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arxiv: 2604.27477 · v1 · submitted 2026-04-30 · 🌌 astro-ph.GA · astro-ph.CO

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The Critical Mass in Galaxy Evolution

Preetish K. Mishra , Changbom Park , Jaehyun Lee , Yohan Dubois , Christophe Pichon , Juhan Kim , Brad Gibson
Authors on Pith no claims yet

Pith reviewed 2026-05-07 08:17 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords critical masshot gas halogalaxy evolutionstar formation efficiencygas accretionbaryon retentionstellar-to-total mass ratiosimulation
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The pith

A redshift-independent critical mass around 10^{12.5} solar masses arises when stable hot gas halos form and suppress cool gas inflows, slowing star formation relative to total mass growth.

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

The paper decomposes the stellar-to-total mass ratio in simulated galaxies and traces its turnover to a single physical threshold. At this mass, galaxies develop stable hot halos that block cool gas from reaching the center, cutting the efficiency of turning available baryons into new stars. Total halo mass then grows faster than stellar mass, producing measurable shifts in gas fractions and baryon retention. A reader would care because the threshold holds at every redshift examined, offering a gravitational mechanism for the breaks seen in many galaxy scaling relations rather than a time-dependent process. The work also flags a lower-mass secondary threshold where gas retention itself peaks before hot-gas effects take over.

Core claim

At M_tot approximately 10^{12.5} solar masses, a dynamically stable hot gas halo develops that suppresses cool gas inflow. This reduces in-situ star formation efficiency so that total mass growth outpaces stellar mass growth. The hot gas reservoir therefore increases while stellar mass growth slows, producing upturns in M_gas/M_tot and M_bar/M_tot together with a downturn in M_*/M_bar that drives the observed turnover in the stellar-to-total mass ratio. The same critical mass appears independent of redshift. A secondary transition occurs near 10^{11} solar masses where the baryon retention fraction reaches its maximum.

What carries the argument

The dynamically stable hot gas halo that forms at the critical mass and suppresses cool gas accretion, thereby lowering in-situ star formation efficiency.

If this is right

  • M_tot growth exceeds in-situ M_* growth once the hot halo forms.
  • The hot gas reservoir grows while stellar mass growth slows.
  • Upturns appear in both M_gas/M_tot and M_bar/M_tot.
  • A downturn in M_*/M_bar produces the stellar-to-total mass ratio turnover.
  • Gas retention fraction peaks at a secondary critical mass near 10^{11} solar masses.

Where Pith is reading between the lines

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

  • The redshift-independent threshold points to a gravitational potential depth that could unify quenching mechanisms across cosmic time.
  • Measurements of circumgalactic medium temperature and kinematics around galaxies at this mass could directly confirm the stable hot halo.
  • Varying feedback prescriptions in simulations would shift the exact location of the critical mass and thereby calibrate subgrid models.
  • The same halo-stability criterion might predict a corresponding break in the efficiency of AGN feedback or in the morphology of the circumgalactic medium.

Load-bearing premise

The simulation accurately reproduces the formation and stability of hot gas halos and the resulting cutoff of cool gas inflows at the identified mass scale without dominant numerical or subgrid effects that would move the threshold.

What would settle it

Direct observations or higher-resolution simulations showing that cool gas continues to accrete efficiently onto galaxies near 10^{12.5} solar masses, with no corresponding downturn in the stellar-to-baryon mass ratio, would falsify the mechanism.

Figures

Figures reproduced from arXiv: 2604.27477 by Brad Gibson, Changbom Park, Christophe Pichon, Jaehyun Lee, Juhan Kim, Preetish K. Mishra, Yohan Dubois.

Figure 1
Figure 1. Figure 1: 2D histogram of M∗/Mtot versus Mtot for cen￾tral galaxies in the HR5 simulation at a redshift of 0.625. The gray scale bar indicates the number of galaxies in each bin. The black dots and the dotted curved line show the binned median M∗/Mtot and the interpolated relation, re￾spectively. The dashed curves represent the 16th–84th per￾centile range of M∗/Mtot at a fixed Mtot. Galaxies with log(Mtot/M⊙) ≥ 12 (… view at source ↗
Figure 2
Figure 2. Figure 2: Left: The redshift evolution of the median M∗/Mtot for galaxies in our sample. Right: The evolution of median M∗/Mtot as function of total mass of galaxies. Black dots and the dashed line indicate the median stellar mass–total mass relation at the final redshift snapshot of the HR5 simulation, as shown in view at source ↗
Figure 3
Figure 3. Figure 3: The evolution of SBR as a function of redshift (top left) and total mass (top right), and the evolution of BRF as a function of redshift (bottom left) and total mass (bottom right). The colored solid lines and shaded region has same meaning as in previous figure. The circle and square markers indicate the redshift and total mass at which galaxies reached their peak M/Mbar and peak M/Mtot, respectively, dur… view at source ↗
Figure 5
Figure 5. Figure 5: Normalized median rate of change of the stel￾lar-to-total mass ratio, d dt  M∗ Mtot  , as a function of the total mass of central galaxies. Contributions from in-situ star for￾mation and ex-situ accretion are shown by open boxes (solid lines) and filled circles (dotted lines), respectively; error bars indicate the uncertainty on the median. Owing to the small number of galaxies in the highest-mass bins, … view at source ↗
Figure 6
Figure 6. Figure 6: Top: The median hot gas mass fraction of galax￾ies as a function of total mass. Bottom: The median frac￾tion of gas able to cool within the dynamical timescale as a function of total mass. In both panels, error bars indicate the uncertainty on the median, and colors represent the red￾shifts z = 5, 2, and 0.625. Error bars and connecting lines are omitted for the highest-mass bins due to low number statisti… view at source ↗
Figure 7
Figure 7. Figure 7: Left: Redshift evolution of the median total mass of galaxies, marked with mass scale associated important transitions. The solid line and shade regions denote median mass and its uncertainty. The open circle, filled triangles, and open squares indicate mass scale associated with peak Mgas/Mtot, MISM/Mgas and d dt  M∗ Mtot  |in-situ SF respectively. Grey dashed lines show linear fits to the open circles … view at source ↗
Figure 8
Figure 8. Figure 8: Median AGN injection rate as function of redshift. The lines denote the evolutionary trajectory of galaxies, color coded by their final total mass. The color coding scheme remains same as in view at source ↗
Figure 9
Figure 9. Figure 9: Hot gas fraction (fhot ≡ Mhot gas/Mtot) as a function of total mass for galaxies from the HR5 simulation at z = 0.625 (red line). The shaded region represents the 16th–84th percentile scatter in each bin. Observational data from N. Lyskova et al. (2023) (z < 0.2) and P. Popesso et al. (2024) (z < 0.2) are shown as blue symbols. The dashed black line shows the empirical fhot–M200 scaling relation from P. Po… view at source ↗
read the original abstract

We investigate the physical origin of critical mass, a threshold where many galaxy properties and scaling relations undergo fundamental transitions, using the Horizon Run 5 simulation. Focusing on massive ($M_{\rm tot} \geq 10^{12}{\rm M_\odot}$) central galaxies, we examine the mass-dependent turnover of the stellar-to-total mass ratio (STR) and the physical processes driving it. We decompose STR into the stellar-to-baryon mass ratio ($M_*/M_{\rm bar}$) and baryon retention fraction ($M_{\rm bar}/M_{\rm tot}$) to examine galaxies' ability to retain baryons and convert them into stars. We find that STR evolution is dominated by variation in $M_*/M_{\rm bar}$, which changes by over a factor of three, peaking within a narrow range of $M_{\rm tot} \sim 10^{12.4\text{--}12.7}{\rm M_\odot}$ independent of redshift, while $M_{\rm bar}/M_{\rm tot}$ varies by at most 30%. A redshift-independent critical mass at $M_{\rm tot} \sim 10^{12.5}{\rm M_\odot}$ ($M_* \sim 10^{10.7}{\rm M_\odot}$) arises from the changing nature of gas accretion. At this scale, a dynamically stable hot gas halo develops that suppresses cool gas inflow, reducing in-situ star formation efficiency such that $M_{\rm tot}$ growth exceeds in-situ $M_{*}$ growth. Consequently, the hot gas reservoir grows while $M_{*}$ growth slows, producing upturns in $M_{\rm gas}/M_{\rm tot}$ and $M_{\rm bar}/M_{\rm tot}$ and a downturn in $M_{*}/M_{\rm bar}$ that ultimately drives the STR turnover. We also identify a secondary critical mass at $M_{\rm tot} \approx 10^{11}{\rm M_\odot}$ (or $M_{*} \approx 10^{9\text{--}9.5}{\rm M_\odot}$) where gas retention fraction peaks, above which increasing hot gas fraction gradually suppresses in-situ star formation efficiency.

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

3 major / 3 minor

Summary. The paper analyzes central galaxies with M_tot >= 10^12 M_sun in the Horizon Run 5 simulation to identify the physical driver of a critical mass scale. It decomposes the stellar-to-total mass ratio (STR) into the stellar-to-baryon ratio (M*/M_bar) and baryon retention fraction (M_bar/M_tot), finding that STR evolution is dominated by a factor-of-three variation in M*/M_bar that peaks at a redshift-independent M_tot ~ 10^{12.4-12.7} M_sun. The authors attribute the associated downturn in M*/M_bar to the formation of a dynamically stable hot gas halo that suppresses cool inflows, thereby lowering in-situ star-formation efficiency while M_tot continues to grow; this produces upturns in M_gas/M_tot and M_bar/M_tot. A secondary critical mass near 10^11 M_sun is also reported where gas retention peaks.

Significance. If the central claim is robust, the work supplies a concrete, simulation-derived mechanism for the well-known transition in galaxy scaling relations around 10^{12.5} M_sun, directly linking the turnover to the shift from cold-mode to hot-mode accretion and the stability of virialized halos. The decomposition into retention and conversion efficiencies is a useful diagnostic that could be applied to other simulations or observations. The redshift-independent location of the primary critical mass, derived empirically rather than by construction, strengthens its potential utility as a benchmark for semi-analytic models and hydrodynamical codes.

major comments (3)
  1. [§3] §3 (results on mass-dependent trends): the location of the critical mass is reported as the narrow interval 10^{12.4-12.7} M_sun where M*/M_bar peaks, yet no quantitative procedure (binning scheme, derivative threshold, or bootstrap significance test) is described for identifying this interval or for confirming its redshift independence. Without these details the claimed precision and universality cannot be evaluated.
  2. [§4.2] §4.2 (discussion of hot-halo mechanism): the assertion that a 'dynamically stable hot gas halo develops that suppresses cool gas inflow' is central to the causal explanation, but the text provides neither radial inflow-rate profiles, t_cool/t_ff distributions, nor radial-velocity histograms at the quoted mass scale. These diagnostics are required to demonstrate that the suppression is resolved and not an artifact of the subgrid cooling or AGN feedback implementation.
  3. [Methods] Methods and §5 (simulation robustness): all results are obtained from a single run of Horizon Run 5. No resolution-convergence tests, variations in subgrid parameters, or cross-code comparisons are presented for the 10^{12}-10^{13} M_sun regime where hot-halo stability is known to be numerically sensitive. This omission leaves open the possibility that the reported critical mass shifts by several tenths of a dex under different numerics.
minor comments (3)
  1. [§1] The abstract and §1 introduce STR without an explicit equation; adding M_*/M_tot = (M_*/M_bar) × (M_bar/M_tot) early would improve readability.
  2. [Figures] Figures displaying M*/M_bar versus M_tot (presumably Figs. 3-5) should include bootstrap or jackknife error bands on the binned medians and on the location of the turnover to allow readers to judge the statistical significance of the redshift-independent claim.
  3. [§4.3] The secondary critical mass at ~10^{11} M_sun is mentioned only briefly; a short dedicated paragraph or table entry would clarify whether it is identified by the same decomposition procedure.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their constructive and detailed report, which highlights important areas for clarification and strengthening. We address each major comment below, indicating revisions where appropriate. Our responses focus on improving the manuscript's transparency and robustness without altering the core findings.

read point-by-point responses

  1. Referee: §3 (results on mass-dependent trends): the location of the critical mass is reported as the narrow interval 10^{12.4-12.7} M_sun where M*/M_bar peaks, yet no quantitative procedure (binning scheme, derivative threshold, or bootstrap significance test) is described for identifying this interval or for confirming its redshift independence. Without these details the claimed precision and universality cannot be evaluated.

    Authors: We agree that explicit details on the identification procedure will improve reproducibility. The interval was identified from the binned M*/M_bar–M_tot relations (0.1 dex logarithmic bins) as the contiguous range containing the peak value at each redshift. In the revised manuscript we will add a description of the binning scheme, define the interval quantitatively as the mass range where M*/M_bar remains within 10% of its maximum, and include bootstrap-resampled uncertainties on the peak location. A new table will tabulate the peak mass and its 1σ uncertainty at z = 0, 0.5, 1, and 2, confirming consistency within uncertainties and thereby supporting the claimed redshift independence. revision: yes

  2. Referee: §4.2 (discussion of hot-halo mechanism): the assertion that a 'dynamically stable hot gas halo develops that suppresses cool gas inflow' is central to the causal explanation, but the text provides neither radial inflow-rate profiles, t_cool/t_ff distributions, nor radial-velocity histograms at the quoted mass scale. These diagnostics are required to demonstrate that the suppression is resolved and not an artifact of the subgrid cooling or AGN feedback implementation.

    Authors: We acknowledge that direct kinematic and thermodynamic diagnostics would provide stronger causal evidence. The Horizon Run 5 snapshot outputs available for the full sample do not contain the particle-level time series required for inflow-rate profiles or t_cool/t_ff maps. In revision we will add radial profiles of gas temperature, density, and specific entropy for a representative subsample of galaxies at the critical mass, which illustrate the emergence of a stable hot atmosphere. We will also expand the discussion to reference analytic expectations for the cold-to-hot accretion transition and note consistency with trends reported in other simulations, while explicitly stating the limitations of the available data products. revision: partial

  3. Referee: Methods and §5 (simulation robustness): all results are obtained from a single run of Horizon Run 5. No resolution-convergence tests, variations in subgrid parameters, or cross-code comparisons are presented for the 10^{12}-10^{13} M_sun regime where hot-halo stability is known to be numerically sensitive. This omission leaves open the possibility that the reported critical mass shifts by several tenths of a dex under different numerics.

    Authors: We recognize the value of numerical robustness checks. Horizon Run 5 is a single, fixed-resolution, large-volume run; performing additional simulations with varied resolution or subgrid physics is computationally prohibitive within the scope of this study. In the revised Methods section we will detail the relevant resolution and subgrid parameters for the 10^{12}–10^{13} M_sun range. In §5 we will add a dedicated paragraph discussing potential numerical sensitivities, citing prior convergence tests from the Horizon Run series and noting that the reported critical mass is consistent with independent results from IllustrisTNG and EAGLE at similar masses. revision: partial

standing simulated objections not resolved
  • Full resolution-convergence tests, subgrid parameter variations, and new cross-code comparisons for the 10^{12}–10^{13} M_sun regime cannot be performed, as they would require additional large-volume simulations beyond the resources available for this work.

Circularity Check

0 steps flagged

No significant circularity; critical mass identified empirically from simulation measurements

full rationale

The paper measures the turnover in stellar-to-total mass ratio (STR) and its decomposition into M*/M_bar and M_bar/M_tot directly from Horizon Run 5 simulation outputs for central galaxies above 10^12 M_⊙. The redshift-independent critical mass at M_tot ∼ 10^{12.5} M_⊙ is located where M*/M_bar peaks and declines, with the physical mechanism (stable hot halo suppressing cool inflows) inferred from the same simulation's gas temperature, accretion, and halo stability diagnostics. No fitted parameter is renamed as a prediction, no load-bearing step reduces to a self-citation or self-defined ansatz, and the central claim does not rely on uniqueness theorems imported from prior author work. The derivation remains self-contained against the simulation data without circular reduction to inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the fidelity of the Horizon Run 5 hydrodynamic simulation for modeling gas accretion modes and halo thermodynamics; the critical mass values are empirically located in the simulation outputs rather than derived from first principles.

free parameters (1)
  • Critical mass location = ~10^{12.5} M_⊙
    The specific mass scale (~10^12.5 M_⊙) at which the hot halo effect dominates is identified by inspecting the peak in M_*/M_bar across the simulated galaxy population.
axioms (2)
  • domain assumption Horizon Run 5 accurately reproduces the transition from cold-mode to hot-mode gas accretion and the stability of hot gas halos at the relevant mass scale.
    Invoked to interpret the suppression of in-situ star formation as the driver of the STR turnover.
  • domain assumption The decomposition STR = (M_*/M_bar) × (M_bar/M_tot) cleanly separates baryon retention from star-formation efficiency without significant cross-talk from other processes.
    Used throughout to attribute the turnover primarily to variation in M_*/M_bar.

pith-pipeline@v0.9.0 · 5728 in / 1845 out tokens · 105958 ms · 2026-05-07T08:17:32.425709+00:00 · methodology

discussion (0)

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Works this paper leans on

65 extracted references · 65 canonical work pages

  1. [1]

    1999, XSPEC: An X-ray spectral fitting package,, Astrophysics Source Code Library, record ascl:9910.005 http://ascl.net/9910.005 Astropy Collaboration, Robitaille, T

    Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A. M., Sip˝ ocz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f

    work page doi:10.1051/0004-6361/201322068 2013

  2. [2]

    K., Glazebrook K., Brinkmann J., Ivezi \'c Z ., Lupton R

    Baldry, I. K., Glazebrook, K., Brinkmann, J., et al. 2004, ApJ, 600, 681, doi: 10.1086/380092

    work page doi:10.1086/380092 2004

  3. [3]

    S., Wechsler R

    Behroozi, P. S., Wechsler, R. H., & Conroy, C. 2013, ApJ, 770, 57, doi: 10.1088/0004-637X/770/1/57

    work page Pith review doi:10.1088/0004-637x/770/1/57 2013

  4. [4]

    A., Lu, Y., Benson, A., Katsianis, A., & Barraza, M

    Blanc, G. A., Lu, Y., Benson, A., Katsianis, A., & Barraza, M. 2019, ApJ, 877, 6, doi: 10.3847/1538-4357/ab16ec

    work page doi:10.3847/1538-4357/ab16ec 2019

  5. [5]

    M., & Schaye, J

    Booth, C. M., & Schaye, J. 2010, MNRAS, 405, L1, doi: 10.1111/j.1745-3933.2010.00832.x 13 12.0 12.5 13.0 13.5 14.0 14.5 15.0 log(Mtot/M⊙) 0.025 0.050 0.075 0.100 0.125 0.150 0.175 fhot ≡ Mhot gas /Mtot HR5 ( z = 0.625) Lyskova+2023 (z < 0.2) Popesso+2024 ( z < 0.2) Popesso+2024: fhot − M200 relation Figure 9.Hot gas fraction (f hot ≡M hot gas/Mtot) as a f...

    work page doi:10.1111/j.1745-3933.2010.00832.x 2010

  6. [6]

    2012, MNRAS, 420, 1825, doi: 10.1111/j.1365-2966.2011.19805.x

    Booth, C. M., & Schaye, J. 2011, MNRAS, 413, 1158, doi: 10.1111/j.1365-2966.2011.18203.x

    work page doi:10.1111/j.1365-2966.2011.18203.x 2011

  7. [7]

    2024, MNRAS, 531, 84, doi: 10.1093/mnras/stae1122

    Boubel, P., Colless, M., Said, K., & Staveley-Smith, L. 2024, MNRAS, 531, 84, doi: 10.1093/mnras/stae1122

    work page doi:10.1093/mnras/stae1122 2024

  8. [8]

    Choi, Y.-Y., Park, C., & Vogeley, M. S. 2007, ApJ, 658, 884, doi: 10.1086/511060

    work page doi:10.1086/511060 2007

  9. [9]

    , keywords =

    Correa, C. A., Schaye, J., Wyithe, J. S. B., et al. 2018, MNRAS, 473, 538, doi: 10.1093/mnras/stx2332

    work page doi:10.1093/mnras/stx2332 2018

  10. [10]

    2024, , 684, A75, 10.1051/0004-6361/202346698

    Curti, M., Maiolino, R., Curtis-Lake, E., et al. 2024, A&A, 684, A75, doi: 10.1051/0004-6361/202346698

    work page doi:10.1051/0004-6361/202346698 2024

  11. [11]

    Davies, L. J. M., Robotham, A. S. G., Lagos, C. d. P., et al. 2019, MNRAS, 483, 5444, doi: 10.1093/mnras/sty3393

    work page doi:10.1093/mnras/sty3393 2019

  12. [12]

    A., Heckman, T

    Dekel, A., & Birnboim, Y. 2006, Monthly Notices of the Royal Astronomical Society, 368, 2–20, doi: 10.1111/j.1365-2966.2006.10145.x

    work page doi:10.1111/j.1365-2966.2006.10145.x 2006

  13. [13]

    Origin of the Golden Mass of Galaxies and Black Holes

    Dekel, A., Lapiner, S., & Dubois, Y. 2019, https://arxiv.org/abs/1904.08431

    work page Pith review arXiv 2019

  14. [14]

    and Peirani, S

    Dubois, Y., Peirani, S., Pichon, C., et al. 2016, MNRAS, 463, 3948, doi: 10.1093/mnras/stw2265

    work page doi:10.1093/mnras/stw2265 2016

  15. [15]

    2015, MNRAS, 452, 1502, doi:10.1093/mnras/stv1416

    Dubois, Y., Volonteri, M., Silk, J., et al. 2015, MNRAS, 452, 1502, doi: 10.1093/mnras/stv1416

    work page doi:10.1093/mnras/stv1416 2015

  16. [16]

    2022, The Astrophysical Journal, 927, 204, doi: 10.3847/1538-4357/ac51ca

    Enia, A., Talia, M., Pozzi, F., et al. 2022, The Astrophysical Journal, 927, 204, doi: 10.3847/1538-4357/ac51ca

    work page doi:10.3847/1538-4357/ac51ca 2022

  17. [17]

    2013, MNRAS, 432, 23, doi: 10.1093/mnras/stt308

    Gruppioni, C., Pozzi, F., Rodighiero, G., et al. 2013, MNRAS, 432, 23, doi: 10.1093/mnras/stt308

    work page doi:10.1093/mnras/stt308 2013

  18. [18]

    The nature, luminosity function, and star formation history of dusty galaxies up to z ≃ 6

    Gruppioni, C., B´ ethermin, M., Loiacono, F., et al. 2020, A&A, 643, A8, doi: 10.1051/0004-6361/202038487

    work page doi:10.1051/0004-6361/202038487 2020

  19. [19]

    , author =

    Habouzit, M., Volonteri, M., & Dubois, Y. 2017, MNRAS, 468, 3935, doi: 10.1093/mnras/stx666

    work page doi:10.1093/mnras/stx666 2017

  20. [20]

    2012, MNRAS, 420, 1825, doi: 10.1111/j.1365-2966.2011.19805.x

    Hahn, O., & Abel, T. 2011, MNRAS, 415, 2101, doi: 10.1111/j.1365-2966.2011.18820.x

    work page doi:10.1111/j.1365-2966.2011.18820.x 2011

  21. [21]

    E., Park, C., Mishra, P

    Hong, S. E., Park, C., Mishra, P. K., et al. 2024, ApJ, 977, 183, doi: 10.3847/1538-4357/ad9276

    work page doi:10.3847/1538-4357/ad9276 2024

  22. [22]

    Hopkins, A. M. 2004, ApJ, 615, 209, doi: 10.1086/424032

    work page doi:10.1086/424032 2004

  23. [23]

    P., Giovanelli, R., & Brinchmann, J

    Huang, S., Haynes, M. P., Giovanelli, R., & Brinchmann, J. 2012, ApJ, 756, 113, doi: 10.1088/0004-637X/756/2/113

    work page doi:10.1088/0004-637x/756/2/113 2012

  24. [24]

    Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55

    work page doi:10.1109/mcse.2007.55 2007

  25. [25]

    S., Chung, H., & Yoon, Y

    Jeong, D., Hwang, H. S., Chung, H., & Yoon, Y. 2025, ApJ, 982, 11, doi: 10.3847/1538-4357/adb1be

    work page doi:10.3847/1538-4357/adb1be 2025

  26. [26]

    2003, MNRAS, 339, 937, doi: 10.1046/j.1365-8711.2003.06241.x G¨ otberg, Y., de Mink, S

    Kauffmann, G., Heckman, T. M., White, S. D. M., et al. 2003, MNRAS, 341, 33, doi: 10.1046/j.1365-8711.2003.06291.x

    work page doi:10.1046/j.1365-8711.2003.06291.x 2003

  27. [27]

    , keywords =

    Kawinwanichakij, L., Silverman, J. D., Ding, X., et al. 2021, ApJ, 921, 38, doi: 10.3847/1538-4357/ac1f21

    work page doi:10.3847/1538-4357/ac1f21 2021

  28. [28]

    , archivePrefix = "arXiv", eprint =

    Kelvin, L. S., Driver, S. P., Robotham, A. S. G., et al. 2014, MNRAS, 444, 1647, doi: 10.1093/mnras/stu1507

    work page doi:10.1093/mnras/stu1507 2014

  29. [29]

    D., Drew, J

    Kendall, M. G., & Stuart, A. 1977, The Advanced Theory of Statistics, Vol. 1: Distribution Theory, 4th edn. (London: Charles Griffin & Company) Kereˇ s, D., Katz, N., Weinberg, D. H., & Dav´ e, R. 2005, MNRAS, 363, 2, doi: 10.1111/j.1365-2966.2005.09451.x

    work page doi:10.1111/j.1365-2966.2005.09451.x 1977

  30. [30]

    2006, The Astrophysical Journal, 639, 600–616, doi: 10.1086/499761

    Kim, J., & Park, C. 2006, The Astrophysical Journal, 639, 600–616, doi: 10.1086/499761

    work page doi:10.1086/499761 2006

  31. [31]

    2023, ApJ, 951, 137, doi: 10.3847/1538-4357/acd251

    Kim, J., Lee, J., Laigle, C., et al. 2023, ApJ, 951, 137, doi: 10.3847/1538-4357/acd251

    work page doi:10.3847/1538-4357/acd251 2023

  32. [32]

    Kravtsov, A

    Kravtsov, A. V., Vikhlinin, A. A., & Meshcheryakov, A. V. 2018, Astronomy Letters, 44, 8, doi: 10.1134/S1063773717120015

    work page doi:10.1134/s1063773717120015 2018

  33. [33]

    2021, MNRAS, 505, 172, doi: 10.1093/mnras/stab1205

    Lapiner, S., Dekel, A., & Dubois, Y. 2021, MNRAS, 505, 172, doi: 10.1093/mnras/stab1205

    work page doi:10.1093/mnras/stab1205 2021

  34. [34]

    , keywords =

    Lapiner, S., Dekel, A., Freundlich, J., et al. 2023, MNRAS, 522, 4515, doi: 10.1093/mnras/stad1263 14 Lara-L´ opez, M. A., Hopkins, A. M., L´ opez-S´ anchez, A. R., et al. 2013, Monthly Notices of the Royal Astronomical Society, 434, 451–470, doi: 10.1093/mnras/stt1031 Le Bail, A., Daddi, E., Elbaz, D., et al. 2024, A&A, 688, A53, doi: 10.1051/0004-6361/202347465

    work page doi:10.1093/mnras/stad1263 2023

  35. [35]

    N., et al

    Lee, J., Shin, J., Snaith, O. N., et al. 2021, ApJ, 908, 11, doi: 10.3847/1538-4357/abd08b

    work page doi:10.3847/1538-4357/abd08b 2021

  36. [36]

    , keywords =

    Lee, J. H., Park, C., Hwang, H. S., & Kwon, M. 2024, ApJ, 966, 113, doi: 10.3847/1538-4357/ad3448

    work page doi:10.3847/1538-4357/ad3448 2024

  37. [37]

    and Challinor, A

    Lewis, A., Challinor, A., & Lasenby, A. 2000, ApJ, 538, 473, doi: 10.1086/309179

    work page doi:10.1086/309179 2000

  38. [38]

    V., Pontzen, A., et al

    Lucie-Smith, L., Peiris, H. V., Pontzen, A., et al. 2025, PhRvD, 112, 063541, doi: 10.1103/vh8n-9cr2

    work page doi:10.1103/vh8n-9cr2 2025

  39. [39]

    I., et al

    Lyskova, N., Churazov, E., Khabibullin, I. I., et al. 2023, MNRAS, 525, 898, doi: 10.1093/mnras/stad2305

    work page doi:10.1093/mnras/stad2305 2023

  40. [40]

    Cosmic Star Formation History

    Madau, P., & Dickinson, M. 2014, ARA&A, 52, 415, doi: 10.1146/annurev-astro-081811-125615

    work page Pith review doi:10.1146/annurev-astro-081811-125615 2014

  41. [41]

    1998, ApJ, 498, 106, doi: 10.1086/305523

    Madau, P., Pozzetti, L., & Dickinson, M. 1998, ApJ, 498, 106, doi: 10.1086/305523

    work page doi:10.1086/305523 1998

  42. [42]

    2023, A&A, 678, A83, doi: 10.1051/0004-6361/202347052 M´ erida, R

    Magnelli, B., G´ omez-Guijarro, C., Elbaz, D., et al. 2023, A&A, 678, A83, doi: 10.1051/0004-6361/202347052 M´ erida, R. M., Sawicki, M., Iyer, K. G., et al. 2025, arXiv e-prints, arXiv:2509.22871, doi: 10.48550/arXiv.2509.22871

    work page doi:10.1051/0004-6361/202347052 2023

  43. [43]

    K., Rana, D., & More, S

    Mishra, P. K., Rana, D., & More, S. 2023, MNRAS, 526, 2403, doi: 10.1093/mnras/stad2914

    work page doi:10.1093/mnras/stad2914 2023

  44. [44]

    Mowla, L., Wel, A. v. d., Dokkum, P. v., & Miller, T. B. 2019, The Astrophysical Journal Letters, 872, L13, doi: 10.3847/2041-8213/ab0379

    work page doi:10.3847/2041-8213/ab0379 2019

  45. [45]

    2017, A&A, 602, A5, doi: 10.1051/0004-6361/201629436

    Novak, M., Smolˇ ci´ c, V., Delhaize, J., et al. 2017, A&A, 602, A5, doi: 10.1051/0004-6361/201629436

    work page doi:10.1051/0004-6361/201629436 2017

  46. [46]

    C., Rossi, E

    Ocvirk, P., Pichon, C., & Teyssier, R. 2008, MNRAS, 390, 1326, doi: 10.1111/j.1365-2966.2008.13763.x

    work page doi:10.1111/j.1365-2966.2008.13763.x 2008

  47. [47]

    Tracing the galaxy-halo connection with galaxy clustering in COSMOS-Web from <i>z</i> = 0.1 to <i>z</i> ∼ 12

    Paquereau, L., Laigle, C., McCracken, H. J., et al. 2025, A&A, 702, A163, doi: 10.1051/0004-6361/202553828

    work page doi:10.1051/0004-6361/202553828 2025

  48. [48]

    Blanton, M. R. 2007, The Astrophysical Journal, 658, 898–916, doi: 10.1086/511059

    work page doi:10.1086/511059 2007

  49. [49]

    2009, ApJ, 691, 1828, doi: 10.1088/0004-637X/691/2/1828

    Park, C., & Choi, Y.-Y. 2009, ApJ, 691, 1828, doi: 10.1088/0004-637X/691/2/1828

    work page doi:10.1088/0004-637x/691/2/1828 2009

  50. [50]

    R., & Choi, Y.-Y

    Park, C., Gott, III, J. R., & Choi, Y.-Y. 2008, ApJ, 674, 784, doi: 10.1086/524192

    work page doi:10.1086/524192 2008

  51. [51]

    2022, The Astrophysical Journal, 937, 15, doi: 10.3847/1538-4357/ac85b5 Planck Collaboration, Ade, P

    Park, C., Lee, J., Kim, J., et al. 2022, The Astrophysical Journal, 937, 15, doi: 10.3847/1538-4357/ac85b5 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016, A&A, 594, A13, doi: 10.1051/0004-6361/201525830

    work page doi:10.3847/1538-4357/ac85b5 2022

  52. [52]

    2024, arXiv e-prints, arXiv:2411.16555, doi: 10.48550/arXiv.2411.16555

    Popesso, P., Biviano, A., Marini, I., et al. 2024, arXiv e-prints, arXiv:2411.16555, doi: 10.48550/arXiv.2411.16555

    work page doi:10.48550/arxiv.2411.16555 2024

  53. [53]

    C., Trainor, R

    Raptis, M., Rudie, G. C., Trainor, R. F., et al. 2025, arXiv e-prints, arXiv:2512.00162, doi: 10.48550/arXiv.2512.00162

    work page doi:10.48550/arxiv.2512.00162 2025

  54. [54]

    E., & Volonteri, M

    Reines, A. E., & Volonteri, M. 2015, ApJ, 813, 82, doi: 10.1088/0004-637X/813/2/82

    work page doi:10.1088/0004-637x/813/2/82 2015

  55. [55]

    R., La Barbera, F., et al

    Roy, N., Napolitano, N. R., La Barbera, F., et al. 2018, MNRAS, 480, 1057, doi: 10.1093/mnras/sty1917

    work page doi:10.1093/mnras/sty1917 2018

  56. [56]

    2003, MNRAS, 339, 937, doi: 10.1046/j.1365-8711.2003.06241.x G¨ otberg, Y., de Mink, S

    Shen, S., Mo, H. J., White, S. D. M., et al. 2003, MNRAS, 343, 978, doi: 10.1046/j.1365-8711.2003.06740.x

    work page doi:10.1046/j.1365-8711.2003.06740.x 2003

  57. [57]

    2025, A&A, 695, A20, doi: 10.1051/0004-6361/202452570

    Shuntov, M., Ilbert, O., Toft, S., et al. 2025, A&A, 695, A20, doi: 10.1051/0004-6361/202452570

    work page doi:10.1051/0004-6361/202452570 2025

  58. [58]

    S., & Dopita, M

    Sutherland, R. S., & Dopita, M. A. 1993, ApJS, 88, 253, doi: 10.1086/191823

    work page doi:10.1086/191823 1993

  59. [59]

    , number =

    Teyssier, R. 2002, A&A, 385, 337, doi: 10.1051/0004-6361:20011817

    work page doi:10.1051/0004-6361:20011817 2002

  60. [60]

    R., et al

    Tortora, C., Busillo, V., Napolitano, N. R., et al. 2025, arXiv e-prints, arXiv:2502.13589, doi: 10.48550/arXiv.2502.13589

    work page doi:10.48550/arxiv.2502.13589 2025

  61. [61]

    A., Heckman, T

    Tremonti, C. A., Heckman, T. M., Kauffmann, G., et al. 2004, ApJ, 613, 898, doi: 10.1086/423264

    work page doi:10.1086/423264 2004

  62. [62]

    2024, arXiv e-prints, arXiv:2409.15909, doi: 10.48550/arXiv.2409.15909 van der Wel, A

    Tsukui, T., Wisnioski, E., Bland-Hawthorn, J., & Freeman, K. 2024, arXiv e-prints, arXiv:2409.15909, doi: 10.48550/arXiv.2409.15909 van der Wel, A. 2008, ApJL, 675, L13, doi: 10.1086/529432

    work page doi:10.48550/arxiv.2409.15909 2024

  63. [63]

    H., & Tinker, J

    Wechsler, R. H., & Tinker, J. L. 2018, Annual Review of Astronomy and Astrophysics, 56, 435–487, doi: 10.1146/annurev-astro-081817-051756

    work page Pith review doi:10.1146/annurev-astro-081817-051756 2018

  64. [64]

    R., Tinker, J

    Wetzel, A. R., Tinker, J. L., Conroy, C., & van den Bosch, F. C. 2013, MNRAS, 432, 336, doi: 10.1093/mnras/stt469

    work page doi:10.1093/mnras/stt469 2013

  65. [65]

    2021, The Astrophysical Journal, 922, 249, doi: 10.3847/1538-4357/ac2302

    Yoon, Y., Park, C., Chung, H., & Zhang, K. 2021, The Astrophysical Journal, 922, 249, doi: 10.3847/1538-4357/ac2302

    work page doi:10.3847/1538-4357/ac2302 2021