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REVIEW 3 major objections 4 minor 2 cited by

The cosmic globular cluster formation history in the E-MOSAICS simulations

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2412.04105 v1 pith:NZVYJ5ZT submitted 2024-12-05 astro-ph.GA

Philipp S. Joschko , J. M. Diederik Kruijssen , Sebastian Trujillo-Gomez , Joel L. Pfeffer , Nate Bastian , Robert A. Crain , Marta Reina-Campos This is my paper · ORCID
classification astro-ph.GA
keywords globularclusterscosmicclusterformationhistoryratedensitysurvivorbiasdownsizinggalaxystarevolutionhigh-redshift
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

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.

What carries the argument

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 $z\approx 2.5$.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

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.

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 (3)
  1. [Abstract vs. Section 3.1] 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.
  2. [Section 3.1, Fig. 1] 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.
  3. [Section 2, Tables 1–2, Appendix A] 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.
minor comments (4)
  1. [Section 3.2] 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.
  2. [Abstract and Table 1] 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.
  3. [Introduction and Figure 7] 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}.
  4. [Abstract and Section 2] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported GC formation histories are forward simulation outputs, not fits; the abstract-vs-Section 3.1 peak-redshift discrepancy is an internal consistency issue, not a circular reduction.

full rationale

The paper's central quantities (z_peak of GC, star, and cluster formation; median formation redshifts; the 1.1-1.6 offset; the survivor-bias lag) are read directly from the E-MOSAICS simulation output after applying a stated GC selection. No parameter is fitted to these target results in this paper, so the fitted-input-called-prediction pattern does not apply. The GC definition (Tables 1-3) is an input assumption carried from Hughes et al. (2022) and Reina-Campos et al. (2022b); while this is load-bearing in the sense that different cuts would shift numbers, the paper discloses the underdisruption motivation and Appendix A shows the upper metallicity cuts only change the GCFRD at z < about 2, leaving the z about 2.5 peak and the z = 2-4 conclusions unaffected. That is a limitation and a correctness risk, not a circular reduction. The model's validity is supported by earlier E-MOSAICS papers that compare against external observations (blue tilt, GC mass function, radial profiles) and by an independent comparison to Choksi & Gnedin (2019); self-citations therefore do not carry the argument alone. The survivor-bias statement is an interpretation of the selection of surviving clusters, but the 1-2 Gyr lag is a model output rather than an input, so it is not definitional. The main issue found is internal: the abstract says the peak GC formation redshift increases weakly with galaxy mass, whereas Section 3.1 reports z_peak,GCFR = {4, 3.5, 2.5, 2} for increasing mass (a decrease), and Section 3.2 reports a weak increase in the median formation redshift (z = 2.3-2.8); the highest-mass bin contains only six galaxies. These are consistency and robustness problems, not circularity. Hence no circular step can be exhibited and the score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper contributes predictions, not derivations; its central claim rests on inherited model components (EAGLE galaxy formation, MOSAICS cluster formation and disruption) and on the specific definitions of what counts as a GC in each galaxy mass bin. No new entities are introduced.

free parameters (3)
  • Galaxy-mass-dependent GC lower mass thresholds (Table 1) = 1e4, 3e4, 1e5 M_sun for log(M_star/M_sun) < 9, 9-10, >= 10
    These thresholds define which surviving clusters are counted as GCs; they directly set the normalization and redshift distribution of the GC formation histories. They are adopted from Schechter function fits in Hughes et al. (2022) and are not derived in this paper.
  • Upper metallicity limits for clusters (Table 2) = [Fe/H] upper bounds from -1.0 to -0.3 depending on galaxy mass
    These cuts remove high-metallicity clusters to compensate for underdisruption of clusters in the model. Appendix A shows they change the GC formation rate densities by more than an order of magnitude at z < 2, so they are consequential for recent epochs.
  • Metal-poor/metal-rich GC metallicity cuts (Table 3) = [Fe/H] cuts from -1.2 to -0.8 by galaxy mass
    The metallicity-separated formation histories (Section 3.3) depend on these cuts, which are taken from Reina-Campos et al. (2022b).
assumptions (4)
  • domain assumption EAGLE 'Recalibrated' model with its feedback and star formation prescriptions produces a realistic galaxy population in a cosmological volume.
    The entire analysis takes the simulated galaxies as a faithful representation of real galaxies; this is the substrate on which cluster formation is overlaid.
  • domain assumption The MOSAICS cluster formation efficiency and disruption model (Kruijssen 2012; Pfeffer et al. 2018) correctly describes the formation and survival of massive star clusters.
    The fiducial cluster formation model is adopted without re-validation here; the survivor-bias interpretation in Section 3.5 follows directly from this disruption model.
  • domain assumption Globular clusters are the surviving high-mass tail of the general cluster population, with no special formation mechanism at high redshift.
    Stated in Section 3: 'this is consistent with the premise of the models used in this work, which is that GCs are the result of intense star and cluster formation throughout cosmic history.'
  • domain assumption A 34.37 cMpc box is representative enough to infer the cosmic GC formation history, despite the acknowledged underestimate of the cosmic SFRD.
    Section 3.5 admits the volume underproduces L* galaxies and misses early star formation peaks; the authors argue the relative shifts between formation histories would persist. The volume-integrated GCFRD peak at z ~ 2.5 is the central example of a claim resting on this assumption.

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Pith. "Pith review of The cosmic globular cluster formation history in the E-MOSAICS simulations." pith.science (2026). https://pith.science/paper/NZVYJ5ZT

@misc{pith2026241204105,
  author       = {Pith},
  title        = {Pith review of: The cosmic globular cluster formation history in the E-MOSAICS simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NZVYJ5ZT}},
  note         = {Machine review of arXiv:2412.04105}
}
abstract

We present a comprehensive analysis of globular cluster (GC) formation and evolution across the $34^3$ Mpc$^3$ volume of the E-MOSAICS galaxy formation simulations. Defining GCs as surviving, high-mass ($>10^5$ M$_\odot$) clusters, we analyse their formation histories as a function of their metallicity and host galaxy mass, also distinguishing between central and satellite galaxies. The redshift of peak GC formation rate increases weakly with galaxy mass, decreases with metallicity, and does not differ between centrals and satellites. The epoch of peak GC formation precedes that of the stars by a factor of $1.1{-}1.6$, primarily due to `downsizing', i.e. low-mass galaxies form their stars later. Consequently, this offset decreases with galaxy mass, leading to nearly coeval stellar and GC populations in massive galaxies ($>10^{11}$ M$_\odot$). GCs themselves do not exhibit strong downsizing, because they predominantly formed at early cosmic epochs conducive to the formation (through high gas pressures) and survival (through high galaxy merger and GC migration rates) of massive, compact stellar systems. The total GC formation rate in the volume peaks at $z\approx 2.5$, shortly before star formation peaks at $z\approx 2$, but well after the general cluster formation rate at $z\approx 4$, reflecting a survivor bias where surviving GCs formed more recently. We find that GC formation commenced early, at $z>10$, such that the results of this work may provide a framework for interpreting direct observations of proto-GC formation with the JWST, especially as these observations accumulate to enable statistical studies.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    astro-ph.GA 2025-05 reject novelty 6.0 of 10

    For 27 massive ellipticals, the paper finds that offset above the globular cluster system-halo mass relation correlates with shallower red globular cluster density profiles, suggesting major mergers set the scatter.

  2. The Formation of Globular Clusters

    astro-ph.GA 2025-01 unverdicted novelty 3.0 of 10

    Globular clusters are best understood as the surviving remnants of ordinary, high-pressure star formation in high-redshift galaxies.

Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.