The [C II] line emission as an interstellar medium probe in the MARIGOLD galaxies

Cristiano Porciani; Emilio Romano-D\'iaz; Prachi Khatri

REVIEW 3 major objections 4 minor 1 cited by

The [C II] line emission as an interstellar medium probe in the MARIGOLD galaxies

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper claims that a principal-component-based prescription using [C II] luminosity, short-timescale star formation rate, and metallicity predicts molecular gas mass in high-redshift galaxies with scatter reduced by a factor of 2.3…

desk verdict Solid simulation study, but the headline 2.3x gain is in-sample and the [C II] post-processing rests on an untested cell-decoupling assumption. read the letter →

arxiv 2411.09755 v2 pith:QMOTEZTR submitted 2024-11-14 astro-ph.GA

Prachi Khatri , Emilio Romano-Díaz , Cristiano Porciani This is my paper · ORCID

classification astro-ph.GA

keywords [CII]emissionmoleculargasmasshigh-redshiftgalaxiesluminosityfunctionprincipalcomponentanalysisMARIGOLDsimulationsstarformationrategas-phasemetallicity

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 uses cosmological simulations of galaxies at redshifts 3 to 7 to test whether the brightness of the [C II] 158 micron line can reliably measure molecular gas mass. It finds that the simple [C II]-to-molecular-gas relation has hidden secondary dependencies on how fast stars are forming and on metallicity, and that accounting for these dependencies improves molecular gas predictions by a factor of 2.3. Among all galaxy properties tested, [C II] emission correlates most tightly with the total mass of metals in the gas phase, raising the possibility that the line can also serve as a metallicity probe. The result matters because [C II] is one of the few bright lines visible from high-redshift galaxies, so a practical calibration would let observers measure molecular gas without relying on fainter CO emission.

What carries the argument

The central machinery is the PCA-based calibration (Eq. 6), for example at z=4: log(M_mol/M_sun) = 4.11 + 0.47 log(L([C II])/L_sun) + 0.59 log(SFR5/M_sun/yr) + 0.01 log(SFR200/M_sun/yr) + 0.09[12+log(O/H)]. It is derived by performing a principal component analysis in the five-dimensional space of scaled variables and setting the last principal component, dominated by M_mol, to zero. The [C II] luminosities feeding this relation come from a plane-parallel, slice-by-slice escape-probability radiative transfer calculation using HYACINTH chemistry, with the total galaxy luminosity taken as the sum of radiatively decoupled cells.

What would settle it

Run the same MARIGOLD galaxy snapshots through a full three-dimensional radiative transfer calculation that includes inter-cell absorption, and compare the resulting galaxy-integrated L([C II]) with the decoupled-cell sum; a difference larger than the roughly 30% level quoted in the Cloudy validation would require revising the PCA calibration and the M_mol and M_metal relations built on it.

Watch

Extended reading notes

Core claim

Working from the MARIGOLD simulations, which track non-equilibrium abundances of H2, CO, C, and C+ on the fly, and post-processing the [C II] emission with a slice-based radiative transfer model, the paper establishes that the L([C II])-M_mol relation carries a strong secondary dependence on the star formation rate averaged over 5 Myr and a weaker dependence on gas-phase metallicity. Including these variables through a principal component analysis yields a redshift-dependent linear prescription that predicts the true molecular gas mass with a scatter of 0.11-0.20 dex, about 2.3 times tighter than the best two-variable fit. The same analysis shows that L([C II]) has the tightest correlation with the gas-phase metal mass, M_metal, among the tested galaxy properties, and that the [C II] luminosity function is always better described by a double power law than by a Schechter function.

Load-bearing premise

All luminosities are computed under the assumption that [C II] photons escaping one simulation cell travel unattenuated to the galaxy edge, so if neighboring cells absorb a significant fraction of the escaping radiation, every luminosity-based calibration would shift.

Editorial extensions

If this is right

At a given [C II] luminosity, galaxies with higher short-timescale SFR and higher metallicity have higher molecular gas masses, so single-parameter calibrations underpredict M_mol for the most massive systems.
A simpler three-variable PCA relation using M_mol, L([C II]), and SFR5 recovers molecular gas within a factor of 1.7 at z=3 and 2.5 at z=7, and stays within roughly a factor of 2.5 when typical observational uncertainties are added.
Because L([C II]) correlates most tightly with M_metal among the studied properties, the line can serve as a metallicity indicator for high-redshift galaxies.
The [C II] luminosity function evolves rapidly, with a 600-fold increase in the number density of L([C II]) ~ 10^9 L_sun emitters between z=7 and z=3, and it is well fitted by a double power law with no exponential cutoff at the bright end.
Galaxies whose [C II] extends at least twice as far as their star formation activity make up about 20% at z=5 and 10% at z=4, and these galaxies preferentially have a roughly 5-7 times higher fractional satellite contribution to the [C II] emission.

Reading between the lines

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

One implicit testable extension is to apply the PCA calibration to observed high-redshift galaxy samples with [C II], SFR, and metallicity measurements and compare the resulting molecular gas masses with dynamical mass estimates; agreement would validate the absolute luminosity scale.
The tight L([C II])-M_metal correlation may partly reflect the known mass-metallicity relation, so separating metal mass from metallicity in observed samples would clarify whether [C II] traces the metal reservoir or the metal concentration.
The double power-law bright end implies that line-intensity mapping experiments should see a larger shot-noise contribution from bright [C II] emitters than predicted by models with an exponential cutoff, offering a direct observational discriminator.
A natural next step is to check whether the redshift evolution of the PCA coefficients mirrors the evolution of depletion time and CO-dark gas fraction, which would link the calibration to the underlying physics of molecular gas excitation.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This is a solid simulation study worth serious refereeing. The headline result—a factor-2.3 improvement in M_mol prediction from a PCA-based calibration—is real but currently an in-sample claim; treat the absolute number with caution until they do out-of-sample validation. The paper also introduces a genuinely new finding: [C II] emission in these simulated galaxies correlates most tightly with gas-phase metal mass, tighter than with SFR, M_mol, or total gas.

What the paper does well: it uses the MARIGOLD cosmological simulations (z=3-7) with on-the-fly non-equilibrium H2, CO, C, and C+ chemistry, post-processes [C II] with a well-documented radiative transfer model, and validates it against Cloudy over a broad grid. The agreement within 30-50% is acceptable given typical observational uncertainties. The comparisons with observed LFs, [C II]-SFR relations, and stacked radial profiles are honest and generally favorable. The statistics of extended [C II] emission (R>=2 in ~20% at z=5, ~10% at z=4) are new and contextualized against ALPINE observations.

Soft spots in proportion to their seriousness. First, the PCA coefficients and the claimed scatter reduction are fitted and evaluated on the same simulated sample. Bootstrapping does not guard against overfitting. A simple cross-validation split or leave-one-snapshot-out test would make the claim robust. Without it, the "factor of 2.3" should be described as an in-sample calibration gain, not a predictive improvement. Second, the cell-to-cell radiative decoupling assumption is load-bearing and only heuristically justified. The stress-test note is correct: with 32 pc cells and line widths of a few km/s, the velocity-shear argument is plausible but not guaranteed. The Cloudy validation uses a single slab and cannot constrain inter-cell transfer. I would not reject the paper over this—it is a standard approximation and the authors flag it—but they should either run a sensitivity test with different effective line widths or soften the absolute calibration claims. Third, no code or data release is mentioned, which limits reproducibility but is not a fatal flaw.

Citation pattern is fine; the self-citations to their own chemistry model are appropriate. The paper is a legitimate contribution that belongs in a serious refereed journal. I would send it to review and ask the referee to pressure-test the PCA validation and the decoupling assumption. After minor-to-moderate revisions, it will be a useful and likely well-cited reference.

Referee Report

3 major / 4 minor

Summary. Using the MARIGOLD cosmological simulation suite at redshifts 3 ≤ z ≤ 7, the authors post-process simulated galaxies with the HYACINTH sub-grid chemistry model and solve for [C II] 157.74 μm line emission, including intra-cell optical depth effects while treating individual cells as radiatively decoupled from one another. They construct [C II] luminosity functions, compare them with ALPINE/REBELS and previous models, derive galaxy-integrated and resolved L([C II])–SFR relations, and investigate L([C II]) as a molecular gas tracer. The central new result is a PCA-based prescription (Eq. 6, Table 5) that incorporates SFR5, SFR200, and gas-phase metallicity as secondary dependencies in the L([C II])–M_mol relation and is claimed to improve M_mol prediction by a factor of 2.3. The paper further reports that [C II] correlates most tightly with gas-phase metal mass among the explored properties, and that about 20% (10%) of simulated galaxies at z=5 (z=4) have [C II] emission extending at least twice as far as the star formation activity.

Significance. If the calibration claim holds, the paper provides a practical route to molecular gas mass estimates in high-redshift galaxies using [C II] plus a short-timescale SFR indicator, which is directly relevant to ALMA and NOEMA programs. The study is also useful for its luminosity-function predictions and for quantifying the incidence of extended [C II] emission. The strengths are the on-the-fly non-equilibrium chemistry, the detailed and documented post-processing radiative-transfer model in Appendices A and B, the explicit comparisons with observed luminosity functions and resolved Σ[C II]–ΣSFR relations, and the transparent reporting of fitted coefficients and dispersions. The main weaknesses are the untested cell-to-cell radiative decoupling assumption and the in-sample evaluation of the PCA gain; both are load-bearing for the headline claims but appear fixable with additional analysis.

major comments (3)

[Sect. 3 and Appendix A/B, Eq. (A.14)] The cell-to-cell radiative decoupling assumption is load-bearing for every luminosity-based calibration in the paper, but it is justified only by the statement that velocity differences between neighbouring cells should exceed the intrinsic line width, with no quantitative test. The line widths implied by Eq. (A.14) at the minimum cell size (Δx_min = 32 pc in M25) are only a few km/s, which is comparable to the rotational shear across adjacent cells in high-redshift galaxies, so the stated condition is not guaranteed. The Cloudy validation in Appendix B is a single plane-parallel slab and cannot constrain inter-cell transfer. If a non-negligible fraction of photons escaping one cell is absorbed by neighbouring dense cells, the total L([C II]), the luminosity function, and especially the SFR-dependent part of the PCA calibration will shift. Please add a quantitative test of the velocity-shear condition across the simulated cell population, or perform a 3D radiative transfer calculation on a representative subset, and report how the absolute luminosity, the LF, and the PCA coefficients change.
[Sect. 7.2, Table 5, Fig. 12] The central claim of a factor-of-2.3 improvement in M_mol prediction is evaluated on the same simulated sample used to fit the PCA coefficients and the two-variable M_mol–L([C II]) baseline. Adding predictors in a PCA or regression always reduces in-sample scatter, and the bootstrap procedure only estimates coefficient uncertainties; it does not test out-of-sample predictive performance. Overfitting therefore cannot be excluded. Please provide a cross-validated comparison (for example k-fold or train/test splits) for both the PCA prescription and the linear baseline, reporting the dispersions obtained out of sample. This is necessary before the factor-2.3 improvement can be interpreted as a genuine predictive gain.
[Appendix B] The validation against Cloudy shows deviations up to ±50%, with a pattern that depends on density and metallicity: the model overpredicts L([C II]) at low density and high metallicity and underpredicts it at intermediate densities. The statement that 30–50% is smaller than typical observational uncertainties does not address the calibration problem: a differential error between dense star-forming cells and diffuse cells will bias the secondary SFR and metallicity dependencies that enter Eq. (6) and the claimed scatter reduction. Please propagate the Appendix B deviations through the PCA calibration, or recalibrate the radiative-transfer model, and demonstrate that the factor-2.3 improvement survives.

minor comments (4)

[Sect. 7] The sentence 'We also report in In Fig. 9' contains a duplicated 'in In' and should be corrected.
[Sect. 6.3 and Fig. 7] The text refers to Vallini et al. (2015) relations with N=1 and N=3, while the figure caption and the earlier text state N=1 and N=2; please reconcile the notation.
[Appendix A] The sentence 'we take N=3 for simplicity, but in practice, use 20 slices in each slice' should read '20 slices in each cell'; the current wording is confusing.
[Table 5] At z=7 the bootstrap uncertainty on the metallicity coefficient d is ±2.80, far larger than the other coefficients, indicating that the five-variable PCA is poorly constrained at that redshift; this should be noted in the text when comparing the five- and three-variable prescriptions.

Circularity Check

1 steps flagged · score 6.0 of 10

In-sample PCA fit is presented as a predictive improvement; the 2.3x gain is measured on the same galaxies used to fit the relation.

fitted input called prediction [Sect. 7.2, Eq. (6), Table 5, Fig. 12]
"We also contrast this with the M_mol obtained from the best-fit relation between M_mol and L[C ii]. The latter shows approximately 2.3 times higher scatter. The 1-sigma standard deviation between the true M_mol and the predicted M_mol using the PCA-based relation is 0.13 implying that for most (95%) of the galaxies, the PCA relation predicts the true molecular gas mass within a factor of about 1.8 while using the two variable linear best-fit, the molecular gas mass is predicted within a factor of 4."

The PCA-based relation in Eq. (6) is fitted to the same simulated galaxy sample on which its performance is then measured, with log(M_mol) itself one of the five input variables to the PCA. The reported factor-of-2.3 improvement is the ratio of in-sample residual scatters of two fits evaluated on that same sample. For nested models, adding the SFR5 predictor cannot increase the in-sample scatter, so some improvement is guaranteed by the fitting procedure rather than by genuine predictive skill. The bootstrapping analysis only resamples the same galaxies and does not provide a held-out or cross-validated test. Thus the headline claim that accounting for secondary dependencies improves the M_mol prediction by a factor of 2.3 is an in-sample fitted-input-called-prediction result.

full rationale

The paper has a substantial body of independent content: the [C II] emission is computed with a post-processing radiative-transfer model validated against Cloudy in Appendix B, and the predicted luminosity functions, [C II]-SFR relations, and luminosity densities are compared with external observational data such as ALPINE, REBELS, and Zanella et al. (2018). The HYACINTH sub-grid model is a self-citation, but it is externally benchmarked against PDR codes and is not used as an unverified uniqueness argument, so it does not constitute circularity. The one genuinely circular step is the central predictive claim in Sect. 7.2: the PCA calibration is derived from, and evaluated on, the same simulated galaxies, and the 2.3x improvement therefore reflects in-sample curve fitting rather than an out-of-sample prediction. This makes the headline 'improvement' partially circular, while the rest of the paper's conclusions remain largely independent.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities. Its central quantitative claims rest on fitted calibrations (PCA and OLS coefficients) and on a set of modeling assumptions inherited from Hyacinth and from the [C II] radiative transfer treatment. The most consequential assumptions are the radiative decoupling of cells and the sub-grid ISM model; both are reasonable and partially validated, but they are not derived from first principles or directly confirmed by observations.

free parameters (4)

PCA coefficients a, b, c, d, e for the M_mol calibration = Listed in Table 5 per redshift; e.g., at z=4: a=0.47, b=0.59, c=0.01, d=0.09, e=4.11
Fitted to the simulated galaxy sample in Sect. 7.2 to predict M_mol from L([C II]), SFR5, SFR200, and 12+log(O/H). The reported factor 2.3 improvement is measured on the same sample.
Best-fit slope and intercept for L([C II])-SFR and L([C II])-M_mol relations = Table 3, e.g., at z=4: a=0.921, b=6.985 for SFR; a=0.772, b=0.742 for M_mol
Ordinary least squares fits to the simulated galaxies at each redshift; these define the baseline calibrations used for comparison with the PCA-based prescription.
Double power-law LF parameters: log(phi*), log(L*), alpha, beta = Table 2, e.g., z=3: log(phi*)=-1.00, log(L*)=7.37, alpha=-1.22, beta=-2.65
MCMC fits to the simulated [C II] luminosity functions; used for LF evolution and luminosity density estimates.
Sub-grid density PDF and temperature-density relation parameters from Hyacinth = Not re-fitted here; adopted from Khatri et al. (2024) and Hu et al. (2021)
These control the distribution of densities and temperatures within each cell, which directly determines C+ abundances and the [C II] excitation calculation. They are inputs from prior work, not fitted in this paper.

assumptions (6)

domain assumption Cells are radiatively decoupled when computing the total [C II] luminosity of a galaxy
Sect. 3 states that the total luminosity is the sum of cell luminosities without inter-cell absorption. This is valid only if velocity differences between cells exceed the intrinsic line width; if not, the absolute luminosities and calibrations would be affected.
domain assumption The sub-grid density PDF and the metallicity-dependent temperature-density relation from Hu et al. (2021) describe the unresolved ISM structure
Adopted from the Hyacinth model; these determine the H2, CO, C, and C+ abundances used in the [C II] calculation and the density slices in the radiative transfer.
domain assumption A two-level statistical equilibrium model with collisional rates from Goldsmith et al. (2012) and no FUV pumping describes the C+ line excitation
Appendix A uses a two-level system with collisions by H2, H, and electrons, plus CMB radiation. Soft UV pumping at 1330 angstroms is neglected, and electron temperature is set equal to kinetic temperature, which could introduce systematic errors in some phases.
domain assumption The simulated galaxy sample is representative of the observed high-redshift galaxy population used for comparison
The MARIGOLD boxes are 25 and 50 Mpc with resolution limits, AGN feedback is not included, and star formation is H2-based. The authors compare with ALPINE and REBELS galaxies and find broad agreement, but selection effects and missing physics could bias the calibration.
ad hoc to paper Dropping the fifth principal component and renormalizing yields a valid M_mol relation
In Sect. 7.2, the last principal component (PC5, dominated by M_mol) contains only 0.35% of the variance, so it is set to zero and the remaining coefficients are renormalized to solve for M_mol. This assumes the data lie approximately on a four-dimensional hyperplane.
standard math Standard statistical tools (MCMC, PCA, bootstrap) provide unbiased parameter estimates and uncertainty ranges
Used for LF fitting, identifying secondary dependences, and estimating coefficient errors. These are well-established methods, though the bootstrap does not provide out-of-sample validation.

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Cite this review

Pith. "Pith review of The [C II] line emission as an interstellar medium probe in the MARIGOLD galaxies." pith.science (2026). https://pith.science/paper/QMOTEZTR

@misc{pith2026241109755,
  author       = {Pith},
  title        = {Pith review of: The [C II] line emission as an interstellar medium probe in the MARIGOLD galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QMOTEZTR}},
  note         = {Machine review of arXiv:2411.09755}
}

abstract

The [C II] fine-structure line at 157.74 $\mu$m is one of the brightest far-infrared emission lines and an important probe of galaxy properties like the star formation rate (SFR) and the molecular gas mass ($M_{\mathrm{mol}}$). Using high-resolution numerical simulations, we test the reliability of the [C II] line as a tracer of $M_{\mathrm{mol}}$ in high-redshift galaxies and investigate secondary dependences of the [C II]-$M_{\mathrm{mol}}$ relation on the SFR and metallicity. We investigate the time evolution of the [C II] luminosity function (LF) and the relative spatial extent of [C II] emission and star formation. We post-process galaxies from the MARIGOLD simulations at redshifts $3 \le z \leq 7$ to obtain their [C II] emission. These simulations were performed with the sub-grid chemistry model, HYACINTH, to track the non-equilibrium abundances of $\mathrm{H_2}$, $\mathrm{CO}$, $\rm C$ and $\mathrm{C^+}$ on the fly. Based on a statistical sample of galaxies at these redshifts, we investigate correlations between the [C II] line luminosity, L([C II]), and the SFR, the $M_{\mathrm{mol}}$, the total gas mass and the metal mass in gas phase ($M_{\mathrm{metal}}$). We find that accounting for secondary dependencies in the L([C II])-$M_{\mathrm{mol}}$ relation improves the $M_{\mathrm{mol}}$ prediction by a factor of 2.3. The [C II] emission in our simulated galaxies shows the tightest correlation with $M_{\mathrm{metal}}$. About 20% (10%) of our simulated galaxies at $z=5$ ($z=4$) have [C II] emission extending $\geq 2$ times farther than the star formation activity. The [C II] LF evolves rapidly and is always well approximated by a double power law that does not show an exponential cutoff at the bright end. We record a 600-fold increase in the number density of L([C II]) $\sim 10^9 \, \mathrm{L_{\odot}}$ emitters in 1.4 Gyr.

Figures

Figures reproduced from arXiv: 2411.09755 by the authors.

**Figure 1.** Face-on view of a simulated galaxy at 𝑧 = 4. From left to right, the columns show the surface density of young stars (with ages ≤ 200 Myr), total gas (including H2) surface density, H2 surface density, and [C ii] surface brightness. In each panel, the circle indicates 0.1 times the virial radius of the parent DM halo. stellar half-mass radius𝑟1/2,∗ (that is, the radius containing half of the stellar mass within 0.1𝑅… view at source ↗

**Figure 2.** Conditional [Cii] LF from the M25 (dashed lines) and M50 (solid lines) simulations at redshifts 𝑧 = 5 and 3 for central galaxies (left panels), satellites galaxies (middle panels), and all galaxies (right panels). The coloured lines show the CLF of emitters residing in DM halos in different 𝑀halo bins and the black lines show the total LFs. The dotted grey line in the right panels denotes the luminosity threshold, 𝐿… view at source ↗

**Figure 3.** Simulated [Cii] LF compared with observational estimates. The coloured lines represent the best-fit DPL – Eq. (2) – to the simulated LF and the shaded area represents the central 68% credibility range obtained using the MCMC chains. Black stars represent the observational estimates at 𝑧 ∼ 4.5 from the ALPINE survey (Yan et al. 2020) and the grey arrow shows the lower limit from Swinbank et al. (2012) based on observ… view at source ↗

Figures from the paper (13 more)

**Figure 4.** Figure 4: Comparison of the cosmic [Cii] luminosity density (𝜌[C ii]) for different luminosity cuts in the Marigold simulations with observational estimates from ALPINE (Loiacono et al. 2021) – clustered and field estimates in pink and blue, respectively; from REBELS (Aravena …

**Figure 5.** Figure 5: Distribution of the Marigold galaxies in the SFR-𝑀mol plane at different redshifts. These are shown as purple hexbins, where the counts are sampled logarithmically. mass (Sect. 7) using a statistical sample of simulated galaxies. For this, we only consider central gala…

**Figure 6.** Figure 6: SFR versus 𝑀∗ in the Marigold galaxies at different redshifts compared with observational estimates of the main-sequence (MS) of star-forming galaxies. These include the MS relations from Schreiber et al. (2015, black) and Popesso et al. (2023, red) at the respective r…

**Figure 7.** Figure 7: [Cii] − SFR relation from the Marigold simulations at 3 ≤ 𝑧 ≤ 7 compared with observations. The simulated galaxy population is represented as purple hexbins, with the colour indicating the galaxy counts per bin. The red line showing the best-fit to these galaxies (see …

**Figure 8.** Figure 8: Spatially resolved [Cii] −SFR relation for the Marigold galaxies at 𝑧 = 4. The galaxies are divided into different stellar-mass bins (the number of galaxies in each bin is indicated in the legend). The solid lines show the median Σ[Cii] as a function of the SFR surface…

**Figure 9.** Figure 9: [Cii] − 𝑀mol relation from our simulations compared with observations. The simulated galaxies are represented by purple hexbins, where the colour indicates the number of galaxies in each bin. The solid red line gives the ordinary least squares linear fit to these galax…

**Figure 10.** Figure 10: Probability distribution function of the conversion factor 𝛼[C ii] exhibited by our simulated galaxies at different redshifts [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]

**Figure 11.** Figure 11: Conversion factor 𝛼[Cii] in our simulated galaxies as a function of gas metallicity (panel 𝑎), the SFR averaged over the last 5 Myr (panel 𝑏), the SFR averaged over the last 200 Myr (panel 𝑐), and the SFR change diagnostic 𝑅5−200 (panel 𝑑, see text) at different redsh…

**Figure 12.** Figure 12: Comparison of the predicted molecular gas mass estimates with the true molecular gas mass using two different approaches for simulated galaxies at 𝑧 = 4. Panel 𝑎 shows the performance of the best-fit relation between 𝑀mol and 𝐿[Cii] , while panels 𝑏 − 𝑑 present result…

**Figure 13.** Figure 13: Comparison of the simulated and observed stacked (radial) surface brightness profiles of the [C [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]

**Figure 14.** Figure 14: Example illustrating the calculation of the [PITH_FULL_IMAGE:figures/full_fig_p018_14.png]

**Figure 15.** Figure 15: Distribution of our galaxies at redshift [PITH_FULL_IMAGE:figures/full_fig_p019_15.png]

**Figure 16.** Figure 16: Comparison of𝑟90, [C ii] and 𝑟90, SFR for simulated galaxies at redshifts 𝑧 = 5 (left) and 4 (right). The galaxies are colour-coded by their multicomponent extent parameter E defined as the ratio of the 𝑟90 and 𝑟70 values of the [Cii] surface brightness profile. The s…

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

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