REVIEW 3 major objections 5 minor 288 references
The canonical CO-to-H2 factor of 0.8 for early dusty galaxies is not forced by the data; two gas-mass methods and realistic size estimates leave near-Milky-Way values (2–4.3) dynamically viable.
Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →
T0 review · deepseek-v4-flash
2026-08-01 15:22 UTC pith:TM6H3OCC
load-bearing objection A careful, honest paper showing alpha_CO=0.8 is not uniquely required for unlensed DSFGs, but its near-Galactic alpha_CO claim rests on one untested pivot: G/D=100. the 3 major comments →
Vz-GAL Dusty Star-Forming Galaxies: Revisiting the CO-H2 Conversion Factor Tension
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The paper establishes that the canonical α_CO = 0.8 conversion factor is not uniquely favored by dynamical constraints on high-redshift dusty star-forming galaxies. For 12 unlensed Vz-GAL sources, dust-SED and TUNER large-velocity-gradient modeling give mutually consistent gas masses, α_CO ≈ 1.5–11.5, medians near 3.4 and 5.1. With realistic cold-gas radii (radiative-transfer or 2.5× dust radii), the isotropic virial estimate yields upper limits α_CO ≤ 4.5 and ≤ 10.6, encompassing the gas-based values. The GN20 case study shows resolved gas geometry and kinematics recover the mass a "mixed" rotating-disk estimator misses, reconciling LVG-derived α_CO with dynamics.
What carries the argument
Two dynamical estimators carry the argument: the isotropic virial estimator, M_dyn ∝ (FWHM)² R_eff, treats the galaxy as a pressure-supported sphere, while the proposed "mixed" estimator, M_dyn = (v_rot² + kσ₀²)R_eff/G with k = 3, models a rotating turbulent thick disk. The decisive input is the effective radius: compact dust radii suppress dynamical masses and force low α_CO, whereas radiative-transfer (LVG) radii — about twice the dust radius — or a fiducial 2.5×R_dust restore consistency. The gas masses come from two methods sharing a fixed gas-to-dust ratio of 100: dust-SED (GMBB) fitting anchored by resolved dust sizes, and the TUNER large-velocity-gradient code jointly fitting the CO l
Load-bearing premise
The entire near-Galactic conclusion rests on fixing the gas-to-dust mass ratio at 100 in both gas-mass methods: if the true ratio were much lower, as for metal-poor gas, both methods would yield α_CO ≈ 0.8–1.0 and the claimed tension would vanish, and the paper sets aside its own free-G/D fits (150–380) as unrealistic without direct metallicity measurements.
What would settle it
Two observations would settle the claim. First, resolve the CO(1–0) emission of the 12 modeled galaxies: if the cold-gas radii match the compact dust radii rather than the assumed ~2× larger extents, the isotropic virial upper limits fall back below the gas-based α_CO and the near-Galactic conclusion collapses. Second, measure metallicities (e.g., via far-infrared fine-structure lines or dust-to-metal calibration) for a handful of these sources: a gas-to-dust ratio near 25–30 would rescale both gas masses down ~3–4×, putting α_CO back at roughly 0.8–1.0.
If this is right
- If α_CO is near-Galactic rather than 0.8, the molecular gas masses of these dusty galaxies are roughly a factor of five larger, implying lower star-formation efficiencies and longer gas-depletion times than commonly quoted.
- Realistic cold-gas extents push the isotropic virial upper limits to α_CO ≤ 4.5 (narrow-line group) and ≤ 10.6 (broad-line group), fully bracketing the gas-based values, so no dynamical argument uniquely favors the low conversion factor.
- α_CO appears to vary from source to source with ISM conditions; applying a universal 0.8 indiscriminately would systematically underestimate molecular gas reservoirs in many high-redshift dusty galaxies.
- Inclinations inferred from dust morphology can misrepresent the gas disk (GN20: dust implies ~67°, resolved gas ~30°), so disk-based dynamical masses need resolved cold-gas kinematics to be reliable.
- Multi-phase ISM structure, with low-J CO tracing extended diffuse gas and higher-J lines tracing dense gas, makes single-transition α_CO calibrations an oversimplification for extreme starbursts.
Where Pith is reading between the lines
- The near-Galactic conclusion rests entirely on the fixed gas-to-dust ratio of 100: direct metallicity measurements showing sub-solar abundances (G/D ~ 25–30) would rescale both gas-mass methods down to α_CO ≈ 0.8–1.0, dissolving the tension in the opposite direction — a test the paper's own free-G/D fits anticipate but cannot resolve.
- The radius logic yields a sharp, checkable prediction: resolved CO(1–0), [CI], or [CII] mapping of these 21 galaxies should reveal cold-gas disks roughly twice the dust radii; if the gas turns out to be as compact as the dust, the dynamical case for α_CO > 2 largely evaporates.
- If near-Galactic α_CO survives, the implied gas fractions and depletion times for early-universe starbursts must be revised upward, shifting estimates of the cosmic molecular gas budget at z ~ 2–4 — a consequence the paper gestures at but does not quantify.
- The "mixed" estimator's failure on unresolved data — it needs implausibly face-on inclinations to match the virial estimator — is a caution that generalizes beyond DSFGs to any survey deriving disk dynamical masses from integrated linewidths alone.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper uses the largest homogeneous sample of 21 unlensed Vz-GAL DSFGs at z~1-4 with VLA CO(1-0) detections and resolved ALMA 1mm dust sizes, down-selecting 12 galaxies for robust gas-mass modeling. Molecular gas masses are derived with two methods: a general modified blackbody (GMBB) dust SED fit with fixed G/D=100, and the TUNER LVG radiative-transfer framework using the same G/D and dust opacity normalization. Both yield α_CO ~1.5-11.5, with medians ~3-5, in contrast to the commonly adopted α_CO=0.8. These gas masses are compared with isotropic virial and 'mixed' rotating thick-disk dynamical mass estimators using dust, LVG, and fiducial 2.5×R_dust radii. The paper concludes that current data do not require α_CO=0.8 and that intermediate to near-Galactic values remain dynamically viable once gas geometry, dust properties, and G/D uncertainties are considered.
Significance. If the main conclusion is accepted, the paper is important because it challenges the routine adoption of α_CO=0.8 for high-z DSFGs and does so with a homogeneous, carefully selected sample that includes CO(1-0) luminosities and resolved dust sizes. Strengths include the transparent statement of shared assumptions between methods, a very useful GN20 case study that decomposes the impact of individual parameters on dynamical α_CO limits, and a clear demonstration that the isotropic virial estimator with realistic gas extents yields upper limits that encompass the gas-based values. The weaker, but defensible, claim that current dynamical data do not exclude near-Galactic α_CO is significant. However, the quantitative gas-based medians are conditional on an untested G/D=100 and on a single dust-opacity normalization, so the paper is best read as a viability argument rather than a measurement of α_CO. With the sensitivity analysis recommended below, the manuscript would make a solid contribution to the α_CO debate.
major comments (3)
- [§3.2.1–§3.2.2, Tables 3, 6, 8] The quantitative backbone of the conclusion is the fixed G/D=100 plus the Draine et al. (2014) dust opacity normalization. Both gas-mass estimators scale linearly with G/D, so the median α_CO values ~3–5 are directly proportional to this assumed ratio. The paper itself reports that leaving G/D free in TUNER yields G/D~150–380 and α_CO~7–22 (§3.2.2), and excludes these as unrealistic based on literature expectations rather than sample metallicity measurements. No direct metallicity or G/D constraint is presented for the Vz-GAL objects. A true ratio in the range 25–50 would bring the gas-based α_CO to ~0.8–1.5 and dissolve the claimed tension; the §3.2.3 statement that the results 'statistically favor' a Milky Way-like value is therefore not supported by the data as presented. At minimum, the paper needs a sensitivity analysis propagating the G/D uncertainty (and ideally external metallici
- [§3.2.2, Eq. (6), Table 6, Fig. 6] The TUNER-based α_CO is not an independent gas-mass estimate in the way the 'two complementary methods' framing implies. The model is fit to the observed CO(1–0) and higher-J CO lines, and α_CO,LVG is defined as M_H2,LVG / L'_CO(1-0),LVG, where the model CO(1–0) luminosity is matched to the observed value within ~0.1 dex for most sources. The agreement between method-1 and method-2 is therefore partly by construction: both share G/D=100 and κ_ν, and the CO luminosity enters the TUNER fit itself. The text acknowledges the non-independence, but the consistency argument should be downweighted or a version of the TUNER analysis that does not feed the observed CO(1–0) luminosity into the α_CO determination should be presented.
- [§4.2, Table 8] The mixed estimator is shown to systematically underestimate M_dyn for unresolved data, and the paper ultimately relies on the isotropic virial estimator with enlarged radii for its headline upper limits. This is transparent, but it leaves the quantitative α_CO upper limits (Table 8, columns g–h) resting on R_LVG or 2.5×R_dust. R_LVG comes from the same TUNER model whose G/D and opacity assumptions are at issue, and 2.5×R_dust is a fiducial literature factor, not a measured cold-gas size for this sample. The central claim should be phrased as 'these values are not excluded by current dynamical constraints' rather than as a positive preference for near-Galactic α_CO, and the illustrative character of the enlarged-radius limits should be stated in the abstract or summary.
minor comments (5)
- [Title/affiliations] The running title contains typographical artifacts: 'F orming' and 'F actor T ension'; the affiliation carries 'Departement' instead of 'Department'.
- [Table 2, note g] Using the CO(5–4) linewidth for HerBS-191 instead of the CO(1–0) FWHM affects the Group-2 dynamical limits. This is important enough to be stated in the main text, not only in a table note.
- [Fig. 6 caption] The phrase 'median underestimation of ~0.10 dex' should be 'median underprediction' to make clear it is the model, not the data, that lies low.
- [Table 8] The repeated column labels (a)–(h) in the table notes are confusing. Please use distinct column identifiers or a clearer shorthand in the caption and notes.
- [§4.3, Table 7] The 'Difference [dex]' column is ambiguous regarding sign convention. Specify explicitly whether positive values correspond to increases or decreases in α_CO relative to the baseline.
Circularity Check
TUNER-based α_CO divides by the model-fitted CO(1-0) luminosity, and the free-G/D fit that would give α_CO~7-22 is discarded in favor of a fixed G/D=100; the near-Galactic α_CO result is therefore partly loaded into the input calibration rather than independently measured.
specific steps
-
fitted input called prediction
[§3.2.2, Eq. (6), Table 6, Fig. 6 (right)]
"MH2,L VG=α CO,L VG·L′ CO(1−0),L VG (Eq. 6). ... Our best-fit models fit the observed CO(1–0) line luminosities within the error bars, with a median underestimation of∼0.10 dex."
The LVG-derived conversion factor is defined as the ratio of the model-inferred gas mass to the model-reproduced CO(1-0) luminosity. Because TUNER is fitted to the observed CO(1-0) line (along with the higher-J SLED and dust SED), L'_CO(1-0),LVG is not an independent observable. Thus α_CO,LVG is partly a re-expression of the fitting procedure and of the assumed G/D=100, rather than an independent measurement of the CO-to-H2 conversion factor. The dust-SED method (method 1) does not share this particular issue because it uses the observed L'_CO in the denominator.
-
other
[§3.2.2 (free-G/D test; fixed G/D adopted; Eqs. 5-6)]
"We have also fixed the G/D ratio to 100, i.e., the same as that used in §3.2.1. We further tested TUNER L VG models with the G/D ratio left as a free parameter. The resulting fits produced median G/D ratios of∼150–380, with 9/12 sources favoring values above 200. These solutions implyα CO values of∼7–22 ... Given that such large G/D ratios are not generally expected ... we chose to adopt a fixed G/D ratio of 100."
By Eq. (5), M_gas = G/D × M_dust and α_CO = M_gas/L'_CO, so every gas-based α_CO in Tables 3 and 6 scales linearly with the adopted G/D. The paper first fits G/D freely and obtains α_CO ~7-22, then rejects those fits as unrealistic and fixes G/D=100, yielding α_CO ~3-5. The headline 'intermediate to near-Galactic values remain viable' is therefore to first order enforced by the choice G/D=100 rather than independently inferred from the data. This is a partially circular/assumption-forced step, although the dynamical upper limits provide some independent constraint.
full rationale
The paper contains substantial independent content: it uses observed CO(1-0) luminosities, ALMA-resolved dust sizes, and dynamical estimators built from observed FWHMs, and it tests the interpretation against the resolved GN20 case. The dust-SED method (Eq. 5) is not circular in the strict sense: it combines an observed CO luminosity with a continuum-derived dust mass and an externally assumed G/D=100. The isotropic virial upper limits are also a legitimate, partly independent check. However, two steps undermine the claim that the near-Galactic α_CO values are a 'prediction' rather than a consequence of the input calibration. First, the TUNER-derived α_CO (Eq. 6) uses the model-fitted CO(1-0) luminosity as its denominator; because TUNER is fitted to the observed CO(1-0) line, this α_CO is a re-expression of the fit rather than an independent measurement. Second, the paper explicitly fits G/D as a free parameter, obtains α_CO~7-22, declares those G/D values unrealistic, and fixes G/D=100; since all gas masses scale linearly with G/D, the resulting α_CO~3-5 is largely imposed by that fixed input. The paper is transparent about the G/D dependence and states that the conclusion is conditional, which keeps this from being fully circular, but the central 'near-Galactic' result is partly loaded into the assumed gas-to-dust ratio. Hence a score of 4 is appropriate: there is real independent content, but some of the derived α_CO values reduce by construction to the adopted calibration.
Axiom & Free-Parameter Ledger
free parameters (7)
- Gas-to-dust mass ratio (G/D) =
100
- Dust opacity normalization (κ_ν) =
0.047 m^2/kg at 850 µm
- Intrinsic disk thickness (q0) =
0.2
- Pressure-support coefficient (k) =
3
- Rotation-to-FWHM factor =
0.5
- Velocity dispersion (σ0) =
31-38 km/s
- Fiducial gas-to-dust size ratio =
2.5
axioms (5)
- standard math Spatially flat ΛCDM cosmology (Planck 2020)
- domain assumption Dust emission traces a circular inclined disk
- domain assumption Molecular gas is smoothly distributed on scales exceeding the dust radius
- domain assumption Solar metallicity (G/D=100) in high-z DSFGs
- standard math Virial estimator factor 6.7
read the original abstract
The CO luminosity-to-H$_2$ mass conversion factor ($\alpha_{CO}$) remains a debated uncertainty in determining molecular gas masses of high-redshift dusty star-forming galaxies (DSFGs). Dynamical mass constraints have often favored $\alpha_{CO}=0.8$~$M_{\odot}~{(K~km~{s}^{-1}~{pc}^{2})}^{-1}$, whereas dust- and radiative-transfer-based methods imply higher values. We revisit this ``tension" using the largest homogeneous sample of 21 unlensed $z\sim1-4$ DSFGs, with securely measured \coonezero luminosities from the VLA \vzgal survey and resolved ($\sim{0.1}^{\prime\prime}$) ALMA 1~mm dust continuum imaging. For 12 galaxies with robust modeling constraints, we derive molecular gas masses using dust spectral energy distribution modeling and the TUNER LVG framework, adopting a solar-metallicity gas-to-dust mass ratio of 100. Although not fully independent due to shared assumptions on dust properties, these approaches yield mutually consistent gas masses corresponding to $\alpha_{CO}\sim1.5-11.5$, with a median near the Galactic $\alpha_{CO}=4.3$. Isotropic virial dynamical masses agree with these gas masses when realistic molecular gas sizes are adopted, while our proposed ``mixed" (rotating, pressure-supported, thick-disk) estimator systematically underestimates dynamical masses, producing low $\alpha_{CO}$ limits. Using GN20 ($z=4.055$) as a case study, we show that resolved gas geometry and kinematics reconcile the discrepancy with LVG-derived $\alpha_{CO}$. Our results suggest that current data do not require $\alpha_{CO}=0.8$, and intermediate to near-Galactic values remain dynamically viable given uncertainties in gas geometry, dust properties, and gas-to-dust ratios. Further progress in calibrating $\alpha_{CO}$ in the early universe will require resolved molecular gas observations, physically motivated ISM modeling, and stringent constraints on dust properties.
Figures
Reference graph
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The ISM Properties and Gas Kinematics of a Redshift 3 Massive Dusty Star-forming Galaxy. , keywords =. doi:10.3847/1538-4357/aaf860 , archivePrefix =. 1812.06095 , primaryClass =
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[56]
^ 3D BAROLO: a new 3D algorithm to derive rotation curves of galaxies. , keywords =. doi:10.1093/mnras/stv1213 , archivePrefix =. 1505.07834 , primaryClass =
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[57]
Galactic Dynamics: Second Edition
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[58]
The ALMA-ALPAKA survey. I. High-resolution CO and [CI] kinematics of star-forming galaxies at z = 0.5-3.5. , keywords =. doi:10.1051/0004-6361/202346444 , archivePrefix =. 2303.16227 , primaryClass =
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Clumpy star formation and an obscured nuclear starburst in the luminous dusty z = 4 galaxy GN20 seen by MIRI/JWST. , keywords =. doi:10.1051/0004-6361/202348845 , archivePrefix =. 2312.03074 , primaryClass =
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[60]
Direct detection of cool molecular gas in a star-forming galaxy at z=7.31. , keywords =. doi:10.1093/mnras/stag924 , archivePrefix =. 2606.13393 , primaryClass =
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HerMES: Candidate Gravitationally Lensed Galaxies and Lensing Statistics at Submillimeter Wavelengths. , keywords =. doi:10.1088/0004-637X/762/1/59 , archivePrefix =. 1205.3778 , primaryClass =
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Candidate Gravitationally Lensed Dusty Star-forming Galaxies in the Herschel Wide Area Surveys. , keywords =. doi:10.3847/0004-637X/823/1/17 , archivePrefix =. 1601.03401 , primaryClass =
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[63]
A search for the lenses in the Herschel Bright Sources (HerBS) sample. , keywords =. doi:10.1093/mnras/staa506 , archivePrefix =. 2002.08373 , primaryClass =
Pith/arXiv arXiv 2002
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[64]
IRAM 30-m-EMIR redshift search of z = 3-4 lensed dusty starbursts selected from the HerBS sample. , keywords =. doi:10.1093/mnras/staa1664 , archivePrefix =. 2006.05992 , primaryClass =
Pith/arXiv arXiv 2006
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Resolved CO(1-0) Emission and Gas Properties in Luminous Dusty Star-forming Galaxies at z = 2-4. , keywords =. doi:10.3847/1538-4357/acb6f7 , archivePrefix =. 2301.12976 , primaryClass =
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[66]
The rapid assembly of an elliptical galaxy of 400 billion solar masses at a redshift of 2.3. , keywords =. doi:10.1038/nature12184 , archivePrefix =. 1305.4930 , primaryClass =
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[67]
Herschel-ATLAS: A Binary HyLIRG Pinpointing a Cluster of Starbursting Protoellipticals. , keywords =. doi:10.1088/0004-637X/772/2/137 , archivePrefix =. 1302.4436 , primaryClass =
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[68]
Hyperluminous starburst gives up its secrets. , keywords =. doi:10.1093/mnras/stz2180 , archivePrefix =. 1908.03199 , primaryClass =
Pith/arXiv arXiv 1908
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[69]
Witnessing the Birth of the Red Sequence: ALMA High-resolution Imaging of [C II] and Dust in Two Interacting Ultra-red Starbursts at z = 4.425. , keywords =. doi:10.3847/0004-637X/827/1/34 , archivePrefix =. 1601.07549 , primaryClass =
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A dust-obscured massive maximum-starburst galaxy at a redshift of 6.34. , keywords =. doi:10.1038/nature12050 , archivePrefix =. 1304.4256 , primaryClass =
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[71]
HerMES: ALMA Imaging of Herschel-selected Dusty Star-forming Galaxies. , keywords =. doi:10.1088/0004-637X/812/1/43 , archivePrefix =. 1504.05256 , primaryClass =
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An Extreme Protocluster of Luminous Dusty Starbursts in the Early Universe. , keywords =. doi:10.3847/1538-4357/aaa1f1 , archivePrefix =. 1709.02809 , primaryClass =
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[73]
Confirming Herschel Candidate Protoclusters from ALMA/VLA CO Observations. , keywords =. doi:10.3847/1538-4357/ab002a , archivePrefix =. 1905.08813 , primaryClass =
Pith/arXiv arXiv 1905
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[74]
The Evolution of the Baryons Associated with Galaxies Averaged over Cosmic Time and Space. , keywords =. doi:10.3847/1538-4357/abb82e , archivePrefix =. 2009.11126 , primaryClass =
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[76]
Imaging the Molecular Gas Properties of a Major Merger Driving the Evolution of a z = 2.5 Submillimeter Galaxy. , keywords =. doi:10.1088/2041-8205/733/1/L11 , archivePrefix =. 1104.4348 , primaryClass =
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[77]
Extended Cold Molecular Gas Reservoirs in z -0.5ex = 3.4 Submillimeter Galaxies. , keywords =. doi:10.1088/2041-8205/739/1/L31 , archivePrefix =. 1105.4177 , primaryClass =
Pith/arXiv arXiv 2041
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[78]
Blind Detections of CO J = 1-0 in 11 H-ATLAS Galaxies at z = 2.1-3.5 with the GBT/Zpectrometer. , keywords =. doi:10.1088/0004-637X/752/2/152 , archivePrefix =. 1204.4706 , primaryClass =
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[79]
A survey of the cold molecular gas in gravitationally lensed star-forming galaxies at z > 2. , keywords =. doi:10.1093/mnras/stw275 , archivePrefix =. 1602.00652 , primaryClass =
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Cool Gas in High-Redshift Galaxies. , keywords =. doi:10.1146/annurev-astro-082812-140953 , archivePrefix =. 1301.0371 , primaryClass =
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[81]
A Total Molecular Gas Mass Census in Z 2-3 Star-forming Galaxies: Low-J CO Excitation Probes of Galaxies Evolutionary States. , keywords =. doi:10.3847/0004-637X/827/1/18 , archivePrefix =. 1606.02309 , primaryClass =
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[82]
First Redshift Determination of an Optically/Ultraviolet Faint Submillimeter Galaxy Using CO Emission Lines. , keywords =. doi:10.1088/0004-637X/705/1/L45 , archivePrefix =. 0909.3177 , primaryClass =
discussion (0)
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