{"id":"b1f214bf-20b8-4dc4-b895-22e4428ad6be","arxiv_id":"2412.04105","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Using the E-MOSAICS simulations, the paper predicts that surviving globular clusters formed mainly at z = 2 to 4, with the cosmic GC formation rate density peaking at z about 2.5.","lead":"This paper analyzes how globular clusters formed across cosmic time in a large cosmological simulation, finding that surviving clusters formed mostly at redshifts 2 to 4, later than all clusters but earlier than most stars. It offers observers a framework for interpreting JWST sightings of young globular clusters at high redshift.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Abstract and Section 3.1 disagree on the sign of the mass dependence of the peak GC formation redshift, undermining the central claim as stated.","rationale":"The reader's conditional verdict already flags the contradiction between the abstract and Section 3.1, but the formal 'weakest_assumption' field names the GC definitions as the load-bearing assumption. I agree that the GC definitions are important, but I find the internal contradiction more directly damaging to the central claim as stated in the abstract. The central claim includes a specific statement about the sign of the mass dependence; when the body of the paper reports the opposite sign, the claim is not reproducible from the paper as written. This is not a matter of external calibration or model choice, but an internal logical inconsistency that must be resolved before the result can be accepted. The proposed test targets exactly this: re-deriving the peak redshifts with uncertainties and checking the ordering. If the ordering is actually flat or decreasing, the abstract and possibly Section 3.2's interpretation of the median ages need revision. The paper has clear strengths: it uses a well-established simulation suite, includes explicit caveats about volume size and metallicity cuts, and the Appendix quantifies the impact of the metallicity cuts. But the mass-dependence claim is central to the abstract and is currently self-contradictory. I therefore keep the reader's CONDITIONAL verdict unchanged, with the condition being a clear resolution of this contradiction and reporting of uncertainties on peak redshifts.","tokens_in":19345,"tokens_out":5023,"duration_ms":51666,"concrete_test":"Extract the median GCFR curves for the four galaxy mass bins from the E-MOSAICS data, smooth each curve (e.g., with a Gaussian filter in log-redshift), and compute the peak redshift for each bin with bootstrap resampling over galaxies (or jackknife over the six galaxies in the top bin). Determine whether the four peak redshifts are monotonically ordered and whether the 68% bootstrap intervals overlap. If the intervals overlap or the ordering is not monotonic in a single direction, then the abstract's 'increases weakly' claim cannot be distinguished from a flat or decreasing trend, and the text must be corrected accordingly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing concern is the internal inconsistency in the paper's central claim about the mass dependence of the peak GC formation redshift. The abstract states that \"the redshift of peak GC formation rate increases weakly with galaxy mass\", but Section 3.1 reports z_peak,GCFR = {4, 3.5, 2.5, 2} for the four mass bins in order of increasing galaxy mass, i.e., a clear decrease. Section 3.2 further complicates the picture by reporting that the median GC formation redshift increases with galaxy mass (from z~2.3 to 2.8), which is a different statistic but may be what the abstract intended. The peak values are quoted without uncertainties, and the highest-mass bin contains only six galaxies, making the reported ordering statistically fragile. If the abstract is wrong, the paper's summary misrepresents the result; if Section 3.1 is wrong, then the mass-dependence claim is not robust. Either way, the central claim as stated is not currently supported by the paper's own reported numbers.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses the E-MOSAICS cosmological simulations to compute the formation histories of globular clusters (GCs), all stellar clusters, and stars in a 34.37 cMpc box, split by host galaxy stellar mass, metallicity, and central/satellite status. It reports that the peak of GC formation occurs at z ≈ 2–4, before the peak of star formation by a factor 1.1–1.6 in age, with the offset driven mainly by the later star formation in low-mass galaxies. It also reports a volume-integrated GC formation rate density peaking at z ≈ 2.5, after the general cluster formation rate density at z ≈ 4, which it attributes to a survivor bias. The paper is positioned as providing a framework for interpreting JWST observations of proto-GCs.","tokens_in":19454,"tokens_out":5284,"duration_ms":55181,"significance":"If the results hold, this is one of the first cosmologically representative, hydrodynamical-simulation-based predictions of the cosmic GC formation history. The paper is transparent about its sample selection: it tabulates the mass and metallicity cuts, shows percentile spreads in the formation histories, and includes an appendix quantifying the effect of the upper metallicity cuts. The comparison of surviving GCs with progenitor GCs gives a concrete, falsifiable prediction about the observable offset between JWST proto-GC counts and z=0 GC age distributions. However, the central mass-dependence claim in the abstract is not consistent with the numbers reported in Section 3.1, and the statistical robustness of the highest-mass bin is weak, so the paper needs revision before the headline result can be accepted.","major_comments":[{"comment":"The abstract states that \"the redshift of peak GC formation rate increases weakly with galaxy mass,\" but Section 3.1 reports z_peak,GCFR = {4, 3.5, 2.5, 2} \"in order of increasing galaxy mass\", which is a monotonic decrease. Section 4, item 1, instead says the peak is \"nearly constant at z = 2–4\". The paper must specify whether the headline statistic is the peak or the median formation redshift. If the peak is meant, the abstract is wrong; if the median is meant (Section 3.2 gives z = 2.3–2.8), then the abstract and Section 3.1 need to be rewritten consistently. As written, the paper's central claim is not supported by its own reported numbers.","section":"Abstract vs. Section 3.1"},{"comment":"The four z_peak,GCFR values, including the z ≈ 2 value for the highest-mass bin, are quoted as exact numbers without uncertainties. The highest-mass bin contains only 6 galaxies (Fig. 1), even though it contains 16,747 GCs, so the median formation history of that bin can be dominated by very few hosts. The monotonic mass ordering of the peaks is therefore statistically fragile. The authors should provide per-bin uncertainties (e.g. bootstrap resampling over galaxies) and explicitly state the caveat before drawing the mass-dependence conclusion.","section":"Section 3.1, Fig. 1"},{"comment":"The GC definition is load-bearing for every quantitative result, but its sensitivity is not tested. Table 1 adopts galaxy-mass-dependent lower mass limits (10^4, 3×10^4, and 10^5 M_sun) justified by the need to fit the Schechter truncation mass, not by an independent physical definition of a GC; the abstract's uniform \">10^5 M_sun\" definition is inconsistent with this table. Appendix A only tests the upper metallicity cuts, not the lower mass thresholds or the Table 3 metallicity splits, so the dependence of the reported peak redshifts on these choices is unknown. A robustness test, for example recomputing the main figures with a uniform 10^5 M_sun cut or with varied thresholds, is needed to establish that the formation-history claims are not artifacts of the selection.","section":"Section 2, Tables 1–2, Appendix A"}],"minor_comments":[{"comment":"The list of median cluster formation redshifts, z = {2.5, 2.2, 2.9, 3.3} for increasing galaxy mass, is not monotonic, so the accompanying sentence that the median formation redshift \"increases with galaxy mass\" is difficult to verify; the per-bin GC median redshifts should be given explicitly.","section":"Section 3.2"},{"comment":"The abstract's definition of GCs as \"high-mass (>10^5 M_sun) clusters\" conflicts with Table 1, which uses lower mass limits of 10^4 and 3×10^4 M_sun for lower-mass galaxies; if the abstract is intended as a simplification, it should say so or specify the mass-dependent threshold.","section":"Abstract and Table 1"},{"comment":"There is a typo \"overabundence\" in the Introduction, and the axis labels in Figure 7 contain \"yr□1 Mpc□3\" placeholders; these should be typeset as yr^{-1} Mpc^{-3}.","section":"Introduction and Figure 7"},{"comment":"The volume is described as \"34^3 Mpc^3\" in the abstract and as a cube with 34.37 cMpc side length in the text; the units and number should be made consistent (comoving Mpc^3) throughout.","section":"Abstract and Section 2"}],"recommendation":"major_revision","confidential_remarks":"The main issue is the internal inconsistency between the abstract and Section 3.1 on the sign of the mass dependence of the GC formation peak, together with the fragility of the highest-mass bin. These are fixable with a careful rewrite and uncertainty estimates. I do not see grounds for rejection, but the paper should not be accepted until the headline claim is stated consistently and the selection sensitivity is quantified."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a transparent, useful model-prediction paper with one real internal inconsistency that needs to be fixed before the abstract should be quoted. The new things are the volume-integrated GC formation rate density in a 34 cMpc E-MOSAICS volume, the explicit comparison between progenitor and surviving GC formation histories (the survivor-bias offset), and the mass-dependent trends from ~3000 galaxies rather than a handful of zoom-ins. That is a genuine step beyond Reina-Campos et al. (2019) and Choksi & Gnedin (2019).\n\nThe paper does several things well. It tabulates the GC selection cuts, shows percentiles, and includes an appendix quantifying how the upper metallicity cuts affect the formation-rate densities. It also reproduces the earlier Milky Way-mass result with 110 galaxies instead of 10, which is reassuring. The central claims are model predictions, not fits, so the circularity burden is low.\n\nThe soft spot is the abstract vs. body contradiction. The abstract says 'the redshift of peak GC formation rate increases weakly with galaxy mass,' but Section 3.1 reports z_peak,GCFR = {4, 3.5, 2.5, 2} for the four mass bins in order of increasing mass. That is a decrease, not an increase. Section 3.2 does report the median GC formation redshift increasing from z~2.3 to 2.8 with mass, which is a different statistic and may be what the abstract intended, but the abstract specifically says 'peak.' As written, the central mass-dependence claim is not supported by the paper's own numbers. Also, the peak redshifts are quoted without uncertainties, and the highest-mass bin contains only six galaxies, so the ordering is fragile. The GC definition cuts are load-bearing, though the paper is reasonably open about that, and Appendix A shows the metallicity cuts mainly affect z<2. No analysis code or data products are provided.\n\nI'd send this to a serious referee. It's a useful framework for JWST proto-GC studies, and the survivor-bias prediction is worth having on the record. But I'd ask the authors to resolve the contradiction, report uncertainties on peak redshifts, and ideally release the analysis scripts before it's used as a definitive reference.","headline":"Useful and transparent model-prediction paper, but the abstract contradicts the body on the sign of the mass dependence of peak GC formation redshift, and that needs fixing before the paper is quoted.","tokens_in":20145,"tokens_out":2334,"would_cite":true,"duration_ms":22712,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Across a simulated cosmic volume, surviving globular clusters form mainly at redshifts $z\\approx 2$–$4$, peaking at $z\\approx 2.5$—before the peak of star formation and after the peak of all clusters—and this ordered sequence is the…","keywords":["globular clusters","cosmic globular cluster formation history","formation rate density","survivor bias","downsizing","galaxy formation","star cluster evolution","high-redshift star formation"],"falsifier":"Count proto-globular-cluster candidates in deep infrared images across many fields and compare the redshift distribution of their formation with the age distribution of surviving globular clusters in local galaxies; if the proto-cluster formation rate peaks at $z\\approx 4$ with no later offset, or the measured peak of surviving cluster ages shifts strongly with host galaxy mass, the predicted survivor-bias peak at $z\\approx 2.5$ and the weak mass dependence would be ruled out.","tokens_in":19073,"feed_emoji":"🔭","tokens_out":8830,"duration_ms":80423,"temperature":0.7,"pith_summary":"Across a simulated cube of universe roughly 34 comoving megaparsecs on a side, this paper asks when the globular clusters that survive today actually formed, and how that timing depends on host galaxy mass, metallicity, and environment. It aims to establish that the cosmic globular cluster formation history is a peaked curve: surviving massive clusters form mainly at redshifts $z\\approx 2$–$4$, with the volume-integrated rate peaking at $z\\approx 2.5$, about a factor of 1.1–1.6 before the peak of star formation but well after the peak of ordinary cluster formation at $z\\approx 4$. The paper attributes the late peak relative to all clusters to survivor bias: clusters that survive to $z=0$ preferentially formed recently, because older clusters have had more time to be disrupted. The result matters because it turns globular clusters into a testable probe of early galaxy formation, and gives deep infrared surveys a concrete statistical prediction for where proto-globular-cluster candidates should be found.","feed_headline":"Globular clusters were born in a cosmic burst at z≈2.5","feed_subtitle":"Simulations place surviving globular cluster formation at z=2–4, before most stars, ready for deep telescopes to test.","key_machinery":"The machinery is a cosmological hydrodynamical simulation coupled to a subgrid model for star cluster formation and disruption. The cluster formation efficiency depends on local gas pressure and the initial cluster mass function varies with environment, while surviving clusters are tracked through stellar evolution, two-body relaxation, and tidal shocks, with clusters disrupted by dynamical friction removed in post-processing. The load-bearing step is the definition of a 'globular cluster' in post-processing: a surviving cluster above a host-mass-dependent mass threshold, restricted to metallicities below a host-mass-dependent ceiling. Comparing the formation rate density of these survivors with the formation rate density of all clusters of initial mass above $10^5\\,\\mathrm{M}_\\odot$ isolates the survivor bias that shifts the peak from $z\\approx 4$ to $z\\approx 2.5$.","core_discovery":"The paper's central claim is that surviving globular clusters—defined by mass thresholds from $10^4$ to $10^5\\,\\mathrm{M}_\\odot$ depending on host galaxy, with upper metallicity cuts to remove artificially underdisrupted clusters—follow a formation history that peaks at $z=2$–$4$ with almost no dependence on host mass. The peak globular cluster formation redshift shifts only weakly with galaxy mass, from $z\\approx 4$ in the lowest-mass bins to $z\\approx 2$ in the most massive galaxies, whereas the star formation peak moves from $z\\approx 0.5$ to $z\\approx 2.5$ across the same mass range. As a result, globular clusters are older than the bulk of stars by a factor of 1.6–1.7 in low-mass galaxies and by only about 1.1 in galaxies above $10^{11}\\,\\mathrm{M}_\\odot$; this offset is mostly stellar downsizing, not globular-cluster downsizing. Metal-rich globular clusters form later than metal-poor ones, with the age gap growing toward lower galaxy masses, and globular cluster ages show no offset between central and satellite galaxies. The total formation rate density peaks at $z\\approx 2.5$ for surviving globular clusters, at $z\\approx 4$ for clusters with initial masses above $10^5\\,\\mathrm{M}_\\odot$, and at $z\\approx 2$ for stars; the 1–2 Gyr shift in the median is the signature of survivor bias. Formation began above $z>10$, with up to 10 per cent of globular cluster mass in low-mass galaxies already in place then.","pith_inferences":["A reader could infer that any observationally selected sample defined by present-day survival will inherit a similar 1–2 Gyr peak shift, so comparisons between proto-cluster surveys and surviving cluster age distributions must correct for survival bias before interpreting the offset as a change in formation physics.","Extending the same logic, the predicted near-constancy of the globular cluster formation peak across host mass implies that a single fixed mass cut applied to all galaxies would create an artificial downsizing signal; observational samples should apply completeness corrections that vary with host galaxy mass.","The paper's environmental mechanism—that globular clusters form wherever gas pressures are high enough—predicts that high-redshift proto-globular-cluster candidates should be preferentially found in dense, high-pressure regions of galaxies, a spatially testable extension with resolved infrared spectroscopy.","Because the simulated volume under-represents Milky Way-mass galaxies, a larger cosmological volume would likely move the volume-integrated peak to slightly lower redshift while preserving the relative ordering of the peaks; this is an extrapolation, not a paper claim."],"forward_implications":["The volume-integrated globular cluster formation rate peaks at redshift $z\\approx 2.5$, about a factor of 1.1–1.6 earlier than the star formation peak and roughly 1–2 Gyr after the general cluster formation peak.","The peak globular cluster formation redshift varies only weakly with host galaxy mass, from $z\\approx 4$ in galaxies below $10^9\\,\\mathrm{M}_\\odot$ to $z\\approx 2$ above $10^{11}\\,\\mathrm{M}_\\odot$, so globular clusters do not show the strong downsizing seen for stars.","Massive galaxies above $10^{11}\\,\\mathrm{M}_\\odot$ form their globular clusters nearly at the same time as their stars, while low-mass galaxies form globular clusters long before most of their stars, with relative ages up to a factor of 1.6–1.7.","Globular cluster formation began at $z>10$, and in galaxies below $10^9\\,\\mathrm{M}_\\odot$ up to 10 per cent of surviving globular cluster mass was in place then, which deep surveys can test.","Metal-rich globular clusters consistently form after metal-poor ones, and the delay grows toward lower host galaxy masses."],"supporting_citations":[{"why":"Introduces the subgrid cluster formation model in cosmological simulations, with environmental cluster formation efficiency and disruption by tidal shocks, the base machinery for these histories.","marker":"Pfeffer et al. 2018"},{"why":"Presents the full simulation suite and documents the underdisruption of metal-rich clusters that motivates the metallicity cuts.","marker":"Kruijssen et al. 2019a"},{"why":"Supplies the galaxy-mass-dependent metallicity ranges and metal-poor/metal-rich cuts adopted in the globular cluster selection.","marker":"Reina-Campos et al. 2022b"},{"why":"Provides the observed host-galaxy-dependent truncation masses on which the minimum globular cluster mass thresholds are based.","marker":"Hughes et al. 2022"},{"why":"Provides the physical model for environmentally dependent cluster formation efficiency used to assign cluster formation.","marker":"Kruijssen 2012"},{"why":"Semi-analytic prediction for the cosmic globular cluster formation history against which this paper compares, confirming the qualitative survivor-bias offset.","marker":"Choksi & Gnedin 2019"},{"why":"The observed cosmic star formation history used as the reference for the stellar formation rate density and peak.","marker":"Madau & Dickinson 2014"}],"fun_headline_variants":["Surviving globular clusters peak at z≈2.5, not z≈4","Globular clusters precede stars: peak z=2.5 vs z=2","GC formation peak at z=2.5, but all clusters peak at z=4","Mass matters little: GCs form in a z=2–4 burst"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The mass thresholds and metallicity cuts used to decide which simulated clusters count as globular clusters are taken from prior observational fits and from the need to remove artificially underdisrupted clusters; if those cuts do not match the real globular cluster population, the peak redshifts, their mass dependence, and the survivor-bias offset would all shift, and the most massive host bin contains only six galaxies.","fun_headline_variants_meta":{"raw":{"variants":["Surviving globular clusters peak at z≈2.5, not z≈4","Globular clusters precede stars: peak z=2.5 vs z=2","GC formation peak at z=2.5, but all clusters peak at z=4","Mass matters little: GCs form in a z=2–4 burst"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000826,"raw_usage":{"total_tokens":3754,"prompt_tokens":1229,"completion_tokens":2525,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":845,"completion_tokens_details":{"reasoning_tokens":2443}},"tokens_in":845,"tokens_out":2525,"duration_ms":21121,"temperature":1.0,"reasoning_tokens":2443,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:45:22.309420+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Count proto-globular-cluster candidates in deep infrared images across many fields and compare the redshift distribution of their formation with the age distribution of surviving globular clusters in local galaxies; if the proto-cluster formation rate peaks at $z\\approx 4$ with no later offset, or the measured peak of surviving cluster ages shifts strongly with host galaxy mass, the predicted survivor-bias peak at $z\\approx 2.5$ and the weak mass dependence would be ruled out.","supporting_citations":[{"cited_title":"E., Pfeffer , J","cited_arxiv_id":null,"evidence_quote":"Provides the observed host-galaxy-dependent truncation masses on which the minimum globular cluster mass thresholds are based."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the physical model for environmentally dependent cluster formation efficiency used to assign cluster formation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Semi-analytic prediction for the cosmic globular cluster formation history against which this paper compares, confirming the qualitative survivor-bias offset."}],"review_version":1}