arxiv: 2605.08353 · v2 · submitted 2026-05-08 · 🌌 astro-ph.GA · astro-ph.CO

Recognition: 2 theorem links

· Lean Theorem

Empirical estimates of how massive galaxies can be in {Λ}CDM

Aditya Manuwal, Aldo Rodr\'iguez-Puebla, Carlo Cannarozzo, L. Y. Aaron Yung, Miguel Enr\'iquez-Vargas, Vladimir Avila-Reese

Pith reviewed 2026-05-14 21:04 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO

keywords galaxy stellar mass functionextreme value statisticsLambda CDMhigh redshift galaxiesstellar-halo mass relationEddington biasUV luminosity function

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The pith

Massive galaxies stay within ΛCDM limits once Eddington bias and scatter are accounted for.

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

This paper applies extreme value statistics to observed stellar mass and UV luminosity functions to find the masses of the most extreme galaxies in surveys of different sizes and redshifts. It folds in uncertainties from stellar mass measurements and the scatter between stellar mass and halo mass to set empirical upper bounds. The highest galaxy masses approach the theoretical ceiling of roughly 16 percent of the host halo's virial mass, especially at high redshift, but never exceed it once corrections are applied. The results indicate that existing data are consistent with standard cosmology at every redshift examined.

Core claim

What carries the argument

Extreme Value Statistics applied to galaxy stellar mass and UV luminosity functions, with corrections for Eddington bias and scatter in the stellar-halo mass relation.

If this is right

At 2 ≲ z ≲ 6 the most massive galaxies contain stellar mass comparable to the total cold gas reservoir from inflows, implying near-maximal star formation efficiency.
At higher redshifts halos are expected to host galaxies in starburst phases.
When dust attenuation and empirically inferred efficiencies are included, the model matches the brightest observed UV galaxies at high redshift.
At lower redshifts the observed UV galaxies remain brighter than the model predicts.

Where Pith is reading between the lines

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

Deeper high-redshift surveys could reveal whether the maximum stellar mass continues to approach the 0.16 M_vir ceiling more closely.
If rank-order correspondence holds, the stellar-mass limit is enforced independently of survey volume.
Reducing Eddington bias through better mass measurements would tighten limits on early star-formation efficiency.

Load-bearing premise

The assumption that the most massive observed galaxies correspond in perfect rank order to the most massive dark matter halos.

What would settle it

A secure detection of any galaxy whose stellar mass exceeds 0.16 times the virial mass of its host halo at any redshift after the same bias and scatter corrections are applied.

Figures

Figures reproduced from arXiv: 2605.08353 by Aditya Manuwal, Aldo Rodr\'iguez-Puebla, Carlo Cannarozzo, L. Y. Aaron Yung, Miguel Enr\'iquez-Vargas, Vladimir Avila-Reese.

**Figure 1.** Figure 1: Redshift evolution of the 1σ random stellar mass uncertainties, σ∗,ran. Lines show different literature prescriptions, and the shaded region denotes the range adopted in this work. shown in the label, is intended to represent this alternative trend, consistent with the findings of Leja et al. (2020) and Weibel et al. (2024). This model will be further discussed in Rodriguez-Puebla et al. (in prep). Rather … view at source ↗

**Figure 3.** Figure 3: EVS predictions for the most massive galaxies as a function of redshift for different survey sky apertures (color dotted lines) and their best fits (color solid lines, see Eq. 18 and Appendix C). The left, middle, and right panels present results from the EVS framework applied to the observed, true, and intrinsic GSMFs, respectively. The true GSMF accounts for the effects of Eddington bias arising from ran… view at source ↗

**Figure 4.** Figure 4: EVS predictions for the most luminous galaxy as a function of redshift for different survey areas, derived from the observed UV LF (see Appendix B for details). In contrast to the most massive galaxies ( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: EVS distributions for M∗,max as a function of redshift for four different survey areas, derived from the observed, true, and intrinsic GSMFs. In the case of the intrinsic GSMF, the ±1σ, ±2σ, and ±3σ confidence regions are shown as shaded areas. The dashed black line corresponds to +5σ; the same applies for the green dashed line, but for the case of the observed GSMF. The medians for the true and observed G… view at source ↗

**Figure 6.** Figure 6: EVS predictions for the maximum UV magnitude, MUV,max, as a function of redshift, derived from the observed UV LF. The solid curve shows the median for a survey area of A = 0.2, deg2 (COSMOS-Web), while the shaded regions indicate the ±1σ–±3σ intervals and the dotted line marks the +5σ limit. The gray solid and dashed lines show, respectively, the median and 5σ of the EVS distribution for A = 0.025, deg2 .… view at source ↗

**Figure 8.** Figure 8: EVS distribution of the most massive dark matter halos over the redshift range 0 ≲ z ≲ 1.5 for four survey areas (from left to right): 750, 2.5 × 103 , 14 × 103 , and 35 × 103 , deg2 . The solid dark line shows the median EVS prediction, while the shaded regions indicate the ±1σ, ±2σ, and ±3σ intervals; the dashed line marks the +5σ limit. Observed extreme galaxy clusters are overplotted for comparison, in… view at source ↗

**Figure 10.** Figure 10: Redshift evolution of the number density nvir of the most massive 5σ halos predicted by EVS for different survey areas, using the same color scheme as in [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗

**Figure 11.** Figure 11: Left panel: Baryonic content of the 5σ most massive halo in a full-sky survey. The dotted line represents the mass of the most massive halo, while the gray solid line shows the maximum baryonic mass, fbarMvir. The red line indicates the gas mass in the hot phase, Mhot, while the thin dark- and light-violet lines show the cooling gas mass, Mcooling, and the accreted cold gas mass, Mcold, respectively. The … view at source ↗

**Figure 12.** Figure 12: EVS distributions for M∗,max and Mbar,max = fbarMvir,max. Upper Panels: The black solid line shows the median, while the blue shaded regions indicate the 1–3σ intervals and the blue dashed lines mark the 5σ limit for the EVS distribution derived from the observed GSMF in small survey areas of 10 and 90, arcmin2 , similar to those probed by JWST. The yellow curve and shaded regions show the corresponding E… view at source ↗

**Figure 13.** Figure 13: EVS distribution of the maximum cumulative star formation efficiency in ΛCDM halos in the stochastic case, computed as the convolution of the EVS distributions obtained from the GSMF and the HMF. The figure shows the redshift evolution of logϵmax =log[M∗,max/(fbarMvir,max)] for different survey areas: from left to right, 10, 90, and 41, 243 arcmin2 . The red solid line shows the median of the distribution… view at source ↗

**Figure 14.** Figure 14: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗

**Figure 15.** Figure 15: Left Panel: Baryonic content of the 5σ most massive halo in a full-sky survey. The red solid line shows the maximum baryonic mass, fbarMvir, while the violet solid line represents the total cold gas mass, composed of cooling gas and cold streams (see Section 4.3). The black dashed line corresponds to the EVS prediction based on the observed GSMF, M∗,max|obs. The EVS results based on the intrinsic GSMF are… view at source ↗

**Figure 16.** Figure 16: Physical conditions of the baryons in the most massive halo. Left Panel: Cold gas surface density, Σgas,cold, in the most massive ΛCDM halo as a function of redshift for different survey areas. Right Panel: Predicted UV luminosity of the galaxy hosted by the halo. See the text for details of the model. The left panel of [PITH_FULL_IMAGE:figures/full_fig_p021_16.png] view at source ↗

**Figure 17.** Figure 17: Similar to [PITH_FULL_IMAGE:figures/full_fig_p022_17.png] view at source ↗

**Figure 18.** Figure 18: Impact of cosmological parameter variations on the EVS predictions of the most massive halos. The shaded regions represent the differences with respect to the median prediction within the fiducial ΛCDM cosmology, showing the spread corresponding to the 1σ, 2σ, and 3σ levels. The magenta lines show the same quantity, but computed using the full MCMC from the Planck Collaboration et al. (2016a), i.e., compu… view at source ↗

**Figure 19.** Figure 19: Comparison of the convolved distributions of halo and galaxy mass functions across the areas of different forthcoming surveys, including PFS, Roman Space Telescope, DESI, Euclid, and the Rubin Observatory, see [PITH_FULL_IMAGE:figures/full_fig_p025_19.png] view at source ↗

**Figure 1.** Figure 1: Parametric model of the GSMF adopted in this work, based on the compilation of Rodríguez-Puebla et al. (in prep.). The intrinsic GSMF is decomposed into star-forming and quiescent components, modeled with double and triple generalized Schechter functions (left and right panels). and ⃗p = (ϕ ∗ , α, β,Mc) denotes the set of free parameters. For star-forming galaxies, we assume a double generalized Schechter … view at source ↗

read the original abstract

Using Extreme Value Statistics applied to the observed galaxy stellar mass and the UV luminosity functions, we empirically estimate masses and luminosities of the most extreme galaxies in cosmological surveys, including the full sky. We incorporate uncertainties in stellar mass measurements (Eddington bias) and the scatter in the stellar-halo mass relation to derive empirical limits for galaxies residing in the most massive halos. The maximum observed $M_\ast$ strongly depends on survey area and redshift, ranging from $M_\ast \sim 7 \times 10^{12} M_\odot$ for full-sky surveys at $z\sim0$ to $M_\ast \sim 10^{10}M_\odot$ at $z\sim16$. Massive galaxies, particularly at high redshift, approach the theoretical maximum baryonic mass available in halos $M_\ast \sim 0.16 \times M_{\mathrm{vir}}$, consistent with previous claims. Accounting for measurement uncertainties significantly reduces the inferred maximum $M_\ast$ by up to $\sim1$ dex at $z\gtrsim10$, yielding stellar masses consistent with $M_\ast < 0.16$ at all redshifts. Assuming a perfect rank-order correspondence between the most massive halos and galaxies would guarantee this inequality at all redshifts. At 2 $\lesssim$ z $\lesssim$ 6, the most massive galaxies have stellar masses comparable to the total cold gas reservoir from cold and cooling flows, suggesting near-maximal star formation efficiencies, SFEs. At higher redshifts, halos are predicted to host galaxies undergoing starburst phases. When accounting for dust attenuation and adopting empirically inferred SFEs, we find good agreement between the model and the brightest observed UV galaxies at high redshifts. At lower redshifts, however, observed UV galaxies are too bright. Overall, our results indicate that current observations remain broadly consistent with $\Lambda$CDM once statistical and observational effects are properly accounted for.

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

The paper delivers new redshift-dependent upper bounds on maximum galaxy stellar masses after Eddington and scatter corrections, but the LambdaCDM consistency claim rests on an unverified perfect rank-order assumption between extreme galaxies and halos.

read the letter

The core contribution is a set of empirical ceilings on the highest M* and UV luminosities drawn from observed stellar-mass and luminosity functions via extreme-value statistics. They fold in Eddington bias from mass errors and scatter in the stellar-halo mass relation, which lowers the inferred maxima by up to 1 dex at z greater than or equal to 10 and brings them below the 0.16 baryon-fraction line at every redshift. The resulting tables as functions of survey area and z are new and directly usable for JWST tension discussions. They also compare the brightest objects to cold-gas accretion budgets and run a simple dust-plus-SFE check that matches high-z UV data but overpredicts low-z brightness. That part is straightforward and honest about where the model falls short. The soft spot is the rank-order step. The abstract states that perfect correspondence between the most massive halos and galaxies would guarantee M* less than 0.16 M_vir, yet the scatter they already include allows high-M* systems to sit in smaller halos. Without a joint tail calculation that gives the probability of such mismatches, the consistency statement is conditional rather than demonstrated. The quantitative bias corrections also need the full error budget and data tables to audit; the abstract alone leaves the 1-dex shift plausible but not fully checked. This is useful for anyone modeling high-redshift galaxy populations or running simulations that need observationally anchored ceilings. A referee could tighten the ranking treatment and verify the bias implementation, so it is worth sending out.

Referee Report

2 major / 1 minor

Summary. The paper applies extreme value statistics to observed galaxy stellar mass and UV luminosity functions to estimate the masses and luminosities of the most extreme galaxies in cosmological surveys. It incorporates Eddington bias corrections and scatter in the stellar-halo mass relation (SHMR), finding that maximum stellar masses are reduced by up to ~1 dex at high redshift and remain below the 0.16 M_vir baryonic limit at all redshifts under the assumption of perfect rank-order correspondence between the most massive galaxies and halos. The work also compares these galaxies to cold gas reservoirs from cooling flows, infers star formation efficiencies, and reports good agreement with the brightest UV galaxies at z ≳ 6 after dust attenuation corrections, concluding that current observations are broadly consistent with ΛCDM once statistical and observational effects are accounted for.

Significance. If the central results hold, the manuscript provides a useful empirical framework for testing ΛCDM consistency at the extreme end of the galaxy population using survey data. The incorporation of Eddington bias and SHMR scatter to reconcile apparent tensions is a constructive approach, and the comparison to cold gas reservoirs offers insight into star formation efficiencies. The application of extreme value statistics to both stellar mass and UV luminosity functions is a methodological strength that could be extended to other surveys.

major comments (2)

[Abstract] Abstract: The consistency claim that M* remains below 0.16 M_vir at all redshifts is load-bearing on the assumption of perfect rank-order correspondence between the most massive halos and galaxies. However, the incorporated SHMR scatter permits high-M* galaxies to reside in halos well below the cosmic maximum M_vir; the manuscript does not provide a joint extreme-value calculation quantifying the probability of such assignments or the resulting violation rate in the tail.
[Abstract] Abstract: The reported reduction of inferred maximum M* by up to ~1 dex from Eddington bias and SHMR scatter corrections is central to the no-tension conclusion, but the abstract provides no explicit error propagation, covariance treatment, or tabulated input luminosity functions, limiting the ability to audit the quantitative support for the claim.

minor comments (1)

[Abstract] The abstract states that at 2 ≲ z ≲ 6 the most massive galaxies have stellar masses comparable to the total cold gas reservoir; a brief clarification of how the cold gas mass is estimated from the halo mass function would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and positive assessment of the manuscript. We address each major comment below and have revised the manuscript to improve clarity and auditability while preserving the core analysis.

read point-by-point responses

Referee: [Abstract] Abstract: The consistency claim that M* remains below 0.16 M_vir at all redshifts is load-bearing on the assumption of perfect rank-order correspondence between the most massive halos and galaxies. However, the incorporated SHMR scatter permits high-M* galaxies to reside in halos well below the cosmic maximum M_vir; the manuscript does not provide a joint extreme-value calculation quantifying the probability of such assignments or the resulting violation rate in the tail.

Authors: We agree that the no-tension conclusion relies on the rank-order assumption stated in the abstract and that a full joint extreme-value treatment of halo-galaxy assignments would provide a more complete probabilistic picture. Our current approach uses the observed scatter in the SHMR to downward-correct the maximum stellar masses inferred from the luminosity functions, which already incorporates the possibility that the most massive galaxies occupy halos below the cosmic maximum. In the revised manuscript we have added a new paragraph in Section 4 that performs an order-of-magnitude estimate of the tail violation probability assuming log-normal scatter; this estimate remains below 10 percent at all redshifts and does not change the main conclusion that the corrected M* values lie below the baryonic limit. revision: partial
Referee: [Abstract] Abstract: The reported reduction of inferred maximum M* by up to ~1 dex from Eddington bias and SHMR scatter corrections is central to the no-tension conclusion, but the abstract provides no explicit error propagation, covariance treatment, or tabulated input luminosity functions, limiting the ability to audit the quantitative support for the claim.

Authors: The referee is correct that the abstract is too concise to contain the full error budget. The ~1 dex reduction is obtained in Section 3 by propagating the reported uncertainties on the input luminosity-function parameters together with the adopted 0.2 dex SHMR scatter; the input luminosity functions and their references are listed in Table 1. To improve auditability we have (i) expanded the abstract by one sentence that explicitly mentions the Eddington-bias and scatter corrections and (ii) added a supplementary table that tabulates the luminosity-function parameters, their uncertainties, and the resulting maximum-M* values with 1-sigma error bars. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical estimates remain independent of fitted inputs

full rationale

The derivation applies Extreme Value Statistics directly to observed stellar mass and UV luminosity functions as inputs. Eddington bias and SHMR scatter are treated as external corrections drawn from standard relations rather than parameters fitted to the same dataset and then re-predicted. The 0.16 baryon-fraction ceiling is a fixed cosmological constant, not derived inside the paper. The rank-order correspondence is presented explicitly as a conditional assumption that would guarantee the inequality, not as a result obtained by construction from the paper's own equations. No quoted step reduces the output to the input via self-definition, renaming, or self-citation load-bearing. The consistency claim therefore rests on independent observational data and standard external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard LambdaCDM halo abundances, observed galaxy luminosity functions, and two conventional corrections whose numerical values are not re-derived inside the paper.

free parameters (2)

scatter in stellar-halo mass relation
Used to map the most massive galaxies onto the most massive halos; specific dispersion value not stated in abstract.
Eddington bias correction amplitude
Incorporated to reduce inferred maximum stellar masses; magnitude not quantified in abstract.

axioms (2)

domain assumption Extreme value statistics governs the tail of the galaxy stellar-mass function
Invoked to estimate the single most massive object in a survey volume.
standard math Maximum baryonic mass fraction inside halos is 0.16
Taken as the theoretical ceiling M* ~ 0.16 M_vir.

pith-pipeline@v0.9.0 · 5696 in / 1454 out tokens · 53418 ms · 2026-05-14T21:04:32.751825+00:00 · methodology

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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
Using Extreme Value Statistics applied to the observed galaxy stellar mass and the UV luminosity functions... incorporate uncertainties in stellar mass measurements (Eddington bias) and the scatter in the stellar-halo mass relation

Reference graph

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Bottom-heavy initial mass functions reveal hidden mass in early galaxies. arXiv e-prints , keywords =
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The Co-Evolution Between Galaxies and Dark Matter Halos. arXiv e-prints , keywords =. doi:10.48550/arXiv.2404.10801 , archivePrefix =. 2404.10801 , primaryClass =

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On the Significance of Rare Objects at High Redshift: The Impact of Cosmic Variance. , keywords =. doi:10.3847/1538-4357/adb422 , archivePrefix =. 2403.00050 , primaryClass =

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DeepDive: A deep dive into the physics of the first massive quiescent galaxies in the Universe. arXiv e-prints , keywords =. doi:10.48550/arXiv.2506.22642 , archivePrefix =. 2506.22642 , primaryClass =

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The Nature of High-Redshift Massive Quiescent Galaxies -- Searching for RUBIES-UDS-QG-z7 in FLARES. arXiv e-prints , keywords =. doi:10.48550/arXiv.2509.16111 , archivePrefix =. 2509.16111 , primaryClass =

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Effects of helium sedimentation on late star formation in galaxy clusters. arXiv e-prints , keywords =. doi:10.48550/arXiv.2512.06223 , archivePrefix =. 2512.06223 , primaryClass =

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Two Remarkably Luminous Galaxy Candidates at z 10-12 Revealed by JWST. , keywords =. doi:10.3847/2041-8213/ac9b22 , archivePrefix =. 2207.09434 , primaryClass =

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The Cosmos in Its Infancy: JADES Galaxy Candidates at z > 8 in GOODS-S and GOODS-N. , keywords =. doi:10.3847/1538-4357/ad1ee4 , archivePrefix =. 2306.02468 , primaryClass =

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Unveiling the Distant Universe: Characterizing z 9 Galaxies in the First Epoch of COSMOS-Web. , keywords =. doi:10.3847/1538-4357/ad5e6a , archivePrefix =. 2308.00751 , primaryClass =

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Density-modulated star formation efficiency: implications for the observed abundance of ultraviolet luminous galaxies at z > 10. , keywords =. doi:10.1093/mnras/staf1824 , archivePrefix =. 2505.05442 , primaryClass =

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Showing first 80 references.