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arxiv: 2604.19529 · v1 · submitted 2026-04-21 · 🌌 astro-ph.GA

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Cosmic evolution of the [CII]-to-molecular gas relation

C\'edric Accard , Florent Renaud , Katarina Kraljic , Diana Ismail , Matthieu B\'ethermin , Oscar Agertz
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Pith reviewed 2026-05-10 02:16 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords CII emissionmolecular gasconversion factorhigh-redshift galaxiesISM phasescosmological simulationsgalaxy evolution
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The pith

No single conversion factor from [CII] luminosity to molecular gas mass works across all redshifts.

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

The paper tracks the [CII] 158 micron line and its link to molecular gas mass in a cosmological zoom-in simulation of a Milky Way-like galaxy from redshift 10 down to 0.2. It generates synthetic observations by post-processing the simulation outputs with radiative transfer. The conversion factor between [CII] luminosity and molecular gas mass changes by nearly three orders of magnitude as the galaxy's interstellar medium grows more metal-rich and less merger-dominated. This matters because [CII] is a key observable for inferring gas reservoirs in distant galaxies, yet a fixed conversion would produce large systematic errors at early times. The emission stays spatially tied to molecular gas, but its strength relative to the gas mass depends on metallicity, the balance of ISM phases, and dynamical events.

Core claim

The global L_[CII]-M_mol relation evolves from a steep, [CII]-deficient regime at very low metallicity to an almost linear behaviour, similar to calibrations at z approximately 2, once the ISM reaches Z greater than or equal to 0.05-0.1 solar at z less than or equal to 5. Over this evolution, alpha_[CII] spans nearly three orders of magnitude, from greater than 10,000 down to approximately 10 solar masses per solar luminosity, even though the [CII] emission remains spatially correlated with the molecular gas. A unique, redshift-independent alpha_[CII] therefore cannot recover molecular gas masses across the regimes explored. [CII] remains a viable tracer of molecular gas at very high redshif

What carries the argument

The redshift-dependent [CII]-to-molecular gas conversion factor alpha_[CII], measured globally and at 100 parsec scales from synthetic data cubes, which varies with the evolving metallicity, ISM phase mix, and merger activity in the simulation.

If this is right

  • At very high redshifts, [CII] traces molecular gas only when conversion factors explicitly account for metallicity, ISM phase mix, and merger events.
  • The L_[CII]-M_mol and L_[CII]-SFR relations approach linear behaviour once metallicity exceeds roughly 0.05 solar, resembling z approximately 2 calibrations.
  • Spatially resolved (100 pc) [CII] emission stays correlated with molecular gas even while the global conversion factor varies by orders of magnitude.
  • Merger-driven changes in ISM phase structure introduce additional offsets in alpha_[CII] beyond the metallicity trend.

Where Pith is reading between the lines

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

  • High-redshift surveys that apply local alpha_[CII] values may systematically underestimate molecular gas masses in metal-poor systems.
  • The metallicity dependence found here could be tested directly by pairing [CII] maps with metallicity diagnostics in future ALMA or JWST observations.
  • Similar conversion-factor evolution may apply to other tracers such as CO lines, affecting gas-mass estimates in the same high-z regime.
  • Galaxy-formation models that assume a fixed [CII] conversion would mispredict star-formation efficiencies at z greater than 5.

Load-bearing premise

The Vintergatan zoom-in simulation plus Skirt post-processing faithfully reproduces the ISM phase structure, metallicity distribution, and [CII] excitation conditions in real high-redshift galaxies.

What would settle it

Independent measurements of molecular gas mass (for example via CO or dust) and [CII] luminosity in a statistical sample of z greater than 5 galaxies that yield a constant alpha_[CII] near the local value would falsify the predicted strong redshift evolution.

Figures

Figures reproduced from arXiv: 2604.19529 by C\'edric Accard, Diana Ismail, Florent Renaud, Katarina Kraljic, Matthieu B\'ethermin, Oscar Agertz.

Figure 1
Figure 1. Figure 1: (Left panel) Relation between [C ii] luminosity and molecular gas mass in Vintergatan. Filled circles show the snapshots of Vintergatan, colour-coded by redshift. The blue dashed line and shaded area are the calibration and scatter of Zanella et al. (2018), derived for main-sequence galaxies with log(M⋆/M⊙) ≈ 10 − 11 at z ≈ 2. The orange dashed line is from Madden et al. (2020), based on nearby star-formin… view at source ↗
Figure 2
Figure 2. Figure 2: Redshift evolution of the gas metallicity distribution in Vinter￾gatan. The colour map shows, at each redshift, the fraction of pixels per metallicity bin, while the orange line and shaded band give the mass￾weighted average metallicity and the 16th–84th percentiles of the pixel distribution. molecular gas mass to the total [Cii] luminosity in each snap￾shot, to the distribution of local conversion factors… view at source ↗
Figure 3
Figure 3. Figure 3: Redshift evolution of the [C ii]–to–molecular-gas conversion fac￾tor α[C ii] . The blue colour map shows the distribution of pixel-wise α[C ii] values, the orange line traces the global conversion factor, and the orange shaded region marks the 16th–84th percentile range of the re￾solved values. Black and purple hatched rectangles indicate the ranges from the Zanella et al. (2018) calibration and the SERRA … view at source ↗
Figure 4
Figure 4. Figure 4: Recovery fraction of the total molecular gas mass inferred from different [C ii]–based estimators as a function of redshift. The blue line shows the recovery fraction when the true molecular surface density is summed only over [C ii]–emitting pixels. The green solid and dashed lines show the results from the resolved relations including both Σ[C ii] and metallicity, and Σ[C ii] alone, respectively. The bla… view at source ↗
Figure 5
Figure 5. Figure 5: Phase diagram of the total gas contents in Vintergatan. The horizontal solid line marks the temperature of T = 2×104 K used to define cold gas. Dashed and dotted vertical lines represent the density of 0.1 cm−3 and 10 cm−3 adopted to identify neutral and molecular gas, respectively. surface density in each pixel. Both prescriptions behave similarly and, once evaluated on all [C ii]-emitting pixels, recover… view at source ↗
Figure 6
Figure 6. Figure 6: Phase diagrams of the 2D projected molecular gas. Orange contours show the [C ii] emission across all gas phases, ranging from 101 to 106 L⊙ kpc−2 in steps of 1 dex. 10 8 6 4 2 0 Redshift 0.0 0.2 0.4 0.6 0.8 1.0 Fraction of [CII] emitted from each phase Molecular Atomic Major merger −2.5 −2.0 −1.5 −1.0 −0.5 0.0 log10 (Z/Z ) [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Fractional [C ii] contribution from the molecular and atomic gas phases as a function of redshift. For each snapshot we compute the [C ii] luminosity emitted by the molecular and atomic phases separately and plot, as filled circles, the fraction of the total [C ii] luminosity that arises from each phase. Points are colour-coded by the global gas metallic￾ity. Vertical grey bands indicate the redshift exten… view at source ↗
read the original abstract

The [CII] 158 $\mu$m line is widely used to trace star formation and the gas contents of high-redshift galaxies. However, it remains unclear under which physical conditions it reliably traces the molecular reservoir, and whether a unique conversion factor $\alpha_{\rm [CII]}$ can be applied across cosmic time. We investigate the evolution of the relation between the [CII] luminosity and molecular gas mass from $z\simeq10$ to $z\simeq0.2$ using the Vintergatan simulation, a high-resolution cosmological zoom-in of a Milky Way-like galaxy. We post-process the snapshots with the Skirt radiative transfer code to generate synthetic [CII] data cubes. We measure global and spatially resolved (100 pc) relations between [CII] luminosity ($L_{\rm [CII]}$), star formation rate (SFR), and molecular gas mass ($M_{\rm mol}$). We follow the redshift evolution of the [CII]-to-molecular gas conversion factor $\alpha_{\rm [CII]}$, and link these trends to the evolution of the interstellar medium (ISM) phases. The global $L_{\rm [CII]}$-$M_{\rm mol}$ and $L_{\rm [CII]}$-SFR relations evolve from a steep, [CII]-deficient regime at very low metallicity to an almost linear behaviour, similar to calibrations at $z\approx2$, once the ISM reaches $Z \gtrsim 0.05$-$0.1\,Z_\odot$ at $z\lesssim5$. Over this evolution, $\alpha_{\rm [CII]}$ spans nearly three orders of magnitude, from $\gtrsim 10^4$ down to $\approx10 \,\rm{M_\odot\,L_\odot^{-1}}$, even though the [CII] emission remains spatially correlated with the molecular gas. A unique, redshift-independent $\alpha_{\rm [CII]}$ therefore cannot recover molecular gas masses across the regimes we explore. [CII] remains a viable tracer of molecular gas at very high redshifts, but only when used with conversion factors that explicitly account for metallicity, ISM phase mix, and merger events.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses the Vintergatan cosmological zoom-in simulation of a Milky Way-like halo, post-processed with the SKIRT radiative transfer code, to track the redshift evolution (z≈10 to z≈0.2) of the [CII] 158 μm luminosity–molecular gas mass relation. Synthetic [CII] data cubes are generated to measure global and 100-pc resolved L_[CII]–M_mol and L_[CII]–SFR relations, from which the conversion factor α_[CII] is derived and linked to ISM phase evolution, metallicity, and merger activity. The key result is that α_[CII] varies by nearly three orders of magnitude, precluding a unique redshift-independent value, while [CII] remains a viable tracer only when metallicity-, phase-, and merger-dependent corrections are applied.

Significance. If the reported trends hold, the work supplies a physically motivated framework for interpreting high-redshift [CII] observations, demonstrating that forward-modeling from hydrodynamics plus line transfer can reveal when and why [CII] fails as a direct molecular-gas tracer. The absence of circularity—trends emerge from the simulation rather than being tuned to observations—is a clear strength, as is the explicit connection between α_[CII] evolution and ISM phase partitioning. The result would affect ALMA-based gas-mass estimates at z≳5 and motivate metallicity-dependent conversion factors in future surveys.

major comments (2)
  1. [abstract and results] The central claim that no unique, redshift-independent α_[CII] recovers M_mol across regimes rests on trends extracted from a single Vintergatan zoom-in of one Milky Way-like halo. Because the reported three-order-of-magnitude variation in α_[CII] is driven by this halo’s specific metallicity build-up, merger sequence, and ISM phase partitioning, it is unclear whether the same evolution applies to galaxies with different stellar masses, assembly histories, or feedback implementations at z≳5 (abstract and results sections).
  2. [methods and discussion] The assumption that the Vintergatan + SKIRT pipeline faithfully reproduces high-redshift ISM conditions is load-bearing for the conclusion that [CII] remains viable only with explicit corrections. No quantitative assessment is provided of how changes in sub-grid physics, spatial resolution, or [CII] excitation assumptions would alter the derived α_[CII](z) trends (methods and discussion sections).
minor comments (2)
  1. [results] Clarify the exact spatial scale and aperture used for the 'global' versus '100 pc resolved' relations; the transition between them is not numerically specified.
  2. [results] Add a brief table or figure panel showing the redshift evolution of mean metallicity and molecular gas fraction alongside α_[CII] to make the causal links more transparent.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have prompted us to clarify several aspects of our analysis. We respond to each major comment below and indicate the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [abstract and results] The central claim that no unique, redshift-independent α_[CII] recovers M_mol across regimes rests on trends extracted from a single Vintergatan zoom-in of one Milky Way-like halo. Because the reported three-order-of-magnitude variation in α_[CII] is driven by this halo’s specific metallicity build-up, merger sequence, and ISM phase partitioning, it is unclear whether the same evolution applies to galaxies with different stellar masses, assembly histories, or feedback implementations at z≳5 (abstract and results sections).

    Authors: We agree that the study is based on a single high-resolution zoom-in simulation of a Milky Way-like halo. This setup was selected to enable a self-consistent, high-fidelity tracking of one galaxy’s ISM evolution from z≈10 to z≈0.2. The reported variation in α_[CII] is physically tied to the secular increase in gas-phase metallicity and the associated shift in ISM phase partitioning, both of which are generic processes expected to operate across galaxies of different masses. The precise redshift at which the transition to a near-linear L_[CII]–M_mol relation occurs will, however, depend on a galaxy’s specific assembly history and feedback implementation. In the revised manuscript we will add an explicit paragraph in the discussion section that states this limitation, cautions against over-generalizing the quantitative α_[CII](z) curve, and notes that the qualitative conclusion (no unique redshift-independent conversion factor) follows from the metallicity dependence itself, which is a robust feature of the underlying physics. revision: partial

  2. Referee: [methods and discussion] The assumption that the Vintergatan + SKIRT pipeline faithfully reproduces high-redshift ISM conditions is load-bearing for the conclusion that [CII] remains viable only with explicit corrections. No quantitative assessment is provided of how changes in sub-grid physics, spatial resolution, or [CII] excitation assumptions would alter the derived α_[CII](z) trends (methods and discussion sections).

    Authors: We recognize that a quantitative sensitivity study varying sub-grid physics, resolution, or the [CII] excitation treatment is not presented. Performing such a study would require a new suite of simulations and is beyond the computational scope of the present work. The Vintergatan model has been validated against a range of observational diagnostics at both low and high redshift, and SKIRT is a standard, well-tested radiative-transfer code. In the revised manuscript we will expand the methods and discussion sections with a qualitative assessment of how plausible changes in these ingredients could affect the results, drawing on existing literature that explores [CII] emission under different ISM conditions and resolutions. We will emphasize that the dominant driver of the α_[CII] evolution is the large-scale metallicity build-up rather than small-scale details of the sub-grid modeling. revision: partial

Circularity Check

0 steps flagged

No circularity: forward-modeling yields emergent α_[CII] trends

full rationale

The paper runs the Vintergatan zoom-in simulation, post-processes snapshots with Skirt to produce synthetic [CII] cubes, then directly computes global and resolved L_[CII]–M_mol relations and the resulting α_[CII](z) from those outputs. No observational data are used to fit α_[CII], no self-referential definitions equate inputs to outputs, and no uniqueness theorems or prior self-citations are invoked as load-bearing premises for the central claim. The reported three-order-of-magnitude variation and the conclusion that a redshift-independent factor fails both follow from the hydrodynamics, metallicity build-up, and radiative transfer inside the model rather than being presupposed by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the fidelity of one particular hydrodynamical simulation and its post-processing; no independent observational calibration or cross-check against multiple codes is described in the abstract.

axioms (2)
  • domain assumption The Vintergatan simulation and its sub-grid physics accurately capture the metallicity evolution and ISM phase structure of high-redshift galaxies.
    Invoked when interpreting the simulated [CII] luminosities as representative of real galaxies.
  • domain assumption The Skirt radiative transfer code correctly computes the [CII] 158 micron emission given the simulated gas and radiation field.
    Required for generating the synthetic data cubes used to measure the relations.

pith-pipeline@v0.9.0 · 5742 in / 1637 out tokens · 44635 ms · 2026-05-10T02:16:11.896591+00:00 · methodology

discussion (0)

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