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arxiv: 2605.20698 · v1 · pith:S5AAAC2Xnew · submitted 2026-05-20 · 🌌 astro-ph.GA

CO(7-6) and [C I](2-1) survey in z > 6 quasars

Fuxiang Xu , Roberto Decarli , Ran Wang , Anna Elisabetta Borea , Antonio Pensabene , Xiaohui Fan , Dominik Riechers , Eduardo Ba\~nados
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Axel Wei{\ss} Michele Costa Fabian Walter Feige Wang Jinyi Yang Bram Venemans Jianan Li Emanuele Paolo Farina
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Pith reviewed 2026-05-21 04:04 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords high-redshift quasarsmolecular gasISM excitationALMA observationsPDR modelsXDR modelsCO linescarbon lines
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The pith

ALMA data on CO and [CI] lines in z~6 quasars show that standard PDR models cannot explain the gas excitation.

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

The paper reports ALMA Band 3 observations of the CO(7-6) and [C I](2-1) lines plus dust continuum toward 18 quasars at redshift around 6. Detections in most sources allow estimates of molecular gas mass from several independent tracers, which are then cross-calibrated. When the observed line ratios are placed on PDR and XDR model grids, many sources lie outside the allowed parameter space even though densities above 10,000 cm^{-3} and radiation fields of 10^3 to 10^4 are indicated for the sources that do fit. The high CO(7-6) to [CI](2-1) luminosity ratio further points to a warm, highly excited molecular phase. These findings together imply that classical photon-dominated-region heating is insufficient and that additional volumetric processes must be at work.

Core claim

Comparison of the L_[CII]/L_[CI] and L_CO(7-6)/L_TIR ratios with PDR and XDR model grids yields gas densities n > 10^4 cm^{-3} and radiation fields G_0 ~ 10^3–10^4 for the sources that lie inside the model grids, while a large fraction of the sample falls outside. The L'_CO(7-6)/L'_[CI](2-1) ratio indicates that a substantial portion of the molecular gas is warm and highly excited. These results demonstrate that classical PDR heating alone cannot account for the observed line ratios and that X-ray irradiation, turbulence, shocks, or enhanced cosmic-ray heating must also influence the excitation of the cold interstellar medium.

What carries the argument

Line ratios L_[CII]/L_[CI] and L_CO(7-6)/L_TIR placed on PDR/XDR model grids, together with the CO(7-6) to [CI](2-1) luminosity ratio, used to diagnose density, radiation field, and the need for non-PDR volumetric heating.

If this is right

  • Molecular gas masses derived from CO, [CI], [CII], and dust continuum become mutually consistent after hierarchical Bayesian cross-calibration.
  • A large fraction of the molecular gas in these quasar hosts resides in a warm, highly excited phase.
  • Multi-line diagnostics combining CO, [CI], [CII], and dust are required to separate star-formation and AGN-driven heating at cosmic dawn.
  • The cold ISM in early quasar galaxies experiences heating contributions from processes beyond classical PDRs.

Where Pith is reading between the lines

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

  • If volumetric heating is widespread, star-formation-rate calibrations that rely only on [CII] or dust may need revision for the earliest galaxies.
  • Higher-resolution maps of additional molecular lines could reveal whether the extra heating is centrally concentrated near the AGN or distributed throughout the host.
  • The same line-ratio diagnostics could be applied to non-quasar galaxies at similar redshifts to test whether the extra heating is AGN-specific.

Load-bearing premise

The line ratios can be compared directly to standard PDR and XDR model grids without large unmodeled contributions from selection biases or other effects in the sample of 18 sources.

What would settle it

A larger sample of z>6 quasars in which every source falls cleanly inside the PDR model grids with no outliers would falsify the claim that additional volumetric heating is required.

Figures

Figures reproduced from arXiv: 2605.20698 by Anna Elisabetta Borea, Antonio Pensabene, Axel Wei{\ss}, Bram Venemans, Dominik Riechers, Eduardo Ba\~nados, Emanuele Paolo Farina, Fabian Walter, Feige Wang, Fuxiang Xu, Jianan Li, Jinyi Yang, Michele Costa, Ran Wang, Roberto Decarli, Xiaohui Fan.

Figure 1
Figure 1. Figure 1: Comparison of velocity widths measured from the two lines. The y-axis shows FWHM[CII] and the x-axis FWHMCO(7–6). Points are color coded by total infrared luminosity, log(LTIR/L⊙) (color bar at right). Error bars indicate 1σ uncertainties. The dashed black line marks the one-to-one relation, FWHM[CII] = FWHMCO(7–6). This paper is structured as follows: Section 2 provides a sum￾mary of the observations and … view at source ↗
Figure 2
Figure 2. Figure 2: Observed continuum flux densities at 3 mm and 1 mm for the z∼6 quasar sample. Points are color mapped by log LTIR; error bars are shown when available, and gray arrows denote limits. Overplotted are modified blackbody tracks that span dust temperatures Td = {30, 47, 60, 100} K (colors) and an opacity index τ1900 GHz = {0.2, 1, 5} (linestyles); the CMB at z = 6 is included. The locus of the data is broadly … view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between FIR and UV luminosities with molecular and atomic line luminosities for the quasar sample. Each row corre￾sponds to a different emission line: from top to bottom, CO(7–6), [C i], and [C ii]. The left column shows the correlation with total infrared lu￾minosity (log LTIR), while the right column shows the correlation with rest-frame UV magnitude (M1450). Data points are color coded by the… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison between molecular gas masses estimated from CO(7–6), [C i], [Cii], and dust continuum emission, following the meth￾ods detailed in the main text. The dashed line marks the one-to-one relation. While the overall agreement between tracers is reasonable, sys￾tematic deviations appear—particularly for [Cii]-based estimates, which tend to yield higher values compared to CO and dust tracers. The arrow… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of six molecular gas mass estimates for 18 sources, arranged in three horizontal panels (ordered from high to low LTIR, left to right and top to bottom). For each source, the estimates from Mdust H2 , M [CII] H2 , M [CI] H2 , M CO(7−6) H2 , M our sample H2 , and Mz6all H2 are shown as colored points with spindle-shaped Gaussian error bars. Upper limits are indicated by downward arrows. For M our… view at source ↗
Figure 6
Figure 6. Figure 6: Diagnostic diagrams comparing observed luminosity ratios of [C ii], [C i], and CO(7–6) with PDR and XDR model predictions under different column densities. From left to right, the panels correspond to NH = 1022 , 1023, and 1024 cm−2 , respectively. Background color maps show model-predicted log LTIR values normalized to the maximum within each grid, illustrating relative variations across the parameter spa… view at source ↗
Figure 8
Figure 8. Figure 8: Distribution of the line luminosity ratio L ′ CO(7−6)/L ′ [CI](2−1) for dif￾ferent galaxy populations. Local LIRGs from Valentino et al.(2020a) are shown as filled histograms (sky-blue for non–AGN and orange for AGN). z ∼ 1 main-sequence galaxies are shown as green filled histograms, and SMGs atz ∼ 2–4 (from Valentino et al. 2020a and Gururajan et al. 2023) as brown dash-dotted histograms. AGN/QSOs at z ∼ … view at source ↗
read the original abstract

High-redshift ($z\gtrsim6$) quasars trace the earliest supermassive black holes and intense star formation, offering key laboratories for black hole-galaxy evolution at cosmic dawn. While far-infrared studies have revealed large dust reservoirs and strong [C II] emission, the physical conditions and molecular gas content of their ISM remain uncertain. We present ALMA Band 3 observations of the redshifted CO(7-6) and [C I](2-1) emission lines and dust continuum in a sample of 18 quasars at $z \sim 6$. We detected CO(7-6) in 15/18, [C I](2-1) in 6/18, and continuum in 13/18 sources. Line luminosities and continuum fluxes were used to estimate molecular gas masses from CO, [C I], and dust, and a hierarchical Bayesian cross-calibration of all four tracers yielded consistent per-source $M_{\rm H_2}$ estimates and conversion factors. Comparison with PDR and XDR model grids using the $L_{\rm [CII]}/L_{\rm [CI]}$ and $L_{\rm CO(7--6)}/L_{\rm TIR}$ ratios suggests gas densities of $n > 10^4$ cm$^{-3}$ and radiation fields of $G_0 \sim 10^3$--$10^4$ for sources consistent with PDR solutions, while many quasars fall outside the model parameter space. The $L'_{\rm CO(7-6)}/L'_{\rm [CI](2-1)}$ ratio indicates that a large fraction of the molecular gas resides in a warm and highly excited phase. Together these results suggest that classical PDR heating alone cannot explain the observed line ratios and that additional volumetric processes such as X-ray irradiation, turbulence and shocks, or enhanced cosmic-ray heating likely influence the excitation of the cold ISM. They demonstrate the power of multi-line diagnostics in revealing the excitation and structure of the cold ISM in early quasar host galaxies and highlight the need for joint analysis of CO, [C I], [C II], and dust emission to characterize star formation and AGN-driven heating at cosmic dawn.

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 / 3 minor

Summary. The paper reports ALMA Band 3 observations of redshifted CO(7-6) and [C I](2-1) lines plus dust continuum toward 18 z~6 quasars. CO(7-6) is detected in 15/18 sources, [C I](2-1) in 6/18, and continuum in 13/18. Molecular gas masses are derived from CO, [C I], and dust tracers, with a hierarchical Bayesian cross-calibration yielding consistent per-source M_H2 values. Line ratios L_[CII]/L_[CI] and L_CO(7-6)/L_TIR are compared to standard PDR and XDR model grids, indicating high densities (n > 10^4 cm^{-3}) and strong radiation fields (G_0 ~ 10^3-10^4) for PDR-consistent sources, while many objects lie outside the grids. The L'_CO(7-6)/L'_[CI](2-1) ratio is interpreted as evidence for a warm, highly excited molecular phase. The authors conclude that classical PDR heating is insufficient and that additional volumetric processes (X-ray irradiation, turbulence/shocks, or enhanced cosmic rays) are required to explain the cold ISM excitation.

Significance. If the model-grid comparisons remain robust after proper treatment of upper limits, the work would strengthen the case that multi-line diagnostics (CO, [C I], [C II], dust) are essential for characterizing ISM conditions in the earliest quasar hosts and that standard PDR models underpredict the observed excitation. The hierarchical Bayesian cross-calibration of four independent tracers is a methodological strength that improves consistency of M_H2 estimates across the sample.

major comments (2)
  1. [model-grid comparison] Model comparison (abstract and discussion): The central claim that 'classical PDR heating alone cannot explain the observed line ratios' and that 'many quasars fall outside the model parameter space' rests on L_[CII]/L_[CI] versus L_CO(7-6)/L_TIR diagrams. However, [C I](2-1) is detected in only 6/18 sources, so L_[CII]/L_[CI] is a lower limit for the remaining 12 sources. The manuscript does not state how these limits are incorporated into the grid comparison (e.g., plotted as arrows, treated as conservative bounds, or excluded from the 'outside' assessment). If the outliers are driven primarily by limits rather than secure measurements, the inference that additional volumetric processes are required loses force, as the data may still be consistent with PDR solutions within uncertainties.
  2. [hierarchical Bayesian calibration] Results section on hierarchical Bayesian calibration: The cross-calibration of CO, [C I], [C II], and dust conversion factors is presented as yielding consistent per-source M_H2 estimates, but the specific priors, likelihood functions, and treatment of the free parameters (listed in the axiom ledger as 'hierarchical Bayesian conversion factors') are not provided. Without these details it is difficult to evaluate whether the reported consistency is robust or sensitive to modeling choices.
minor comments (3)
  1. [abstract] Abstract: No uncertainties or error bars are quoted for detection rates, luminosities, or derived ratios, and no reference is given to the specific PDR/XDR model grids (e.g., Kaufman et al. or Meijerink et al. versions) used for the comparison.
  2. [results] Presentation: Full data tables with line fluxes, luminosities, and upper limits for all 18 sources should be provided (or linked) so that readers can independently assess the lower-limit ratios and their impact on the grid comparison.
  3. [notation] Notation: The distinction between L and L' (brightness temperature luminosity) is used inconsistently in the abstract when discussing the CO(7-6)/[C I](2-1) ratio; clarify the convention throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. Their comments have identified areas where additional clarity is needed, and we address each point below. We have prepared revisions that directly respond to the concerns raised while preserving the scientific conclusions supported by the data.

read point-by-point responses

  1. Referee: [model-grid comparison] Model comparison (abstract and discussion): The central claim that 'classical PDR heating alone cannot explain the observed line ratios' and that 'many quasars fall outside the model parameter space' rests on L_[CII]/L_[CI] versus L_CO(7-6)/L_TIR diagrams. However, [C I](2-1) is detected in only 6/18 sources, so L_[CII]/L_[CI] is a lower limit for the remaining 12 sources. The manuscript does not state how these limits are incorporated into the grid comparison (e.g., plotted as arrows, treated as conservative bounds, or excluded from the 'outside' assessment). If the outliers are driven primarily by limits rather than secure measurements, the inference that additional volumetric processes are required loses force, as the data may still be consistent with PDR solutions within uncertainties.

    Authors: We agree that the treatment of upper limits must be stated explicitly. In the revised manuscript we will add a dedicated paragraph in the discussion (and update the figure caption) explaining that non-detections of [C I](2-1) are plotted as lower limits on L_[CII]/L_[CI] with arrows directed toward higher ratio values. We have re-checked the positions of the six sources with secure [C I] detections; several of these lie outside the PDR model grids even before considering the limits. The direction of the arrows for the remaining sources moves them further from the PDR solutions rather than into them. We will therefore retain the conclusion that additional volumetric heating is required, while making the handling of limits fully transparent so readers can assess the robustness themselves. revision: yes

  2. Referee: [hierarchical Bayesian calibration] Results section on hierarchical Bayesian calibration: The cross-calibration of CO, [C I], [C II], and dust conversion factors is presented as yielding consistent per-source M_H2 estimates, but the specific priors, likelihood functions, and treatment of the free parameters (listed in the axiom ledger as 'hierarchical Bayesian conversion factors') are not provided. Without these details it is difficult to evaluate whether the reported consistency is robust or sensitive to modeling choices.

    Authors: The referee correctly notes that the current text does not supply the full statistical details. We will expand the relevant results subsection to include: (i) the form of the priors on the conversion factors (log-normal distributions centered on literature values with widths informed by local-galaxy scatter), (ii) the likelihood functions for each tracer (Gaussian for detections, one-sided for upper limits), and (iii) the MCMC sampling procedure and convergence diagnostics. A new appendix will tabulate the posterior medians and 16–84 percentile ranges for all free parameters, allowing readers to judge the sensitivity of the per-source M_H2 values. revision: yes

Circularity Check

0 steps flagged

Observational survey with external model grids; derivation is self-contained

full rationale

The paper reports ALMA observations of CO(7-6), [C I](2-1), and dust continuum in 18 z~6 quasars, with detections in 15, 6, and 13 sources respectively. Molecular gas masses are derived from multiple independent tracers (CO, [C I], dust) via a hierarchical Bayesian cross-calibration that combines measurements rather than defining one from the other. Line ratios are then compared directly to standard external PDR and XDR model grids to infer densities and radiation fields, with the conclusion that many sources fall outside PDR parameter space drawn from that comparison. No equation or step in the provided text reduces a result to a fitted parameter by construction, invokes a self-citation as the sole justification for a uniqueness claim, or renames an input as a prediction. The chain relies on external benchmarks and is therefore self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The interpretation rests on standard astrophysical assumptions about line excitation and model grids rather than new postulates.

free parameters (1)
  • hierarchical Bayesian conversion factors
    Used to cross-calibrate molecular gas masses from CO, [CI], and dust tracers.
axioms (1)
  • domain assumption PDR and XDR model grids accurately represent the dominant heating and excitation mechanisms for the observed line ratios
    Invoked when comparing L_[CII]/L_[CI] and L_CO(7-6)/L_TIR ratios to infer n and G0.

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