1–0) to CO(5–4) maps for star-forming galaxies at z = 0.8–3.5, and compares the CO emission with the underlying H2 mass distribution. The central claims are that the CO-to-H2 conversion factor αCO rises from about 1–5 M⊙ (K km s−1 pc2)−1 in the central 1–3 kpc of massive galaxies to values exceeding 100 at ~15 kpc, that CO half-light radii are on average 27–29% smaller than H2 half-mass radii with roughly 30% of the H2 mass lying beyond two CO half-light radii, and that CO excitation ratios increase toward galaxy centers and with redshift, reaching suprathermal values in warm, dense gas. The paper argues that these results imply that a single αCO cannot be used to trace H2 across z = 1–3 disks and that combined CO plus H2 corrections will be needed for resolved observations.

Significance. If these predictions hold, they are directly relevant to the interpretation of current and upcoming resolved CO observations at z = 1–3: the paper provides a physically motivated, spatially resolved αCO prescription, predicts quantitative size-ratio corrections, and makes falsifiable predictions for CO line-ratio gradients. The work is carefully presented, with percentile spreads, a localized ISRF treatment that improves agreement with z = 0 GMC data, clear comparisons to observed sizes and line ratios, and an explicit list of caveats. The target z = 1–3 outputs are forward predictions rather than fits to the same data, so the exercise is not circular. The main weakness is that the headline quantitative claims depend strongly on the assumed cosmic-ray ionization rate scaling, which is both ambiguously written in Eq. (9) and acknowledged in Sec. 4.2 to be potentially overestimated in galaxy centers; no robustness test is provided. This needs to be addressed before the magnitude of the αCO gradient and the size ratios can be fully endorsed.

major comments (2)
  1. [Sec. 4.2; Eq. (9); Fig. 4; Table 1] The central quantitative claims—the αCO gradient in Fig. 4 and the CO half-light to H2 half-mass radius ratios in Table 1—are directly affected by the assumed cosmic-ray ionization rate. Sec. 4.1 states that the higher gas temperature caused by increased ISRF and CR strength raises the CO(1–0) brightness and thus lowers αCO in the centers. The authors acknowledge in Sec. 4.2 that the linear Σ_SFR–ξ_CR scaling 'may not hold in all environments', and, citing Krumholz et al. (2023), that starburst systems may have only moderately enhanced CR rates, which would imply that central CR heating is overestimated in the present model. Yet no alternative CR prescription or sensitivity test is presented. I request a robustness test with a plausible alternative CR treatment (e.g., a capped CR enhancement or the Krumholz et al. prescription) recomputing at least the αCO(r) profiles, the r31(r) profiles, and the Table 1 size ratios. Without such a test, the magnitude of the predicted αCO range and the 27–29% size ratios are not demonstrated to be robust to an uncertainty the authors themselves flag.
  2. [Sec. 2.2.3; Eq. (9); Sec. 4.2] The description of the CR normalization is internally inconsistent and invites a factor-of-10 misreading. The text says 'assuming ζ−16 = 0.1 is the CR ionization rate and ξ_CR,MW = 10−16 s−1 is the CR field in the solar neighborhood'. If ζ−16 is a dimensionless prefactor, calling it the ionization rate is wrong; if ζ−16 is already a rate, multiplying it by ξ_CR,MW double-counts the normalization. The product of the two values is 10−17 s−1, consistent with the '10^-17 s^-1' stated in Sec. 4.2, but a reader implementing Eq. (9) literally from Sec. 2.2.3 could easily adopt 10−16 s−1. Please rewrite the sentence and Eq. (9) so that ζ−16 is unambiguously a dimensionless scaling relative to ξ_CR,MW, or state the solar-neighborhood CR ionization rate directly and use only one symbol for it.
minor comments (4)
  1. [Sec. 2.3; Figs. 3–7; Table 1] The number of galaxies entering each redshift–stellar mass bin after the merger and convergence cuts is not reported anywhere. Because some bins are strongly affected by the merger cut (the text notes only one high-mass z = 2.5–3.5 galaxy and omits that bin), the 16th–84th percentile spreads would be much more interpretable if N per bin were given in each panel or in Table 1.
  2. [Sec. 2.2.2; Sec. 3.1] The definition of the molecular gas mass used for αCO includes the helium contribution (0.4×M_C) and is used interchangeably with M_H2. Since αCO is then effectively a molecular-gas-to-CO ratio rather than a pure H2-to-CO ratio, the comparison to literature αCO values (e.g., the observed values discussed in Sec. 4.1) should state explicitly whether the observational values include helium (i.e., the usual 1.36 correction).
  3. [Fig. 8] The observational data points ('diamonds') in Fig. 8 are not individually identified or assigned uncertainties. Please add a legend or a caption note specifying which source (Kaasinen, Ikeda, Rizzo, Tadaki, and where applicable individual galaxies) corresponds to each symbol, so that the comparison is reproducible.
  4. [Sec. 2.3] The prose in Sec. 2.3 says the three bins are 'around z=1,2,3', while the figures use z=0.8–1.2, z=1.8–2.2, and z=2.5–3.5. This is clear in the figures, but the text should use the wider labels consistently to avoid confusion between the snapshot centers and the bin edges.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the predicted radial alpha_CO, excitation, and size trends are forward-model outputs from a pipeline validated on external z=0 data, not fits to the quantities being predicted.

full rationale

The predicted radial alpha_CO profiles, CO excitation gradients, and half-light-to-half-mass size ratios are not fitted to the quantities they are used to claim. SLICK's sub-resolution cloud properties (Eqs. 2-4), the chemical network, the ISRF and CR prescriptions (Eqs. 8-9), and Despotic's line solver are fixed inputs adopted from prior work; alpha_CO = M_H2 / L'_CO is computed as an output of that forward model, not imposed as a target. The only calibration against data is the z=0 M_H2-L'_CO comparison from Garcia et al. (2024), which is an external benchmark outside this paper's target (resolved z=1-3 CO emission); using it as a validation anchor does not make the z=1-3 predictions fitted. The CR-Sigma_SFR scaling in Eq. (9) is a clearly stated modeling assumption rather than a hidden restatement of the results, and Sec. 4.2 explicitly concedes that overestimating the CR ionization rate could overpredict the line ratios and that the assumed scaling 'may not hold in all environments'; this is an acknowledged uncertainty to be explored with alternative CR prescriptions, not a circular reduction. No equation or fitting step makes the headline alpha_CO range, the r1/2,CO/r1/2,H2 ~ 0.7 values, or the suprathermal r31 values equal to any input by construction.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The model depends on several calibrated normalizations (CR rate, ISRF, GMC pressure-radius relation, dust scaling) and domain assumptions about unresolved ISM physics. None of these is a new physical entity; they are extrapolations of local calibrations to z=1-3. The CR normalization is the most fragile because the paper uses two different values and states the line ratios are sensitive to it.

free parameters (7)
  • CR ionization rate normalization (ζ_-16, ξ_CR,MW) = ζ_-16=0.1, ξ_CR,MW=10^-16 s^-1 (Sec 2.2.3); 10^-17 s^-1 (Sec 4.2)
    Sets CR heating in DESPOTIC; drives high-J CO excitation and suprathermal line ratios. The paper states two different values.
  • Solar-neighborhood SFR surface density Σ_SFR,MW = 790 M_sun Myr^-1 kpc^-2
    Normalizes the localized UV ISRF strength chi in Eq. 8; controls cloud heating and CO luminosity.
  • GMC pressure-radius normalization (P_ext/k_B, M_C) = 10^4 cm^-3 K and 290 M_sun
    Eq. 2 sets cloud radius from external pressure and cloud mass; determines density and line excitation.
  • Dust absorption coefficient κ_abs and β_UV,MW = κ_abs=1.078e5 cm^2 g^-1; β_UV,MW≈0.5
    Eqs. 6-7 set UV attenuation and ISRF; calibrated to MW extinction curve and gas surface density.
  • Dust-to-gas ratio relation coefficients = log DGR = 2.445 log(Z/Zsun) - 2.029; DMR_MW=0.44
    Scales dust abundance and dust-gas coupling (Eqs. 10-11), affecting CO formation and gas heating.
  • Virial parameter α_vir = 1
    Assumes clouds are virialized to set velocity dispersion and clumping; affects CO line brightness.
  • Nearest-neighbor count for ISRF = 64
    Number of neighboring particles used to compute local SFR density and ISRF; chosen after comparing number vs distance thresholds.
assumptions (6)
  • domain assumption Each SIMBA gas particle represents a virialized molecular cloud with a power-law density profile (Eq. 3) and pressure-radius relation (Eq. 2).
    Sub-resolution ISM model; if z=1-3 cloud populations differ from local GMCs, all CO maps and alpha_CO gradients change.
  • domain assumption DESPOTIC equilibrium chemistry, thermal balance, and escape-probability radiative transfer correctly predict CO line luminosities for such clouds.
    Required to compute CO(1-0) through CO(5-4); extrapolated from z=0 validation to z=1-3.
  • ad hoc to paper The CR ionization rate scales linearly with local SFR surface density (Eq. 9).
    Boosts high-J excitation in centers; authors note starbursts may have only moderately enhanced CR rates.
  • ad hoc to paper The ISRF strength is set by the 64 nearest-neighbor particles with dust attenuation (Eqs. 6-8).
    Choice of neighbor count affects chi and hence CO luminosity; motivated by agreement with z=0 GMC data.
  • domain assumption SIMBA's sub-resolution H2 prescription (Krumholz & Gnedin 2011) and dust evolution correctly trace molecular gas at z=1-3.
    Input H2 masses and metallicities set the denominator of alpha_CO and the chemistry.
  • domain assumption X-ray/AGN heating is negligible for J≤5 CO lines in the selected main-sequence galaxies.
    Authors exclude AGN; X-rays can dominate high-J CO excitation in AGN hosts.

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Cite this review

Pith. "Pith review of Predicting the resolved CO emission of $z=1-3$ star-forming galaxies." pith.science (2026). https://pith.science/paper/TMQRGUCX

@misc{pith2026250613899,
  author       = {Pith},
  title        = {Pith review of: Predicting the resolved CO emission of $z=1-3$ star-forming galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TMQRGUCX}},
  note         = {Machine review of arXiv:2506.13899}
}
abstract

(Abridged) Resolved observations of the CO emission from $z=1-3$ star-forming galaxies are becoming increasingly common, with new high-resolution surveys on the horizon. We aim to inform the interpretation of this resolved CO emission by creating synthetic observations and testing to what extent routinely observed CO transitions can be used to trace H$_2$ across galaxy disks. To this end, we extract $z=1-3$ massive star-forming galaxies (on and above the main sequence) from the SIMBA cosmological simulation and predict their spatially resolved CO(1$-$0)-to-CO(5$-$4) emission using the $\texttt{SLICK}$ pipeline, which combines sub-resolution modeling of the cloud population with the DESPOTIC spectral line calculation code. We find that the CO(1$-$0)-to-H$_2$ ratio ($\alpha_{\rm CO}$) varies significantly within these galaxy disks$-$from values of $\sim1-5$ $\mathrm{M_\odot}$ (K km s$^{-1}$ pc$^2$)$^{-1}$ in the central 1-3 kpc of the most massive galaxies to $>100$ $\mathrm{M_\odot}$ (K km s$^{-1}$ pc$^2$)$^{-1}$ at $\sim$ 15 kpc. Thus, the use of a single $\alpha_{\rm CO}$ to derive the H$_2$ surface density leads to severe underestimates of the H$_2$ contribution in its outskirts. As expected, higher-$J$ CO transitions trace molecular gas in the centers at higher densities, whereas CO(1$-$0) better traces the more diffuse, extended molecular gas. We see significant variations in the CO excitation, with CO(3$-$2)/CO(1$-$0) line luminosity ratios of the most massive galaxies at $z\sim2$ declining from $\sim$ 0.9 in the galaxy centers to $\sim$ 0.1 in the outskirts. On average, line ratios increase substantially toward higher redshifts and lower galaxy stellar masses. We predict that tracing molecular gas with CO beyond 3-5 kpc of cosmic noon galaxies will be challenging with current facilities due to the drastic increase in $\alpha_{\rm CO}$.

Figures

Figures reproduced from arXiv: 2506.13899 by the authors.

Figure 1
Figure 1. Different treatments of the interstellar radiation field, as shown through the correlation between the clouds’ H2 mass vs. CO(1–0) luminosity: the left-hand panel shows a non-localized implementation (i.e., same ISRF for all clouds in a galaxy) whereas the right-hand panel shows the localized treatment (considering the 64 nearest-neighboring clouds). Slick’s clouds are indicated by the hexagonal bins, where the colo… view at source ↗
Figure 2
Figure 2. Example of the resolved CO emission and H [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Average radial profiles of CO surface brightness and H [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Average radial profile of the CO-to-H2 conversion factor (αCO), for different transitions (shown in the legend on the right). The x axis is plotted in log scale. The solid lines represent the median αCO, averaged across the entire galaxy sample shown in each panel. The…
Figure 5
Figure 5. Figure 5: Average radial profile of the CO line luminosity ratios, in the same bins of redshift (columns) and stellar mass (rows) as the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Histogram of the size ratio of CO(1–0) half-light radii [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Histograms of the size ratios of (a) CO(3–2) half-light [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: CO half-light radii as a function of galaxy stellar mass, in three redshift bins (one for each panel, as labelled at top), for [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Average radial profile of abundances of HI, H [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: αCO vs. gas-phase metallicity per pixel, including the pixels of all synthetic CO(1–0) maps for the entire z=1–3 sample. The color-coding represents the number of pixels per hexbin as shown via a color bar on the right of the figure. The columns again show different r…
Figure 11
Figure 11. Figure 11: αCO vs. UV field strength, χ, per pixel. The column and row separation, and color-coding are the same as for [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: αCO vs. hydrogen number density per pixel. The column and row separation, and color-coding are the same as for [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]
Figure 13
Figure 13. Figure 13: αCO vs. non-thermal velocity dispersion per pixel. The column and row separation, and color-coding are the same as for [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]

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Forward citations

Cited by 2 Pith papers

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