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arxiv: 2605.26209 · v1 · pith:HIZHYPMRnew · submitted 2026-05-25 · 🌌 astro-ph.GA

How galaxies acquire their stellar mass at high redshift: High star formation efficiencies and the relative roles of dust and initial mass function

Hao Fu , Francesco Shankar , Fabio Fontanot , Andrea Lapi , Feng Yuan , Mohammadreza Ayromlou , Daniel Roberts , Lumen Boco
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Nicola Menci Emiliano Merlin Laura Pentericci Mengyuan Xiao
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Pith reviewed 2026-06-29 21:18 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords high-redshift galaxiesstar formation efficiencyinitial mass functiondust attenuationUV luminosity functionstellar mass functionsemi-empirical modeling
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The pith

Massive high-redshift galaxies formed stars at efficiencies of 0.8-0.9 before dropping to 0.2-0.3, requiring variable IMFs when dust is accounted for

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

A semi-empirical model assigns star formation rates to dark matter halos by matching observed UV luminosity functions to halo accretion rates at each redshift. Stellar masses are built by integrating these rates along halo progenitor lines, making the star formation efficiency a direct output. The model finds that massive galaxies at z around 9-10 experienced bursty star formation with efficiencies peaking at 0.8-0.9, then settling to lower values. Dust increases the predicted star formation rates at z less than 8, while top-heavy initial mass functions reduce the efficiencies by a factor of 2-3 to prevent values above 1. This setup reproduces the stellar mass function, clustering, and main sequence without modeling feedback or cooling.

Core claim

Massive galaxies grew their stellar mass with a bursty star formation at z∼9-10, with the SFE reaching high peaks of 0.8-0.9 at z>9 and lowering to standard values of 0.2-0.3 below z≲9. The presence of dust could enhance the predicted SFRs at z≲8, and switching to top-heavy IMFs reduces the SFEs by a factor of 2-3, highlighting the need for a variable IMF to avoid unphysical SFEs, especially in the presence of dust.

What carries the argument

The SFR-halo accretion rate relation obtained via abundance matching of observed UV luminosity functions to dark matter halo accretion rate distributions.

Load-bearing premise

The abundance matching between UV luminosity functions and halo accretion rates correctly assigns the star formation rates to halos without needing to model cooling, feedback, or stochastic processes.

What would settle it

Measurements of the initial mass function or direct star formation efficiencies in z>9 galaxies showing no need for top-heavy IMFs or efficiencies remaining below 0.5 would falsify the requirement for variable IMFs and high efficiencies.

Figures

Figures reproduced from arXiv: 2605.26209 by Andrea Lapi, Daniel Roberts, Emiliano Merlin, Fabio Fontanot, Feng Yuan, Francesco Shankar, Hao Fu, Laura Pentericci, Lumen Boco, Mengyuan Xiao, Mohammadreza Ayromlou, Nicola Menci.

Figure 1
Figure 1. Figure 1: Distribution of the TNG subhaloes on the star formation rate-halo accretion rate plane (blue dots), and median star formation rate-halo accretion rate relations from the TNG (blue lines) and computed using the TNG’s inputs via the abundance matching described in Section 2.2 (orange dashed lines) at redshifts z = 6 − 11. The subplots in each panel show the distribution normalised to unity of the star format… view at source ↗
Figure 2
Figure 2. Figure 2: Star formation rate function at from redshifts z = 6 to 11. The data points with error bars show the data from HST (blue squares, pink pluses and grey pentagons; Bouwens et al. 2015, 2021, 2022), UltraVISTA/COSMOS and UKIDSS (orange rhombuses; Bowler et al. 2015), WUDS (green dots; Pelló et al. 2018), PEARLS+JWST (yellow stars; Adams et al. 2024), JWST-PRIMER (red triangles; Donnan et al. 2024), JWST ERO+E… view at source ↗
Figure 4
Figure 4. Figure 4: Evolution of the cosmic stellar mass density. The blue solid line shows the cosmic star formation history computed by integrating the cosmic star formation rate density retrieved from our star formation rate functions shown in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: Upper panel: Star formation rate-halo accretion rate relation from redshift z = 6 to 11, from the abundance matching. The cyan coloured area shows the redshift evolution region of the relation from z = 0 to 6, as presented in Fu et al. (2025a) and Fu et al. (2025b). Cen￾tral panel: Halo accretion rate function in the same redshift bins. Lower panel: Star formation rate from the TNG simulation compared to t… view at source ↗
Figure 5
Figure 5. Figure 5: Galaxy stellar mass function at redshifts z = 6, 7 and 8. The blue solid lines show the prediction from decode’s reference model and the blue dashed lines show the scenario with dust correction (as we will discuss in Section 4.7). Our results are compared with the observational data from HST/CANDELS (green dots with error bars; Stefanon et al. 2021), JWST NIRCam (blue squares with error bars; Weibel et al.… view at source ↗
Figure 6
Figure 6. Figure 6: Stellar mass-halo mass relation at redshifts z = 6, 7 and 8. The upper and lower panels show the stellar mass and stellar-to-halo mass ratio as a function of halo mass, respectively. The right labels in the lower panels represent the star formation efficiency, defined as ϵ⋆ = M⋆/(Mh fb). Our results (blue solid lines) are compared to the observational measurements from Stefanon et al. (2021, green dots wit… view at source ↗
Figure 7
Figure 7. Figure 7: Galaxy bias as a function of redshift for UV magnitude MUV ≲ −19 (blue solid line) and MUV ≲ −17 (orange dashed line). We com￾pare our predictions to the observed galaxy bias from Subaru/Hyper Suprime-Cam (cyan triangles with error bars; Harikane et al. 2016), JWST JADES (blue dots with error bars; Dalmasso et al. 2024a), HST CANDELS (red squares with error bars; Dalmasso et al. 2024b) and JWST NIRCam/gris… view at source ↗
Figure 8
Figure 8. Figure 8: Upper panel: Stellar mass growth of galaxies in different mass bins as a function of redshift. The red dots with error bars show three massive galaxies in the JWST sample from Xiao et al. (2024). The mas￾sive candidates detected by de Graaff et al. (2025) and Wang et al. (2024b) are also plotted as a reference (purple square and green tri￾angles with error bars). The red lines and shaded areas show the mea… view at source ↗
Figure 9
Figure 9. Figure 9: Average star formation rate evolution for galaxies selected in our catalogue with stellar mass M⋆ ∼ 1011 M⊙ at redshift z ≃ 5 (red dashed line). We compare our results to the star formation histories inferred for the JWST ZF-UDS-7329 galaxy from Prospector and FAST++ (M⋆ = 1011 M⋆ at z = 3.2; Glazebrook et al. 2024; blue and orange lines with shaded areas), JWST RUBIES-EGS-49140 (M⋆ = 1.5 × 1011 M⋆ at z = … view at source ↗
Figure 10
Figure 10. Figure 10: Star formation rate-stellar mass relation at redshifts z = 6, 7 and 8. The predictions from decode (blue solid lines and shaded areas) are compared to the observational determinations Spitzer+Herschel (grey solid lines; Popesso et al. 2023), JWST JADES/CEERS (red dashed and green dash-dotted lines; Clarke et al. 2024) and COSMOS/SMUVS, JWST JADES/GOODS-S and MIDIS/XDF (yellow dotted lines; Ri￾naldi et al.… view at source ↗
Figure 12
Figure 12. Figure 12: Upper panel: Stellar mass growth of galaxies in the same largest stellar mass bins as in [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 11
Figure 11. Figure 11: Initial mass function from Salpeter (1955, black dotted line), Kroupa (2001, black dashed line) and Chabrier (2003, black dash-dotted line), compared to the bottom-light (gold solid line) and top-heavy (red solid line) toy model IMFs parametrised in terms of Larson (1998) formula. The green shaded area represents the range of variation of the integrated galaxy-wide initial mass function for star formation… view at source ↗
read the original abstract

JWST has measured an unprecedented abundance of galaxies above $z\gtrsim 4-5$, whose formation and evolution are still difficult to reconcile within traditional galaxy evolution models in a $\Lambda$CDM framework. Here, we present a study on the star formation histories of these high-redshift galaxies between $z\simeq5-12$ via a data-driven semi-empirical model that uses the observed UV LFs as input to retrieve SFRs, naturally bypassing any uncertain modelling of cooling, feedback and/or stochastic processes. Galaxy stellar masses are progressively built in time by integrating their SFRs assigned along their progenitor haloes via the SFR-halo accretion rate relation, derived from abundance matching between the input observed UV LFs with the dark matter halo accretion rate distributions at each redshift. This makes the SFEs a full prediction of the model rather than a tuned input, serving as a natural baseline to test burstiness, dust attenuation, or IMF variations. Our approach naturally reproduces the total stellar mass function, the large-scale clustering, and the star-forming main sequence. We find that massive galaxies grew their stellar mass with a bursty star formation at $z\sim9-10$, broadly in agreement with the star formation histories inferred from spectral energy distribution fitting, with the SFE reaching high peaks of $0.8-0.9$ at $z>9$ and lowering to standard values of $0.2-0.3$ below $z\lesssim9$. We find that the presence of dust could enhance the predicted SFRs at $z\lesssim8$, better reproducing the observed SFRs of massive dusty galaxies, and increase the SFEs to values close to or even above unity at $z \gtrsim 8$. Finally, switching to top-heavy IMFs reduces the SFEs by a factor of $2-3$, highlighting the need for a variable IMF as an inevitable ingredient in the evolution of galaxies at high redshifts to avoid unphysical SFEs, especially in the presence of dust.

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

2 major / 1 minor

Summary. The manuscript presents a data-driven semi-empirical model that derives SFRs for high-redshift galaxies by abundance matching observed UV luminosity functions to dark matter halo accretion rate distributions at each redshift, then integrates these SFRs along progenitor halo tracks to construct stellar mass assembly histories between z~5-12. The model claims this approach yields SFEs as predictions rather than inputs, reproduces the stellar mass function, large-scale clustering, and star-forming main sequence, and finds bursty star formation in massive galaxies at z~9-10 with SFEs peaking at 0.8-0.9 at z>9 before declining to 0.2-0.3 at z≲9; it further argues that dust attenuation and top-heavy IMFs are required to avoid unphysical SFEs near or above unity.

Significance. If the abundance-matching step is robust and the monotonic mapping assumption holds, the work supplies a useful empirical baseline for high-z galaxy growth that highlights the potential necessity of variable IMFs and bursty SF at early times, while matching several key observables without explicit tuning of feedback or cooling. This could inform interpretations of JWST data on early stellar mass buildup.

major comments (2)
  1. [Abstract] Abstract and description of the SFR-halo accretion rate relation: the relation is obtained by abundance matching the input observed UV LFs to halo accretion distributions, after which the same UV LFs are used to assign SFRs and integrate stellar masses. This makes the reported SFE peaks (0.8-0.9 at z>9) effectively the conversion factors needed to match the input data by construction, undermining the claim that SFEs are independent predictions of the model.
  2. [Abstract] Abstract and results on burstiness and SFE: the model concludes bursty SF at z~9-10 from the derived histories, yet the abundance-matching procedure assumes a monotonic, tight UV-to-halo-accretion mapping that may not hold under bursty SF (where instantaneous UV luminosity need not trace time-averaged accretion). No test of this assumption or error propagation on the matching step is reported, which is load-bearing for the quantitative SFE values and the necessity of variable IMF.
minor comments (1)
  1. The abstract states the model reproduces the star-forming main sequence but provides no quantitative comparison metrics or redshift range for this reproduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and have made revisions to the manuscript to improve clarity regarding the model's assumptions and methodology.

read point-by-point responses

  1. Referee: [Abstract] Abstract and description of the SFR-halo accretion rate relation: the relation is obtained by abundance matching the input observed UV LFs to halo accretion distributions, after which the same UV LFs are used to assign SFRs and integrate stellar masses. This makes the reported SFE peaks (0.8-0.9 at z>9) effectively the conversion factors needed to match the input data by construction, undermining the claim that SFEs are independent predictions of the model.

    Authors: We clarify that while the SFR-halo accretion rate relation is derived via abundance matching to the observed UV LFs, the SFEs are not input parameters but are calculated as the ratio of the assigned SFR to the expected baryonic accretion rate. This allows the model to predict stellar mass growth without presupposing the efficiency. The claim of 'predictions' refers to the fact that no functional form or redshift evolution for SFE was assumed a priori. We have revised the abstract to better articulate this point. revision: partial

  2. Referee: [Abstract] Abstract and results on burstiness and SFE: the model concludes bursty SF at z~9-10 from the derived histories, yet the abundance-matching procedure assumes a monotonic, tight UV-to-halo-accretion mapping that may not hold under bursty SF (where instantaneous UV luminosity need not trace time-averaged accretion). No test of this assumption or error propagation on the matching step is reported, which is load-bearing for the quantitative SFE values and the necessity of variable IMF.

    Authors: The potential inconsistency between the monotonic mapping assumption and bursty star formation is a valid concern. Our model uses the mean relation at each redshift, and the bursty appearance in the assembly histories stems from the varying accretion rates of individual haloes. We did not include a dedicated test or error propagation in the original submission. To address this, we have added text in the methods and discussion sections noting this limitation and its implications for the quantitative SFE values and the interpretation of IMF variations. This revision acknowledges the approximation while maintaining the utility of the mean relations derived. revision: yes

Circularity Check

1 steps flagged

SFE peaks presented as predictions but obtained directly via abundance matching to the input UV LFs

specific steps
  1. fitted input called prediction [Abstract]
    "This makes the SFEs a full prediction of the model rather than a tuned input, serving as a natural baseline to test burstiness, dust attenuation, or IMF variations. ... Galaxy stellar masses are progressively built in time by integrating their SFRs assigned along their progenitor haloes via the SFR-halo accretion rate relation, derived from abundance matching between the input observed UV LFs with the dark matter halo accretion rate distributions at each redshift."

    The SFR-halo relation is obtained by abundance matching the same observed UV LFs that supply the SFRs; the resulting SFEs are therefore the numerical factors needed to match the input UV LF abundances to halo accretion rates at each z. Reporting these SFEs as model predictions and concluding bursty SF or variable IMF necessity from their high values is circular because the values are forced by the matching step itself.

full rationale

The paper derives the SFR-halo accretion rate relation by abundance matching the observed UV luminosity functions (the sole data input) to halo accretion rate distributions, then assigns SFRs along progenitor tracks and integrates to obtain stellar masses and SFEs. The reported SFE values (0.8-0.9 at z>9) are therefore the exact conversion factors required to reproduce the input UV LF number densities at each redshift; labeling them 'full predictions' and using them to infer burstiness or variable IMF necessity is a fitted-input-called-prediction pattern. The model does reproduce other observables (SMF, clustering) by construction from the same matching, but the central SFE claim reduces to the input data rather than an independent derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that abundance matching between UV LFs and halo accretion rates supplies a complete SFR assignment without additional physics; no free parameters are explicitly introduced in the abstract, and no new entities are postulated.

axioms (1)
  • domain assumption Abundance matching between observed UV luminosity functions and dark matter halo accretion rate distributions at each redshift accurately assigns SFRs to haloes while bypassing modelling of cooling, feedback and stochastic processes.
    This premise is invoked in the abstract as the core of the data-driven approach that makes SFEs a prediction.

pith-pipeline@v0.9.1-grok · 5958 in / 1480 out tokens · 36112 ms · 2026-06-29T21:18:42.624370+00:00 · methodology

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