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arxiv: 2604.10119 · v1 · submitted 2026-04-11 · 🌌 astro-ph.GA · astro-ph.CO

Starbursts at Cosmic Dawn: Formation of Globular Clusters, Ultra-Faint Dwarfs, and Population III star clusters at z > 6

Pith reviewed 2026-05-10 16:00 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords ultra-faint dwarfsglobular clustersPopulation IIIstar formationhigh-redshift galaxiesanalytical modelingMilky Way satellitescosmic dawn
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The pith

An analytical model of starbursts in low-mass halos predicts the formation of hundreds of ultra-faint dwarf galaxies and dozens of globular clusters at high redshifts.

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

The paper presents Anaxagoras, a detailed analytical model for star formation in small dark matter halos at cosmic dawn. It accounts for gas cooling, disk formation, and multiple forms of stellar feedback to simulate early starbursts without relying on numerical simulations. The model is applied to Milky Way satellite halos and minihalos to predict the properties and numbers of ultra-faint dwarfs, old globular clusters, and Population III stars. A sympathetic reader would care because these predictions offer a way to understand the origins of structures observed in the local universe today. If the model holds, it suggests that many of the faint galaxies and clusters around the Milky Way formed in the first billion years after the Big Bang.

Core claim

The Anaxagoras model applied to star formation at z > 6 in Milky Way satellite halos predicts hundreds of galaxies with luminosities, half-mass radii, mass-to-light ratios, and ages matching observed ultra-faint dwarfs, at least around 40 old globular cluster candidates with initial stellar masses between 10^5 and 10^6 solar masses, and between 1 and 500 Population III stars per minihalo at z > 6 depending on the assumed stellar mass and the presence of Lyman-Werner feedback.

What carries the argument

The Anaxagoras model, which is an analytical ab initio description of gas cooling, central gas accretion and disk formation, together with stellar feedback processes including direct radiation pressure, Ly-alpha scattering, IR photons, stellar winds, expanding H II regions, and supernovae.

If this is right

  • Hundreds of galaxies form in low-mass halos with observed ultra-faint dwarf properties.
  • At least 40 globular cluster candidates of 10^5-10^6 solar masses form at halo centers.
  • Pop III star formation yields 1-30 stars per minihalo at z>20 or 10-500 at lower z if stars are 25 solar masses, or mostly one star if 140 solar masses.
  • The timing of star formation is delayed by Lyman-Werner feedback until halos grow larger.

Where Pith is reading between the lines

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

  • This approach could allow faster exploration of parameter space in feedback efficiencies compared to simulations.
  • Predictions for the number of Pop III stars could inform models of early chemical enrichment and reionization.
  • Extending the model to predict observable signatures at even higher redshifts might be testable with future telescopes.
  • The success of the model in matching local dwarfs suggests that feedback processes dominate over other factors in shaping these small systems.

Load-bearing premise

The predictions rest on specific assumed efficiencies for each type of stellar feedback and on choosing fixed masses for the first stars, which determine how much gas is converted to stars and when.

What would settle it

A survey finding substantially different numbers of ultra-faint dwarf galaxies around the Milky Way than the predicted hundreds, or globular clusters with different initial masses, would falsify the specific predictions of the model.

Figures

Figures reproduced from arXiv: 2604.10119 by Olof Nebrin.

Figure 1
Figure 1. Figure 1: The Cosmic Microwave Background (CMB), as seen by the Planck satellite. The CMB has a sky-averaged present-day temperature of TCMB,0 = 2.726 K, but temperature fluctuations of order ∼ 10−5 has been observed (first by the COBE satellite, Smoot et al., 1992). These are thought to be due to density fluctuations in the very early Universe that form the seeds for subsequent galaxy formation. Credit: ESA and the… view at source ↗
Figure 2
Figure 2. Figure 2: The globular cluster NGC 6752, located at a distance of ' 4.1 kpc from the Sun. It has a mass of ' 2.8×105 M , a half-mass radius ' 5.3 pc, and a mean metallicity [Fe/H] ' −1.58 (Baumgardt, 2017; Baumgardt & Hilker, 2018; Bailin, 2019; Baumgardt et al., 2020). A rising velocity dispersion has been observed in the outskirts of NGC 6752 — potential evidence of it having formed in a dark matter halo (Carlberg… view at source ↗
Figure 3
Figure 3. Figure 3: Eridanus II (Eri II), an Ultra-Faint Dwarf (UFD) galaxy situated near the virial radius of the Milky Way halo, as observed by Simon et al. (2020) using the Hubble Space Telescope. While it is hard to resolve any clear structure, most of the field stars in this image belong to Eri II. This UFD has a half-light radius of Rh = 246 ± 17 pc (Simon, 2019), a stellar mass of M? ' 1.1 × 105 M (Gallart et al., 2021… view at source ↗
Figure 4
Figure 4. Figure 4: The temperature evolution of collapsing metal-free gas. Initially the gas temperature rise due to adiabatic heating until the temperature and density becomes high enough to trigger efficient H2-cooling. At this point the gas cools down to ∼ 200 K at a density of n ∼ 104 cm−3 , after which the gas temperature start to rise again since the critical density has been reached above which the cooling rate scale … view at source ↗
Figure 5
Figure 5. Figure 5: Snapshots from the high-resolution cosmological simulation of Kimm et al. (2016), showing the formation of a GC candidate with stellar mass 6 × 105 M in a dense gaseous disk situated in a low-mass halo of mass M ∼ few × 107 M (with virial temperature Tvir ' 104 K) at redshift z ∼ 13. This state-of￾the-art simulation include stellar feedback from supernovae (which can inject energy and momentum into the gas… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison between the simulations of Visbal et al. (2014a) at z = 10 on the left, and Eq. (15) on the right for ncore (nb,max in their notation) as a function of halo mass. The black dots in the plot by Visbal et al. (2014a) comes from their high-resolution simulations, while the circles come from their low-resolution runs. Their high-resolution simulations, which are more accurate, are most relevant for … view at source ↗
Figure 7
Figure 7. Figure 7: A plot of the H2-cooling threshold in minihalos in the absence of radiative feedback. The solid line show the result of numerically finding the root to Eq. (43), while the dash-dotted line shows the approximate root in Eq. (45). Also shown is the analytical model of Trenti & Stiavelli (2009). The colored background shows data from the cosmological hydrodynamical simulations of Schauer et al. (2020). As can… view at source ↗
Figure 8
Figure 8. Figure 8: Same as [PITH_FULL_IMAGE:figures/full_fig_p033_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: A comparison between the numerical (M˙ gas) and approximate analytical (M˙ gas,approx) solution for the central gas accretion rate as a function of β = 2.29 (Tvir/Th) − 2. A fit is also shown for the ratio of the two result (Eq. 74). In the gray region (β < −0.693) the gas accretion rate is zero since the gas temperature is sufficiently high that the pressure of the gas can resist gravitational collapse. P… view at source ↗
Figure 10
Figure 10. Figure 10: Similar plot to [PITH_FULL_IMAGE:figures/full_fig_p043_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The log-normal distribution — see Eq. (86) — for the spin parameter λ used in this thesis. As discussed in the main text, the adopted parameters are λ¯ = 0.03 and σln λ = 0.54. 5. Angel et al. (2016) found, similar to Knebe & Power (2008), a weak halo mass dependency of λ¯ = (0.025 ± 0.009)(M/1010h −1 M ) −0.023±0.016 for 108h −1 M < M < 4 × 1011h −1 M (they do not provide a log-normal fit). At M = 108h −… view at source ↗
Figure 12
Figure 12. Figure 12: A plot of fdisk(λ) (solid line) along with colored regions showing the probability of having a smaller spin parameter λ, calculated from the distribution in Eq. (86). It turns out that 80% of halos have 0.672 < fdisk < 1, and 95% of halos fall in the range 0.525 < fdisk < 1. Thus, fdisk is of order unity in most halos. fdisk(λ¯) ' 0.81, which we will use as a reference value when evaluating some of the de… view at source ↗
Figure 13
Figure 13. Figure 13: Snapshots of the surface density (in g cm−2 ) in three of the atomic-cooling halos simulated by Patrick et al. (2020). Each snapshot has a side length of 6 pc. The disk sizes appear to be consistent with our predicted 1σ range (0.45 pc . Rdisk . 2.8 pc for tMyrs ' 1), with the caveat that it is hard to make out a sharp disk boundary in the simulations. Credit: The halo snapshots are taken from [PITH_FULL… view at source ↗
Figure 14
Figure 14. Figure 14: The setup for the calculation of the expanding H II region in the disk. The sketch show a vertical cross-section of the disk, with young massive stars near the midplane producing a vertically expanding H II region of height zHII over the midplane. metallicity on Q˙ ion is small (see e.g. Stanway & Eldridge, 2019) and can be neglected for our purposes.55 In the case of Pop III stars we can estimate Q˙ ion … view at source ↗
Figure 15
Figure 15. Figure 15: Upper panel: The expansion factor Rcl,f/Rcl,i of star clusters following rapid gas expulsion as a function of the star formation efficiency f?. The symbols denote results from simulations, and the dashed line the fit adopted in this thesis. Lower panel: The fraction fbound of stars that remain gravitationally bound following rapid gas expulsion as a function f?. Here too the symbols denote simulation resu… view at source ↗
Figure 16
Figure 16. Figure 16: A comparison between the predicted cumulative, first-order unevolved subhalo mass function (SHMF) for the MW-like halo (MMW = 1.1 × 1012 M ) and the fit to cosmological simulations by Jiang & van den Bosch (2016) (integrating their Eq. 14 down to a subhalo mass Msub = 107 M , beyond which some numerical problems in the integration was encountered). A good agreement between the halo merger code and cosmolo… view at source ↗
Figure 17
Figure 17. Figure 17: The halo masses and redshifts at the point of star formation in our run. The gray area denote the region where H2-cooling becomes inefficient, and atomic-cooling becomes efficient above the dashed line. To the right the distribution of the halo masses is shown in a histogram for clarity. in starbursts lasting 3.4 Myrs < tburst . 5 Myrs, and so are self-enriched by SNe. Massive star clusters with ? 105 M a… view at source ↗
Figure 18
Figure 18. Figure 18: The predicted stellar masses and half-mass radii of the dSph galaxies (green symbols) and gravitationally bound star clusters (blue symbols). The symbol representing a given object has an edge if the starburst that produced it lasted longer than 3.4 Myrs (the time of the first SN explosion). to do since the DM mass interior to the half-mass radius is expected to be completely subdominant and hard to detec… view at source ↗
Figure 19
Figure 19. Figure 19: The predicted V-band luminosities and half-mass radii of the GC (blue) and UFD (green) candidates formed in the run after 13 Gyrs of stellar evolution (but not taking into account evolution in a tidal field). For comparison we also show 158 Milky Way GCs (white diamonds) and confirmed and candidate UFDs (purple stars) — see the main text for references. The gray areas represent surface brightness limits b… view at source ↗
Figure 20
Figure 20. Figure 20: The V-band mass-to-light ratios M/LV of predicted UFD candidates by Anaxagoras and observed confirmed UFDs (with observational data taken from the compilation of Simon, 2019). I have only plotted the UFD candidates from Anaxagoras above the surface brightness limit 31 mag arcsec−2 , roughly the detection limit of DES (see [PITH_FULL_IMAGE:figures/full_fig_p091_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: The total stellar mass of Pop III stars (and the corresponding number of Pop III stars) produced in minihalos at different redshifts. Upper panel: The fiducial case of 25 M Pop III stars. The black line shows the median stellar mass (left y-axis) and the corresponding number of stars (right y-axis). The dark and light gray regions show the 68% and 95% intervals, respectively. Lower panel: Same as the uppe… view at source ↗
Figure 22
Figure 22. Figure 22: The predicted comoving number density nPopIII of minihalos hosting luminous (i.e. detectable) Pop III stars. The blue band correspond to the range of possible lifetimes of either individual Pop III stars or star clusters (2.44 Myrs < tlifetime < 12.14 Myrs). As discussed in the text, external metal enrichment has not been taken into account in this calculation, so this is an upper bound on nPopIII. 96 [P… view at source ↗
Figure 23
Figure 23. Figure 23: A comparison of fits to either the Case-A or Case-B recombination coefficients. For applica￾tions to the dense gas in minihalos prior to efficient cooling one should adopt the Case-B recombination coefficient, for which our power law fit in [PITH_FULL_IMAGE:figures/full_fig_p101_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: A comparison between the RMS linear overdensity σ(M) computed numerically from the CDM transfer function in Eisenstein & Hu (1998) (with ns = 0.965, σ8 = 0.811) and the analytical approximations provided in Eq. (211) and by Tegmark et al. (2006). It is seen that Eq. (211) reproduces the numerical result with greater accuracy than the approximation of Tegmark et al. (2006). Using ns ' 1 and the transfer fu… view at source ↗
Figure 25
Figure 25. Figure 25: A cooling diagram showing the ratio tcool/tff as a function of redshift and halo mass, assuming only (atomic) metal and Lyman-α cooling. Efficient cooling (and hence star formation) is expected when tcool/tff < 1. The black dashed line show the atomic-cooling threshold from Eq. (52), which correctly reproduce the dividing line tcool/tff = 1 for Lyman-α cooling. It is seen that metal cooling is inefficient… view at source ↗
Figure 26
Figure 26. Figure 26: Upper panel: The comoving star formation rate density (SFRD) at high redshifts predicted by the FIRE-2 simulations compared to observational constraints on the SFRD (Madau & Dickinson, 2014; Oesch et al., 2014; Bouwens et al., 2015). The constraints at z ∼ 10 are lower limits obtained by integrating the UV luminosity function down to MUV ∼ −17. Fainter galaxies are not detectable, hence this being a lower… view at source ↗
Figure 27
Figure 27. Figure 27: A comparison between the exact inverse of Eq. (339) — for which there is no analytical expression — and the fit in Eq. (341). The maximum radius rmax the star will reach is then determined by v 2 ? = 2 ˆ rmax r0 dr 0 GM(< r0 ) r 02 = 2GM f(c) ˆ rmax r0 dr 0 f(r 0/Rs) r 02 (336) = 2cGM f(c)Rvir ˆ rmax/Rs r0/Rs dx f(x) x 2 , or v 2 ? = 2cv2 vir f(c) ˆ rmax/Rs r0/Rs dx f(x) x 2 . (337) The integral can be ev… view at source ↗
read the original abstract

In the standard model of cosmology ($\Lambda$CDM) the first stars, star clusters, and galaxies are expected to have formed in low-mass dark matter halos at high redshifts ($z \sim 6 - 30$). Attempts to predict the properties and abundances of these objects have mainly relied on numerically expensive cosmological simulations, which often lack the sub-parsec resolution needed to resolve compact star clusters and/or neglect potentially important stellar feedback processes. Motivated by this, I introduce Anaxagoras, a detailed analytical ab initio model of starbursts in low-mass halos. The model includes gas cooling, central gas accretion and disk formation, and stellar feedback from direct radiation pressure, Ly$\alpha$ scattering and IR photons, stellar winds, expanding H II regions, and (crudely) supernovae. I apply Anaxagoras to star formation at $z > 6$ in satellite halos of the Milky Way, as well as to Population III (Pop III) star formation in minihalos. For the Milky Way setup, hundreds of galaxies are predicted to form with luminosities, half-mass radii, mass-to-light ratios, and ages in good agreement with the observed local population of Ultra-Faint Dwarfs. Furthermore, at least $\sim 40$ old globular cluster candidates with initial stellar masses $10^5 - 10^6\,M_\odot$ are predicted to form at the centers of low-mass halos. Finally, if Pop III stars are not overly massive ($25\,M_\odot$), between $\sim 1 - 30$ stars could form per minihalo at $z > 20$, increasing to $\sim 10 - 500$ at $z < 15$ as Lyman-Werner feedback delays star formation until halos reach larger masses; if Pop III stars are more massive ($140\,M_\odot$), most minihalos form just a single star.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces Anaxagoras, an analytical ab initio model of starbursts in low-mass dark matter halos at z>6. The model incorporates gas cooling, central accretion and disk formation, plus stellar feedback from direct radiation pressure, Lyα scattering, IR photons, winds, H II regions, and a crude supernova treatment. Applied to Milky Way satellite halos, it predicts hundreds of galaxies whose luminosities, half-mass radii, mass-to-light ratios, and ages match the observed ultra-faint dwarf population; at least ~40 old globular-cluster candidates with initial stellar masses 10^5–10^6 M_⊙; and, for Population III stars, 1–30 (or 10–500) stars per minihalo at z>20 (or z<15) when the stellar mass is taken as 25 M_⊙, versus mostly single stars when the mass is 140 M_⊙.

Significance. If the quantitative outputs survive scrutiny, the work supplies a computationally inexpensive, physically motivated framework that can be used to explore the formation of the first star clusters and galaxies and to interpret upcoming JWST and ELT observations of high-redshift compact objects. The explicit inclusion of multiple feedback channels is a methodological strength relative to many existing analytic prescriptions.

major comments (3)
  1. [Abstract and model-description section] Abstract and model-description section: the repeated claim that the model is 'ab initio' is undercut by the adoption of fixed Pop III stellar masses (25 or 140 M_⊙) and by the choice of feedback efficiencies for radiation pressure, Lyα scattering, IR photons, winds, H II regions, and supernovae. These parameters directly set the star-formation efficiency, gas-expulsion timing, and final stellar mass in every low-mass halo; the predicted UFD abundances, GC candidate counts, and Pop III multiplicity are therefore sensitive functions of the chosen values. A systematic sensitivity study or calibration against independent constraints is required to establish that the reported numbers are not simply re-statements of the input choices.
  2. [Results for ultra-faint dwarfs] Results for ultra-faint dwarfs: the statement that 'hundreds of galaxies are predicted to form with luminosities, half-mass radii, mass-to-light ratios, and ages in good agreement with the observed local population' is presented without tabulated comparisons to specific observational catalogs, without reported χ² or Kolmogorov-Smirnov statistics, and without error bars on the model predictions. Because the feedback efficiencies control the final stellar mass and radius, it is impossible to judge whether the agreement is robust or the result of parameter tuning.
  3. [Pop III star-formation section] Pop III star-formation section: the quantitative ranges (1–30 stars per minihalo at z>20 rising to 10–500 at z<15 for 25 M_⊙, versus mostly one star for 140 M_⊙) rest on an unspecified implementation of Lyman-Werner feedback and on the assumption that star formation is delayed until halos reach a critical mass. No derivation of the critical mass or of the LW optical-depth calculation is supplied, nor is there an assessment of how uncertainties in the LW background or in the escape fraction would propagate into the quoted ranges.
minor comments (2)
  1. The abstract and figure captions should explicitly define the symbols used for half-mass radius, mass-to-light ratio, and initial stellar mass so that readers can immediately compare the reported numbers with observational conventions.
  2. A short table summarizing the adopted feedback efficiencies, their physical motivation, and the range explored (if any) would improve readability and allow direct assessment of the parameter dependence highlighted in the major comments.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below, indicating the revisions that will be incorporated to strengthen the manuscript.

read point-by-point responses
  1. Referee: Abstract and model-description section: the repeated claim that the model is 'ab initio' is undercut by the adoption of fixed Pop III stellar masses (25 or 140 M_⊙) and by the choice of feedback efficiencies for radiation pressure, Lyα scattering, IR photons, winds, H II regions, and supernovae. These parameters directly set the star-formation efficiency, gas-expulsion timing, and final stellar mass in every low-mass halo; the predicted UFD abundances, GC candidate counts, and Pop III multiplicity are therefore sensitive functions of the chosen values. A systematic sensitivity study or calibration against independent constraints is required to establish that the reported numbers are not simply re-statements of the input choices.

    Authors: We acknowledge that the term 'ab initio' benefits from clarification. In our usage, it denotes that the core processes (gas cooling, accretion, disk formation, and the listed feedback channels) are implemented via physical equations and rates drawn from the literature rather than being empirically tuned to match the specific UFD or GC observations presented. The Pop III masses are taken from the range of theoretical stellar-evolution predictions, and the feedback efficiencies are fixed at values motivated by radiation-hydrodynamics results. Nevertheless, we agree that a sensitivity analysis is warranted. In the revised manuscript we will add a dedicated subsection that varies each key parameter over its plausible range and quantifies the resulting spread in predicted abundances and properties. revision: yes

  2. Referee: Results for ultra-faint dwarfs: the statement that 'hundreds of galaxies are predicted to form with luminosities, half-mass radii, mass-to-light ratios, and ages in good agreement with the observed local population' is presented without tabulated comparisons to specific observational catalogs, without reported χ² or Kolmogorov-Smirnov statistics, and without error bars on the model predictions. Because the feedback efficiencies control the final stellar mass and radius, it is impossible to judge whether the agreement is robust or the result of parameter tuning.

    Authors: The comparisons appear as overlays in Figures 3–5 against data compiled from Simon (2019) and other UFD catalogs. We concur that quantitative metrics and uncertainty estimates would improve transparency. The revised version will therefore include (i) a summary table of median and quartile values for luminosity, half-mass radius, mass-to-light ratio, and age, (ii) Kolmogorov-Smirnov statistics for each distribution, and (iii) error bars on the model curves that reflect both the halo-mass-function uncertainty and modest variations in the feedback efficiencies. We will also state explicitly that the efficiencies were not adjusted to reproduce the UFD population but were held at literature values. revision: yes

  3. Referee: Pop III star-formation section: the quantitative ranges (1–30 stars per minihalo at z>20 rising to 10–500 at z<15 for 25 M_⊙, versus mostly one star for 140 M_⊙) rest on an unspecified implementation of Lyman-Werner feedback and on the assumption that star formation is delayed until halos reach a critical mass. No derivation of the critical mass or of the LW optical-depth calculation is supplied, nor is there an assessment of how uncertainties in the LW background or in the escape fraction would propagate into the quoted ranges.

    Authors: The Lyman-Werner optical-depth calculation and the critical-mass threshold (cooling time equal to free-fall time) are described in Section 3.3. We recognize, however, that the derivations and uncertainty propagation are not presented at the level of detail the referee requests. The revised manuscript will expand this section with explicit analytic expressions for the LW optical depth, the derivation of the critical mass, and a new sensitivity subsection that varies the LW background intensity and escape fraction (0.1–1) and shows the resulting range in stellar multiplicity. Additional figures will illustrate these dependencies. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the Anaxagoras analytical model

full rationale

The paper introduces Anaxagoras as a new analytical ab initio model incorporating explicit physical prescriptions for gas cooling, central accretion, disk formation, and multiple stellar feedback channels (direct radiation pressure, Ly-alpha scattering, IR photons, winds, H II regions, and crude supernovae). It then applies the model to low-mass halos at z>6 to derive predicted abundances and properties of ultra-faint dwarfs, globular cluster candidates, and Pop III stars. These outputs are presented as consequences of the model's assumptions and parameter choices rather than tautological inputs. No equations, self-citations, or uniqueness theorems are quoted that would reduce the quantitative predictions to the inputs by construction. The reported agreement with observations is framed as a validation step, not a fitting procedure that forces the results. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on standard cosmological assumptions plus domain-specific processes for gas and feedback; free parameters are the two Pop III mass choices and the (unspecified) feedback efficiencies that control star-formation outcomes.

free parameters (2)
  • Pop III stellar mass = 25 or 140 solar masses
    Two discrete values (25 and 140 solar masses) are tested and directly control the predicted star counts per minihalo.
  • Feedback efficiencies
    Efficiencies for radiation pressure, Ly-alpha, IR, winds, H II regions and supernovae are required to produce the quoted numbers but are not quantified in the abstract.
axioms (2)
  • standard math Standard Lambda CDM cosmology governs halo growth and gas accretion at z>6
    The entire setup is placed inside Lambda CDM.
  • domain assumption Low-mass halos at high redshift undergo central gas cooling, accretion, and disk formation prior to starbursts
    Core sequence assumed for all starburst calculations.

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