Synergising semi-analytical models and hydrodynamical simulations to interpret JWST data from the first billion years

Joakim Rosdahl; Martin G. Haehnelt; Pratika Dayal; Romain Teyssier; Taysun Kimm; Valentin Mauerhofer

REVIEW 3 major objections 4 minor 1 cited by

Synergising semi-analytical models and hydrodynamical simulations to interpret JWST data from the first billion years

T0 review · 3 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Two physical mechanisms explain JWST's bright galaxies at $z \geq 11$.

desk verdict Solid, careful model comparison; the eIMF path is a genuine prediction, the eSFE path is tuned, and the stochastic sampling needs a joint-distribution check. read the letter →

arxiv 2502.02647 v2 pith:DXQPKHO5 submitted 2025-02-04 astro-ph.GA

Valentin Mauerhofer , Pratika Dayal , Martin G. Haehnelt , Taysun Kimm , Joakim Rosdahl , Romain Teyssier This is my paper · ORCID

classification astro-ph.GA

keywords high-redshiftgalaxiesreionisationUVluminosityfunctionstellarinitialmassstarformationefficiencyJWSTsemi-analyticgalaxyradiation-hydrodynamicssimulation

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

The paper argues that the bright galaxies JWST sees in excess at $z \geq 11$ can be explained by either of two physical mechanisms: a stellar initial mass function that becomes top-heavy in low-metallicity, high-redshift systems, or a star formation efficiency that rises with redshift. Both prescriptions reproduce the observed ultraviolet luminosity function when inserted into a semi-analytic model whose star-forming gas properties are sampled from a high-resolution radiation-hydrodynamics simulation, so the comparison is anchored in simulated interstellar-medium physics rather than free fitting alone. The paper also claims that star formation in galaxies below about $10^9\,M_\odot$ of stars supplies roughly 85% of the ionising photons down to the midpoint of reionisation at $z \sim 7$, identifying low-mass galaxies as the key reionisation sources. If correct, the JWST bright-end excess is not a crisis for galaxy formation, and the reionising population is pinned to a specific, faint class of galaxies.

What carries the argument

The load-bearing machinery is the transfer of interstellar-medium statistics from the high-resolution SPHINX20 radiation-hydrodynamics simulation into the DELPHI semi-analytic model: probability distributions of cold gas fraction (gas below 1000 K) and star formation efficiency (stars younger than 30 Myr divided by cold gas mass) are sampled by Monte Carlo for each halo, injecting stochastic, bursty star formation. Two luminosity-boosting prescriptions are layered on top: the eIMF model makes the stellar mass function increasingly top-heavy at low metallicity and high redshift, raising the UV luminosity and ionising-photon output per unit stellar mass; the eSFE model raises cold gas fractions and star formation efficiencies in massive halos above $z\sim7$, saturating at fixed values at $z\ge14$. These ingredients turn the semi-analytic model into an ensemble whose bright end can match JWST while its faint end is set by simulated interstellar-medium physics.

What would settle it

A JWST/NIRSpec measurement of the ionising photon production efficiency $\xi_{\rm ion}$ in bright galaxies at $z \sim 12-17$ would settle the eIMF model, which predicts $\log_{10}\xi_{\rm ion}\simeq25.55\,[{\rm Hz\,erg^{-1}}]$ against roughly $25.2$ for the other models; likewise, a stellar mass function measurement at $M_\ast\sim10^9\,M_\odot$ and $z\sim12$ would test the eSFE model, which predicts a number density about 100 times that of the fiducial model.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the overabundance of bright galaxies at $z \geq 11$ is reproduced by two distinct and physically motivated prescriptions, not by exotic sources: the eIMF model, in which the stellar initial mass function becomes increasingly top-heavy at low metallicity and high redshift, and the eSFE model, in which the cold gas fraction and star formation efficiency of massive halos increase with redshift above $z \sim 7$. Both match the observed ultraviolet luminosity function from $z \sim 5$ out to $z \sim 15-20$ once dust attenuation is included at low redshift, with dust negligible above $z \sim 12$. The paper further establishes that, in every model consistent with reionisation constraints, galaxies with stellar masses below roughly $10^9\,M_\odot$ provide about 85% of the escaping ionising photons down to the reionisation midpoint at $z \sim 7$. The models also place the mass-metallicity relation in place by $z\sim17$ and bracket current measurements of UV spectral slopes, Balmer break strengths, and ionising photon production efficiencies, with the eIMF model predicting a factor 2--2.5 higher $\xi_{\rm ion}$ at $z \geq 12$.

Load-bearing premise

The load-bearing premise is that the probability distributions of cold gas fraction and star formation efficiency measured in the simulated low-mass halos carry over unchanged to the much more massive halos that the semi-analytic model produces, and that in the eSFE model these quantities rise to fixed high values at $z\ge14$; if real massive halos do not follow that extrapolation, the predicted abundance of bright galaxies at $z>10$ changes.

Editorial extensions

If this is right

If the central claim is right, the JWST bright-end excess at $z \geq 11$ is reproduced within standard structure formation, with no need for additional sources such as faint active galactic nuclei to explain the ultraviolet luminosity function.
The eIMF and eSFE models predict stellar mass functions that differ by more than 2.5 orders of magnitude at $M_\ast \sim 10^9\,M_\odot$ and $z \sim 12$, so jointly measured luminosity and stellar mass functions will separate the two mechanisms.
Because sub-$10^9\,M_\odot$ galaxies dominate the reionisation budget, deeper surveys should find that the sources completing reionisation are mostly fainter than current JWST detection limits.
The eIMF model predicts $\xi_{\rm ion}\sim10^{25.55}\,{\rm Hz\,erg^{-1}}$ for faint galaxies at $z \gtrsim 12$, a factor 2--2.5 above the other models, making ionising photon production efficiency a direct observational test of a top-heavy IMF.
Dust attenuation shapes the bright end of the UV luminosity function only at $z \lesssim 11$; at higher redshifts the intrinsic and observed luminosity functions coincide, so dust cannot mask a model failure there.

Reading between the lines

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

We infer that the current JWST bright-end data, taken alone, cannot distinguish between the two mechanisms; the degeneracy has to be broken by stellar mass functions or spectral indicators, a point the paper itself makes.
If low-mass galaxies supply most of the ionising photons, then bright-galaxy surveys may be probing the wrong population for understanding reionisation; the relevant sources sit near or below current detection limits.
The eSFE model's assumed saturation values at $z\ge14$ ($f_\ast=0.8$, $f_{\rm cold}=0.5$) could be checked directly with larger-volume radiation-hydrodynamics simulations; if those simulations find lower efficiencies in massive halos, the eSFE bright end would weaken.
A natural testable extension is to combine the eIMF prediction of high $\xi_{\rm ion}$ with 21-cm observations of the reionisation midpoint: the model's larger photon output requires a lower escape fraction to match the timing, and future neutral-hydrogen measurements could verify that combination.

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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

Bottom line: this paper deserves a serious referee. The eIMF half of the argument is a real prediction; the eSFE half is built to reproduce the excess it then claims to explain. And the stochastic-sampling ambiguity in Sect. 2.2 could be load-bearing, so it should be fixed before the bright-end match is treated as physical.

What's genuinely new: feeding SPHINX20 cold-gas fractions and SFE distributions into DELPHI as stochastic draws, the eSFE variant itself, and the unusually broad comparison against UV LFs, stellar mass functions, dust masses, beta slopes, Balmer breaks, xi_ion, and reionisation history. The multi-observable sweep is systematic and the paper is clearly written. The eIMF model's form is imported from earlier independent work, but using it here to match the JWST bright end at z>11 is a legitimate, non-tuned success.

Now the soft spots, in proportion. First, eSFE: the high-z boost (f*=0.8, fcold=0.5 at z>=14, with a weighted average between z=7 and 14) is introduced to lift the bright end to the observed level. The paper does call it an 'extreme model', but the abstract still presents both eIMF and eSFE as successful explanations; that circularity should be made much more explicit. Second, the reionisation analysis fits a constant fesc per model to match reionisation history. The claim that low-mass galaxies (M*<1e9 Msun) provide about 85% of ionising photons is robust to that fit because a constant fesc cancels in the cumulative distribution, but the fitted fesc values themselves are not constraints. Third, the stress-test concern is real: the methods text says 'standard Monte Carlo sampling' of 'the sphinx probability distribution', but the figures show marginal PDFs and the text never states that fcold and f_sphinx are drawn jointly. If they are sampled independently, the product fcold*f_sphinx is uncalibrated to SPHINX20's joint behaviour, and the artificial starbursts could sit exactly on the z>11 bright end. That would weaken both the fiducial model's underprediction and the eIMF/eSFE 'success'. The eIMF model is less exposed because its luminosity boost comes from the IMF rather than the sampling, but the bright-end LF in all models depends on this sampling.

Who this is for: anyone working on JWST UV LFs or reionisation sources. The eIMF model produces concrete, testable signatures (xi_ion, Balmer breaks, metal enrichment) that make the paper worth citing. Treat the eSFE model as an upper envelope, not a physical proposal.

Recommendation: send to peer review. Ask the authors to (a) validate that the sampled fcold*f_sphinx product reproduces SPHINX20's joint distribution, (b) separate the tuned eSFE from the predictive eIMF in the abstract and conclusions, and (c) downplay the fitted fesc as an inference.

Referee Report

3 major / 4 minor

Summary. The paper couples the DELPHI semi-analytic galaxy formation model to ISM properties measured in the SPHINX20 radiation-hydrodynamics simulation. Cold gas fractions fcold and star formation efficiencies f_sphinx are Monte Carlo sampled from SPHINX20 PDFs, introducing stochastic star formation into DELPHI. Three models are compared: a fiducial model using the SPHINX20-derived distributions, an eIMF model with a metallicity- and redshift-dependent top-heavy IMF, and an eSFE model with ad hoc increasing star formation efficiency and cold gas fraction for massive halos at z>7. The fiducial model underpredicts the bright end of the observed UV LF at z>=11, while the eIMF and eSFE models reproduce it. The paper additionally compares stellar mass functions, dust masses, mass-metallicity relations, UV slopes, Balmer breaks, and xi_ion against JWST and ALMA data, and uses the models to infer that galaxies with M*<10^9 Msun provide about 85% of the escaping ionizing photons down to z~7.

Significance. If the results hold, the paper provides a useful demonstration that a semi-analytic model can use resolved hydrodynamical simulation results to generate stochastic star formation and make multi-observable predictions for JWST. The eIMF model's agreement with the z>=11 bright-end UV LF is a genuine prediction in the sense that the IMF prescription is imported from prior cluster-formation simulations and not tuned to the JWST LF, and the paper gives a broad set of falsifiable predictions (xi_ion, beta slopes, Balmer breaks, SMF separation, luminosity density evolution) that can discriminate between the models. The reionization source claim is also presented with two escape-fraction prescriptions, which strengthens its qualitative robustness. However, the central claim that both the eIMF and eSFE models explain the bright JWST excess is currently conditional on two load-bearing issues: the stochastic sampling of fcold and f_sphinx is not shown to preserve the joint SPHINX20 distribution, and the eSFE boost is imposed by hand rather than derived or independently calibrated.

major comments (3)

[Sects. 2.2-2.3, Eq. (2)] The stochastic sampling of fcold and f_sphinx is underspecified in a way that directly affects the central claim. Equation (1) defines f_sphinx as M_*[<30 Myr]/(M_g fcold), so the physical quantity that sets the new stellar mass in Eq. (2) is the product fcold*f_sphinx = M_*[<30 Myr]/M_g. The manuscript displays only marginal PDFs of fcold and f_sphinx (Figs. 2 and 3) and states that DELPHI halos are assigned values by 'standard Monte Carlo sampling' of the SPHINX20 distributions. If fcold and f_sphinx are drawn independently from their marginals, the product distribution will not reproduce the joint distribution realized in SPHINX20, and rare combinations of high cold gas fraction and high recent SFE could be generated artificially. Such artificial bursts are exactly the rare objects that populate the bright end of the z>=11 UV LF and contribute to the reionizing photon budget. The authors should state whether the draws are joint and should validate that the sampled product distribution matches the SPHINX20 distribution of M_*[<30 Myr]/M_g. If the draws are in fact independent, the analysis must be rerun by sampling from the joint fcold-f_sphinx distribution before the fiducial underprediction and the eIMF/eSFE 'success' can be interpreted.
[Sect. 2.6.2 and Table 1] The eSFE model's high-redshift boost is imposed rather than derived. The model sets f*(Mh,z)=0.8 and fcold=0.5 for massive halos at z>=14, with a linear interpolation between the SPHINX20 values at z=7 and these imposed values at z=14. No independent physical motivation or calibration is provided for these specific numbers beyond the need to increase the bright-end UV LF. Consequently, the eSFE agreement with the z>=11 JWST data in Fig. 7 is partly a consequence of construction, and it cannot be presented on the same footing as the eIMF model in the abstract's claim that both models 'can explain' the abundance of bright galaxies. The eSFE model should be explicitly reframed as a deliberately extreme scenario, or its parameter values should be calibrated against independent high-resolution simulations or observations, before it is used to support the paper's main conclusion.
[Sect. 2.2] The extrapolation of SPHINX20 PDFs to the most massive DELPHI halos is a key uncertainty for the bright end. As the text acknowledges, at any redshift DELPHI contains halos up to two orders of magnitude more massive than the most massive SPHINX20 halos, and those massive halos are assigned fcold and f_sphinx from smaller systems. The argument that this induces limited error relies on visual convergence of the PDFs for the few most massive SPHINX20 bins. Because the z>=11 bright-end LF is one of the two central claims, the paper should quantify the sensitivity of the bright-end results to this mass matching, for example by testing an alternative extrapolation or by checking against a larger-volume simulation with more massive halos.

minor comments (4)

[Sect. 4.1, Eq. (10)] Equation (10) contains an unresolved citation placeholder '(?)' that should be replaced with the intended reference.
[Sect. 1] The citation list in the discussion of accreting black holes includes '?;' between references; this placeholder needs to be fixed.
[Sect. 2.2 and Figs. 2-3] The text says the PDFs are built in stellar mass bins, while Figs. 2 and 3 and the assignment procedure at the end of the section use halo mass bins; this inconsistency should be resolved.
[Fig. 17] The right panel does not show the uncertainty ranges from the five random-seed runs; adding them or stating that they are omitted for clarity would make the presentation consistent with the left panel.

Circularity Check

1 steps flagged · score 6.0 of 10

The eSFE branch reproduces the z≥11 bright-end excess by construction, while the eIMF branch provides an independent check.

fitted input called prediction [Sec. 2.6.2 (eSFE definition) and Sec. 3.1 (UV LF comparison)]
"The second model we explore is termed the evolving star formation efficiency model ('SFE'). ... For more massive halos, at z ≥ 14, we have f∗(Mh, z) = 0.8, and in between those redshifts we do a weighted average: f∗(Mh, z) = (14− z)/7· f sphinx∗ +(z−7)/7·0.8. The same holds for fcold(Mh, z), but with a value of 0.5 at z≥ 14."

The eSFE model is introduced (Sect. 2.6) as a way to 'boost galaxy luminosities at z >~ 11', and its only high-redshift ingredients are the imposed values f*=0.8 and fcold=0.5 for massive halos at z≥14. These are precisely the halos that dominate the bright end of the z≥11 UV LF. The later statement (Sect. 3.1) that this model 'successfully reproduces JWST observations of the UV LF' is therefore not an independent test: raising the SFE of the bright-host halos raises their UV luminosity by construction. No external calibration or first-principles constraint is given for the 0.8/0.5 values, so the eSFE half of the central claim reduces to the chosen input.

full rationale

The paper's main circularity is confined to the eSFE branch. The eIMF branch is imported from external star-cluster simulations (Chon et al. 2022) and is not tuned to the JWST LF, so its z≥11 agreement is an independent test. The fiducial model is calibrated to z~5−9 UV LF and SMF via fw and rgas, and its z>10 underprediction is an honest extrapolation, not a fit. The constant fesc is fit to reionisation history, but because it is mass-independent it does not force the conclusion that M*<10^9 Msun galaxies provide ~85% of ionising photons; that decomposition is a model output. The stochastic sampling of fcold and f_sphinx from marginal distributions could be a calibration weakness (the joint product distribution is not validated), but this is a correctness/robustness concern rather than a circular reduction. Overall, one of the two explanatory models (eSFE) has its success built in, so the combined claim 'both models can explain the bright-end excess' is partially circular.

Assumptions & free parameters 4 free parameters · 8 assumptions · 0 invented entities

The central predictions rest on a chain of imported physical assumptions, a handful of fitted numbers, and two deliberately ad hoc model ingredients. The most important imported inputs are the SPHINX20 ISM distributions and the eIMF prescription from Chon et al. (2022). The fitted numbers are the SN feedback coupling (fw=0.04), the dust/gas radius normalisation, and the per-model escape fraction used for reionisation. The eSFE high-z boost is an ad hoc construction whose role should be discounted when interpreting the bright-end match.

free parameters (4)

f_w (SNII energy coupling fraction) = 0.04 (fiducial, eIMF, eSFE); 0.06 in delphi23
Chosen to match the observed redshift evolution of the UV LF at z<~10 (Sect. 2.3, Table 1).
r_gas normalisation (gas+dust distribution radius) = r_gas = 4.5 * lambda * r_vir * (1+z)/6 with lambda=0.04
Chosen to match the UV LF and ALMA dust observables at z~5-7 (Sect. 2.5, Table 1).
Constant escape fraction fesc = 15.2% (fiducial), 5.7% (eIMF), 15.4% (eSFE), 13.1% (delphi23)
Fit per model to reproduce reionisation constraints on the neutral hydrogen fraction (Sect. 4.1, Table 1).
eSFE high-z SFE boost = f*=0.8 and fcold=0.5 for massive halos at z>=14; linear interpolation for 7<z<14
Ad hoc values chosen by hand so that the eSFE model matches the bright-end UV LF at z>11 (Sect. 2.6.2).

assumptions (8)

standard math Sheth-Tormen halo mass function and Parkinson binary merger trees describe the dark matter halo population.
Used to build DELPHI halo assemblies from z=4.5 back to z=40.8 (Sect. 2.1).
domain assumption SPHINX20's sub-grid star formation and feedback recipes, including a boosted SN rate, produce realistic high-z galaxy populations.
The cold gas fractions and star formation efficiencies from SPHINX20 are the physical input to DELPHI (Sect. 2.2).
domain assumption The 1000 K temperature threshold defines the cold gas reservoir relevant for star formation and dust growth.
Cold gas is defined as T<1000 K; this choice sets fcold and affects dust grain growth and destruction (Sect. 2.2).
domain assumption Metals, dust and gas are perfectly mixed, and the dust geometry is described by a simple radius r_gas with a fixed spin parameter.
This determines dust attenuation, UV slopes and Balmer breaks; the authors acknowledge the simplification in Sect. 5.
domain assumption The eIMF prescription from Chon et al. (2022), where fmassive depends on metallicity and redshift, describes the stellar IMF in high-z galaxies.
Equations (7) and (8) set the top-heavy IMF used in the eIMF model; imported from star cluster simulations.
domain assumption Instantaneous recycling approximation for metal and dust production.
Invoked in Sect. 2.4 and later identified as a likely cause of missing low-mass, high-metallicity systems (Sect. 5).
ad hoc to paper The eSFE boost and its linear redshift interpolation are a valid representation of star formation in massive halos at z>7.
f*=0.8 and fcold=0.5 at z>=14 are chosen by hand, with no external calibration; this is the main ad hoc ingredient (Sect. 2.6.2).
ad hoc to paper A single constant escape fraction per model captures the ionising photon escape physics.
The global fesc is fit to reionisation data; the alternative Chisholm et al. (2022) beta-dependent prescription is tested and rejected (Sect. 4).

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Pith. "Pith review of Synergising semi-analytical models and hydrodynamical simulations to interpret JWST data from the first billion years." pith.science (2026). https://pith.science/paper/DXQPKHO5

@misc{pith2026250202647,
  author       = {Pith},
  title        = {Pith review of: Synergising semi-analytical models and hydrodynamical simulations to interpret JWST data from the first billion years},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DXQPKHO5}},
  note         = {Machine review of arXiv:2502.02647}
}

abstract

The field of high redshift galaxy formation has been revolutionised by JWST, which is yielding unprecedented insights on galaxy assembly at early times. Our key aim is to study the physical mechanisms that can explain the unexpected abundance of bright galaxies at $z \geq 11$, as well as their metal enrichment and spectral properties. We also use recent data to determine the key sources of reionisation. To do so, we implement cold gas fractions and star formation efficiencies derived from the SPHINX20 high-resolution radiation-hydrodynamics simulation into DELPHI, a semi-analytic model that tracks the assembly of dark matter halos and their baryonic components from $z \sim 4.5-40$. In addition, we explore two different methodologies to boost galaxy luminosities at $z \geq 11$: a stellar initial mass function (IMF) that becomes increasingly top-heavy with decreasing metallicity and increasing redshift (eIMF model), and star formation efficiencies that increase with increasing redshift (eSFE model). Our key findings are: (i) both the eIMF and eSFE models can explain the abundance of bright galaxies at $z \geq 11$; (ii) dust attenuation plays an important role for the bright-end of the UV LF at $z \leq 11$; (iii) the mass-metallicity relation is in place as early as $z \sim 17$ in all models although its slope is model-dependent; (iv) within the spread of both models and observations, all of our models are in good agreement with current estimates of $\beta$ slopes at $z \sim 5-17$ and Balmer break strengths at $z \sim 6-10$; (v) in the eIMF model, galaxies at $z\geq12$ or with $\rm{M_{UV}}\geq-18$ show values of $\xi_{\rm{ion}} \sim 10^{25.55}~{\rm [Hz~erg^{-1}]}$, twice larger than in other models; (vi) star formation in galaxies below $10^{9}\rm{M_{\odot}}$ is the key driver of reionisation, providing the bulk ($\sim 85\%$) of ionising photons down to its midpoint at $z \sim 7$.

Figures

Figures reproduced from arXiv: 2502.02647 by the authors.

**Figure 1.** Halo mass functions obtained from the sphinx20 and delphi models, shown using blue and green histograms, respectively, as marked. The left and right panels show results at z ∼ 5 and 9, respectively. such that Mi g = (Ωb/Ωm)Mh. If any halo has progenitors, its initial gas mass is the sum of the final gas mass brought in by merging progenitors - after star formation and the resulting supernova (SN) feedback (Sect. 2… view at source ↗

**Figure 2.** Fraction of halos with a cold gas fraction (fcold) below the value shown on the horizontal axis from the sphinx20 simulations, for the mass bins marked, at z = 5 (left panel) and z = 9 (right panel). The cold gas fraction is defined as the fraction of gas mass that is below 1000 K, within the virial radius of the halo. 0.0 0.1 0.2 0.3 0.4 0.5 f sphinx * 0.0 0.2 0.4 0.6 0.8 1.0 f r a c tio n o f h alo s ( f sp hin x … view at source ↗

**Figure 3.** Fraction of halos with a star formation efficiency value (f sphinx ∗ ) below the value shown on the horizontal axis from the sphinx20 simulations, for the mass bins marked, at z = 5 (left panel) and z = 9 (right panel). The star formation efficiency is defined as the ratio between the mass of stars younger than 30 Myr and the cold gas mass; if a halo has no cold gas mass, we define its star formation efficiency to b… view at source ↗

Figures from the paper (13 more)

**Figure 5.** Figure 5: Evolution of the stellar metal yields (solid lines) and total yields (metals and gas return fraction - dashed lines) per unit stellar mass as a function of metallicity, for the redshifts marked, for the eIMF model. The dashed purple line shows the metallicity-dependent…

**Figure 6.** Figure 6: As a function of metallicity, we show the ratio between the ionising photon production rates (intrinsic UV luminosities) in the eIMF and fiducial model using solid (dashed) lines at the marked redshifts. (2020), the results of which are shown in [PITH_FULL_IMAGE:figu…

**Figure 7.** Figure 7: Redshift evolution of the UV LF between z ∼ 5 − 20, as marked. In each panel, we show a comparison of the fiducial model, and the eIMF and eSFE models against the results from delphi23 (Mauerhofer & Dayal 2023) for both the intrinsic (dashed lines) and dust attenuated …

**Figure 8.** Figure 8: Redshift evolution of the UV luminosity density at z ∼ 5 − 21. Solid lines show the mean of five runs for each model, using dust attenuated values of ρUV integrating down to observed magnitude limits of MUV < ∼ −17. Shaded areas show the maximum and minimum values ass…

**Figure 9.** Figure 9: Redshift evolution of the SMF at z ∼ 5 − 20, for the different model explored in this work. Solid lines show the mean results from five runs of each model with shaded areas showing the associated maximum and minimum values. The bottom right panel shows the SMF integrat…

**Figure 10.** Figure 10: Evolution of the dust mass as a function of stellar mass at z ∼ 5 − 17 for the different models studied in this work, as marked. Lines represent the mean of the five runs with different seeds for each model; shaded areas represent the range between the minima and maxi…

**Figure 11.** Figure 11: Gas-phase metallicity as a function of stellar mass at z ∼ 5 − 17, as marked. Lines represent the mean of the five runs with different seeds for each model; shaded areas represent the range between the minima and maxima shown by the 16th and 84th percentiles, respecti…

**Figure 12.** Figure 12: Ultraviolet spectral slopes (β), using the Calzetti dust extinction law, as a function of the observed UV magnitude at z ∼ 5−17, as marked. Lines represent the mean of the five runs with different seeds for each model; shaded areas represent the range between the mini…

**Figure 13.** Figure 13: Balmer break strength as a function of the observed UV magnitude at z ∼ 6 − 17, as marked. Lines represent the mean of the five runs with different seeds for each model; shaded areas represent the range between the minima and maxima shown by the 16th and 84th percenti…

**Figure 14.** Figure 14: Ionising photon production efficiency (ξion) as a function of the observed UV magnitude. Lines represent the mean of the five runs with different seeds for each model; shaded areas represent the range between the minima and maxima shown by the 16th and 84th percentile…

**Figure 15.** Figure 15: Evolution of the ionising photon rate density as a function of redshift. In both panels, for reference, the solid lines represent the intrinsic ionising photon density for the different models studied, as marked. Shaded regions highlight the spread from the minimum to…

**Figure 16.** Figure 16: Cumulative emissivity of ’escaping’ ionising photons as a function of stellar mass for the new models explored in this work (fiducial, eIMF and eSFE), as marked. Solid and dashed lines show results at z ∼ 7 and 10, respectively. For the sake of clarity, we limit resu…

**Figure 17.** Figure 17: Volume filling fraction of neutral hydrogen as a function of redshift. In the left panel, we carry out calculations assuming a constant global escape fraction (fesc), as marked, given by the best fit to a selection of observational data (Jung et al. 2020; Gaikwad et a…

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