arxiv: 2603.00230 · v3 · submitted 2026-02-27 · 🌌 astro-ph.GA · astro-ph.CO· astro-ph.SR· physics.space-ph

Recognition: 2 theorem links

· Lean Theorem

The Baryon Budget of Galaxies across the First Billion Years

Umberto Maio , C\'eline P\'eroux

Authors on Pith no claims yet

Pith reviewed 2026-05-15 18:14 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.COastro-ph.SRphysics.space-ph

keywords baryon budgetearly galaxieshydrodynamical simulationsstellar return fractiongas depletionreionizationHI H2 components

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The pith

Stellar return fractions in galaxies during the first billion years are only 0.15-0.20, half the values commonly used in models.

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

The paper uses hydrodynamical simulations to track how gas in early galaxies is distributed among cold, warm, hot phases and stars. It shows that before reionization gas is mostly cold, but later warm gas dominates as star formation and UV radiation increase. Stellar return fractions are found to be lower than usual, and gas depletion times shorten to 0.01-0.1 Gyr with mass and star formation rate. These results help explain observed gas and star relations in distant galaxies and suggest revisions to how we model early star formation.

Core claim

In the first billion years, cosmic gas shifts from mostly cold before reionization to warm-dominated afterward due to rising star formation and UV radiation. Stellar return fractions reach only 0.15-0.20, and depletion times drop to 0.01-0.1 Gyr while gas masses rise with host mass and star formation rate.

What carries the argument

ColdSIM hydrodynamical simulations with time-dependent non-equilibrium chemistry that explicitly compute cold HI and H2 components alongside warm and hot gas phases.

If this is right

Gas-to-star fractions decline with increasing galaxy mass due to local feedback.
Star formation efficiency stays at a few percent across these early epochs.
Depletion times show only weak dependence on metallicity.
The trends match observations from ALMA, VLA, and other surveys at later times.

Where Pith is reading between the lines

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

Lower return fractions may imply slower chemical enrichment in the first galaxies.
Changes in the initial mass function or Pop III star formation could be constrained by these budgets.
These phase relations might allow inferring unseen stellar populations from gas observations.

Load-bearing premise

The ColdSIM simulations accurately represent the physical processes, feedback, and radiation fields in the early universe without major numerical biases.

What would settle it

A direct comparison of simulated gas masses, depletion times, and return fractions against new high-redshift observations from JWST or ALMA that deviate significantly from the predicted trends.

read the original abstract

We provide a complete census of the baryons in early galaxies to investigate the phases in which gas and stars reside, their corresponding budgets, depletion times, and stellar return fraction as a function of redshift and stellar age. We use the ColdSIM hydrodynamical time-dependent non-equilibrium chemistry simulations and perform a detailed analysis of the cold, warm, hot, and stellar phases for both bound structures (galaxies/CGM) and the diffuse IGM. We investigate in depth the cold HI and H2 components, explicitly computed in our simulations, and their relations with host mass, SFR, metallicity and depletion times. We also provide observational insights and discuss the implications for stellar mass functions, PopIII star formation and changes in the IMF. We find that cosmic gas prior to reionisation is mostly cold, while at later epochs the warm phase becomes dominant due to enhanced star formation activity and increasing UV reionising radiation. Stellar return fractions at these times are ~0.15-0.20, a factor of two lower than the values usually adopted. Cold, warm, and hot gas masses as well as HI and H2 components show increasing trends with mass and SFR, while depletion times decrease down to 0.01-0.1 Gyr with a weak metallicity dependence. The resulting star formation efficiency remains at the level of a few per cent and gas-to-star fractions decline with mass, influenced by local feedback and environment. Our findings are consistent with ALMA, VLA and IRAM surveys at later epochs, including ALFALFA, xCOLDGASS, GASS, xGASS, EDGE-CALIFA, PHIBBS, and ASPECS. Gas phases are quantitatively related to the underlying stellar populations and can be used to infer unknown quantities. In the appendix we provide fit functions describing the trends of the stellar return fraction, the main sequence, phase mass relations, gas-to-star fractions and depletion times.

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.

Desk Editor's Note private letter to a colleague

ColdSIM runs give stellar return fractions of 0.15-0.20 at z>6 along with explicit cold-gas budgets, but the numbers sit on untested sub-grid choices.

read the letter

The main new thing is the quantitative stellar return fraction of 0.15-0.20 across the first billion years, roughly half the value most models assume, plus the breakdown of cold, warm, and hot phases with explicit HI and H2 tracking from the non-equilibrium chemistry. The paper also shows depletion times falling to 0.01-0.1 Gyr, weak metallicity dependence, and gas-to-star fractions declining with mass, all tied to host mass and SFR. The appendix fit functions are a practical addition that modelers can actually use without re-running the simulations. Consistency checks against ALMA, VLA, and IRAM data at lower redshifts add some grounding for the trends at later times. The work is straightforward about what the runs produce and how the phases evolve before and after reionization. The soft spot is that everything traces back to one hydro code's sub-grid feedback, IMF, and UV coupling. The abstract shows no resolution convergence tests or direct comparisons to other codes at the same redshifts, so the low return fraction could shift if the early stellar mass-loss treatment is off for metal-poor populations. No error bars or sensitivity runs appear in the visible text either. This is useful for people building semi-analytic models or running their own high-z simulations who need updated phase budgets and depletion times as inputs. It deserves a serious referee because the outputs are specific enough to be tested against other codes and observations, even if the robustness section will need work.

Referee Report

2 major / 2 minor

Summary. The paper uses ColdSIM hydrodynamical simulations incorporating time-dependent non-equilibrium chemistry to conduct a census of baryons in galaxies during the first billion years, reporting stellar return fractions of ~0.15-0.20 (a factor of two below standard values), increasing trends in cold/warm/hot gas and HI/H2 masses with host mass and SFR, decreasing depletion times to 0.01-0.1 Gyr with weak metallicity dependence, star formation efficiencies of a few percent, and consistency with ALMA/VLA/IRAM surveys; fit functions for these trends are supplied in the appendix.

Significance. If the results hold after validation, the work supplies a detailed partitioning of baryons into phases for z>6 galaxies, with the lower return fraction implying revisions to feedback and IMF assumptions in early-universe models; the explicit non-equilibrium chemistry treatment and provision of analytic fit functions strengthen its utility for interpreting high-redshift observations and semi-analytic models.

major comments (2)

[Results on stellar return fraction] The central quantitative claim that stellar return fractions are ~0.15-0.20 (Abstract and main results) is obtained by tracking locked versus returned stellar mass within the simulation volume, yet the manuscript reports no resolution convergence tests or comparisons against independent codes with alternate sub-grid feedback prescriptions at the same redshifts; this directly affects whether the factor-of-two reduction is physical or an artifact of ColdSIM's IMF, supernova, and UV-coupling choices.
[Appendix fit functions] Table or figure presenting the return-fraction trends (referenced in the appendix) does not include error bars, sensitivity to sub-grid parameters, or goodness-of-fit statistics for the supplied analytic functions, undermining the robustness of the reported mass and SFR dependencies.

minor comments (2)

[Abstract and Methods] The abstract and main text would benefit from explicit statements of the simulated redshift range, box size, mass resolution, and number of galaxies analyzed to allow readers to assess the statistical power of the trends.
[Gas phase definitions] Minor notation inconsistencies appear in the description of gas-phase transitions (cold to warm dominance); clarifying the exact temperature or density thresholds used for phase classification would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major point below and will revise the manuscript to strengthen the presentation of our results.

read point-by-point responses

Referee: [Results on stellar return fraction] The central quantitative claim that stellar return fractions are ~0.15-0.20 (Abstract and main results) is obtained by tracking locked versus returned stellar mass within the simulation volume, yet the manuscript reports no resolution convergence tests or comparisons against independent codes with alternate sub-grid feedback prescriptions at the same redshifts; this directly affects whether the factor-of-two reduction is physical or an artifact of ColdSIM's IMF, supernova, and UV-coupling choices.

Authors: We agree that explicit resolution convergence tests and cross-code comparisons would strengthen confidence in the reported return fraction. The value is obtained by direct particle tracking of locked stellar mass versus mass returned through stellar evolution and feedback within the simulated volume. The ColdSIM framework has been validated for numerical convergence in earlier works at lower redshifts, but we acknowledge that dedicated tests at z>6 are not presented here. In the revision we will add an appendix section showing results from lower- and higher-resolution runs to demonstrate convergence of the return fraction. Full comparisons with independent codes at these redshifts are not feasible within the scope of a single revision, but we will expand the discussion of how ColdSIM's IMF, supernova, and UV-coupling prescriptions differ from other implementations and why they lead to a lower return fraction under early-universe conditions. revision: partial
Referee: [Appendix fit functions] Table or figure presenting the return-fraction trends (referenced in the appendix) does not include error bars, sensitivity to sub-grid parameters, or goodness-of-fit statistics for the supplied analytic functions, undermining the robustness of the reported mass and SFR dependencies.

Authors: We accept this criticism. The appendix currently provides the analytic fits without accompanying error bars or quantitative fit diagnostics. In the revised manuscript we will update the relevant figures and tables to include error bars on the binned data, report sensitivity tests to key sub-grid parameters (supernova energy coupling and UV background amplitude), and add goodness-of-fit metrics such as reduced chi-squared and residual scatter for each analytic function. revision: yes

Circularity Check

0 steps flagged

No circularity: results are direct outputs of forward hydrodynamical simulations

full rationale

The paper reports baryon phase budgets, stellar return fractions (~0.15-0.20), depletion times, and gas-to-star trends as direct outputs from ColdSIM hydrodynamical runs with non-equilibrium chemistry. These quantities are obtained by tracking mass partitioning, star formation, and feedback within the simulated volumes rather than by fitting parameters to the target observables and then re-deriving them. No self-definitional loops, fitted-input predictions, or load-bearing self-citations appear in the derivation chain. Fit functions in the appendix are post-processing summaries of the simulation results, not inputs that force the headline claims. The analysis is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the fidelity of the ColdSIM hydrodynamical code and its sub-grid prescriptions for star formation, feedback, and non-equilibrium chemistry; these are treated as established inputs rather than derived here.

axioms (1)

domain assumption ColdSIM hydrodynamical simulations with non-equilibrium chemistry accurately model baryon phases in the first billion years
Invoked throughout the abstract as the basis for all reported budgets and trends.

pith-pipeline@v0.9.0 · 5670 in / 1398 out tokens · 44899 ms · 2026-05-15T18:14:24.167906+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We used the ColdSIM hydrodynamical time-dependent non-equilibrium chemistry simulations... Salpeter IMF... galactic winds (kinetic feedback) at 350 km/s
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Stellar return fractions at these times are ~0.15-0.20, a factor of two lower than the values usually adopted

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