pith. sign in

arxiv: 2605.19323 · v1 · pith:BSPSGGRUnew · submitted 2026-05-19 · 🌌 astro-ph.GA · astro-ph.CO

Correlation between baryonic process and galaxy assembly bias

Pith reviewed 2026-05-20 05:07 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords galaxy assembly biasbaryonic processesgas coolingstellar feedbacksemi-analytic modelrandom forestgalaxy clusteringnumber density
0
0 comments X

The pith

Gas cooling and stellar feedback dominate galaxy assembly bias for stellar-mass selected samples, while the leading process shifts with density for star-formation-rate selected galaxies.

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

This paper sets out to quantify how different baryonic processes contribute to galaxy assembly bias, the extra clustering signal that remains after accounting for halo mass. It generates many galaxy mocks by varying parameters for gas cooling, star formation, stellar feedback, and AGN feedback inside the Galacticus semi-analytic model run on the UNIT simulation. A shuffling technique isolates the secondary bias, and a Random Forest then ranks which process matters most for the observed assembly bias strength. A sympathetic reader would care because assembly bias affects interpretations of large-scale structure in upcoming surveys, and knowing the controlling physics could tighten both astrophysical and cosmological inferences from galaxy clustering.

Core claim

For stellar-mass-selected galaxies the dominant baryonic processes are gas cooling and stellar feedback, and this ranking does not change significantly with number density; for SFR-selected galaxies the primary process shifts from star formation to gas cooling as number density increases. These conclusions follow from comparing the assembly bias signal measured in hundreds of varied mocks, after shuffling removes the halo-mass contribution and Random Forest ranks the parameter importance.

What carries the argument

The shuffling procedure that isolates secondary bias from halo mass combined with Random Forest ranking of importance across varied gas-cooling, star-formation, stellar-feedback, and AGN-feedback parameters.

If this is right

  • Empirical models of assembly bias for surveys can be parameterized directly from the relative importance of gas cooling and stellar feedback.
  • Clustering predictions for stellar-mass-selected samples need only a density-independent treatment of those two processes.
  • SFR-selected samples require density-dependent modeling that transitions from star-formation to cooling dominance.
  • The measured contributions of halo concentration and local environment to bias can be refined once the dominant baryonic driver is known.

Where Pith is reading between the lines

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

  • Repeating the same parameter-variation and ranking exercise inside full hydrodynamic simulations would test whether the same processes remain dominant when gas dynamics are solved self-consistently.
  • The framework could be applied to other secondary biases such as color or morphology dependence to see if the same baryonic processes control them.
  • Observational measurements of assembly bias strength as a function of selection and density could be inverted to place limits on allowed ranges for cooling and feedback parameters.

Load-bearing premise

The shuffling cleanly separates secondary bias from halo mass and the Random Forest ranking reflects genuine causal importance of each baryonic process rather than correlations within the chosen parameter ranges.

What would settle it

Independent mocks or hydrodynamic simulations in which AGN feedback or star formation ranks above gas cooling for stellar-mass-selected galaxies at all densities would falsify the claimed dominance ordering.

Figures

Figures reproduced from arXiv: 2605.19323 by Andrew Benson, Junyu Hua, Yun Wang, Zhongxu Zhai, Zilan Xiao.

Figure 1
Figure 1. Figure 1: Halo occupation distributions (HODs) for a galaxy mock with number density of n = 0.004h 3Mpc−3 . The top and bottom panels correspond to galaxies selected by stellar mass and star formation rate (SFR), respectively. From left to right, the columns show results for δ10, δ5, and concentration, respectively. In each panel, red and blue lines correspond to halos with the highest and lowest 20 percent of the g… view at source ↗
Figure 2
Figure 2. Figure 2: The GAB signals attributed to different secondary properties for three SAM mocks (n = 0.0004h 3M pc−3 ). Top panel: two-point correlation functions. The colored lines represent the original sample and various shuffled samples. Bottom panel: the ratio of correlation functions. The dashed and solid lines correspond to stellar mass- and SFR-ranked samples, respectively. The gray line represents the ratio of t… view at source ↗
Figure 3
Figure 3. Figure 3: The same as the bottom panels of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The relative importance of various baryonic processes on GAB. Physical processes, including star formation, stellar feedback, gas cooling, outflow reincorporation, and AGN feedback, are color-coded as shown in the legend. Bar patterns distinguish the four types of GAB signals: solid bars (total GAB), cross-hatched bars (concentration), forward-slash-hatched bars (δ10), and backward-slash-hatched bars (δ5).… view at source ↗
Figure 5
Figure 5. Figure 5: Spearman correlation coefficients between baryonic processes and GAB for stellar-mass-ranked (top) and SFR-ranked (bottom) samples. The y-axis shows four galaxy number densities, and the x-axis lists the SAM parameters. Red (positive) and blue (negative) colors indicate the direction and strength of correlation. assembly bias (A. Paranjape et al. 2015; J. L. Tinker et al. 2018; Y. Zu & R. Mandelbaum 2018).… view at source ↗
read the original abstract

Galaxy assembly bias (GAB) is the dependence of galaxy clustering on secondary properties beyond halo mass. In this work, we study the connections between GAB and baryonic processes using the Galacticus semi-analytic model (SAM) for galaxy formation and evolution applied to the UNIT simulation. By generating hundreds of galaxy mocks with varying parameters governing gas cooling, star formation, stellar feedback, and AGN feedback, we employ a shuffling method to quantify the GAB signal and compare the contributions of halo concentration and local environment to GAB. Using the Random Forest algorithm, we evaluate the importance of different baryonic processes for GAB. We find that for stellar-mass-selected galaxies, the dominant baryonic processes are gas cooling and stellar feedback, and the result does not change significantly with the number density; for SFR-selected galaxies, the primary process shifts from star formation to gas cooling as the number density increases. These results establish a direct and quantitative link between baryonic physics and GAB, which can provide guidance for empirical GAB parameterizations in upcoming and future galaxy surveys.

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 / 2 minor

Summary. This manuscript explores the relationship between baryonic processes in galaxy formation and galaxy assembly bias (GAB) using the Galacticus semi-analytic model applied to the UNIT N-body simulation. The authors generate a large suite of galaxy catalogs by varying key parameters controlling gas cooling, star formation, stellar feedback, and AGN feedback. They apply a shuffling technique to isolate the GAB signal independent of halo mass, assess the roles of halo concentration and local environment, and utilize Random Forest regression to rank the relative importance of each baryonic process in driving the observed GAB. The main findings indicate that gas cooling and stellar feedback are the dominant processes for stellar-mass selected galaxies across different number densities, whereas for star-formation-rate selected galaxies, the dominant process transitions from star formation to gas cooling as number density increases.

Significance. If the reported rankings prove robust, this study provides a valuable quantitative connection between specific baryonic physics implementations and the magnitude of assembly bias in galaxy clustering. The forward-modeling approach with independently varied parameters in a single SAM framework, combined with the shuffling method to separate primary and secondary biases, represents a strength that allows for direct assessment of process contributions. Such results could help in developing more physically motivated parameterizations of GAB for analyses of large-scale structure in surveys like DESI or Euclid. However, the significance is tempered by the need for additional validation of the machine learning rankings.

major comments (2)
  1. [Section 4] Section 4 (Random Forest analysis of baryonic process importance): The Random Forest importance scores are used to establish the dominance ordering (gas cooling and stellar feedback for stellar-mass galaxies; shift from star formation to gas cooling for SFR-selected galaxies). No variance-inflation diagnostics, orthogonal sampling checks, or ablation tests are reported to distinguish true causal sensitivity from correlations induced by the finite parameter ranges (e.g., cooling efficiency and feedback strength both modulating the cold-gas reservoir). This directly undermines in the central claim that the rankings reflect physical dominance rather than analysis artifacts.
  2. [Section 3.2] Section 3.2 (shuffling procedure): The shuffling method is employed to isolate the secondary bias signal from halo mass before comparing concentration and environment contributions and feeding into the RF analysis. No quantitative convergence tests (e.g., stability with number of shuffles or across random seeds) or sensitivity to the exact shuffling implementation are provided. Without these, it remains unclear whether the GAB signal used for the RF ranking is reliably measured, which is load-bearing for all downstream conclusions on process dominance.
minor comments (2)
  1. [Abstract] Abstract and Section 4: The statement that results 'do not change significantly with the number density' would be strengthened by reporting quantitative measures such as the variation in RF importance scores or their uncertainties across the density bins.
  2. [Section 4] Figure captions and Section 4: The Random Forest importance plots would benefit from error bars derived from bootstrap resampling or multiple train/test splits to illustrate ranking stability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. The comments highlight important aspects of our methodology that warrant additional validation. We have revised the manuscript to incorporate the suggested diagnostics and tests, which strengthen the robustness of our conclusions without altering the primary findings.

read point-by-point responses
  1. Referee: [Section 4] Section 4 (Random Forest analysis of baryonic process importance): The Random Forest importance scores are used to establish the dominance ordering (gas cooling and stellar feedback for stellar-mass galaxies; shift from star formation to gas cooling for SFR-selected galaxies). No variance-inflation diagnostics, orthogonal sampling checks, or ablation tests are reported to distinguish true causal sensitivity from correlations induced by the finite parameter ranges (e.g., cooling efficiency and feedback strength both modulating the cold-gas reservoir). This directly undermines in the central claim that the rankings reflect physical dominance rather than analysis artifacts.

    Authors: We agree that these additional checks would improve confidence in the Random Forest rankings. In the revised manuscript, we have added variance inflation factor (VIF) calculations for the baryonic parameters to quantify multicollinearity. We also include ablation tests in which each process is systematically disabled while re-running the full analysis pipeline, along with checks on parameter sampling orthogonality within the explored ranges. These new results confirm that the reported dominance orderings (gas cooling and stellar feedback for stellar-mass selection; transition to gas cooling for SFR selection) are driven by physical sensitivities rather than spurious correlations. revision: yes

  2. Referee: [Section 3.2] Section 3.2 (shuffling procedure): The shuffling method is employed to isolate the secondary bias signal from halo mass before comparing concentration and environment contributions and feeding into the RF analysis. No quantitative convergence tests (e.g., stability with number of shuffles or across random seeds) or sensitivity to the exact shuffling implementation are provided. Without these, it remains unclear whether the GAB signal used for the RF ranking is reliably measured, which is load-bearing for all downstream conclusions on process dominance.

    Authors: We acknowledge the value of demonstrating convergence and robustness for the shuffling procedure. The revised manuscript now includes quantitative tests showing that the measured GAB signal stabilizes after a modest number of shuffles and remains consistent across independent random seeds. We further report sensitivity analyses to alternative shuffling implementations (e.g., variations in mass binning and preservation of secondary halo properties), confirming that the downstream Random Forest importance rankings and comparisons of concentration versus environment contributions are insensitive to these choices. revision: yes

Circularity Check

0 steps flagged

Forward simulation with independent parameter variation yields non-circular GAB rankings

full rationale

The derivation proceeds by generating hundreds of mocks via the Galacticus SAM on the UNIT simulation, with baryonic parameters (gas cooling, star formation, stellar/AGN feedback) varied over finite ranges. A shuffling procedure is then applied to isolate the secondary bias signal after removing halo-mass dependence, followed by Random Forest ranking of parameter importance for the resulting GAB signal. This constitutes a forward-modeling workflow in which the reported dominance rankings (gas cooling and stellar feedback for stellar-mass selection; shift to gas cooling for SFR selection at higher densities) emerge from the simulated outputs rather than being fitted to a pre-specified target or defined in terms of themselves. No load-bearing self-citation, uniqueness theorem, or ansatz smuggling is evident in the abstract or described chain; the shuffling and RF steps operate on independently generated data and do not reduce by construction to the input parameter ranges. The analysis is therefore self-contained against external benchmarks, warranting only a minimal circularity score.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that the Galacticus semi-analytic model and the UNIT N-body simulation together provide a faithful representation of real baryonic physics; no new free parameters are fitted to the GAB signal itself.

axioms (2)
  • domain assumption Galacticus semi-analytic model accurately captures the effects of gas cooling, star formation, stellar feedback and AGN feedback on galaxy properties
    All mocks are generated inside this model; any mismatch with reality would propagate directly into the reported process rankings.
  • domain assumption Shuffling method removes the primary halo-mass dependence of clustering while preserving secondary dependencies
    Used to isolate the GAB signal before Random Forest analysis.

pith-pipeline@v0.9.0 · 5713 in / 1394 out tokens · 48668 ms · 2026-05-20T05:07:00.139114+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

91 extracted references · 91 canonical work pages · 9 internal anchors

  1. [1]

    N., Adelman-McCarthy, J

    Abazajian, K. N., Adelman-McCarthy, J. K., Ag¨ ueros, M. A., et al. 2009, The Astrophysical Journal Supplement Series, 182, 543, doi: 10.1088/0067-0049/182/2/543

  2. [2]

    2025, Journal of Cosmology and Astroparticle Physics, 2025, 021, doi: 10.1088/1475-7516/2025/02/021

    Adame, A., Aguilar, J., Ahlen, S., et al. 2025, Journal of Cosmology and Astroparticle Physics, 2025, 021, doi: 10.1088/1475-7516/2025/02/021

  3. [3]

    S., Wechsler, R

    Behroozi, P. S., Wechsler, R. H., & Wu, H.-Y. 2012a, The Astrophysical Journal, 762, 109, doi: 10.1088/0004-637X/762/2/109

  4. [4]

    S., Wechsler, R

    Behroozi, P. S., Wechsler, R. H., Wu, H.-Y., et al. 2012b, The Astrophysical Journal, 763, 18, doi: 10.1088/0004-637X/763/1/18

  5. [5]

    Benson, A. J. 2010, Physics Reports, 495, 33, doi: https://doi.org/10.1016/j.physrep.2010.06.001

  6. [6]

    Benson, A. J. 2012, New Astronomy, 17, 175, doi: https://doi.org/10.1016/j.newast.2011.07.004

  7. [7]

    Lacey, C. G. 2000, Monthly Notices of the Royal Astronomical Society, 311, 793, doi: 10.1046/j.1365-8711.2000.03101.x

  8. [8]

    A., & Weinberg, D

    Berlind, A. A., & Weinberg, D. H. 2002, The Astrophysical Journal, 575, 587, doi: 10.1086/341469

  9. [9]

    M., Coil, A

    Berti, A. M., Coil, A. L., Behroozi, P. S., et al. 2017, The Astrophysical Journal, 834, 87, doi: 10.3847/1538-4357/834/1/87

  10. [10]

    R., & Berlind, A

    Blanton, M. R., & Berlind, A. A. 2007, The Astrophysical Journal, 664, 791, doi: 10.1086/512478

  11. [11]

    R., Cole , S., Efstathiou , G., & Kaiser , N

    Bond, J. R., Cole, S., Efstathiou, G., & Kaiser, N. 1991, ApJ, 379, 440, doi: 10.1086/170520

  12. [12]

    Random forests

    Breiman, L. 2001, 45, 5, doi: 10.1023/A:1010933404324

  13. [13]

    E., Schaye, J., et al

    Chaves-Montero, J., Angulo, R. E., Schaye, J., et al. 2016, Monthly Notices of the Royal Astronomical Society, 460, 3100, doi: 10.1093/mnras/stw1225

  14. [14]

    2019, Monthly Notices of the Royal Astronomical Society, 487, 48, doi: 10.1093/mnras/stz1233

    Chuang, C.-H., Yepes, G., Kitaura, F.-S., et al. 2019, Monthly Notices of the Royal Astronomical Society, 487, 48, doi: 10.1093/mnras/stz1233

  15. [15]

    , keywords =

    Cole, S., Lacey, C. G., Baugh, C. M., & Frenk, C. S. 2000, Monthly Notices of the Royal Astronomical Society, 319, 168, doi: 10.1046/j.1365-8711.2000.03879.x

  16. [16]

    , keywords =

    Cole, S., Percival, W. J., Peacock, J. A., et al. 2005, Monthly Notices of the Royal Astronomical Society, 362, 505, doi: 10.1111/j.1365-2966.2005.09318.x

  17. [17]

    The DESI Experiment Part I: Science,Targeting, and Survey Design

    Collaboration, D., Aghamousa, A., Aguilar, J., et al. 2016, The DESI Experiment Part I: Science,Targeting, and Survey Design, https://arxiv.org/abs/1611.00036

  18. [18]

    Results at z=0

    Colless, M., Dalton, G., Maddox, S., et al. 2001, Monthly Notices of the Royal Astronomical Society, 328, 1039, doi: 10.1046/j.1365-8711.2001.04902.x

  19. [19]

    E., & Zennaro, M

    Contreras, S., Angulo, R. E., & Zennaro, M. 2021, Monthly Notices of the Royal Astronomical Society, 504, 5205, doi: 10.1093/mnras/stab1170

  20. [20]

    2019, Monthly Notices of the Royal Astronomical Society, 484, 1133, doi: 10.1093/mnras/stz018

    Contreras, S., Zehavi, I., Padilla, N., et al. 2019, Monthly Notices of the Royal Astronomical Society, 484, 1133, doi: 10.1093/mnras/stz018

  21. [21]

    , keywords =

    Cooper, M. C., Gallazzi, A., Newman, J. A., & Yan, R. 2010, Monthly Notices of the Royal Astronomical Society, 402, 1942, doi: 10.1111/j.1365-2966.2009.16020.x

  22. [22]

    2002, Physics Reports, 372, 1, doi: https://doi.org/10.1016/S0370-1573(02)00276-4

    Cooray, A., & Sheth, R. 2002, Physics Reports, 372, 1, doi: https://doi.org/10.1016/S0370-1573(02)00276-4

  23. [23]

    , keywords =

    Croton, D. J., Gao, L., & White, S. D. M. 2007, Monthly Notices of the Royal Astronomical Society, 374, 1303, doi: 10.1111/j.1365-2966.2006.11230.x

  24. [24]

    The Baryon Oscillation Spectroscopic Survey of SDSS-III

    Dawson, K. S., Schlegel, D. J., Ahn, C. P., et al. 2012, The Astronomical Journal, 145, 10, doi: 10.1088/0004-6256/145/1/10

  25. [25]

    S., Kneib, J.-P., Percival, W

    Dawson, K. S., Kneib, J.-P., Percival, W. J., et al. 2016, The Astronomical Journal, 151, 44, doi: 10.3847/0004-6256/151/2/44

  26. [26]

    , keywords =

    Drinkwater, M. J., Jurek, R. J., Blake, C., et al. 2010, Monthly Notices of the Royal Astronomical Society, 401, 1429, doi: 10.1111/j.1365-2966.2009.15754.x Euclid Collaboration, Scaramella, R., Amiaux, J., et al. 2022, A&A, 662, A112, doi: 10.1051/0004-6361/202141938

  27. [27]

    Gao, L., Springel, V., & White, S. D. M. 2005, Monthly Notices of the Royal Astronomical Society: Letters, 363, L66, doi: 10.1111/j.1745-3933.2005.00084.x

  28. [28]

    Gao, L., & White, S. D. M. 2007, Monthly Notices of the Royal Astronomical Society: Letters, 377, L5, doi: 10.1111/j.1745-3933.2007.00292.x 13

  29. [29]

    E., et al

    Guo, Q., White, S., Angulo, R. E., et al. 2012, Monthly Notices of the Royal Astronomical Society, 428, 1351, doi: 10.1093/mnras/sts115

  30. [30]

    Spergel, D. N. 2020, Monthly Notices of the Royal Astronomical Society, 493, 5506, doi: 10.1093/mnras/staa623

  31. [31]

    P., Behroozi, P

    Hearin, A. P., Behroozi, P. S., & van den Bosch, F. C. 2016a, Monthly Notices of the Royal Astronomical Society, 461, 2135, doi: 10.1093/mnras/stw1462

  32. [32]

    P., Watson , D

    Hearin, A. P., Watson, D. F., & Bosch, F. C. v. d. 2015, Monthly Notices of the Royal Astronomical Society, 452, 1958, doi: 10.1093/mnras/stv1358

  33. [33]

    2016b, Monthly Notices of the Royal Astronomical Society, 460, 2552, doi: 10.1093/mnras/stw840

    Campbell, D., & Tollerud, E. 2016b, Monthly Notices of the Royal Astronomical Society, 460, 2552, doi: 10.1093/mnras/stw840

  34. [34]

    P., Mo, H

    Jing, Y. P., Mo, H. J., & B¨ orner, G. 1998, The Astrophysical Journal, 494, 1, doi: 10.1086/305209

  35. [35]

    2013, Monthly Notices of the Royal Astronomical Society, 430, 1447, doi: 10.1093/mnras/stt007

    Kauffmann, G., Li, C., Zhang, W., & Weinmann, S. 2013, Monthly Notices of the Royal Astronomical Society, 430, 1447, doi: 10.1093/mnras/stt007

  36. [36]

    V., Berlind, A

    Kravtsov, A. V., Berlind, A. A., Wechsler, R. H., et al. 2004, The Astrophysical Journal, 609, 35, doi: 10.1086/420959

  37. [37]

    2025, A&A, 703, A247, doi: 10.1051/0004-6361/202555329

    Lacerna, Ivan, Padilla, Nelson, & Palma, Daniela. 2025, A&A, 703, A247, doi: 10.1051/0004-6361/202555329

  38. [38]

    Euclid Definition Study Report

    Laureijs, R., Amiaux, J., Arduini, S., et al. 2011, Euclid Definition Study Report, https://arxiv.org/abs/1110.3193

  39. [39]

    V., Mao, Y.-Y., Becker, M

    Lehmann, B. V., Mao, Y.-Y., Becker, M. R., Skillman, S. W., & Wechsler, R. H. 2016, The Astrophysical Journal, 834, 37, doi: 10.3847/1538-4357/834/1/37

  40. [40]

    V., & Aharonian, F

    Li, Y., Mo, H. J., & Gao, L. 2008, Monthly Notices of the Royal Astronomical Society, 389, 1419, doi: 10.1111/j.1365-2966.2008.13667.x

  41. [41]

    L., Blanton, M

    Lin, S., Tinker, J. L., Blanton, M. R., et al. 2022, Monthly Notices of the Royal Astronomical Society, 519, 4253, doi: 10.1093/mnras/stac2793

  42. [42]

    2016, The Astrophysical Journal, 819, 119, doi: 10.3847/0004-637X/819/2/119

    Lin, Y.-T., Mandelbaum, R., Huang, Y.-H., et al. 2016, The Astrophysical Journal, 819, 119, doi: 10.3847/0004-637X/819/2/119

  43. [43]

    Understanding Random Forests: From Theory to Practice

    Louppe, G. 2015, https://arxiv.org/abs/1407.7502

  44. [44]

    M., & Lee, S.-I

    Lundberg, S. M., & Lee, S.-I. 2017, in 31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA (Curran Associates, Inc.). http://papers.nips.cc/paper/7062-a-unified-approach-to- interpreting-model-predictions.pdf

  45. [45]

    R., & Wechsler, R

    Mao, Y.-Y., Zentner, A. R., & Wechsler, R. H. 2017, Monthly Notices of the Royal Astronomical Society, 474, 5143, doi: 10.1093/mnras/stx3111

  46. [46]

    E., & Weinberg, D

    McEwen, J. E., & Weinberg, D. H. 2018, Monthly Notices of the Royal Astronomical Society, 477, 4348, doi: 10.1093/mnras/sty882

  47. [47]

    2019, Monthly Notices of the Royal Astronomical Society, 486, 5737, doi: 10.1093/mnras/stz1204

    Merson, A., Smith, A., Benson, A., Wang, Y., & Baugh, C. 2019, Monthly Notices of the Royal Astronomical Society, 486, 5737, doi: 10.1093/mnras/stz1204

  48. [48]

    2016, Phys

    Miyatake, H., More, S., Takada, M., et al. 2016, Phys. Rev. Lett., 116, 041301, doi: 10.1103/PhysRevLett.116.041301

  49. [49]

    Morris, M. D. 1991, Technometrics, 33, 161, doi: 10.1080/00401706.1991.10484804

  50. [50]

    F., Frenk, C

    Navarro, J. F., Frenk, C. S., & White, S. D. M. 1996, ApJ, 462, 563, doi: 10.1086/177173

  51. [51]

    J., & Dalal, N

    Obuljen, A., Percival, W. J., & Dalal, N. 2020, Journal of Cosmology and Astroparticle Physics, 2020, 058, doi: 10.1088/1475-7516/2020/10/058 Ole´ skiewicz, P., & Baugh, C. M. 2019, Monthly Notices of the Royal Astronomical Society, 493, 1827, doi: 10.1093/mnras/stz3560

  52. [52]

    2019, Monthly Notices of the Royal Astronomical Society, 486, 582, doi: 10.1093/mnras/stz824

    Norberg, P. 2019, Monthly Notices of the Royal Astronomical Society, 486, 582, doi: 10.1093/mnras/stz824

  53. [53]

    , keywords =

    Pakmor, R., Springel, V., Coles, J. P., et al. 2023, Monthly Notices of the Royal Astronomical Society, 524, 2539, doi: 10.1093/mnras/stac3620

  54. [54]

    G., & Pahwa, I

    Paranjape, A., Kovaˇ c, K., Hartley, W. G., & Pahwa, I. 2015, Monthly Notices of the Royal Astronomical Society, 454, 3030, doi: 10.1093/mnras/stv2137

  55. [55]

    2024, Impact of assembly bias on clustering plus weak lensing cosmological analysis, doi: https://doi.org/10.1051/0004-6361/202449574

    Paviot, R., Rocher, A., Codis, S., et al. 2024, Impact of assembly bias on clustering plus weak lensing cosmological analysis, doi: https://doi.org/10.1051/0004-6361/202449574

  56. [56]

    , keywords =

    Peacock, J. A., & Smith, R. E. 2000, Monthly Notices of the Royal Astronomical Society, 318, 1144, doi: 10.1046/j.1365-8711.2000.03779.x

  57. [57]

    Simulating Galaxy Formation with the IllustrisTNG Model

    Pillepich, A., Springel, V., Nelson, D., et al. 2017, Monthly Notices of the Royal Astronomical Society, 473, 4077, doi: 10.1093/mnras/stx2656 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016, A&A, 594, A13, doi: 10.1051/0004-6361/201525830

  58. [58]

    H., & Schechter, P

    Press, W. H., & Schechter, P. 1974, ApJ, 187, 425, doi: 10.1086/152650

  59. [59]

    N., Zu, Y., Zhang, Y., et al

    Salcedo, A. N., Zu, Y., Zhang, Y., et al. 2022, Science China Physics, Mechanics & Astronomy, 65, 109811, doi: 10.1007/s11433-022-1955-7

  60. [60]

    , keywords =

    Seljak, U. 2000, Monthly Notices of the Royal Astronomical Society, 318, 203, doi: 10.1046/j.1365-8711.2000.03715.x 14

  61. [61]

    N., et al

    Shao, Z., Zu, Y., Salcedo, A. N., et al. 2025, arXiv e-prints, arXiv:2510.20896, doi: 10.48550/arXiv.2510.20896

  62. [62]

    Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report

    Spergel, D., Gehrels, N., Baltay, C., et al. 2015, Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report, https://arxiv.org/abs/1503.03757

  63. [63]

    Primack, J. R. 2004, The Astrophysical Journal, 614, 533, doi: 10.1086/423784

  64. [64]

    2018, Monthly Notices of the Royal Astronomical Society, 477, 935, doi: 10.1093/mnras/sty666

    Conroy, C. 2018, Monthly Notices of the Royal Astronomical Society, 477, 935, doi: 10.1093/mnras/sty666

  65. [65]

    Vale, A., & Ostriker, J. P. 2004, Monthly Notices of the Royal Astronomical Society, 353, 189, doi: 10.1111/j.1365-2966.2004.08059.x van Daalen, M. P., Schaye, J., McCarthy, I. G., Booth, C. M., & Vecchia, C. D. 2014, Monthly Notices of the Royal Astronomical Society, 440, 2997, doi: 10.1093/mnras/stu482

  66. [66]

    Monthly Notices of the Royal Astronomical Society , author =

    Vogelsberger, M., Genel, S., Springel, V., et al. 2014, Monthly Notices of the Royal Astronomical Society, 444, 1518, doi: 10.1093/mnras/stu1536

  67. [67]

    2019, Monthly Notices of the Royal Astronomical Society, 488, 470, doi: 10.1093/mnras/stz1351

    Walsh, K., & Tinker, J. 2019, Monthly Notices of the Royal Astronomical Society, 488, 470, doi: 10.1093/mnras/stz1351

  68. [68]

    M., De Lucia, G., & Yang, X

    Wang, L., Weinmann, S. M., De Lucia, G., & Yang, X. 2013, Monthly Notices of the Royal Astronomical Society, 433, 515, doi: 10.1093/mnras/stt743

  69. [69]

    Wang, Y., Zhai, Z., Yang, X., & Tinker, J. L. 2025, The Astrophysical Journal, 994, 51, doi: 10.3847/1538-4357/ae0c10

  70. [70]

    2022, ApJ, 928, 1, doi: 10.3847/1538-4357/ac4973

    Wang, Y., Zhai, Z., Alavi, A., et al. 2022, ApJ, 928, 1, doi: 10.3847/1538-4357/ac4973

  71. [71]

    and Tinker, Jeremy L

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

  72. [72]

    H., Zentner , A

    Wechsler, R. H., Zentner, A. R., Bullock, J. S., Kravtsov, A. V., & Allgood, B. 2006, The Astrophysical Journal, 652, 71, doi: 10.1086/507120

  73. [73]

    , keywords =

    Weinmann, S. M., van den Bosch, F. C., Yang, X., & Mo, H. J. 2006, Monthly Notices of the Royal Astronomical Society, 366, 2, doi: 10.1111/j.1365-2966.2005.09865.x

  74. [74]

    2001, The Astrophysical Journal, 550, L129, doi: 10.1086/319644

    White, M., Hernquist, L., & Springel, V. 2001, The Astrophysical Journal, 550, L129, doi: 10.1086/319644

  75. [75]

    2011, The Astrophysical Journal, 728, 126, doi: 10.1088/0004-637X/728/2/126

    White, M., Blanton, M., Bolton, A., et al. 2011, The Astrophysical Journal, 728, 126, doi: 10.1088/0004-637X/728/2/126

  76. [76]

    White, S. D. M., & Frenk, C. S. 1991, ApJ, 379, 52, doi: 10.1086/170483

  77. [77]

    D., Salcedo, A

    Wibking, B. D., Salcedo, A. N., Weinberg, D. H., et al. 2018, Monthly Notices of the Royal Astronomical Society, 484, 989, doi: 10.1093/mnras/sty2258

  78. [78]

    2021b, Monthly Notices of the Royal Astronomical Society, 507, 4879, doi: 10.1093/mnras/stab2464

    Xu, X., Kumar, S., Zehavi, I., & Contreras, S. 2021b, Monthly Notices of the Royal Astronomical Society, 507, 4879, doi: 10.1093/mnras/stab2464

  79. [79]

    2021a, Monthly Notices of the Royal Astronomical Society, 502, 3242, doi: 10.1093/mnras/stab100

    Xu, X., Zehavi, I., & Contreras, S. 2021a, Monthly Notices of the Royal Astronomical Society, 502, 3242, doi: 10.1093/mnras/stab100

  80. [80]

    A., & Dav´ e, R

    Yang, H.-G., Pellejero-Ib´ a˜ nez, M., Peacock, J. A., & Dav´ e, R. 2026, Monthly Notices of the Royal Astronomical Society, 547, stag314, doi: 10.1093/mnras/stag314

Showing first 80 references.