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REVIEW 3 major objections 4 minor 163 references

Weak lensing mass-richness relation of redMaPPer clusters in the LSST DESC DC2 simulations

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

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Pith's one-line read A simulated LSST-like sky shows that combining cluster counts with weak lensing recovers the mass-richness relation of redMaPPer clusters.

desk verdict A careful, useful simulation-based calibration of a counts+lensing pipeline for LSST cluster cosmology; the selection function is the load-bearing but self-referential piece. read the letter →

arxiv 2502.08444 v2 pith:5CCGGJDT submitted 2025-02-12 astro-ph.CO

Constantin Payerne , Zhuowen Zhang , Michel Aguena , Céline Combet , Thibault Guillemin , Marina Ricci , Nathan Amouroux , Camille Avestruz
show 8 more authors
Eduardo J. Barroso Arya Farahi Eve Kovacs Calum Murray Markus M. Rau Eli S. Rykoff Samuel J. Schmidt the LSST Dark Energy Science Collaboration
This is my paper · ORCID
classification astro-ph.CO
keywords galaxyclustersmass-richnessrelationweakgravitationallensingredMaPPerclusternumbercountsDC2simulationphotometricredshiftsshear-richnesscovariance
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 tries to establish that the mass-richness relation of optically selected galaxy clusters can be inferred reliably from the combination of cluster number counts and weak gravitational lensing, using the mock universe of the DC2 simulation as a testbed for the future LSST survey. The authors fit a six-parameter log-normal scaling relation between halo mass and redMaPPer richness for 3,600 clusters in the range $20<\lambda<200$ and $0.2

What carries the argument

The load-bearing object is the forward model connecting halo mass and richness through $P(\lambda|m,z)$, a six-parameter log-normal scaling relation, combined with the redMaPPer selection function $\Phi(\lambda,m,z)=c(m,z)/p(\lambda,z)$, where completeness $c$ is measured by matching detected clusters to simulated halos and purity is assumed near unity for $\lambda>20$. The lensing side uses the stacked excess surface density $\Delta\Sigma(R)$ predicted by integrating $\Delta\Sigma(R|m,z)$ over the same mass function, completeness, and richness distribution, with the 1-halo term from an NFW profile (or Einasto/Hernquist) plus a concentration-mass relation; a two-step variant fits a mean mass per richness-redshift bin instead. The machinery works by feeding the same selection-function-weighted halo population into both the count prediction and the lensing prediction, so that the complementary degeneracy directions of counts and lensing can break the scaling-relation parameter degeneracies.

What would settle it

Run the same count+lensing fit after adding the stacked shear of unmatched redMaPPer detections to the signal, or after replacing the matching-based completeness with an independently calibrated completeness from injected mock clusters; if the recovered $\ln\lambda_0$ or $\mu_m$ move by more than the reported uncertainties, the selection-function treatment is the source of the bias.

Watch

Extended reading notes

Core claim

The central claim is that a joint count+lensing analysis of redMaPPer clusters in the DC2 simulation recovers the underlying mass-richness relation without strong modeling bias. The authors model the observed richness as a log-normal variable around a mean $\langle\ln\lambda|m,z\rangle = \ln\lambda_0 + \mu_z \ln((1+z)/(1+z_0)) + \mu_m \log_{10}(m/m_0)$, with scatter $\sigma_{\ln\lambda|m,z}$, and predict both cluster counts and stacked excess surface density $\Delta\Sigma(R)$ through the halo mass function weighted by the redMaPPer completeness. Combining counts with either stacked profiles or mean masses tightens constraints on the mean scaling parameters by a factor of about seven and on the scatter parameters by a factor of three to four, and the recovered parameters agree with the fiducial relation from halo-richness matching at the 1-2$\sigma$ level. The paper also claims that the constraints are robust to the choice of concentration-mass relation and to NFW, Einasto, or Hernquist density profiles in the radial fit range $1<R<3.5$ Mpc, and that photo-z systematics and shear-richness covariance produce only small, partially correctable shifts.

Load-bearing premise

The analysis assumes that the redMaPPer completeness measured by matching detected clusters to dark matter halos is accurate and that the roughly 1% spurious detections contribute negligible lensing signal; if unmatched clusters have non-negligible shear or the matching misses real clusters, both the count and stacked-lensing predictions shift and bias the inferred mass-richness relation.

Editorial extensions

If this is right

  • Using either stacked profiles or mean masses in combination with counts gives comparable constraints; errors on $\ln\lambda_0$, $\mu_z$, and $\mu_m$ shrink by roughly a factor of seven relative to single-probe fits.
  • Adopting different concentration-mass relations or dark matter density profiles (NFW, Einasto, Hernquist) shifts the inferred scaling relation by less than about $1\sigma$ when fitting in $1<R<3.5$ Mpc.
  • Photometric redshift errors from a pessimistic template-based estimator bias the normalization by about $1\sigma$; fitting a global multiplicative factor $(1+b)$ jointly with the scaling parameters removes most of this bias.
  • Shear-richness covariance shifts the mass slope $\mu_m$ by up to $0.5\sigma$, an effect comparable to the photo-z shift and larger than the shift from an optimistic machine-learning photo-z estimator.
  • Across all tested analysis configurations, posterior shifts relative to the fiducial relation stay below $2\sigma$, supporting the reliability of the joint count+lensing pipeline for LSST-era cluster cosmology.

Reading between the lines

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

  • The $R>1$ Mpc cut imposed by ray-tracing resolution means the inner region, where profile differences and miscentering matter most, is untested; real LSST data with better small-scale resolution could reveal larger modeling sensitivity than this paper measures.
  • The measured shear-richness covariance is likely suppressed by the simulation's spherical assignment of galaxies in halos, so the 0.5 sigma shift should be treated as a lower bound until triaxial galaxy placement or real data are used.
  • A natural next step is to free the cosmological parameters in the same counts+lensing fit; the complementarity demonstrated here suggests joint cluster cosmology constraints could be substantially tighter than counts alone.
  • The photo-z bracket between pessimistic and optimistic estimators offers a practical calibration strategy for LSST: adopt a fitted multiplicative lensing correction and validate it with spectroscopic subsamples.
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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 constrains the redMaPPer cluster mass-richness relation in the cosmoDC2/DC2 simulation using cluster number counts and either stacked weak-lensing profiles or mean lensing masses, across richness 20<lambda<200 and redshift 0.2<z<1. The analysis uses a six-parameter log-normal scaling relation, a selection function calibrated from the ClEvaR matched cluster-halo catalog, and a fixed simulation cosmology. The authors report that the joint count+lensing analysis recovers the fiducial relation inferred from the matched catalog, that the constraints are robust to concentration-mass relation and density profile choices, that photometric redshift uncertainties introduce about 1 sigma biases which can be mitigated by a fitted multiplicative correction, and that shear-richness covariance shifts results by up to about 0.5 sigma. The paper also provides a quantitative tension metric and makes use of several public DESC software tools.

Significance. If the central claim holds, this is a useful validation of an LSST-era cluster scaling relation pipeline: it is the first redMaPPer mass-richness constraint in cosmoDC2, it explores a broad set of modeling and observational systematics (concentration-mass relations, NFW/Einasto/Hernquist profiles, BPZ/FlexZBoost photo-zs, shear-richness covariance), and it provides a transparent comparison against a fiducial relation. The strengths include the explicit use of public DES C tools, the side-by-side comparison of stacked profiles versus mean masses, and the candid discussion of limitations in Sect. 6.2. Nonetheless, the main validation is against a fiducial relation derived from the same matching that calibrates the selection function, so the external reach of the 'recovery' claim is weaker than the abstract implies; this, together with the diagonal-only lensing covariance, is the main reason the central claim needs additional support.

major comments (3)
  1. [Sect. 3.4 and Eqs. (1), (13), (14)] The central validation claim in Sect. 6.1 rests on agreement with a fiducial relation that is fitted to the same ClEvaR matched catalog (Sect. 3.4.1) that also supplies the selection function c(m,z) entering the count and lensing predictions (Sect. 3.4.2). This makes the agreement an internal consistency test: a systematic error in the matching, such as redshift-dependent incompleteness or residual projection contamination, would shift the model predictions and the reference relation together and would not be detected by the posteriors in Fig. 6. None of the robustness tests in Sect. 5 vary c(m,z), and the purity argument in footnote 9 relies on the same matched catalog. I request a perturbation test of c(m,z) within the uncertainties quoted in Sect. 3.4.2 (for example, using the stated 80% completeness level at M200c > 10^14 Msun) with the resulting shifts in ln lambda0 and mu_m reported, or, failing that, a revised wording that limits the claim to pipeline self-consistency rather than an external recovery of the mass-richness relation.
  2. [Sect. 4.2.2, Eq. (26)] The stacked-lensing likelihood uses only the diagonal of the bootstrap covariance, justified by the noisiness of off-diagonal terms. This is an acknowledged approximation, but the paper's quantitative consistency statements, including the tension values in Sect. 6.1 and Fig. E.1, depend on the covariance being correct; if the off-diagonal elements are positive, as expected from correlated large-scale structure and halo-profile variations, the quoted uncertainties are underestimated. I ask the authors to provide a quantitative check of the off-diagonal-to-diagonal ratio in the fitted 1-3.5 Mpc range, for example by comparing the bootstrap result with an analytic covariance prediction (Wu et al. 2019) or with a smoothed/shrunk bootstrap covariance, and to state whether the parameter shifts and tension values are affected.
  3. [Sect. 5.3.1] The multiplicative correction factor (1+b) is fitted jointly with the scaling parameters and is common to all redshift-richness bins. This can absorb only a monopole normalization error; it cannot correct a photo-z bias that varies with redshift or richness. In the BPZ case the uncorrected shifts in ln lambda0 and mu_m are of order 1 sigma, and the paper does not demonstrate that the factor is not absorbing a redshift-dependent bias. I suggest a diagnostic that fits b per redshift bin (or per redshift-richness bin) and checks whether the b values are consistent, since this directly affects the claim that the photo-z bias is 'mitigated' by the single factor.
minor comments (4)
  1. [Abstract vs. Sect. 5.1 and 6.1] The abstract says the constraints are consistent 'at the 1 sigma level' with the fiducial values, while Sect. 5.1 states the posteriors recover the fiducial values 'at the <2 sigma level' and reports a '>2 sigma tension' in the projected mu_z-sigma_z plane; Sect. 6.1 again says 'consistent at the 1 sigma level.' These statements should be harmonized with the actual tension values reported in Fig. E.1.
  2. [Fig. 7 and Sect. 5.2.1] The figure caption calls the case with concentration left free 'concentration-free,' while the text uses 'free-concentration case'; please use one consistent term throughout.
  3. [Table E.1] The block beginning 'Impact of source photometric redshifts, Sect. 5.3.2' appears to refer to the shear-richness covariance analysis rather than photometric redshifts; the section label should be corrected.
  4. [Eq. (13)] The lower integration limit m_min is not specified in Eq. (13); for consistency with Eq. (1) and Sect. 4.2.1, the adopted value (10^12 Msun) should be stated where the lensing model is first introduced.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the inference uses independent count and lensing data vectors, with the fiducial relation used only as a comparison reference.

full rationale

The central inference is not circular. The data vectors are the redMaPPer cluster counts (Sect. 4.1.1), stacked excess surface density profiles (Sect. 4.1.2), and mean lensing masses (Sect. 4.1.3), all constructed from the simulation catalogs independently of the scaling-relation parameters. The models in Eqs. (1), (13), and (14) use the standard halo mass function, a calibrated completeness c(m,z), and the parametric P(lambda|m,z); the parameters are then sampled from the likelihoods in Eqs. (24), (26), and (27). The fiducial relation from ClEvaR matching (Sect. 3.4.1) is not used as a prior or likelihood term; it is only a posterior reference for the tension metric in Fig. 13 and Eq. (39). Although the completeness calibration and the fiducial relation share the same matched catalog, so that their agreement is an internal-consistency check rather than an external validation, this shared provenance does not make any predicted parameter algebraically equal to an input. The paper explicitly acknowledges the residual systematics: Sect. 2.2 footnote 9 states that neglecting spurious detections is "a strong assumption," and Sect. 6.2 notes that "uncertainties in the selection function may still induce some bias in the recovered parameters." The (1+b) photo-z factor is a fitted nuisance parameter tested for mitigation, not relabeled as a prediction, and the shear-richness covariance is an estimated correction, not a derived output. There is no equation-level reduction of an output to an input, and no load-bearing self-citation chain.

Assumptions & free parameters 7 free parameters · 7 assumptions · 0 invented entities

The inference is built on six fitted scaling parameters, a fitted photo-z bias term, and a set of prior-literature models including the halo mass function, halo bias, NFW profile, and log-normal richness relation, plus a measured selection function. No new physical entities are introduced.

free parameters (7)
  • ln lambda_0 = 3.37 +/- 0.03 (baseline counts plus profiles)
    Normalization of the mean richness at the pivot mass and redshift in Eq. (16).
  • mu_z = 0.08 +/- 0.07 (baseline counts plus profiles)
    Redshift slope of the mean mass-richness relation in Eq. (16).
  • mu_m = 2.18 +/- 0.07 (baseline counts plus profiles)
    Mass slope of the mean relation in Eq. (16), the parameter most sensitive to shear-richness covariance.
  • sigma_ln_lambda_0 = 0.53 +/- 0.03 (baseline counts plus profiles)
    Normalization of the log-normal scatter in Eq. (17).
  • sigma_z = 0.20 +/- 0.11 (baseline counts plus profiles)
    Redshift slope of the scatter in Eq. (17).
  • sigma_m = 0.14 +/- 0.05 (baseline counts plus profiles)
    Mass slope of the scatter in Eq. (17).
  • Photo-z bias correction (1+b) = b = -0.02 +/- 0.03 for BPZ, b = 0.02 +/- 0.03 for FlexZBoost
    Multiplicative factor fitted jointly with the scaling parameters to absorb photometric redshift calibration bias in Section 5.3.1.
assumptions (7)
  • domain assumption The Despali et al. (2015) halo mass function and Tinker et al. (2010) halo bias accurately describe halo abundance and clustering in cosmoDC2.
    Used in Eqs. (1), (13), (14), and (25); calibration uncertainties are not propagated.
  • domain assumption The mass-richness relation is log-normal with mean and scatter given by Eqs. (15) to (17).
    This shape is assumed for both the fiducial and lensing-plus-counts fits.
  • domain assumption The redMaPPer selection function factorizes as Phi = c(m,z) / p(lambda,z), with purity near unity for lambda above 20 and no lensing from spurious detections.
    Eq. (3) and Eq. (13); the text itself flags this as a strong assumption.
  • domain assumption The NFW profile with the Duffy et al. (2008) concentration-mass relation describes the cluster density over the fitted radial range.
    Baseline model in Section 5.1; alternatives are tested in Section 5.2.
  • domain assumption The two-halo term is negligible for R below 3.5 Mpc.
    Motivates the radial cut in Sections 4.1.2 and 5.1; Appendix B tests larger Rmax.
  • ad hoc to paper Off-diagonal elements of the stacked lensing profile covariance are negligible.
    Section 4.2.2 retains only diagonal bootstrap covariance because off-diagonal terms are noisy; Wu et al. (2019) note this can under-estimate uncertainties at large scales.
  • domain assumption Observed and true cluster redshifts are equal in the selection function form.
    Footnote 5 states that observed and true redshifts are considered equal.

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Cite this review

Pith. "Pith review of Weak lensing mass-richness relation of redMaPPer clusters in the LSST DESC DC2 simulations." pith.science (2026). https://pith.science/paper/5CCGGJDT

@misc{pith2026250208444,
  author       = {Pith},
  title        = {Pith review of: Weak lensing mass-richness relation of redMaPPer clusters in the LSST DESC DC2 simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5CCGGJDT}},
  note         = {Machine review of arXiv:2502.08444}
}
abstract

Cluster scaling relations are key ingredients in cluster abundance-based cosmological studies. In optical cluster cosmology, where clusters are detected through their richness, cluster-weak gravitational lensing has proven to be a powerful tool to constrain the cluster mass-richness relation. This work is conducted as part of the Dark Energy Science Collaboration (DESC), which aims to analyze the Legacy Survey of Space and Time (LSST) of the Vera C. Rubin Observatory, starting in 2026. Weak lensing-inferred cluster properties, such as mass, suffer from several sources of bias. We constrain the mass-richness relation of 3,600 clusters detected by the redMaPPer algorithm in the cosmoDC2 extra-galactic mock catalog of the LSST DESC DC2 simulation, covering 440 square degrees, using number count measurements and either stacked weak lensing profiles or mean cluster masses in intervals of richness ($20 < \lambda < 200$) and redshift ($0.2 < z < 1$). We find that, for an LSST-like source galaxy density, our constraints are robust to changes in the concentration-mass relation and dark matter density profile modeling choices, when source redshifts and shapes are perfectly known. We find that photometric redshift uncertainties can introduce bias at the 1$\sigma$ level, which can be mitigated by an overall correction factor, fitted jointly with the scaling parameters. We find that including positive shear-richness covariance in the fit shifts the results by up to 0.5$\sigma$. Our constraints also compare fairly to a fiducial mass-richness relation, obtained from matching cosmoDC2 halo masses to redMaPPer-detected cluster richnesses.

Figures

Figures reproduced from arXiv: 2502.08444 by the authors.

Figure 1
Figure 1. Left: cosmoDC2 halo M200c masses (from the simulation) versus the redMaPPer cluster richnesses. The points are colored with the redMaPPer cluster redshift. The full line is the best-fitted mean richness-mass relation in Eq. (16) at z = 0.4. The dashed lines represent the low mass and low richness cut used on the cosmoDC2-redMaPPer matched catalog for the fit of the fiducial scaling relation. Right: Histogram of rich… view at source ↗
Figure 2
Figure 2. Measured count of redMaPPer cluster as a function of richness, for different richness bins. For each richness-redshift bin, the width of the shaded area represent the width of the richness bin, and the height correspond to the Poisson noise √ N. The steeper slope of cluster counts at intermediate richness (between the second and third richness bin) for all redshift bins is primarily due to the choice of richness bin… view at source ↗
Figure 3
Figure 3. Stacked excess surface density profile as a function of the distance to the cluster center, for different richness bins (colors) and different redshift bins (from top left to bottom right). The error bars are the diagonal elements of the bootstrap covariance matrices. The black dashed vertical line (resp. black filled vertical line) represents the R > 1 Mpc cut (resp. R < 3.5 Mpc cut). 4.1.2. Stacked excess surface … view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Signal-to-noise ratio of the stacked excess surface density profiles, for two different richness bins (left and right panel) and different richness bins (colors). in Sect. 3.3, is used in Eq. (1). The quantity ΣN is the cluster count covariance matrix, which accounts f…
Figure 5
Figure 5. Figure 5: Left: Mean cluster lensing mass as a function of mean richness within the stack, the different colors correspond to the different redshift bins. Right: Mean cluster lensing masses as a function of the DC2 matched masses from the cosmoDC2 dark matter halo catalog. The d…
Figure 6
Figure 6. Figure 6: Left: Posterior distribution of the scaling relation parameters using abundance alone (blue), lensing profiles alone (dashed red), or masses alone (green, full lines). The joint abundance and lensing profiles posterior is displayed in black. Right: Posterior distributi…
Figure 7
Figure 7. Figure 7: Left: Posterior distribution of the scaling relation parameters using count/mass likelihood. The concentration-free case is shown with the dashed lines, the other contours are obtained using various concentration-mass relations from the literature. Right: Posterior dis…
Figure 8
Figure 8. Figure 8: Left: Mean photometric redshift against true cosmoDC2 redshift for BPZ and FlexZBoost methods. Right: distribution of true cosmoDC2 redshifts after our magnitude cuts (black). Upper panel: The blue distribution represents the same distribution after a cut on the probab…
Figure 9
Figure 9. Figure 9: Impact of photometric redshifts of source galaxies on scaling relation parameter estimation. Left: The filled contours show the constraints when using true redshifts of source galaxies. Dashed contours are obtained when considering the BPZ photometric redshifts. Empty …
Figure 10
Figure 10. Figure 10: Binned excess surface density-richness covariance in Eq. (38), as a function of the radius from the cluster center. We stack all clusters between λ ∈ [20, 70) and subdivide by different redshift bins from the top left panel to the bottom right panel. The true redshift…
Figure 11
Figure 11. Figure 11: The covariance in Eq. (38) modeled as a constant bias term bCov(M,z) across radius when binned by richness (left panel) or redshift (right panel). The positive covariance at large scales at lower redshift and richness bins is consistent with expectations from projecti…
Figure 12
Figure 12. Figure 12: Impact of shear-richness covariance on scaling relation parameter estimation. Left: Posterior distribution of the scaling relation parameters with (dashed blue) and without (filled blue) the shear-richness covariance correction in Eq. (35), considering true source gal…
Figure 13
Figure 13. Figure 13: Summary of the constraints on the scaling relation parameters (only ln λ0, µz and µm) obtained in Sect. 5. The vertical shaded region in each subplot represents the fiducial constraints presented in Sect. 3.4.1. For clarity, each color used for the plot corresponds to…

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.