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The Three Hundred Project hydrodynamical simulations: Hydrodynamical weak-lensing cluster mass biases and richnesses using different hydro models

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Two simulation codes with different baryon treatments give consistent weak-lensing mass–richness relations for clusters.

desk verdict Solid extension of the Three Hundred weak-lensing calibration to a second hydro code; the fitting tables are useful, but the redMaPPer agreement is partly tuned by the stellar-mass cut and should be read as conditional. read the letter →

arxiv 2501.14019 v2 pith:FDMNQUHF submitted 2025-01-23 astro-ph.CO astro-ph.GA

Carlo Giocoli , Giulia Despali , Massimo Meneghetti , Elena Rasia , Lauro Moscardini , Stefano Borgani , Giorgio. F. Lesci , Federico Marulli
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Weiguang Cui Gustavo Yepes
This is my paper · ORCID
classification astro-ph.COastro-ph.GA
keywords galaxyclustersweakgravitationallensingmass-richnessrelationhydrodynamicalsimulationsbaryonicfeedbackprojectioneffectsclustercosmologymass-observablerelations
topics Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether the way baryons are treated in simulations changes the masses weak lensing recovers for galaxy clusters, and whether a galaxy-count proxy called richness can still be calibrated to those masses. The answer it defends is no for the first question and yes for the second: the weak-lensing mass bias is the same within uncertainties for the GadgetX and GIZMO-SIMBA hydrodynamical runs and a dark-matter-only run, when the lensing mass is compared with the true mass of the same simulation. The paper then measures the weak-lensing mass–observed richness relation, $\langle\log\lambda_{\rm obs}|M_{\rm wl}\rangle = A(z)+B(z)\log(M_{\rm wl}/M_p)$, and finds both hydro runs consistent within $1\sigma$; in the combined fit the intercept is redshift-independent, the slope is a second-order polynomial in $z$ but nearly flat below $z\simeq0.55$, and the scatter grows linearly with redshift. With a minimum stellar mass of $10^{10}\,h^{-1}\,M_\odot$, the simulated relation lines up with SDSS redMaPPer calibrations, so the fitted relations are offered as model priors for cluster-count cosmology.

What carries the argument

The load-bearing tool is a forward-model weak-lensing pipeline applied to the same 324 clusters run with GadgetX, GIZMO-SIMBA, and a dark-matter-only version. Particles within $\pm5$ Mpc along the line of sight are collapsed onto lens planes for three orthogonal projections, shear maps are sampled at 30 background galaxies per square arcminute, and the excess surface mass density profiles are fitted with a smoothly truncated Navarro-Frenk-White (BMO) profile using a Bayesian Monte Carlo Markov Chain to obtain $M_{\mathrm{wl}}$ and concentration. Richness is defined as the count of haloes and subhaloes above a stellar mass threshold in a cylinder of radius $R_{200}$ and height 10 Mpc, corrected for projected interlopers by subtracting $4/33$ of the halo count in an outer annulus (Eq. 14). The mass–richness relations are extracted by Bayesian linear regression with a Gaussian likelihood that propagates errors on both axes, producing the redshift- and stellar-mass-cut-dependent regression parameters in Tables 1 and 2.

What would settle it

Run the paper's cylinder-count richness estimator on a realistic mock galaxy catalogue that includes photometric noise and selection, then run the redMaPPer cluster finder on the same catalogue: if the redMaPPer richness differs from $\lambda_{\rm obs}$ systematically with mass or redshift beyond the quoted scatter, the calibration would not transfer to real surveys. A direct observational check is to measure the slope and scatter of the mass–richness relation for SDSS redMaPPer clusters at $z<0.3$ with a stellar-mass-complete sample and compare with the $M_{\mathrm{star,min}}=10^{10}\,h^{-1}\,M_\odot$ prediction.

Watch

Extended reading notes

Core claim

The paper establishes that baryonic physics does not break the weak-lensing calibration of cluster masses. Comparing the average weak-lensing mass bias of the two hydro runs with the dark-matter-only reference, the biases agree when each hydro run is compared with its own true mass, while relative to the DM-only mass GadgetX masses run a few percent high and GIZMO-SIMBA a few percent low, with the offsets closing above $M_{200,\mathrm{DM}}\simeq10^{15}\,h^{-1}\,M_\odot$. It then constructs the observed richness from projected halo and subhalo counts with background subtraction, fits $\langle\log\lambda_{\rm obs}|M_{\rm wl}\rangle$ with a Bayesian linear regression, and shows that the two hydro codes give regression parameters consistent within $1\sigma$. In the combined model, the intercept depends only on the stellar mass threshold, the slope follows a second-order polynomial in redshift and stays roughly constant up to $z\simeq0.55$, and the scatter in richness at fixed weak-lensing mass grows linearly with redshift; the scatter is smaller when richness is tied to the true mass. At $M_{\mathrm{star,min}}=10^{10}\,h^{-1}\,M_\odot$ the observed-richness–weak-lensing-mass relation matches SDSS redMaPPer clusters, which is the paper's basis for offering the fits as priors for survey cluster cosmology.

Load-bearing premise

The load-bearing assumption is that counting simulated galaxies above a stellar mass limit in a cylinder and subtracting a fixed background fraction gives the same number that real survey algorithms such as redMaPPer record as richness; if real membership probabilities or the stellar-mass calibration do not match that count, the calibrated mass–richness relation would not apply to observed clusters.

Editorial extensions

If this is right

  • The weak-lensing mass bias of clusters can be calibrated without depending strongly on the galaxy-formation code: GadgetX, GIZMO-SIMBA, and the dark-matter-only run give the same bias and scatter when compared with their own true masses.
  • A single combined weak-lensing mass–observed richness relation, with the fitted redshift and stellar-mass-cut dependence, can be used for mapping survey richnesses to masses for cluster-count cosmology.
  • The slope of the relation stays nearly constant up to $z\simeq0.55$, so low-redshift survey analyses do not need a strongly evolving mass–richness calibration.
  • The scatter of richness at fixed weak-lensing mass grows linearly with redshift and is larger than the scatter at fixed true mass, so redshift-dependent scatter must be included in mass-observable likelihoods.
  • With a $10^{10}\,h^{-1}\,M_\odot$ stellar mass cut, the simulated observed-richness–weak-lensing-mass relation agrees with SDSS redMaPPer calibrations, giving an observational anchor for the simulation-based relation.

Reading between the lines

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

  • Because the paper fixes one source redshift distribution, ignores off-diagonal shape-noise covariance, and does not model mis-centering, the precise redshift trends of the slope and scatter may shift when those survey effects are included; the cross-code consistency is more robust than the absolute parameter values.
  • The $4/33$ geometric background subtraction and hard stellar-mass cuts approximate redMaPPer's probabilistic red-sequence membership; applying the same pipeline inside a mock with photometric errors and running redMaPPer on it would test whether the calibration transfers directly.
  • The small hydro-code-dependent difference in weak-lensing mass relative to the DM-only reference suggests that dark-matter-only halo mass functions could remain usable for very massive clusters, while surveys probing lower masses may need baryon-dependent mass corrections.
  • The match to redMaPPer at one stellar mass cut implies a testable program: add photometric and membership-selection models to the simulations and predict full richness distributions, including the tails that dominate cluster-count systematics.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper uses the Three Hundred project's zoom hydrodynamical simulations (GadgetX and GIZMO-SIMBA) together with a dark-matter-only run, for 324 massive clusters selected by M200 > 8e14 h^-1 Msun at z=0, to quantify weak-lensing (WL) cluster mass biases and to calibrate mass-richness relations up to z=0.94. The authors build simulated convergence/shear maps from random projections, fit smoothly truncated NFW profiles to the excess surface mass density, define an observed richness via cylinder counts of subhaloes above a stellar mass threshold with a geometric background subtraction (Eq. 14), and fit forward and inverse WL mass-richness relations. They report that the two hydrodynamical codes give WL mass-richness relations consistent within 1 sigma, that the intercept is redshift-independent, that the slope is approximately constant below z~0.55 and follows a quadratic in redshift, and that the scatter grows linearly with redshift. They further claim that, with a minimum stellar mass of Mstar,min = 1e10 h^-1 Msun, their relation aligns with SDSS redMaPPer cluster analyses.

Significance. If the central claims hold, the paper provides a valuable controlled comparison of baryonic effects on weak-lensing mass calibration and a useful set of fitting tables for mass-richness calibration. The main strengths are the use of two different hydrodynamical codes with identical initial conditions, a DM-only baseline, nine snapshots, projection-averaged weak-lensing profiles, explicit MCMC regression fits, and compact parameter tables (Tables 1-3) that can be used by future studies. The comparison of scatter at fixed true mass versus fixed weak-lensing mass is also a useful result. However, the survey-facing significance is conditional on the assumed mapping between the simulated cylinder richness and observed richness estimators such as redMaPPer, and on the idealized weak-lensing setup (diagonal covariance, fixed source redshift).

major comments (3)
  1. [§3, Eq. (14) and §3.2] The central claim that the simulated relation aligns with SDSS redMaPPer cluster analyses is not quantitatively validated. The observed richness in Eq. (14) is a cylinder count of subhaloes above a stellar mass threshold with a geometric 4/33 background subtraction, whereas redMaPPer uses red-sequence membership probabilities, an evolving 0.2 L* luminosity threshold, percolation, photometric redshift weighting, and a central galaxy treatment. The paper states in §3.2 that a stellar mass threshold 'better aligns' with redMaPPer, but no test of this mapping is provided. Since Mstar,min is a free parameter and the adopted value 1e10 h^-1 Msun was chosen partly to produce agreement, the claimed alignment may be a tuning artifact rather than evidence that the simulated richness reproduces the observed one. This is load-bearing for the survey-facing calibration. Please either validate the mapping by applying redMaPPer or AMICO to simulated galaxy catalogs, or explicitly reframe the comparison as a test of a simplified stellar-mass-based richness proxy and remove the 'aligns well' claim.
  2. [§2.2–§2.3, Eqs. (8), (12)–(13)] The weak-lensing analysis assumes a diagonal covariance matrix and a fixed source redshift zs=3. The diagonal covariance is acknowledged in the text, but it directly affects the reported 1-sigma consistency between GadgetX and GIZMO-SIMBA and the inferred scatter in the richness-mass relation: off-diagonal terms from correlated large-scale structure can substantially increase the uncertainties on the fitted masses. A fixed source plane at zs=3 is also not representative of typical surveys with broad source redshift distributions and photo-z errors, and it can bias the derived masses differently with redshift. The authors should test the sensitivity of their central WL mass bias and mass-richness scatter results to a more realistic source redshift distribution and to at least a block-diagonal covariance including large-scale structure terms, or restrict the claims accordingly.
  3. [§2.1, §3.1, §4] The sample is selected by M200 > 8e14 h^-1 Msun at z=0, so the richness-mass relations are calibrated on a mass-selected sample rather than on a sample selected by the richness observable. The paper notes that a true mass-selected sample is not strongly affected by Malmquist-Eddington biases, but for application to optically selected cluster surveys the selection function matters and can change both the slope and scatter. The calibration should either be convolved with realistic selection functions or the claims should be limited to the simulated mass-selected sample. This is especially relevant because the comparison with redMaPPer in Fig. 10 assumes that observed optical selection is equivalent to the simulated one.
minor comments (4)
  1. [§3] The text referring to Fig. 7 says that the Chen et al. (2024) model fails for Mstar,min = 10^12.5 h^-1 Msun, but the four panels in Fig. 7 show stellar mass cuts up to 10^10.75 h^-1 Msun; this appears to be a typo and should be corrected.
  2. [Table 2] The last column of Table 2 is missing formatting for the reported errors: entries such as '0.1260.003 + 0.0270.006z' should read 0.126 +/- 0.003 + (0.027 +/- 0.006) z.
  3. [§3.2] The comparison in Fig. 10 uses richnesses rescaled according to Table 5 of McClintock et al. (2019), but the text does not specify whether the simulated Eq. (14) richness is on the same scale as the rescaled redMaPPer richness before the fit; please state explicitly how the rescaling is applied to the simulated values or why it is not needed.
  4. [§2.3] The likelihood in Eqs. (16)–(17) includes the propagated mass uncertainty via B^2 sigma^2_logMwl but does not include an explicit intrinsic scatter parameter; the reported scatter sigma_log lambda_obs is therefore a residual scatter. The paper should clarify whether this residual scatter is meant to include intrinsic scatter and how the absence of an intrinsic scatter term affects the quoted uncertainties.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the mass-richness relation is an independently fitted calibration from simulation outputs, and the redMaPPer comparison uses external published data rather than a fitted parameter renamed as a prediction.

full rationale

The derivation chain is self-contained. Weak-lensing masses are obtained by fitting a truncated NFW profile to simulated shear profiles (Eqs. 9-13), and the observed richness is defined by an explicit counting procedure in Eq. 14, namely cylinder counts with a 4/33 background subtraction. The reported mass-richness relations in Tables 1-3 are Bayesian fits to these measured quantities, not quantities that are defined in terms of the fitted parameters. The claim of agreement with SDSS redMaPPer is an external comparison: the paper rescales literature redMaPPer richnesses using McClintock et al. (2019) Table 5 and compares them with the simulated relation at Mstar,min = 10^10 h^-1 Msun; the stellar mass threshold is not fitted to redMaPPer richness, and the paper does not claim that Eq. 14 reproduces the redMaPPer red-sequence membership algorithm. The self-citations, such as following the lensing procedure of Euclid Collaboration: Giocoli et al. (2024), are not load-bearing because the procedure is fully re-described in Sections 2.2-2.3. The fixed quadratic coefficients in the redshift evolution, c = -0.42 and c = -0.18, are a parameterization choice for the fitted trend, not inputs that force the result. Even if the adopted stellar mass threshold is a post-hoc comparison choice, that is a calibration or validation concern, not circularity. No step reduces, by construction or by self-citation, to its own inputs.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central calibration rests on several chosen inputs: stellar mass cuts, a hand-fixed quadratic coefficient for the slope evolution, a fixed source redshift, an assumed background source density, and a truncation radius. None of these are derived in the paper; they are standard choices or calibration freedoms. No new physical entities are introduced.

free parameters (5)
  • Stellar mass cut Mstar,min = 10^10, 10^10.25, 10^10.5, 10^10.75 h^-1 M_sun
    Richness is defined by the number of galaxies above this threshold; the redMaPPer comparison uses one of these values, so the agreement is partly ensured by this choice (Sec. 3.2).
  • Quadratic redshift coefficient for slope (c) = -0.42 for WLOR, -0.18 for true mass relation
    Chosen independently of the stellar mass cut to describe the redshift evolution of the slope; no derivation is provided (Sec. 3.1, Tables 1-3).
  • Background source density n_gal = 30 galaxies per square arcmin
    Assumed for the WL shape noise term; affects the mass uncertainties and the fitted scatter (Sec. 2.2).
  • Truncation radius factor t = 3
    The BMO profile truncation at Rt=3 R200 is adopted from earlier work; it changes the outer profile and the recovered M200 (Sec. 2.3).
  • Pivot mass Mp = 3e14 h^-1 M_sun
    Used to rescale masses in the richness relation; changes the intercept but not the slope or the conclusions (Sec. 3).
assumptions (5)
  • domain assumption Simulated clusters from The Three Hundred represent real cluster population
    The 324 clusters are selected from MDPL2 with M200>8e14 h^-1 M_sun at z=0 and resimulated; the paper generalizes from this sample to clusters in the mass and redshift range of surveys.
  • standard math NFW and BMO truncated NFW profiles describe the cluster density
    The WL profile model uses a smoothly truncated NFW profile (Eq. 9), with concentration from Eq. 2; this is a standard assumption in the field.
  • domain assumption Subhalo stellar mass tracks observed galaxy population
    Richness is computed by counting subhaloes above a stellar mass cut; no photometric scatter, incompleteness, or membership probability is applied (Eq. 14).
  • domain assumption Diagonal covariance is sufficient for WL mass errors
    The analysis neglects off-diagonal covariance from large-scale structure and sample variance, explicitly stated in Sec. 2.3; this likely underestimates uncertainties.
  • domain assumption Fixed source redshift zs=3 represents background sources
    All lensing maps assume a single source plane at zs=3 instead of a full source redshift distribution (Sec. 2.2).

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Cite this review

Pith. "Pith review of The Three Hundred Project hydrodynamical simulations: Hydrodynamical weak-lensing cluster mass biases and richnesses using different hydro models." pith.science (2026). https://pith.science/paper/FDMNQUHF

@misc{pith2026250114019,
  author       = {Pith},
  title        = {Pith review of: The Three Hundred Project hydrodynamical simulations: Hydrodynamical weak-lensing cluster mass biases and richnesses using different hydro models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FDMNQUHF}},
  note         = {Machine review of arXiv:2501.14019}
}
abstract

The mass of galaxy clusters estimated from weak-lensing observations is affected by projection effects, leading to a systematic underestimation compared to the true cluster mass, varying with both mass and redshift. The magnitude depends on the criteria used to select clusters and the spatial scale over which their mass is measured. We leverage hydrodynamical simulations of galaxy clusters carried out with GadgetX and GIZMO-SIMBA as part of the Three Hundred project. We used them to quantify weak-lensing mass biases with respect also to the results from dark matter-only simulations. We also investigate how the biases propagate into the richness-mass relation. We aim to shed light on the effect of the presence of baryons on the weak-lensing mass bias and also whether this bias depends on the galaxy formation recipe; we seek to model the richness-mass relation that can be used as guidelines for observational experiments for cluster cosmology. We produced weak-lensing simulations of random projections to model the expected excess surface mass density profile of clusters up to redshift $z=1$. We then estimated the observed richness by counting the number of galaxies in a cylinder and correcting by projected contaminants. We derived the weak-lensing mass-richness relation and found consistency across hydrodynamical simulations. The intercept parameter of the relation is independent of redshift but varies with the minimum of the stellar mass to define the richness. At the same time, the slope is relatively constant up to $z=0.55$. The scatter in observed richness at a fixed weak-lensing mass increases linearly with redshift at a fixed stellar mass cut. As expected, we observed that the scatter in richness at a given true mass is smaller than at a given weak-lensing mass. Our results for the weak-lensing mass-richness relation align well with SDSS redMaPPer cluster analyses. [Abridged]

Figures

Figures reproduced from arXiv: 2501.14019 by the authors.

Figure 1
Figure 1. Simulated convergence maps of a cluster lens, namely with ID=4, at zl = 0.22 and considering zs = 3, obtained by collapsing the total mass along the z-projection. The left and the central panels show the results using two different hydro-solvers GadgetX and GIZMO-SIMBA, respectively. In the right panel, we display the convergence map of the same cluster projection simulated using only collisionless dark matter parti… view at source ↗
Figure 2
Figure 2. Excess surface mass density profile of the projections displayed in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Posterior distributions of derived weak-lensing mass and concen￾tration from the three weak-lensing simulations of the cluster of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Average weak-lensing mass biases as a function of the corresponding three-dimensional masses. On the left, the weak lensing masses are relative to their respective total mass; on the right, they are always related to the total mass of the DM-only runs. The top and bott…
Figure 6
Figure 6. Figure 6: Halo and subhalo distribution in the projection x-y considering a field of view of 10 Mpc on a side and ±5 Mpc along the line of sight, ∆H = 10 Mpc, for the GadgetX cluster run. Black circles show the location of the centre of all subhaloes within the halo radius R200,…
Figure 7
Figure 7. Figure 7: Weak-lensing mass-observed richness relation measured for the clusters at redshift z = 0.22 run with GadgetX. The different panels consider different minimum stellar mass cuts Mstar, min, from 1010 to 1010.75h −1M⊙. The weak-lensing masses Mwl are rescaled with respect…
Figure 8
Figure 8. Figure 8: Weak-lensing mass-observed richness relation measured for the clusters at redshift z = 0.22 run with both hydrocodes GadgetX in blue and GIZMO-SIMBA in red, respectively. The blue points are thus the same from [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: Intercept A, slope B, and scatter σlog λobs at a fixed weak-lensing cluster mass as a function of redshift. Blue and red curves refer to the two hydro simulations: GadgetX and GIZMO-SIMBA, respectively. In all panels, the results referring to a given stellar mass cuts …
Figure 10
Figure 10. Figure 10: Observed richness-weak-lensing mass relation comparison with different literature results. We compute our model considering an observed richness with a minimum stellar mass of Mstar, min = 1010 h −1M⊙ and the parameters have been calculated at z = 0.35. All redMaPPer …
Figure 11
Figure 11. Figure 11: True mass-observed richness relation for the clusters at redshift z = 0.22 as measured in both hydro-runs. The solid lines show the linear regression model results, with the shaded region indicating the 1σ uncertainty on the intercept and slope parameters. In each sub…

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Works this paper leans on

110 extracted references · 38 canonical work pages

  1. [1]

    Abbott, T. M. C., Aguena, M., Alarcon, A., et al. 2020, Phys. Rev. D, 102, 023509

    2020

  2. [2]

    Abbott, T. M. C., Aguena, M., Alarcon, A., et al. 2022, Phys. Rev. D, 105, 023520

    2022

  3. [3]

    G., Aguilar, J., Ahlen, S., et al

    Adame, A. G., Aguilar, J., Ahlen, S., et al. 2025, J. Cosmology Astropart. Phys., 2025, 021

    2025

  4. [4]

    2010, MNRAS, 407, 263

    Andreon, S. 2010, MNRAS, 407, 263

    2010

  5. [5]

    2012, A&A, 548, A83

    Andreon, S. 2012, A&A, 548, A83

    2012

  6. [6]

    2016, A&A, 587, A158

    Andreon, S. 2016, A&A, 587, A158

    2016

  7. [7]

    & Bergé, J

    Andreon, S. & Bergé, J. 2012, A&A, 547, A117

    2012

  8. [8]

    & Hurn, M

    Andreon, S. & Hurn, M. 2013, Statistical Analysis and Data Mining: The ASA Data Science Journal, 9, 15

    2013

Show all 110 references
  1. [9]

    2024, Journal of Cosmology and Astroparticle Physics, 2024, 024

    Ansarinejad, B., Raghunathan, S., Abbott, T., et al. 2024, Journal of Cosmology and Astroparticle Physics, 2024, 024

    2024

  2. [10]

    R., Gray, M

    Arthur, J., Pearce, F. R., Gray, M. E., et al. 2017, MNRAS, 464, 2027

    2017

  3. [11]

    A., Fan, X., & Cen, R

    Bahcall, N. A., Fan, X., & Cen, R. 1997, in American Astronomical Society Meeting Abstracts, V ol. 190, American Astronomical Society Meeting Ab- stracts #190, 52.01

    1997

  4. [12]

    A., Marshall, P., & Oguri, M

    Baltz, E. A., Marshall, P., & Oguri, M. 2009, J. Cosmology Astropart. Phys., 2009, 015

    2009

  5. [13]

    2010, Classical and Quantum Gravity, 27, 233001

    Bartelmann, M. 2010, Classical and Quantum Gravity, 27, 233001

    2010

  6. [14]

    & Schneider, P

    Bartelmann, M. & Schneider, P. 2001, Physics Reports, 340, 291

    2001

  7. [15]

    J., Raghunathan, S., Crawford, T

    Baxter, E. J., Raghunathan, S., Crawford, T. M., et al. 2018, MNRAS, 476, 2674

    2018

  8. [16]

    M., Murante, G., Arth, A., et al

    Beck, A. M., Murante, G., Arth, A., et al. 2016, MNRAS, 455, 2110

    2016

  9. [17]

    Becker, M. R. & Kravtsov, A. V . 2011, ApJ, 740, 25

    2011

  10. [18]

    2019, MNRAS, 484, 1598

    Bellagamba, F., Sereno, M., Roncarelli, M., et al. 2019, MNRAS, 484, 1598

    2019

  11. [19]

    2015, py-sphviewer: Py-SPHViewer v1.0.0

    Benitez-Llambay, A. 2015, py-sphviewer: Py-SPHViewer v1.0.0

    2015

  12. [20]

    2023, ApJ, 952, 84

    Bergamini, P., Acebron, A., Grillo, C., et al. 2023, ApJ, 952, 84

    2023

  13. [21]

    2012, MNRAS, 427, 3134

    Boldrin, M., Giocoli, C., Meneghetti, M., & Moscardini, L. 2012, MNRAS, 427, 3134

    2012

  14. [22]

    2016, MNRAS, 457, 2738

    Boldrin, M., Giocoli, C., Meneghetti, M., et al. 2016, MNRAS, 457, 2738

    2016

  15. [23]

    B., Grillo, C., Rosati, P., et al

    Caminha, G. B., Grillo, C., Rosati, P., et al. 2023, A&A, 678, A3

    2023

  16. [24]

    Carbone, C., Fedeli, C., Moscardini, L., & Cimatti, A. 2012, J. Cosmology As- tropart. Phys., 2012, 023

    2012

  17. [25]

    2024, ApJ, 966, 227

    Chen, M., Cui, W., Fang, W., & Wen, Z. 2024, ApJ, 966, 227

    2024

  18. [26]

    2021, Phys

    Costanzi, M., Saro, A., Bocquet, S., et al. 2021, Phys. Rev. D, 103, 043522

    2021

  19. [27]

    Costanzi, M., Sartoris, B., Viel, M., & Borgani, S. 2014, J. Cosmology Astropart. Phys., 10, 081

    2014

  20. [28]

    2022, MNRAS, 514, 977

    Cui, W., Dave, R., Knebe, A., et al. 2022, MNRAS, 514, 977

    2022

  21. [29]

    2018, MNRAS, 480, 2898

    Cui, W., Knebe, A., Yepes, G., et al. 2018, MNRAS, 480, 2898

    2018

  22. [30]

    2016, MNRAS, 458, 4052 D’Addona, M., Mercurio, A., Rosati, P., et al

    Cui, W., Power, C., Knebe, A., et al. 2016, MNRAS, 458, 4052 D’Addona, M., Mercurio, A., Rosati, P., et al. 2024, A&A, 686, A4 Davé, R., Anglés-Alcázar, D., Narayanan, D., et al. 2019, MNRAS, 486, 2827

    2016

  23. [31]

    E., et al

    Despali, G., Giocoli, C., Angulo, R. E., et al. 2016, MNRAS, 456, 2486

    2016

  24. [32]

    & Vegetti, S

    Despali, G. & Vegetti, S. 2017, MNRAS, 469, 1997

    2017

  25. [33]

    M., Li, S

    Diego, J. M., Li, S. K., Amruth, A., et al. 2024, A&A, 689, A167

    2024

  26. [34]

    2009, MNRAS, 399, 497 Euclid Collaboration: Blanchard, A., Camera, S., et al

    Dolag, K., Borgani, S., Murante, G., & Springel, V . 2009, MNRAS, 399, 497 Euclid Collaboration: Blanchard, A., Camera, S., et al. 2020, A&A, 642, A191 Euclid Collaboration: Castro, T., Fumagalli, A., Angulo, R. E., et al. 2023, A&A, 671, A100 Euclid Collaboration: Giocoli, C....

    2009

  27. [35]

    & van de Weygaert, R

    Feldbrugge, J. & van de Weygaert, R. 2024, arXiv e-prints, arXiv:2405.20475

    2024 arXiv

  28. [36]

    2020, A&A, 638, A114

    Finoguenov, A., Rykoff, E., Clerc, N., et al. 2020, A&A, 638, A114

    2020

  29. [37]

    2023, MNRAS, 518, 4238

    Gianfagna, G., Rasia, E., Cui, W., et al. 2023, MNRAS, 518, 4238

    2023

  30. [38]

    2021, A&A, 653, A19

    Giocoli, C., Marulli, F., Moscardini, L., et al. 2021, A&A, 653, A19

    2021

  31. [39]

    2012, MNRAS, 426, 1558

    Giocoli, C., Meneghetti, M., Ettori, S., & Moscardini, L. 2012, MNRAS, 426, 1558

    2012

  32. [40]

    B., Ettori, S., & Moscardini, L

    Giocoli, C., Meneghetti, M., Metcalf, R. B., Ettori, S., & Moscardini, L. 2014, MNRAS, 440, 1899

    2014

  33. [41]

    K., & Tormen, G

    Giocoli, C., Moreno, J., Sheth, R. K., & Tormen, G. 2007, MNRAS, 376, 977

    2007

  34. [42]

    F., et al

    Giocoli, C., Palmucci, L., Lesci, G. F., et al. 2024, A&A, 687, A79

    2024

  35. [43]

    Y ., Kravtsov, A

    Gnedin, O. Y ., Kravtsov, A. V ., Klypin, A. A., & Nagai, D. 2004, ApJ, 616, 16

    2004

  36. [44]

    J., Klein, M., & Dolag, K

    Grandis, S., Bocquet, S., Mohr, J. J., Klein, M., & Dolag, K. 2021, MNRAS, 507, 5671

    2021

  37. [45]

    J., Dietrich, J

    Grandis, S., Mohr, J. J., Dietrich, J. P., et al. 2019, MNRAS, 488, 2041

    2019

  38. [46]

    Grandis, S. et al. 2024, Astron. Astrophys., 687, A178

    2024

  39. [47]

    R., Friedrich, O., & Mana, A

    Gruen, D., Seitz, S., Becker, M. R., Friedrich, O., & Mana, A. 2015, MNRAS, 449, 4264 Article number, page 13 of 15 A&A proofs: manuscript no. aanda

    2015

  40. [48]

    E., Pearce, F

    Haggar, R., Gray, M. E., Pearce, F. R., et al. 2020, MNRAS, 492, 6074

    2020

  41. [49]

    2003, MNRAS, 339, 1155

    Hoekstra, H. 2003, MNRAS, 339, 1155

    2003

  42. [50]

    2013, Space Sci

    Hoekstra, H., Bartelmann, M., Dahle, H., et al. 2013, Space Sci. Rev., 177, 75

    2013

  43. [51]

    2011, MNRAS, 412, 2095

    Hoekstra, H., Hartlap, J., Hilbert, S., & van Uitert, E. 2011, MNRAS, 412, 2095

    2011

  44. [52]

    Hoekstra, H., Yee, H. K. C., & Gladders, M. D. 2004, ApJ, 606, 67

    2004

  45. [53]

    E., et al

    Hoosain, M., Blyth, S.-L., Skelton, R. E., et al. 2024, MNRAS, 528, 4139

    2024

  46. [54]

    Hopkins, P. F. 2015, MNRAS, 450, 53

    2015

  47. [55]

    A., Abel, B., et al

    Ivezic, Z., Tyson, J. A., Abel, B., et al. 2008, eprint arXiv: 0805.2366 [arXiv:0805.2366]

    2008 arXiv

  48. [56]

    A., Axelrod, T., et al

    Ivezic, Z., Tyson, J. A., Axelrod, T., et al. 2009, in Bulletin of the American Astronomical Society, V ol. 41, American Astronomical Society Meeting Ab- stracts #213, 366

    2009

  49. [57]

    2021, MNRAS, 508, 1206

    Jauzac, M., Klein, B., Kneib, J.-P., et al. 2021, MNRAS, 508, 1206

    2021

  50. [58]

    2021, MNRAS, 502, 1494

    Kiiveri, K., Gruen, D., Finoguenov, A., et al. 2021, MNRAS, 502, 1494

    2021

  51. [59]

    2015, Reports on Progress in Physics, 78, 086901

    Kilbinger, M. 2015, Reports on Progress in Physics, 78, 086901

    2015

  52. [60]

    2025, A&A, 695, A216

    Kleinebreil, F., Grandis, S., Schrabback, T., et al. 2025, A&A, 695, A216

    2025

  53. [61]

    2016, MNRAS, 457, 4340

    Klypin, A., Yepes, G., Gottlöber, S., Prada, F., & Heß, S. 2016, MNRAS, 457, 4340

    2016

  54. [62]

    R., et al

    Knebe, A., Gámez-Marín, M., Pearce, F. R., et al. 2020, MNRAS, 495, 3002

    2020

  55. [63]

    Knollmann, S. R. & Knebe, A. 2009, ApJS, 182, 608

    2009

  56. [64]

    2011, arXiv:1110.3193

    Laureijs, R., Amiaux, J., Arduini, S., et al. 2011, arXiv:1110.3193

    2011 arXiv

  57. [65]

    E., Le Brun, A

    Lee, B. E., Le Brun, A. M. C., Haq, M. E., et al. 2018, MNRAS, 479, 890

    2018

  58. [66]

    2023, MNRAS, 523, 1228

    Li, Q., Cui, W., Yang, X., et al. 2023, MNRAS, 523, 1228

    2023

  59. [67]

    I., van de Weygaert, R., Cautun, M., et al

    Libeskind, N. I., van de Weygaert, R., Cautun, M., et al. 2018, MNRAS, 473, 1195

    2018

  60. [68]

    Lima, M. & Hu, W. 2005, Phys. Rev. D, 72, 043006

    2005

  61. [69]

    R., McCullough, J., et al

    MacCrann, N., Becker, M. R., McCullough, J., et al. 2022, MNRAS, 509, 3371

    2022

  62. [70]

    I., Brinchmann, J., et al

    Mainieri, V ., Anderson, R. I., Brinchmann, J., et al. 2024, arXiv e-prints, arXiv:2403.05398

    2024 arXiv

  63. [71]

    2017, MNRAS, 465, 3817

    Malavasi, N., Arnouts, S., Vibert, D., et al. 2017, MNRAS, 465, 3817

    2017

  64. [72]

    B., Allen, S

    Mantz, A. B., Allen, S. W., Morris, R. G., et al. 2016, MNRAS, 463, 3582

    2016

  65. [73]

    2016, Astronomy and Computing, 14, 35

    Marulli, F., Veropalumbo, A., & Moresco, M. 2016, Astronomy and Computing, 14, 35

    2016

  66. [74]

    2019, MNRAS, 485, 498

    Maturi, M., Bellagamba, F., Radovich, M., et al. 2019, MNRAS, 485, 498

    2019

  67. [75]

    N., Gruen, D., et al

    McClintock, T., Varga, T. N., Gruen, D., et al. 2019, MNRAS, 482, 1352

    2019

  68. [76]

    2017, MNRAS, 469, 4899

    Melchior, P., Gruen, D., McClintock, T., et al. 2017, MNRAS, 469, 4899

    2017

  69. [77]

    2023, A&A, 678, L2

    Meneghetti, M., Cui, W., Rasia, E., et al. 2023, A&A, 678, L2

    2023

  70. [78]

    2008, A&A, 482, 403

    Meneghetti, M., Melchior, P., Grazian, A., et al. 2008, A&A, 482, 403

    2008

  71. [79]

    2018, ApJ, 854, 120

    Murata, R., Nishimichi, T., Takada, M., et al. 2018, ApJ, 854, 120

    2018

  72. [80]

    Natarajan, P., Williams, L. L. R., Brada ˇc, M., et al. 2024, Space Sci. Rev., 220, 19

    2024

  73. [81]

    F., Frenk, C

    Navarro, J. F., Frenk, C. S., & White, S. D. M. 1996, ApJ, 462, 563

    1996

  74. [82]

    F., Frenk, C

    Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, ApJ, 490, 493

    1997

  75. [83]

    & Hamana, T

    Oguri, M. & Hamana, T. 2011, MNRAS, 414, 1851

    2011

  76. [84]

    2020, MNRAS, 491, 1643 Planck Collaboration

    Phriksee, A., Jullo, E., Limousin, M., et al. 2020, MNRAS, 491, 1643 Planck Collaboration. 2016, Astron. Astrophys., 594, A13 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2014, A&A, 571, A20

    2020

  77. [85]

    A., Cuesta, A

    Prada, F., Klypin, A. A., Cuesta, A. J., Betancort-Rijo, J. E., & Primack, J. 2012, MNRAS, 423, 3018

    2012

  78. [86]

    2022, A&A, 665, A16

    Ragagnin, A., Meneghetti, M., Bassini, L., et al. 2022, A&A, 665, A16

    2022

  79. [87]

    2015, ApJ, 813, L17

    Rasia, E., Borgani, S., Murante, G., et al. 2015, ApJ, 813, L17

    2015

  80. [88]

    S., Rozo, E., Busha, M

    Rykoff, E. S., Rozo, E., Busha, M. T., et al. 2014, ApJ, 785, 104

    2014

  81. [89]

    N., Wu, H.-Y ., Rozo, E., et al

    Salcedo, A. N., Wu, H.-Y ., Rozo, E., et al. 2024, Phys. Rev. Lett., 133, 221002

    2024

  82. [90]

    A., Bravo-Alfaro, H., Pointecouteau, E., & An- dernach, H

    Santiago-Bautista, I., Caretta, C. A., Bravo-Alfaro, H., Pointecouteau, E., & An- dernach, H. 2020, A&A, 637, A31

    2020

  83. [91]

    2015, MNRAS, 454, 2305

    Saro, A., Bocquet, S., Rozo, E., et al. 2015, MNRAS, 454, 2305

    2015

  84. [92]

    2016, MNRAS, 459, 1764

    Sartoris, B., Biviano, A., Fedeli, C., et al. 2016, MNRAS, 459, 1764

    2016

  85. [93]

    2010, MNRAS, 407, 2339

    Sartoris, B., Borgani, S., Fedeli, C., et al. 2010, MNRAS, 407, 2339

    2010

  86. [94]

    N., et al

    Schneider, P., Asgari, M., Jozani, Y . N., et al. 2022, A&A, 664, A77

    2022

  87. [95]

    2002, A&A, 396, 1

    Schneider, P., van Waerbeke, L., Kilbinger, M., & Mellier, Y . 2002, A&A, 396, 1

    2002

  88. [96]

    Sheth, R. K. & Tormen, G. 1999, MNRAS, 308, 119

    1999

  89. [97]

    2017, MNRAS, 466, 3103

    Simet, M., McClintock, T., Mandelbaum, R., et al. 2017, MNRAS, 466, 3103

    2017

  90. [98]

    2017, MNRAS, 471, 3827

    Singh, S., Mandelbaum, R., Seljak, U., Slosar, A., & Vazquez Gonzalez, J. 2017, MNRAS, 471, 3827

    2017

  91. [99]

    Springel, V ., White, S. D. M., Tormen, G., & Kau ffmann, G. 2001, MNRAS, 328, 726

    2001

  92. [100]

    2024, MNRAS, 528, 4451

    Srivastava, A., Cui, W., Meneghetti, M., et al. 2024, MNRAS, 528, 4451

    2024

  93. [101]

    & Bridle, S

    Takada, M. & Bridle, S. 2007, New Journal of Physics, 9, 446

    2007

  94. [102]

    V ., Klypin, A., et al

    Tinker, J., Kravtsov, A. V ., Klypin, A., et al. 2008, ApJ, 688, 709

    2008

  95. [103]

    1998, MNRAS, 297, 648

    Tormen, G. 1998, MNRAS, 297, 648

    1998

  96. [104]

    1998, MNRAS, 299, 728

    Tormen, G., Diaferio, A., & Syer, D. 1998, MNRAS, 299, 728

    1998

  97. [105]

    2004, MNRAS, 350, 1397 van den Bosch, F

    Tormen, G., Moscardini, L., & Yoshida, N. 2004, MNRAS, 350, 1397 van den Bosch, F. C. 2002, MNRAS, 331, 98

    2004

  98. [106]

    M., Diego, J

    Vega-Ferrero, J., Dana, J. M., Diego, J. M., et al. 2021, MNRAS, 500, 247

    2021

  99. [107]

    2018, ApJ, 868, 130

    Wang, Y ., Pearce, F., Knebe, A., et al. 2018, ApJ, 868, 130

    2018

  100. [108]

    H., Bullock, J

    Wechsler, R. H., Bullock, J. S., Primack, J. R., Kravtsov, A. V ., & Dekel, A. 2002, ApJ, 568, 52

    2002

  101. [109]

    2022, MNRAS, 515, 4471

    Wu, H.-Y ., Costanzi, M., To, C.-H., et al. 2022, MNRAS, 515, 4471

    2022

  102. [110]

    2024, MNRAS, 533, 1048 Article number, page 14 of 15 Giocoli et al

    Zhang, Y ., Guo, H., Yang, X., & Wang, P. 2024, MNRAS, 533, 1048 Article number, page 14 of 15 Giocoli et al. 2024: Hydrodinamical WL mass biases Appendix A: Dark matter-only true mass-richness relations In this appendix, we report the results of the relations between the true...

    2024

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