{"id":"f905dd7e-be59-4504-a5c7-622d9c040846","arxiv_id":"2502.06778","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"From 87 serendipitous CO detections in ALMA calibrator fields, the authors measure the CO luminosity function and molecular gas density from z=0 to 6, finding a peak near z=1.5 followed by a decline of about one dex.","lead":"ALMACAL used ALMA calibration observations, normally discarded, to find 87 galaxies emitting carbon monoxide out to redshift 6, and used them to measure how the total amount of cold molecular gas in the Universe changed over cosmic time. Because the survey uses data that would otherwise be thrown away, it offers a cheap, independent way to track the fuel for star formation and to test how survey design affects cosmic variance.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The z~1.5 peak and high-z decline are prior-dominated: 81/87 sources get J/redshift from SHARK-2 (§3.4.1), no second line confirms them, and the 'lowest-J' check is not an independent test.","rationale":"The reader's weakest assumption and my concern agree. The central claim is that ALMACAL-22 constrains the CO LF and molecular gas density evolution to z~6, with a peak at z~1.5 and a decline of ~1 dex. For that claim to hold, the redshift/J assignment for the 81 sources without optical/NIR counterparts must be statistically unbiased. The paper's own §3.4 states no second transition was identified in any field; §3.4.1 introduces the SHARK-2 probability; §4.5's lowest-J check is not an independent validation; and §4.3/§5.2 concede the highest bin is a lower limit. Each of these is acknowledged in the text, and they are the reason a conditional verdict is appropriate. I do not see a reason to reject: the ALMACAL multi-field design genuinely mitigates cosmic variance, the completeness and fidelity treatment is careful, and the comparison with independent surveys and simulations is broadly consistent. The concern is exactly that the conclusion may be prior-dependent, which is testable by rerunning with an empirical prior. Since the reader already reached CONDITIONAL on this basis, my verdict is UNCHANGED.","tokens_in":30673,"tokens_out":5100,"duration_ms":48993,"concrete_test":"Recompute the CO LF and rho_H2(z) exactly as in §4.2-§4.4, but replace the SHARK-2 redshift/J prior in §3.4.1 with an empirical prior constructed from the combined ASPECS, COLDz, and HDFN CO luminosity functions and their redshift distributions (or, failing that, a uniform-in-log-L' prior over all J=1-6 lines accessible in each cube). Compare the resulting rho_H2(z) and the redshift of the peak to Table 3 and Fig. 6. If the z~1.5 peak and the ~1 dex drop by z=4-6 move by more than the reported 1-sigma uncertainties, the central evolutionary claim is prior-dominated and should be reported as conditional on SHARK-2. If the trend survives unchanged, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.4.1 assigns each of 81 unconfirmed detections a probability distribution over CO transitions and redshifts built from SHARK-2; Eq. (3) then uses those probabilities, with per-transition volumes, to construct the CO LF, and Eq. (5) converts to rho_H2. This makes the central evolutionary trend dependent on the SAM's CO excitation and luminosity function being a faithful prior. The risk is concrete: the r_j->1 conversion factors in §4.2 are as large as 13.86 for CO(6-5) at z>2, so a systematic tendency to up-weight high-J transitions inflates L'_CO and pushes sources to z>2, exactly where the paper reports a ~1 dex decline after the z~1.5 peak. The fidelity is set to unity for the three spectroscopic and three photometric sources, but for the remaining 81 there is no counterpart or second CO line to break the degeneracy, as the paper itself notes in §3.4. The 'lowest-J approach' of §4.5 does not settle this: it is the opposite extreme assumption, shares the same single-line data, ignores the volume weighting of the fiducial analysis, and agrees only within large uncertainties. The z=4-6 bin is additionally a lower limit with only one fitted point above the luminosity threshold (§4.3, §5.2), so the 'constraints to z~6' language overstates the empirical content. This is not a claim that SHARK-2 is wrong; it is a claim that the paper's headline results are not yet demonstrated to be independent of its redshift prior.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper (ALMACAL XIII) presents a blind search for CO emission lines in 1107 ALMA calibrator data cubes from the ALMACAL-22 release, yielding 87 CO candidates with S/N>4. Spectroscopic redshifts are secured for three sources and photometric redshifts for three more; for the remaining 81 sources, redshift and CO J-transition assignments are drawn from probability distributions built from the SHARK-2 semi-analytical model (Section 3.4.1). The authors construct the CO(1-0) luminosity function in six redshift bins using Eq. (3) with 1000 Monte Carlo realizations that sample flux, completeness, fidelity, and the redshift probability, fit Schechter functions with alpha fixed to -0.2, integrate to obtain the molecular gas mass density rho_H2(z), and compare with previous surveys (ASPECS, COLDz, PHIBSS, HDF-N) and simulations. The headline results are that rho_H2 rises to a peak near z~1.5 and declines by about 1 dex toward higher redshift, that the z=4-6 value is only a lower limit, that the results are consistent with the 'bathtub' baryon-cycling model, and that cosmic variance is below 5% thanks to the many independent sightlines.","tokens_in":31050,"tokens_out":19321,"duration_ms":157682,"significance":"The survey strategy is a genuine methodological advance: using many independent ALMA calibrator fields rather than one contiguous area directly mitigates cosmic variance, and the paper's treatment of completeness (injection-recovery grid, Fig. 1), fidelity (negative-source statistics, Eq. 1), uncertainty propagation (1000 realizations over flux, completeness, fidelity, and redshift), the [C ii] interloper estimate, and the exclusion of lines within 2000 km/s of calibrator redshifts is careful and largely reproducible from the text. The catalogue in Table A and the tabulated Schechter parameters are useful community products. If the headline result (rho_H2 peaking near z~1.5 and declining by ~1 dex toward z~4-6) survives the prior-dependence concern raised below, it would provide a cosmic-variance-hardened confirmation of the bathtub model and a new constraint on the molecular gas depletion timescale at high redshift. The principal caveat is that the novel high-redshift decline is claimed precisely in the regime where redshift and J-transition assignments are most dependent on the SHARK-2 prior, and where the z=4-6 bin contains only one fitted data point above the luminosity limit.","major_comments":[{"comment":"For 81 of the 87 sources the redshift and J-transition are assigned in each of the 1000 LF realizations by drawing from the SHARK-2 flux-redshift probability distribution, and Eq. (3) propagates those draws into the CO LF and hence, via Eq. (5), into rho_H2. The assertion in §5.1.2 that 'the final results on the molecular gas mass density and luminosity function are decoupled from the simulation' is therefore load-bearing and is not demonstrated. The lowest-J test of §4.5 is the opposite limiting assumption rather than an independent measurement: it uses the same single-line data, omits the per-transition volume weighting of the fiducial method, and §4.5 itself concedes it 'likely skews the distribution of CO across cosmic epochs'; the agreement in Fig. 6 is within large uncertainties. The close agreement with SHARK-2 in Fig. 9 is then partly by construction. I request a sensitivity analysis with an agnostic prior (for example uniform over J within the detectable redshift range), with the resulting shifts in Phi*, L'*, and rho_H2(z>2) quoted explicitly, and a reframing of the SHARK-2 comparison as a consistency check rather than an independent confirmation.","section":"§3.4.1, §4.2, §5.1.2, §4.5"},{"comment":"The manuscript states in §4.3 that the z=4-6 panel contains only one data point above the luminosity limit and in §5.2 that the z=4-6 rho_H2 is only a lower limit, yet the abstract claims 'strong constraints ... back to z~6' and presents the '~1 dex decline' without qualification. Given the prior-dependence issue above, the high-redshift decline rests on a lower limit whose constituent sources have model-assigned redshifts, and Table 3 omits the z=4-6 bin entirely. Please add the z=4-6 rho_H2 explicitly to Table 3 with lower-limit notation, and revise the abstract and conclusions to state that the z~6 constraint is a lower limit based on a single point above the completeness threshold.","section":"Abstract; §4.3; §5.2; Table 3"},{"comment":"The r_j->1 conversion factors are quoted as {3.33, 5.20, 4.76, 2.70, 0.53} at z<2 and {4.09, 8.24, 12.21, 14.68, 13.86} at z>2 for J=2,...,6, but the defining convention is not stated (whether L'_{CO(1-0)} = r_j->1 x L'_J or L'_J / r_j->1) and the specific Boogaard et al. (2020) table is not identified. As printed, the z<2 sequence is non-monotonic in J, and r_2->1 = 3.33 is hard to reconcile with typical L'_{2-1}/L'_{1-0} values near unity. Because r_6->1 = 13.86 at z>2, a misassignment of a high-J line changes L'_{CO(1-0)} by more than an order of magnitude. Please specify the convention, verify the numerical values against the cited source, and quantify the sensitivity of rho_H2(z>2) to alternative excitation assumptions.","section":"§4.2"}],"minor_comments":[{"comment":"The text contains numerous ligature-rendering artifacts such as 'di fferent', 'e ffective', 'e fficient', 'su fficiently', 'o ffers', and 'di fficult'; these should be resolved in the production version.","section":"Throughout"},{"comment":"The SHARK-2 reference is cited inconsistently: §6 cites 'Lagos et al. 2023' while §3.4.1 and §5.1.2 cite 'Lagos et al. 2024', and both entries appear in the bibliography; please unify the citations.","section":"§3.4.1, §6, References"},{"comment":"When quoting the local faint-end slope from Fletcher et al. (2021), the text reads 'alpha ~ 1.2'; with the convention of Eq. (4) this should be written alpha ~ -1.2 to avoid sign confusion.","section":"§5.1.1"},{"comment":"Conclusions items 4 and 5 state that cosmic variance is 'less than 5%' without the caveat given in §5.3 that the Keenan et al. (2020) prescription may under-estimate field-to-field variance by an order of magnitude at z~2-4 according to Gkogkou et al. (2022); the headline figure should carry that caveat or be attributed explicitly to the D&R10/K20 prescriptions.","section":"§5.3, §6 Conclusions"},{"comment":"The numerical factor 291.0 in pi R^2 * 291.0 is not defined; a brief note on the unit conversion (arcmin^2 to h^-1 Mpc^2) would make the cosmic-variance formula self-contained.","section":"Eq. (7)"},{"comment":"Several catalogue entries have reliability values as low as 0.05-0.15; a sentence in §3.5 explaining how such low-fidelity candidates enter the LF through F_i in Eq. (3) would help readers interpret the catalogue and the stability of the results.","section":"Table A.1"}],"recommendation":"major_revision","confidential_remarks":"The paper is within A&A scope and the data products are valuable, but the headline result (low rho_H2 at z>2, leading to the 'peak at z~1.5 and ~1 dex decline') could plausibly be an artifact of the SHARK-2 redshift/J prior, and the z=4-6 bin is a lower limit with one point. I would not block publication if the authors add a prior-sensitivity analysis, verify the r_j->1 table (which looks like it may contain a bookkeeping error), and temper the abstract. The paper's internal candor about the one-point bin and the lower-limit status is to its credit."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take on Bollo et al. The genuinely new thing is the size of the serendipitous CO sample: 87 detections from ALMA calibrator fields, giving a CO LF to z~6 with field-to-field variance below 5%. That's a real improvement over single-field surveys like ASPECS and COLDz, and the completeness injections and fidelity estimates are careful. The rho_H2 points at z<3 are consistent with previous surveys, and the updated Madau-Dickinson fit plus the baryon-cycle ratios are useful updates.\n\nThe load-bearing soft spot is the redshift assignment. For 81 of 87 sources there is no spectroscopic or photometric redshift; the J transition and redshift come from the SHARK-2 SAM's flux-redshift probability distribution (§3.4.1). Those probabilities go directly into the LF via Eq. 3 and into rho_H2 via Eq. 5. The high-J to CO(1-0) conversion factors are large at z>2 (up to ~14 for CO(6-5)), so if the model overweights high-J transitions, luminosities inflate and sources move to z>2 — exactly where the paper finds the ~1 dex decline after the z~1.5 peak. No second CO line was detected to check the assignments. The 'lowest-J approach' in §4.5 is not an independent test of the model: it is the opposite extreme, uses the same single-line data, ignores the volume weighting, and the authors themselves say it likely overestimates the gas content. So the claim in §5.1.2 that the results are 'decoupled' from SHARK-2 is too strong.\n\nAlso, the z=4-6 bin is a lower limit with one data point above the luminosity threshold, so the abstract's 'strong constraints back to z~6' is overstated. That said, the central z<3 measurements look solid, and the comparison with other surveys is reassuring.\n\nWho's this for? Anyone working on the CO LF or molecular gas density will want this catalogue and the low-cosmic-variance argument. But they should treat the high-z trend as model-informed, not model-independent. A good referee should make the authors re-frame the claims and test the sensitivity to the prior (flat in J, different excitation ratios, etc.). This deserves a serious referee — conditional acceptance at most.","headline":"A careful, low-cosmic-variance CO LF out to z~6, but the headline high-z decline is prior-dominated and needs re-framing.","tokens_in":31600,"tokens_out":4263,"would_cite":true,"duration_ms":34365,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Using ALMA calibrator fields, the paper traces the cosmic molecular gas density back to z ~ 6, finding a peak near z ≈ 1.5 and a decline of about an order of magnitude toward higher redshift.","keywords":["CO luminosity function","molecular gas mass density","ALMACAL","cosmic variance","galaxy evolution","high redshift","ALMA calibration fields","bathtub model"],"falsifier":"Follow up the single-line candidates with a second CO transition, [C I], or dust continuum at the frequencies predicted by SHARK-2; if a large fraction of lines assigned to CO(2-1) at z ≈ 1-1.5 turn out to be CO(1-0) at z ≈ 0.5-0.7, the claimed peak of ρ_H2 near z ≈ 1.5 would move or weaken.","tokens_in":30512,"feed_emoji":"🌌","tokens_out":6113,"duration_ms":50360,"temperature":0.7,"pith_summary":"This paper claims that the cosmic density of molecular gas—the raw fuel for star formation—rose from the present day back to a peak at redshift z ≈ 1.5, and then declined by roughly an order of magnitude toward z ≈ 6. The evidence comes from 87 CO emission-line galaxies found serendipitously in the calibration fields of ALMA, which together cover hundreds of independent sightlines and therefore suffer far less cosmic variance than single contiguous survey areas. If the claim holds, the fuel supply for star formation tracked the rise and fall of cosmic star formation, and the ratio of molecular gas to stellar mass is consistent with a \"bathtub\" model in which gas is continuously replenished while stars form. The global gas depletion timescale, the ratio of molecular gas density to star-formation rate density, is found to be roughly constant across all redshifts.","feed_headline":"Molecular gas peaks at cosmic noon, then drops tenfold","feed_subtitle":"Eighty-seven CO galaxies found in ALMA calibrator fields trace the rise and fall of star-formation fuel from z=0 to z=6.","key_machinery":"The load-bearing machinery is the probabilistic redshift assignment built from the SHARK-2 semi-analytical model: for each single-line detection, a two-dimensional histogram of CO transition flux against redshift is converted into a probability that the line is CO(J→J-1) at a given z, and the analysis is repeated in 1000 Monte Carlo realisations sampling these probabilities together with completeness, fidelity, and flux uncertainties. This turns otherwise ambiguous single-line detections into a statistical sample. On top of that sits the standard conversion from observed CO flux to CO(1-0) luminosity (Solomon et al. 1997) with empirical high-J-to-1-0 ratios, the Schechter-function fit to the CO luminosity function, and the integration of L' Φ(L') to get ρ_H2. The ALMACAL survey design—299 independent calibrator fields rather than one contiguous patch—is what reduces cosmic variance to below about 5 percent.","core_discovery":"The paper's central result is an extended CO luminosity function and a new measurement of the cosmic molecular gas mass density ρ_H2 from z = 0 to z ≈ 6. Using the ALMACAL-22 dataset—archival ALMA calibration observations pruned to high quality—the authors identify 87 CO candidates, assign redshifts by weighting over possible CO(1-0) through CO(6-5) transitions with probability distributions from the SHARK-2 semi-analytical model, and build the luminosity function in six redshift bins. They find that ρ_H2 increases with redshift, peaks near z ≈ 1.5 at log ρ_H2 ≈ 7.4 M⊙ Mpc⁻³, and then declines by about 1 dex toward the highest redshifts, with Schechter-function fits showing a decreasing normalization Φ* and a characteristic luminosity L* that rises to z ≈ 2 and then plateaus. The same data place the molecular-to-atomic gas density ratio peaking near z ≈ 1.5 and a roughly constant global depletion timescale, which the authors interpret as support for the bathtub model of baryon cycling.","pith_inferences":["If SHARK-2's prior is even mildly biased toward CO(2-1), the inferred z ≈ 1.5 peak could be an artifact of the prior; a targeted follow-up of a few dozen candidates would settle whether the peak is real or model-driven.","The tension with ASPECS and HDFN at z > 1—where ALMACAL finds lower ρ_H2—may indicate that small contiguous surveys overestimate the density because of cosmic variance, or that ALMACAL's calibrator fields sit in underdense regions; comparing the two on a common volume would test which.","The method of using archival calibration data as a science survey could be extended to other spectral lines (e.g., [C I], [C II], H2O) and to measure the cosmic density of atomic gas at high redshift, where 21-cm emission is too faint."],"forward_implications":["The cosmic molecular gas density peaks near z ≈ 1.5, placing the maximum supply of star-forming fuel at cosmic noon and supporting the idea that gas consumption tracks the star-formation rate density.","The roughly constant global depletion timescale means that, on cosmic average, galaxies consume their molecular gas on a fixed timescale at every epoch, so changes in ρ_H2 rather than changes in efficiency drive the star-formation history.","The molecular-to-stellar mass density ratio follows the bathtub model: gas must be continuously replenished to sustain the observed star formation, rather than being a one-time reservoir.","Surveys built from many small independent fields, like ALMACAL, keep cosmic variance below about 5 percent, more than an order of magnitude lower than single contiguous fields of similar total area; future molecular-line surveys should adopt this design.","The bright end of the CO luminosity function evolves such that the characteristic luminosity L* rises from z = 0 to z ≈ 2 and then stays flat, while the normalization Φ* falls by a factor of about 3 across the same range."],"supporting_citations":[{"why":"The ALMACAL pilot that established the CO line-search methodology and the probabilistic redshift assignment approach this paper extends.","marker":"Hamanowicz et al. 2022"},{"why":"The ALMACAL-22 data release and pruning that defines the high-quality sample of data cubes used here.","marker":"Bollo et al. 2024"},{"why":"SHARK-2 semi-analytical model, the source of the flux-redshift probability distribution used for redshift assignment.","marker":"Lagos et al. 2024"},{"why":"Supplies the empirical high-J to CO(1-0) luminosity conversion factors used to scale the observed CO fluxes.","marker":"Boogaard et al. 2020"},{"why":"Provides the reference CO luminosity function and the CO transition prior that the SHARK-2 redshift distribution is compared against.","marker":"Boogaard et al. 2023"},{"why":"The ASPECS survey whose CO luminosity function and molecular gas density are the primary comparison at z = 1-3.","marker":"Decarli et al. 2020"},{"why":"The COLDz survey providing comparison CO luminosity function and density estimates at z = 2-3 and z = 5-7.","marker":"Riechers et al. 2020b"},{"why":"The compilation and functional fit of ρ_H2 evolution used to place ALMACAL results in the cosmic baryon cycle context.","marker":"Walter et al. 2020"},{"why":"Provides the atomic gas density and star-formation rate density fits used in the baryon-cycle census.","marker":"Péroux & Howk 2020"},{"why":"Supplies the cosmic variance formula adapted to estimate field-to-field variance in the ALMACAL survey.","marker":"Driver & Robotham 2010"}],"fun_headline_variants":["Molecular gas peaks at cosmic noon, then falls tenfold","ALMA calibrator data reveals gas's rise and fall to z=6","Cosmic molecular gas: peak at z=1.5, then 10x drop","From z=0 to 6: CO gas density peaks at cosmic noon","87 CO galaxies trace molecular gas history to z=6"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the SHARK-2 model's probability distribution correctly assigns the rotational transition and redshift for the 81 of 87 candidates that lack spectroscopic or photometric redshifts; if this prior is wrong, the reconstructed CO luminosities, luminosity function, and molecular gas density would shift.","fun_headline_variants_meta":{"raw":{"variants":["Molecular gas peaks at cosmic noon, then falls tenfold","ALMA calibrator data reveals gas's rise and fall to z=6","Cosmic molecular gas: peak at z=1.5, then 10x drop","From z=0 to 6: CO gas density peaks at cosmic noon","87 CO galaxies trace molecular gas history to z=6"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000954,"raw_usage":{"total_tokens":4125,"prompt_tokens":1058,"completion_tokens":3067,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":674,"completion_tokens_details":{"reasoning_tokens":2981}},"tokens_in":674,"tokens_out":3067,"duration_ms":19216,"temperature":1.0,"reasoning_tokens":2981,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T14:21:08.213291+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Follow up the single-line candidates with a second CO transition, [C I], or dust continuum at the frequencies predicted by SHARK-2; if a large fraction of lines assigned to CO(2-1) at z ≈ 1-1.5 turn out to be CO(1-0) at z ≈ 0.5-0.7, the claimed peak of ρ_H2 near z ≈ 1.5 would move or weaken.","supporting_citations":[{"cited_title":"A., Péroux, C., et al","cited_arxiv_id":null,"evidence_quote":"The ALMACAL pilot that established the CO line-search methodology and the probabilistic redshift assignment approach this paper extends."},{"cited_title":"2024, Astronomy and Astrophysics, 690, A258","cited_arxiv_id":null,"evidence_quote":"The ALMACAL-22 data release and pruning that defines the high-quality sample of data cubes used here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"SHARK-2 semi-analytical model, the source of the flux-redshift probability distribution used for redshift assignment."},{"cited_title":"A., van der Werf, P., Weiss, A., et al","cited_arxiv_id":null,"evidence_quote":"Supplies the empirical high-J to CO(1-0) luminosity conversion factors used to scale the observed CO fluxes."},{"cited_title":"A., Decarli, R., Walter, F., et al","cited_arxiv_id":null,"evidence_quote":"Provides the reference CO luminosity function and the CO transition prior that the SHARK-2 redshift distribution is compared against."},{"cited_title":"2020, ApJ, 902, 110","cited_arxiv_id":null,"evidence_quote":"The ASPECS survey whose CO luminosity function and molecular gas density are the primary comparison at z = 1-3."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the cosmic variance formula adapted to estimate field-to-field variance in the ALMACAL survey."}],"review_version":1}