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The Modeling Landscape of Extragalactic CO in CMB Surveys

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Ignoring CO×CIB would bias future CMB foreground fits by many standard deviations.

desk verdict Useful, transparent uncertainty-quantification of CO×CIB as a CMB foreground; the qualitative claim holds, but the quantitative biases and PCA templates inherit the envelope of 15 CO models plus one CIB model. read the letter →

arxiv 2506.16028 v1 pith:PP5AG2DM submitted 2025-06-19 astro-ph.CO astro-ph.GA

Yogesh Mehta , Anirban Roy , Simon Foreman , Alexander van Engelen , Nick Battaglia This is my paper
classification astro-ph.COastro-ph.GA
keywords extragalacticcarbonmonoxideCMBforegroundscosmicinfraredbackgroundSunyaev-Zel'dovicheffectpowerspectrumprincipalcomponentanalysisFisherforecastlineintensitymapping
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 argues that the cross-correlation between extragalactic carbon monoxide line emission and the cosmic infrared background (CO×CIB) is a foreground that next-generation CMB surveys cannot ignore. Using a grid of 15 CO models, built from five star-formation-rate–halo-mass relations and three SFR–CO luminosity scalings, plus a standard CIB halo model, the authors simulate CO and CIB skies at 90, 150, and 220 GHz. They find that CO alone is too faint to detect in current experiments, but CO×CIB is comparable to the kinetic Sunyaev-Zel'dovich signal and, if omitted from a power-spectrum fit, shifts tSZ, kSZ, and radio-source parameters by amounts near current uncertainties and far above the expected uncertainties of a CMB-S4-like survey. They further show that the full spread of CO×CIB spectra can be captured by three principal-component amplitudes.

What carries the argument

The load-bearing object is the 15-model grid of extragalactic CO prescriptions, each obtained by pairing one of five star-formation-rate–halo-mass relations (Silva15, Fonseca16, TNG100, TNG300, Behroozi19) with one of three SFR–CO luminosity scaling relations (Greve14, Kamenetzky15, Visbal10), applied halo-by-halo to dark-matter-only N-body snapshots and summed along the line of sight. The CIB is modeled with the Shang et al. (2012) halo model, whose parameters were fit to Planck and IRAS data. The argument then runs on two standard tools: the Fisher-matrix bias formula, which converts each simulated CO×CIB spectrum into expected parameter shifts for ACT-like and CMB-S4-like noise, and a principal component analysis (singular value decomposition of the model covariance matrix) that compresses the 15 spectra into a small set of orthogonal templates.

What would settle it

A measurement of the CO×CIB cross-power spectrum at 150 or 220 GHz from an ACT/SPT-like dataset, or from a future CMB-S4-like survey, that falls outside the predicted one-order-of-magnitude band (e.g., $D_\ell^{150}\sim0.5$–$1.8\,\mu\mathrm{K}^2$ at $\ell=3000$) would falsify the model grid; equivalently, a CO luminosity function measured by ALMA/NOEMA at $z\sim1$–$3$ that lies outside the range spanned by the 15 models would break the weakest assumption.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the CO×CIB cross-power spectrum is a major small-scale CMB foreground whose amplitude is robust enough across the model grid to matter, and whose neglect in parameter estimation produces biases that can exceed the statistical errors of upcoming surveys. The authors simulate 15 CO models plus the Shang et al. (2012) CIB model in N-body snapshots, integrate the contributions over redshift with a 50 GHz top-hat bandpass at 90, 150, and 220 GHz, and obtain CO×CIB amplitudes at $\ell=3000$ of roughly $0.34$–$1.08\,\mu\mathrm{K}^2$ at 90 GHz, $0.55$–$1.76$ at 150 GHz, and $1.07$–$5.56$ at 220 GHz, overlapping earlier estimates. A Fisher forecast with a nine-parameter foreground model shows that omitting CO×CIB biases parameters such as $a_{\mathrm{tSZ}}$, $a_{\mathrm{kSZ}}$, and the radio-source amplitude by many tens of standard deviations for a CMB-S4-like survey. A principal component analysis of the model covariance shows that three amplitude parameters suffice to reproduce all 15 spectra within the expected measurement uncertainties.

Load-bearing premise

The whole forecast stands on the assumption that the 15 model combinations (five halo-mass–SFR relations times three SFR–CO scaling laws) span the true range of extragalactic CO luminosity in mass and redshift, and that the single Shang et al. (2012) CIB model is not systematically biased.

Editorial extensions

If this is right

  • Current CMB analyses that fit tSZ, kSZ, and radio foregrounds without a CO×CIB term carry a model-dependent bias; for ACT DR6-like sensitivity the bias is at the level of the reported uncertainties, so existing kSZ constraints may need reinterpretation.
  • Future CMB-S4-like surveys will require a CO×CIB template in their foreground model, otherwise tSZ, kSZ, and radio-source parameters are shifted by many tens of standard deviations.
  • Three PCA amplitudes for CO×CIB are enough to span the modeling uncertainty for such a survey, offering a practical marginalization strategy without committing to one CO model.
  • Because CO×CIB frequency decoherence is driven by CO rather than by the CIB, internal linear combination methods may not cleanly isolate CO, making power-spectrum modeling with PCA templates the safer route.
  • At 150 and 220 GHz the upper end of the predicted CO×CIB range is comparable to the kSZ autospectrum, so CO×CIB is a potential contaminant for kSZ measurements.

Reading between the lines

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

  • The same singular-value-decomposition strategy could be ported to other uncertain line foregrounds, such as [CII], for which halo-model predictions also span wide ranges.
  • The predicted high correlation between CO and the CIB at 90 GHz (~83–93%) implies that a measured CO×CIB spectrum would directly constrain the CO luminosity–halo mass relation, turning CO from a nuisance into a probe of molecular gas at $z\sim1$–3.
  • The authors' CO autospectra are lower than those of earlier works; if a direct CO auto-spectrum measurement later lands above the predicted band, the SFR–CO scaling relations used here may be missing a population of luminous galaxies.
  • One could test the PCA prescription by injecting any of the 15 models into simulated CMB-S4-like data and fitting with only the three amplitudes; the paper explicitly leaves that validation to future work.
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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

3 major / 4 minor

Summary. This paper forward-models the contribution of extragalactic CO line emission and its cross-correlation with the cosmic infrared background (CIB) to CMB temperature power spectra at 90, 150, and 220 GHz. The authors combine five SFR–halo mass relations with three SFR–L_CO scaling relations in LIMpy, apply them to 13 realizations of a 100 Mpc/h N-body simulation, and add the Shang et al. (2012) CIB model. From snapshot-level power spectra they find that CO auto-spectra span 1–2 orders of magnitude but remain below the expected kSZ signal, while the CO×CIB cross-spectrum is comparable to kSZ at 150 and 220 GHz. Using a Fisher-matrix bias calculation, they forecast that neglecting CO×CIB biases foreground parameters at levels comparable to ACT DR6 uncertainties and many times the expected CMB-S4 uncertainties. A PCA of the CO×CIB spectra indicates that three amplitude parameters capture the model range for a CMB-S4-like survey.

Significance. If the quantitative results are robust, this is a timely and useful study for the CMB community: it broadens the set of CO models considered relative to M23 and K24, provides explicit forecasts of the bias from neglecting CO×CIB, and offers a practical PCA-based parameterization for foreground fitting. The simulation pipeline is clearly described and builds on public tools (LIMpy, MP-GADGET), and no CMB foreground data are used to calibrate the models, so the analysis is genuinely forward-modeling rather than circular. The frank discussion of model dependence and the agreement of the CO×CIB range with previous work are strengths. However, the quantitative headline claims inherit two untested assumptions: the 15-model CO grid brackets the true CO population, and the single S12 CIB model correctly describes the halo-mass/redshift distribution of infrared emission relevant for the cross-correlation.

major comments (3)
  1. [Section 2.2 and Section 5 (Eq. 20, Figs. 7–9)] The quantitative bias forecasts rest on a single CIB model (S12), whose parameters are fitted to CIB auto-spectra (Table 1). Auto-spectrum agreement does not uniquely determine the halo-mass/redshift distribution of infrared luminosity that sets the CO×CIB cross-spectrum, so the bias magnitudes in Figs. 7–9 may scale with any systematic error in the S12 halo model. I request a robustness test, e.g., varying S12 parameters (M_eff, δ, or adding a minimum halo mass) or using an alternative CIB halo model, and recomputing the CO×CIB spectra and the Fisher biases. Without such a test, the headline bias numbers are conditional on a single untested CIB assumption.
  2. [Section 4.2, Table 2, and Eq. (1)] The 15-model grid produces CO auto-spectra that are systematically lower than the K24 range, with only a small overlap at the upper end. Since K24's range is anchored to observed CO luminosity functions, the present grid may not bracket the high-luminosity end of the CO population, and the PCA templates of Section 6 and the derived 'three PCs suffice' claim inherit this incompleteness. I recommend adding K24-style models (or the M23 model) to the grid, or at least computing the projection of the K24 spectra onto the first three PCs and reporting the residuals. The current comparison in Tables 2 and 3 at ℓ=3000 alone does not establish that the shapes are captured.
  3. [Sections 4.1–4.3 and Section 6 (Eqs. 25–27)] No error bars or sample-variance estimates are reported for the simulated power spectra, despite the use of 13 independent realizations. The model-to-model spread in Figs. 4–6 and the higher PCs in Fig. 10 (which the authors note are dominated by numerical noise) can only be interpreted as physically meaningful if the simulation noise is subdominant to the differences between models. The PCA convergence test in Eq. (27) uses an analytic experimental covariance but does not include the simulation measurement noise. Please add sample-variance error bars (e.g., from the 13 realizations) and check the sensitivity of the N=3 PCA conclusion to this noise.
minor comments (4)
  1. [Abstract] The phrase 'many times greater than the expected uncertainties expected for future data' contains a doubled 'expected'; please revise.
  2. [Section 2.1, after Eq. (1)] The sentence 'This diverse range of models will allow us to quantify the full range of possible CO signals' overstates the coverage, given that Table 2 shows the grid may not cover the high end of K24; consider softening to 'the range spanned by these models'.
  3. [Section 6, Eqs. (25)–(26)] The notation σ_bin(D^F_ℓ) is introduced as the binned uncertainty, but Eq. (26) defines σ(D^F_ℓ)^2 without explicitly showing the binning; please make the relationship between the binned and unbinned quantities clearer.
  4. [Figure 3] The gray shaded bands with embedded transition labels are visually dense and difficult to read at publication size; consider splitting the three frequency panels or using a separate legend for the line transitions.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: all predicted spectra and Fisher biases are forward-modeled from externally calibrated CO and CIB relations; the LIMpy/Roy et al. (2023) and Battaglia et al. template usage are non-load-bearing self-citations, and the PCA sufficiency test is self-evaluated but explicitly flagged as approximate.

full rationale

The paper's central predictions - the COxCIB cross-spectra and the foreground parameter biases from neglecting them - are forward-modeled from externally calibrated inputs, not fitted to the quantities being predicted. CO luminosities follow Eq. (1), combining five M_halo-SFR relations (Silva et al. 2015; Fonseca et al. 2017; IllustrisTNG; Behroozi et al. 2019) with three SFR-L_CO scaling relations (Greve et al. 2014; Kamenetzky et al. 2016; Visbal & Loeb 2010), all grounded in external galaxy observations and simulations, while the S12 CIB model (Shang et al. 2012) is fitted to Planck and IRAS CIB autospectra (Ade et al. 2014b; McCarthy & Madhavacheril 2021). No COxCIB data, CO auto-spectrum measurement, or CMB foreground dataset is used to calibrate any model parameter, so the cross-spectra in Fig. 4 and the bias forecasts in Figs. 7-9 are genuine model outputs rather than re-labeled fits. The agreement with the independent M23 and K24 calculations (Table 3) provides external corroboration. The LIMpy code (Roy et al. 2023) and the kSZ templates (Battaglia et al. 2012, 2013) involve overlapping authors, but both are public, reproducible tools whose scientific content traces to external calibrations and simulations; per the review rules, such reusable code is real evidence and does not raise the circularity score. The one self-referential element is the Section 6 PCA: the 'three PCs suffice' chi-squared test (Eq. 27) reconstructs the same 15 model spectra from which the PCs were derived, so it measures the intrinsic dimensionality of the model envelope (with the noise weighting providing external content) rather than validating against external data. The paper explicitly flags this as approximate and defers a rigorous simulated-analysis test to future work. Likewise, the bracketing assumption that the 15 models span the true CO luminosity function is a stated modeling assumption, not a derived result, and the conclusion section identifies theoretical model spread as the dominant uncertainty. No derivation step reduces to its own input by construction.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The paper introduces no new fitted parameters or entities; all inputs come from prior literature (S12, Roy et al. 2023 models). The ledger lists the external fitted parameters, modeling choices, and domain assumptions that the forecast claims depend on. The most consequential assumptions are that the 15-model grid brackets the true CO emission and that the single S12 CIB model is adequate for the cross-correlation.

free parameters (5)
  • CO scaling relation intercept and slope (a_CO, b_CO) for Greve14, Kamenetzky15, Visbal10 = from Roy et al. 2023, not given in paper
    Eq. (1) maps SFR to CO line luminosity; these coefficients are calibrated to galaxy samples at z<6.3 and set the overall CO amplitude.
  • S12 CIB model parameters (L0, Meff, delta, beta, gamma, To, alpha) = L0=1.59e-15 Lsun/Msun, Meff=12.6, delta=3.6, beta=1.75, gamma=1.7, To=24.4 K, alpha=0.36
    Table 1; fitted to Planck and IRAS CIB autospectra in Ade et al. (2014b) and McCarthy & Madhavacheril (2021). The CIB model drives the CO×CIB amplitude.
  • SFR-halo mass relation parameters for Behroozi19, Fonseca16, Silva15, TNG100, TNG300 = from respective literature
    These five M_halo-SFR relations determine which halos form stars and therefore CO; they are calibrated to observations or hydrodynamical simulations.
  • Flux cut threshold = 15 mJy
    Section 3.2; replaces pixels above 15 mJy with the mean flux to mimic ACT-like source masking; affects both CO and CIB shot-noise levels and the cross-spectra.
  • Bandpass width = 50 GHz top-hat centered at 90, 150, 220 GHz
    Assumed in Section 3.2; sets which CO transitions and redshifts contribute to each band.
assumptions (7)
  • domain assumption CO luminosity depends on halo mass only through SFR via log10 L_CO = a + b log10 SFR(M_halo), Eq. (1), with no scatter, metallicity, or environment dependence.
    All 15 models are power-law scalings; any real scatter could change the shot-noise and clustering terms of the CO power spectra.
  • domain assumption The CIB luminosity is assigned via the S12 model with a mass-only lognormal L-M relation, Eq. (3), and a single SED for all halos, Eq. (5).
    Section 2.2; the CIB is not varied across models, so the CO×CIB cross-spectrum depends on this one CIB prescription.
  • domain assumption Halo occupation is based on friends-of-friends halos above 2.05e10 Msun/h, with no subhalo treatment.
    Section 3.1; low-mass halos and substructure could contribute to CO and CIB, especially at high redshift.
  • standard math The snapshot-based Riemann sum, Eq. (13), equals the lightcone integral; the authors checked Riemann versus trapezoid equivalence.
    Section 3.2, footnote 1; approximation could introduce small errors in the redshift weighting.
  • ad hoc to paper The 15 models span the plausible range of CO emission.
    This is the load-bearing assumption for all quantitative statements; no coverage guarantee is provided.
  • standard math Fisher matrix bias formula, Eq. (20), linearizes the response of parameters to a small unmodeled component.
    Section 5; for large biases the linear approximation may be inaccurate.
  • ad hoc to paper Principal components computed from the 15-model set provide a sufficient basis for the true CO×CIB spectrum in a CMB-S4-like analysis.
    Section 6; if the true model lies outside the grid, the PCA templates will not capture it.

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Pith. "Pith review of The Modeling Landscape of Extragalactic CO in CMB Surveys." pith.science (2026). https://pith.science/paper/PP5AG2DM

@misc{pith2026250616028,
  author       = {Pith},
  title        = {Pith review of: The Modeling Landscape of Extragalactic CO in CMB Surveys},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PP5AG2DM}},
  note         = {Machine review of arXiv:2506.16028}
}
abstract

Extragalactic carbon monoxide (CO) line emission will likely be an important signal in current and future Cosmic Microwave Background (CMB) surveys on small scales. However, great uncertainty surrounds our current understanding of CO emission. We investigate the implications of this modeling uncertainty on CMB surveys. Using a range of star formation rate and luminosity relations, we generate a suite of CO simulations across cosmic time, together with the broadband cosmic infrared background (CIB). From these, we quantify the power spectrum signatures of CO that we would observe in a CMB experiment at 90, 150, and 220 GHz. We find that the resulting range of CO auto-spectra spans up to two orders of magnitude and that while CO on its own is unlikely to be detectable in current CMB experiments, its cross-correlation with the CIB will be a significant CMB foreground in future surveys. We then forecast the bias on CMB foregrounds that would result if CO were neglected in a CMB power spectrum analysis, finding shifts that can be comparable to some of the uncertainties on CMB foreground constraints from recent surveys, particularly for the thermal and kinetic Sunyaev-Zel'dovich effects and radio sources, and many times greater than the expected uncertainties expected for future data. Finally, we assess how the broad range of multifrequency CO$\times$CIB spectra we obtain is captured by a reduced parameter set by performing a principal component analysis, finding that three amplitude parameters suffice for a CMB-S4-like survey. Our results demonstrate the importance for future CMB experiments to account for a wide range of CO modeling, and that high-precision CMB experiments may help constrain extragalactic CO models.

Figures

Figures reproduced from arXiv: 2506.16028 by the authors.

Figure 1
Figure 1. A lightcone visualization qualitatively depicting both the CO transitions in the foreground and CMB in the back￾ground. When observing the CMB, all CO transitions across cosmic time redshift into the bandpass and contribute to the total measured flux. While we do not use a lightcone approach, our power spectrum-based method is equivalent (see Sec. 3.2 for details). luminosity functions. The result is a nearly two-or… view at source ↗
Figure 2
Figure 2. Our simulated maps of the S12 CIB model and two CO models for several redshifts that contribute to our considered 90 GHz bandpass. For a given CO line, the bandpass selects the source redshifts, while for the CIB, all redshifts contribute to the observed emission. The CO intensity varies significantly with the model choice and is subdominant to the CIB at each snapshot. Both the CIB and CO intensity peak at cosmic n… view at source ↗
Figure 3
Figure 3. Auto-spectra of CO and CIB from our simulations observed at 90, 150, and 220 GHz and ℓ = 3000 as functions redshift. The grey bands correspond to the redshifts that source the various CO lines that contribute to a given observing frequency; the transitions are noted in text boxes centered on their respective grey band. The width of the grey bands corresponds to that of the broad CMB bandpasses of ∆ν = 50 GHz, result… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Auto-power spectra observed at 90, 150, and 220 GHz of CO and CIB and their cross-spectra from our simulations for the variety of models considered, shown as Dℓ ≡ ℓ(ℓ + 1)Cℓ/(2π). Their cross-correlation includes both cross terms, shown in Eq. (16). The range of CO aut…
Figure 5
Figure 5. Figure 5: Auto- and cross-spectra of CO, CIB, and CO × CIB for each frequency pair evaluated at several scales ℓ. The frequency dependence of the CO autospectrum is model-dependent in both amplitude and shape. The CO × CIB spectra are heavily influenced by the CIB spectrum and s…
Figure 6
Figure 6. Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Forecasted parameter shifts on other CMB fore￾ground parameters if the CO × CIB power spectra are not included in the model, given the noise properties of the ACT￾like survey. Each panel corresponds to a parameter that we allow to vary within our foreground model, with…
Figure 8
Figure 8. Figure 8: Forecasted shifts in foreground parameter con￾tours if the CO × CIB power spectra are not included in the model for the ACT-like survey. The presence of a given CO × CIB model (colored contours) shifts the parameters away from the fiducial point (black circles). Note t…
Figure 9
Figure 9. Figure 9: Forecasted parameter shifts on other CMB fore￾ground parameters if the CO×CIB power spectra are not in￾cluded in the model, for the noise properties of the CMB-S4- like survey, as in [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Upper panel: First 5 principal components of the set of CO×CIB angular cross power spectra computed from the models explored in this work. The dominant principal component (“PC 1”) represents the “average shape” of D F ℓ across all models (where F denotes a pair of fr…
Figure 11
Figure 11. Figure 11: Upper panel: The black points show the estimated uncertainties on D ν ℓ from a CMB-S4-like experiment (see main text for details), while the grey bands show the ranges of CO×CIB cross spectra from the models in Sec. 4. Middle panel: First 5 principal components of the…

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