Constraints on the galaxy formation models during epoch of reionization with high redshift observations

Anshuman Acharya; Benedetta Ciardi; Ming Li; Qi Guo; Qing-Bo Ma; Xiao-Rong Chen; Xin Wang

REVIEW 3 major objections 5 minor 62 references

Constraints on the galaxy formation models during epoch of reionization with high redshift observations

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read With a 20% escape fraction, galaxy formation models tuned to JWST data meet the hydrogen budget for reionization at $z>6$.

desk verdict A careful MCMC calibration of L-Galaxies to JWST UVLFs, with a headline photon-budget claim that is true only if you ignore recombinations and take fesc=20% at face value. read the letter →

arxiv 2504.19422 v1 pith:PJ2UYLGP submitted 2025-04-28 astro-ph.CO

Qing-Bo Ma , Xiao-Rong Chen , Ming Li , Qi Guo , Benedetta Ciardi , Anshuman Acharya , Xin Wang This is my paper · ORCID

classification astro-ph.CO

keywords cosmicreionizationgalaxyformationsemi-analyticalmodelsL-GalaxiesescapefractionionizingphotonbudgetUVluminosityfunctionhigh-redshiftgalaxies

open problems Dark Matter

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

This paper asks whether ordinary galaxies can account for cosmic reionization, the phase transition in which the Universe went from neutral to ionized. Using the L-Galaxies semi-analytical models run on the Jiutian-300 dark-matter simulation, with parameters fitted by a Markov Chain Monte Carlo (a standard statistical fitting method) to ultraviolet luminosity functions from JWST and HST at $z=6$--$12$, it finds that all fitted model variants reproduce the observed galaxy properties and produce enough ionizing photons. The load-bearing number is the escape fraction—the share of ionizing photons that leaves a galaxy rather than being absorbed inside it. Assuming a constant 20% escape fraction, every model produces more ionizing photons than the number of hydrogen atoms in the Universe at all $z>6$. Including dust correction inside the fit pushes the star formation efficiency upward and yields about 50% more ionizing photons, while making predicted stellar mass functions agree better with observations; if these results hold, ordinary galaxies with a modest escape fraction can drive reionization, and the choice of whether and how dust is treated in the model matters for the photon budget.

What carries the argument

The argument runs through three linked pieces. First, a Markov Chain Monte Carlo pipeline that randomly samples halo merger trees from the Jiutian-300 N-body simulation, which makes it computationally feasible to fit the 15--16 free parameters of the semi-analytical models to the observed UV luminosity functions; only a handful of parameters are actually well constrained by those data. Second, the L-Galaxies 2015 and 2020 semi-analytical models themselves, which follow galaxy formation along dark-matter merger trees and compute star formation, feedback, and metal enrichment; through BPASS binary stellar-population spectra they assign each galaxy a time-integrated ionizing photon number $\eta_{\rm ion}$. Third, the assumed constant escape fraction of 20% converts the emitted photon density $N_{\rm ion}$ into a comparison with the hydrogen atom density $N_{\rm H}$. The load-bearing relation is the almost-linear power law $\eta_{\rm ion}=A_{\rm ion}(M_{*}/10^{10} M_\odot)^{\alpha_{\rm ion}}$ with $\alpha_{\rm ion}\approx0.9$--$1$: it lets the paper turn observed and predicted stellar mass functions directly into an ionizing photon budget, with dust correction shifting the fitted parameters so that more massive, dusty galaxies form more stars and therefore emit more ionizing photons.

What would settle it

Measure the average escape fraction of ionizing photons from galaxies at $z\approx6$--$8$ with Lyman-continuum observations, for example from JWST or future facilities. This paper itself shows that at an escape fraction of 10% only the 2015-model all-galaxy variants keep $0.1 N_{\rm ion}$ above $N_{\rm H}$ at $z=6$, so an observed escape fraction of 10% or below would falsify the 20%-escape-fraction budget claim for most of the models.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that JWST-era observations of the ultraviolet luminosity function at $z\approx6$--$12$ can pin down enough of the L-Galaxies parameters to turn the model into a reionization budget, and that the budget closes. With the best-fit parameters, both L-Galaxies 2015 and L-Galaxies 2020 reproduce the observed UV luminosity functions, stellar mass functions, star formation rate densities, and ionizing photon emission efficiencies. The time-integrated ionizing photon number per galaxy is nearly proportional to stellar mass, $\eta_{\rm ion}=A_{\rm ion}(M_{*}/10^{10} M_\odot)^{\alpha_{\rm ion}}$ with $\alpha_{\rm ion}\approx0.9$--$1$, so the stellar mass function acts as a photon inventory. Summed over the simulation volume, the predicted ionizing photon number density exceeds the mean hydrogen atom density at $z>6$ once an escape fraction of 20% is assumed; without dust correction, the Fiducial model reaches about 5 times $N_{\rm H}$ at $z=6$. When dust extinction is folded into the MCMC fit, the fitted star formation efficiency rises and gas reincorporation speeds up, producing roughly 50% more ionizing photons at $z=6$ and stellar mass functions that match observations from $z=6$ to $12$ better than the no-dust versions. The paper concludes that galaxy formation models consistent with current high-redshift observations can supply the ionizing photon budget of reionization with a modest, constant escape fraction.

Load-bearing premise

The whole photon-budget result rests on assuming that every galaxy lets a constant 20% of its ionizing photons escape into intergalactic space; if the real escape fraction is lower, most of the models would no longer produce enough photons to complete reionization by $z=6$.

Editorial extensions

If this is right

A constant 20% escape fraction is enough: the modeled high-redshift galaxies alone can keep the Universe ionized at $z>6$, so reionization does not force exotic ionizing sources or escape fractions near unity.
Dust correction should be part of the fitting, not an afterthought: the dust-corrected MCMC runs predict about 50% more ionizing photons at $z=6$ and stellar mass functions consistent with observations down to $z=6$, while the no-dust versions match the stellar mass function only at $z\ge9$.
The two model generations bracket the ionizing budget: L-Galaxies 2015 produces at least twice as many ionizing photons at $z=6$ as L-Galaxies 2020 because its star formation prescription makes low-mass halos form stars earlier, so the photon budget is sensitive to the star-formation physics as well as to the data.
Because $\eta_{\rm ion}$ is nearly proportional to $M_{*}$, high-redshift stellar mass functions serve almost directly as ionizing photon inventories; improving stellar mass function measurements at $z>6$ sharpens the reionization budget.
Only a subset of galaxy-formation parameters is constrained by the UV luminosity function (the star formation efficiency, burst parameters, gas reincorporation and ram-pressure stripping scales in L-Galaxies 2020; star formation efficiency and ejection efficiency in L-Galaxies 2015), leaving other parameters free and making multiple models consistent with the same observations.

Reading between the lines

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

If future observations put the average escape fraction below about 10%, the headline budget closes only for the 2015-model all-galaxy variants; the paper itself notes that most models would not have $0.1 N_{\rm ion}$ above $N_{\rm H}$ at $z=6$. A natural next step is to treat the escape fraction as a fitted parameter rather than an input assumption.
The dust correction implies a testable prediction: massive galaxies at $z\approx6$--$8$ should be dusty enough to explain the suppression of their UV luminosities; infrared and submillimetre observations of the same galaxies could check whether the fitted dust attenuation is real.
The $N_{\rm ion}$ versus $N_{\rm H}$ comparison is a necessary, not sufficient, test of reionization by galaxies: recombinations in a clumpy intergalactic medium increase the required photon budget, so coupling these outputs to radiative transfer would show how much headroom the 20% budget actually leaves.
If the near-universal linear $\eta_{\rm ion}$--$M_{*}$ relation extends beyond the simulated mass range, observers could estimate reionization budgets directly from JWST stellar mass functions, without running full semi-analytical models.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is a solid, careful MCMC calibration of L-Galaxies against JWST/HST UVLFs at z=6-12, and the photon budget result is exactly what the math shows but less than the abstract makes it sound. The genuinely new piece is the explicit dust-correction comparison: when the MCMC fits dust-corrected UVLFs, alpha_H2 rises and the predicted ionizing photon output goes up by ~50%, with better agreement to observed SMFs. That sub-result is well supported and will be useful to anyone modeling reionization sources.

What the paper does well: it applies the Henriques et al. (2013) tree-sampling MCMC technique to 15-16 parameters, and it is honest about the fact that most of those parameters are only weakly constrained by the UVLF. Rather than overstate the best-fit, they run additional 'final' models with only the well-determined parameters changed, then compare against SMF, SFRD, and zeta_ion observations that were not part of the fit. The side-by-side LG15 vs LG20 comparison is informative, and the underlying pipeline looks sound.

The soft spots are real but not fatal. The headline claim -- with fesc=20%, all models produce more ionizing photons than the hydrogen atom density at z>6 -- is a static sum of cumulative emitted photons. It ignores recombinations, which the text itself says can 'substantially increase the required number of photons.' At z=6 the margin for several non-dust models is thin, and the paper reports that at fesc=10% only the LG15 models clear the bar. If a recombination clumping factor of a few is realistic, the claim flips for most models. The bright-end UVLF points are excluded from the fit due to simulation box size; that is defensible, but it is a cut that should not be swept under the rug. The predicted SMF, SFRD, and Nion curves are shown with no uncertainty propagation, so agreement with non-fitted data is hard to weigh quantitatively. And those quantities are not fully independent checks -- they come from the same calibrated model, though at least they are not fitted targets.

The paper is for people doing semi-analytic modeling of reionization and for observers interpreting JWST UVLFs and SMFs. It deserves a serious referee: the issues are fixable with hedging and, ideally, a quick test with a recombination factor. I would send it to peer review rather than desk-reject.

Referee Report

3 major / 5 minor

Summary. The paper calibrates the L-Galaxies 2015/2020 semi-analytic galaxy formation models to high-redshift UV luminosity functions using an MCMC approach applied to merger trees from the Jiutian-300 N-body simulation. Three MCMC runs are performed (LG20 without dust correction, LG20 with dust correction, and LG15 without dust correction), and the resulting parameter sets are used to run seven/eight model variants, including best-fit, 'final' (well-constrained parameters only), and fiducial configurations. The models are compared with JWST/HST observations of UVLFs, stellar mass functions, star formation rate densities, and ionizing photon production efficiencies. The paper's headline results are that, with a constant escape fraction of 20%, all models produce more cumulative ionizing photons than the total number of hydrogen atoms at z>6, and that including dust correction in the MCMC yields a higher star formation efficiency, ~50% more ionizing photons, and better agreement with observed stellar mass functions.

Significance. If established, the results would support two non-trivial conclusions: a standard SAM calibrated only to high-z UVLF data can simultaneously reproduce independent observations (SMF, SFRD, and ζion), and the modeled galaxy population can meet the ionizing photon budget with a modest, constant escape fraction. The paper has clear strengths: the MCMC fits use up-to-date JWST and HST UVLF measurements; the SMF, SFRD, and ζion comparisons are not used as fitting targets, providing a useful validation test; the 'final' model variants mitigate the weak constraints on most SAM parameters; and the ηion–M⋆ power-law and per-baryon ionizing yields are compact, reusable parameterizations. The main weaknesses concern the photon-budget argument: the fesc=20% statement is a static comparison that ignores recombinations, and the margin at z=6 is modest for several models, so the headline claim needs explicit caveats or a full reionization calculation.

major comments (3)

[Abstract; §3.2, bottom panel of Fig. 7] The abstract states that 'with the assumption of escape fraction of 20%, all models produce more ionizing photons than the number of Hydrogen atoms in the Universe at z>6', but the paper's own quantitative analysis evaluates this inequality only at z=6, where the text says 'most cases have 0.2 × Nion > NH at z = 6'. The bottom panel of Fig. 7 and the associated text show that for the Fiducial model Nion is above NH only at z<9.5, implying Nion<NH at z=12. As written, the phrase 'at z>6' is therefore not supported by the plotted redshift evolution; the claim should be rephrased as 'by z=6' or 'at z=6', and the crossing redshift of Nion/NH for each model should be reported.
[§3.2, bottom panel of Fig. 7] The fesc=20% comparison is a static, recombination-free photon budget. The paper itself warns that 'gas recombination can substantially increase the required number of photons, in particular in high density regions'. For the non-dust LG20 models the margin is thin: Fiducial reaches ~5 NH at z=6, so 0.2*Nion is only ≈NH, and with fesc=10% the text states that only the LG15 models would satisfy the inequality. Since fesc is an externally assumed constant rather than a fitted or observationally constrained quantity, the headline conclusion should be framed as a necessary condition for reionization, and the critical clumping/recombination factor or a full reionization calculation should be provided before claiming that the modeled galaxy population can complete reionization.
[§3.2; Table 1; Appendix A] The reported Nion values are quoted without uncertainties, although the MCMC analysis in Appendix A shows that most of the 15–16 fitted parameters are only weakly constrained. The spread between 'bestfit' and 'final' variants is substantial in some cases: at z=6, LG15 bestfit and LG15 final produce ~200% and ~100% more ionizing photons than Fiducial, respectively, a factor-of-two systematic difference in Nion. Because the fesc=20% margin at z=6 is close to unity for several models, this parameter/systematic uncertainty is comparable to the margin and should be propagated into the conclusion, for example by evaluating Nion along the MCMC posterior or across the 'final' parameter choices.

minor comments (5)

[Appendix A, Fig. 11 caption] The caption says '1-σ (68%) and 3-σ (95%)', but 95% corresponds to about 2σ, not 3σ; this should be corrected.
[Fig. 4; bottom panel of Fig. 2] The vertical-axis labels read 'MPc−3' but should read 'Mpc−3'.
[Fig. 12 caption] The caption contains the typo 'volumn' where 'column' was intended.
[§3.1] The text 'the adoption in L15 of a critical mass threshold' should read 'LG15' rather than 'L15'.
[§3.1] The UVLF χ² values quoted for the eight models are not accompanied by the number of data points or reduced-χ² values; providing this information would help the reader compare models on an equal footing.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: MCMC-fitted parameters and independently benchmarked outputs; fesc/recombination caveats are conditionalities, not circular reductions.

full rationale

The derivation is self-contained. Model parameters are fitted to z = 6-12 UVLF observations with an MCMC whose likelihood is explicitly the UVLF chi-square (Appendix A: chi^2 = sum (phi_obs - phi_sim)^2 / sigma_obs^2), and then the quantities presented as predictions (SMF, SFRD, zeta_ion, N_ion) are outputs of the resulting simulations, compared to external data sets that were not fitting targets: Stefanon et al. (2021) and Navarro-Carrera et al. (2024) for SMF, Nakajima et al. (2023) for SFR versus stellar mass, and Castellano et al. (2022), Tang et al. (2023) and Simmonds et al. (2024) for zeta_ion. The SMF agreement is therefore a genuine out-of-sample check rather than a fitted target, and the dust-correction claim ('The inclusion of dust correction within MCMC results in higher star formation efficiency, which predicts ~50% more ionizing photons') is transparently a derived consequence of a fitted star formation efficiency, not a prediction of a quantity that was itself used in the fit. The ionizing photon budget is computed from BPASS SEDs and the integrated star formation history through eta_ion = A_ion (M_* / 10^10 M_sun)^alpha_ion and N_ion = sum eta_ion / V_box, and the comparison with N_H at f_esc = 20% is a stated assumption rather than a fitted or self-defined result. The paper's own caveat in Section 3.2 that 'gas recombination can substantially increase the required number of photons' is a physical limitation of the static budget argument, not a circular step, and the explicit f_esc = 10% sensitivity check makes the conditional nature of the headline claim clear. The self-citations to Ma et al. (2023) and Liu et al. (2024) supply the ionizing photon integration method, but the resulting zeta_ion is validated against external observational determinations, so these citations are not load-bearing in a circular sense. No uniqueness theorem, ansatz, or renamed known result is invoked to force the conclusions.

Assumptions & free parameters 17 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the L-Galaxies SAM prescriptions, the BPASS SED model, the assumed escape fraction, and the N-body halo sample; no new physical entities are introduced. The many MCMC-fitted parameters are listed above because the fitted values determine the predicted UVLF, SMF, and Nion.

free parameters (17)

fesc = 0.2 (assumed constant, not fitted)
Assumed escape fraction of ionizing photons; converts intrinsic Nion to ionizing budget. With fesc=0.1 most models would fail to exceed NH at z=6 (Sec. 3.2).
alpha_H2 (LG20 SF efficiency) = 0.11 LG20 bestfit, 0.19 LG20 dust bestfit, fiducial 0.06
MCMC fit to UVLF; dust-corrected fit requires higher efficiency.
Mcrit_0 (LG15 SF mass threshold) = 0.27 LG15 bestfit, 0.24 LG15 final
MCMC fit; affects faint-end UVLF.
alpha_SF,burst (burst SF efficiency) = 0.65 LG20, 0.25 LG20 dust, 0.6 LG15
MCMC fit for starburst after galaxy mergers.
beta_SF,burst (burst SF index) = 0.21 LG20, 0.27 LG20 dust, 1.9 LG15
MCMC fit for starburst after galaxy mergers.
kAGN (AGN feedback efficiency) = 1.6e-3 LG20, 0.011 LG20 dust, 6.2e-3 LG15
MCMC fit to UVLF; weakly constrained.
fBH (black hole growth efficiency) = 0.07 LG20, 0.049 LG20 dust, 0.082 LG15
MCMC fit to UVLF; weakly constrained.
V_BH (black hole velocity scale) = 730 LG20, 50 LG20 dust, 740 LG15
MCMC fit; extreme dust bestfit value hints at degeneracy.
epsilon_reheat (SN reheat efficiency) = 1.6 LG20, 0.51 LG20 dust, 1.3 LG15
MCMC fit to UVLF.
V_reheat (reheat velocity scale) = 110 LG20, 150 LG20 dust, 320 LG15
MCMC fit to UVLF.
beta_reheat (reheat index) = 4.1 LG20, 3.4 LG20 dust, 0.79 LG15
MCMC fit to UVLF.
eta_eject (ejection efficiency) = 4.7 LG20, 2.8 LG20 dust, 0.28 LG15
MCMC fit; strongly constrained in LG15.
V_eject (ejection velocity scale) = 200 LG20, 490 LG20 dust, 59 LG15
MCMC fit to UVLF.
beta_eject (ejection index) = 2.4 LG20, 4.3 LG20 dust, 1.2 LG15
MCMC fit to UVLF.
gamma_reinc (reincorporation factor) = 7.7e9 LG20, 9.6e8 LG20 dust, 6.5e10 LG15
MCMC fit; lower value in dust case boosts stellar mass in massive halos.
alpha_friction (dynamical friction delay) = 1.8 LG20, 2.3 LG20 dust, 3.8 LG15
MCMC fit to UVLF; weakly constrained.
M_rp (ram-pressure stripping scale) = 2.3e4 LG20, 2.5e4 LG20 dust, 1.4e4 LG15
MCMC fit; selected as well-constrained in LG20.

assumptions (6)

domain assumption Planck 2018 cosmological parameters (Omega_m=0.3111, Omega_b=0.049, h=0.6766, sigma8=0.8102, ns=0.9665) are fixed as inputs.
Adopted in Section 1 for both N-body and SAM; central results depend on this background cosmology.
domain assumption L-Galaxies SAM prescriptions for gas cooling, star formation, feedback, and metal enrichment are a sufficient description of high-z galaxy formation.
The entire analysis is built on the SAM; biases in these prescriptions propagate to UVLF, SMF, and Nion.
domain assumption BPASS binary stellar population SEDs correctly describe the ionizing photon production of high-z stellar populations.
Section 2.2 states ionizing photons are computed on the fly via BPASS; paper notes different SPS can strongly change ionizing budget (Liu et al. 2024).
domain assumption FoF halos with at least 20 dark matter particles (Mhalo > 2e8 Msun/h) provide a complete enough galaxy sample for z=6-12.
Section 2.1; resolution limit is cited as reason results at M1500 > -16 and Mstar < 1e7 might not be robust.
standard math The Henriques et al. (2013) random tree sampling reproduces the full simulation UVLF within 5% except in excluded bright bins.
Appendix A; the MCMC tree sampling relies on this approximation; bins failing the 5% test are removed.
ad hoc to paper A constant escape fraction fesc=20% applies to all galaxies and redshifts.
Introduced in Section 3.2 for the photon budget; not derived from the model or fitted to data; lower values fail the budget.

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Cite this review

Pith. "Pith review of Constraints on the galaxy formation models during epoch of reionization with high redshift observations." pith.science (2026). https://pith.science/paper/PJ2UYLGP

@misc{pith2026250419422,
  author       = {Pith},
  title        = {Pith review of: Constraints on the galaxy formation models during epoch of reionization with high redshift observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PJ2UYLGP}},
  note         = {Machine review of arXiv:2504.19422}
}

abstract

We use high resolution N-body dark matter simulations and L-Galaxies semi-analytical galaxy formation models to explore the high-$z$ galaxy properties and estimate the budget of ionizing photons. The parameters within L-Galaxies are obtained using a Markov Chain Monte Carlo (MCMC) method with high-$z$ galaxy observations from JWST and other telescopes. We consider two versions of L-Galaxies with and without dust correction on galaxy UV luminosities. With the best-fit parameters, both L-Galaxies 2015 and L-Galaxies 2020 reproduce well observations of UV luminosity functions, stellar mass functions, star formation rate densities and ionizing photon emission efficiency. With the assumption of escape fraction of $20\%$, all models produce more ionizing photons than the number of Hydrogen atoms in the Universe at $z>6$. The inclusion of dust correction within MCMC results in higher star formation efficiency, which predicts $\sim 50\%$ more ionizing photons, with better consistency between the predicted stellar mass functions and observations.

Figures

Figures reproduced from arXiv: 2504.19422 by the authors.

**Figure 1.** Halo mass functions (HMF) at z = 14 (red), 12 (magenta), 10 (cyan), 8 (blue) and 6 (yellow). Solid lines refer to results from the Jiutian-300 simulation, while dashed lines are those from Tinker et al. (2008), computed with the COLIBRI library. 2.0 × 108 M⊙/h. They are then used to construct the halo merger trees by following Springel et al. (2005). As a reference, in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Top panel: UV luminosity functions (UVLF, ϕ) at z = 6 to 12 from LG simulation Fiducial (black), LG20 bestfit (cyan), LG20 final (magenta), LG20 dust bestfit (blue), LG20 dust final (red), LG15 bestfit (yellow) and LG15 final (green). The dashed black line (named Fiducial dust) is not a new simulation, but rather Fiducial with a correction for dust. The observational data points are from Bouwens et al. (2021, up tri… view at source ↗

**Figure 3.** Top panel: 2-D distributions of stellar mass M⋆ versus halo mass Mhalo at z = 7 from LG simulation Fiducial, LG20 bestfit, LG20 final, LG20 dust bestfit, LG20 dust final, LG15 bestfit and LG15 final, from left to right and from top to bottom. The dashed black lines are the mean M⋆ of halos with the same Mhalo. The mean curves from all models are also shown in the bottom-right plot with the same legend of [PITH_FULL… view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Redshift evolution of the star formation rate density (SFRD) from LG simulation Fiducial (black), LG20 bestfit (cyan), LG20 final (magenta), LG20 dust bestfit (blue), LG20 dust final (red), LG15 bestfit (yellow) and LG15 final (green). The solid lines refer to resul…

**Figure 5.** Figure 5: Top panel: 2-D distributions of cold gas metallicity Zcoldgas versus stellar mass M⋆ of galaxies at z = 7 from LG simulation Fiducial, LG20 bestfit, LG20 final, LG20 dust bestfit, LG20 dust final, LG15 bestfit and LG15 final, from left to right and from top to bottom. …

**Figure 7.** Figure 7: Top panel: distribution of ionizing photon number nion as a function of M⋆ at z = 7 from LG simulation Fiducial (black), LG20 bestfit (cyan), LG20 final (magenta), LG20 dust bestfit (blue), LG20 dust final (red), LG15 bestfit (yellow) and LG15 final (green). The gray …

**Figure 8.** Figure 8: Top panel: 2-D distributions of ionizing photon emission efficiency ζion versus stellar mass M⋆ at z = 7 from LG simulation Fiducial, LG20 bestfit, LG20 final, LG20 dust bestfit, LG20 dust final, LG15 bestfit and LG15 final, from left to right and from top to bottom. T…

**Figure 9.** Figure 9: Redshift evolution of the average ζion from LG simulation Fiducial (black), LG20 bestfit (cyan), LG20 final (magenta), LG20 dust bestfit (blue), LG20 dust final (red), LG15 bestfit (yellow) and LG15 final (green). The solid lines refer to results when all galaxies are …

**Figure 10.** Figure 10: Top panel: 2-D distributions of ionizing photon production efficiency κion versus stellar mass M⋆ at z = 7 from LG simulation Fiducial, LG20 bestfit, LG20 final, LG20 dust bestfit, LG20 dust final, LG15 bestfit and LG15 final, from left to right and from top to bottom…

**Figure 11.** Figure 11: MCMC sample analysis for 6 free parameters in LG20 (green) without dust correction on UVLF, and LG20 dust (dark blue) with dust correction on UVLF. The first sub-plot in each column is the 1-D distribution of parameter samples, while the others are the 2-D distributio…

**Figure 12.** Figure 12: MCMC sample analysis for 6 free parameters in LG15 without dust correction on UVLF. The first sub-plot in each volumn is the 1-D distribution of parameter samples, while the others are the 2-D distributions. The two contours denote the 1-σ (68%) and 3-σ (95%) range of…

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts ...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix "arXiv" = new.block " " eprint * " " * new.block " " eprint * " " * if if if FUNCTION format.doi doi empty "" " " doi * " " * if FUNCTION format.pid doi empty eprint empty ur...

[3] [3]

ށH( T &[A ) Vs D| & :dd6 5 Rt U V 2 h*Xd

thebibliography [1] 20pt to REFERENCES 6pt =0pt -12pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command E...

2021

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