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arxiv: 2605.06587 · v1 · submitted 2026-05-07 · 🌌 astro-ph.CO · astro-ph.GA

Recognition: unknown

Constraining Galaxy Cluster Triaxiality via Weak Lensing -- I. Preparation for the Rubin Data Beyond Leading Order

Shenming Fu , Radhakrishnan Srinivasan , Tae-hyeon Shin , Rance Solomon , Deric Jones , Camille Avestruz , Yuanyuan Zhang , Michel Aguena
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C\'eline Combet Anthony Englert Benjamin Levine Alex I. Malz Constantin Payerne Marina Ricci Anja von der Linden The LSST Dark Energy Science Collaboration
Authors on Pith no claims yet

Pith reviewed 2026-05-08 05:27 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords weak lensinggalaxy clusterstriaxialityprojected ellipticitydark energy surveyrubin lsstcluster shapes
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The pith

Galaxy clusters exhibit a projected ellipticity of 0.31 when their weak lensing signals are stacked after alignment by satellite galaxies.

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

The paper develops and applies a method to extract the average projected shape of galaxy clusters from weak lensing data by performing axis-aligned stacking and expanding the multipole moments to second order in ellipticity. Using a precursor sample from the Dark Energy Survey Year 3 consisting of redMaPPer clusters with high central-galaxy centering probability, orientations are taken from the satellite galaxy distribution. This yields a measured ensemble ellipticity of 0.310 with an associated axis ratio of 0.527, showing no statistically significant trends with mass or redshift. The measurement is validated on mock catalogs and positioned as preparation for tighter constraints once Rubin Observatory LSST data arrive.

Core claim

Applying the triaxiality module of the Cluster Lensing Mass Modeling software to DES Y3 data, the authors stack weak-lensing signals of clusters aligned according to satellite-galaxy major axes and expand the monopole and quadrupole to second order in ellipticity. For the selected sample they report a projected ellipticity of 0.310^{+0.017}_{-0.016} (axis ratio 0.527^{+0.018}_{-0.019}) that is statistically independent of both cluster mass and redshift within the probed range.

What carries the argument

Axis-aligned stacking of weak-lensing multipoles expanded to second order in ellipticity, with orientations supplied by the satellite galaxy distribution.

If this is right

  • The measured average ellipticity supplies a direct observational anchor for the typical projected shapes assumed in cosmological simulations of cluster formation.
  • Absence of mass and redshift trends implies that a single ellipticity prior can be used across the current sample range without large systematic corrections.
  • Extension of the multipole analysis to second order reduces the leading-order bias in shape recovery for future wide-field surveys.
  • The same pipeline scales directly to LSST, Euclid, and Roman data sets once larger cluster samples become available.

Where Pith is reading between the lines

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

  • If satellite galaxies continue to trace halo axes in larger samples, optical catalogs alone could suffice for shape constraints without requiring multi-wavelength orientation data.
  • The second-order terms may become essential for controlling projection biases in cluster mass calibration at the precision demanded by next-generation surveys.
  • A larger sample would permit binning the ellipticity measurement by additional observables such as dynamical state or concentration to test for hidden dependencies.

Load-bearing premise

Satellite galaxies reliably indicate the major-axis orientation of the underlying dark-matter halo without introducing significant misalignment or selection bias from the centering cut.

What would settle it

Repeating the identical stacking and multipole analysis with cluster orientations taken from an independent tracer such as X-ray isophotes or direct lensing reconstruction and obtaining a statistically different ellipticity value.

Figures

Figures reproduced from arXiv: 2605.06587 by Alex I. Malz, Anja von der Linden, Anthony Englert, Benjamin Levine, Camille Avestruz, C\'eline Combet, Constantin Payerne, Deric Jones, Marina Ricci, Michel Aguena, Radhakrishnan Srinivasan, Rance Solomon, Shenming Fu, Tae-hyeon Shin, The LSST Dark Energy Science Collaboration, Yuanyuan Zhang.

Figure 1
Figure 1. Figure 1: Flowchart of the analysis pipeline. The green parallelograms, blue rectangles, and pink parallelograms show the data, processing steps, and results, respectively. and the stretch (with two components, γ1 and γ2, sep￾arated by 45 degrees) of the background image, respec￾tively. They are connected by derivatives of a lensing potential ϕ that satisfies Eq. 2 and Eq. 3 with sky coor￾dinates. κ = 1 2 (∂11ϕ + ∂2… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the deformation. Top: 2D projection with surface density transformation Σ(p x2 + y 2) → Σ(p qx2 + y 2/q). The iso-density contour changes from a circle to an ellipse with ra￾tio of axes a : b = 1/ √q : √q while the area and mass are unchanged during the transformation. Bot￾tom: Effective 3D structure with density transformation ρ( p x2 + y 2 + z 2) → ρ( p qx2 + y 2/q + z 2). Here, the iso-d… view at source ↗
Figure 3
Figure 3. Figure 3: Dilution factor as a function of the true ellipticity for the baseline sample (defined in Section 2.1) and for the redshift- and richness-split cluster sub-samples (defined in Section 3.4). 10. Build a mapping between input true ellipticities and the mean dilution factor of the cluster sample. Fig￾ure 3 shows the dilution factor as a function of ellipticity for each cluster sample. It grows with ellipticit… view at source ↗
Figure 4
Figure 4. Figure 4: shows the boost factor for each cluster sam￾ple. The error bars are estimated by jackknife. As ex￾pected, the boost factor grows with richness as more cluster members contaminate the background sample. 6 The mean can be higher than the cluster redshift provided by redMaPPer, because these cluster galaxies have photo-zs biased high (T. N. Varga et al. 2019). 10 0 R [Mpc] 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1… view at source ↗
Figure 5
Figure 5. Figure 5: Fitting results for the stacked lensing monopole (Left) and quadrupole (Middle and Right) profiles of the baseline cluster sample (selected by pcen0 > 0.9 and 0.2 < z < 0.65 in DES Y3 redMaPPer). The fitted parameters are shown in view at source ↗
Figure 6
Figure 6. Figure 6: Posterior of the stacked lensing monopole and quadrupole simultaneous fit shown in view at source ↗
Figure 7
Figure 7. Figure 7: Fitted stacked profiles of the selected DES Y3 redMaPPer clusters when split by richness or redshift. The dark (light) shaded area shows the 1σ (2σ) of the confidence interval. The data have been corrected for boost factors. Top two: High and Low redshift bins. Bottom two: High and Low richness bins. The fitted ellipticities are shown in view at source ↗
Figure 8
Figure 8. Figure 8: Halo ellipticity (ϵ) and axis ratio (q) as a function of redshift (Top) or richness/mass (Bottom) for the selected DES Y3 redMaPPer clusters. results of concentration from 2 to 6, indicating that this analysis is not sensitive to halo concentration. The fit￾ted mass is also consistent with the input (difference < 1 % when q > 0.4). In addition, we note that when qtruth ∈ [0.6, 1) the error is < 1 %, but th… view at source ↗
Figure 9
Figure 9. Figure 9: Fitting results for the stacked lensing monopole and quadrupole profiles of clusters with pcen0 > 0.9 and 0.2 < z < 0.65 in DES Y1 redMaPPer. The points with error bars represent the data. The solid curves show the best– fit model predictions. The shaded regions indicate the 1 σ (dark) and 2 σ (light) confidence intervals. Like view at source ↗
Figure 10
Figure 10. Figure 10: Comparison between the true and fitted axis ratios derived from mock catalogs with different concentration values. The red-dashed, solid, and dotted lines correspond to c200c = 2, 4, and 6, respectively. Left: Fitted axis ratio (q) vs. true value (qtruth). Right: Relative error (∆q/qtruth) vs. qtruth. The shaded areas around the lines represent the 1 σ confidence interval for the mock clusters with the co… view at source ↗
Figure 11
Figure 11. Figure 11: Top: Monopole comparison between the ellip￾tical (orange) and spherical NFW profiles (black dotted) of clusters with the same mass, M200c = 2 × 1014M⊙ and con￾centration, c200c = 4 at redshift z = 0.4. We also show the profile of a spherical cluster with 95 % of the mass in crim￾son. Bottom: Fractional difference between the monopoles of the elliptical and the two spherical profiles. We find that the elli… view at source ↗
Figure 12
Figure 12. Figure 12: Top: MagLim galaxy number density stacked along cluster major axes. The contours are set at equal steps in logarithmic scale. The top right panel shows the central half region of the top left panel. Bottom left: Effective radius as a function of axis ratio. Density levels are sampled uniformly in logarithmic space. At each level, pixels with densities within 5 % are selected, and an ellipse is fitted to t… view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of projected halo ellipticity measurements for the selected DES Y3 and SDSS redMaPPer clusters. Left: Ellipticity as a function of redshift. We indicate the measurement from T.-h. Shin et al. (2018) in blue, the baseline sample in black, the low-redshift sample in orange, and the high-redshift sample in red. The horizontal error bar indicates the range of redshifts for the respective cluster sa… view at source ↗
Figure 14
Figure 14. Figure 14: Histogram of the comparison between the major-axis angle of each cluster halo measured from the satellite galaxy distribution vs. the one measured from the particle distribution in SkySim5000. The angle unit is degree. C. THEORY OF MONOPOLE AND QUADRUPOLE C.1. Forms Following the description in Section 3, we give the details of the derivation of the monopole and the quadrupole. First, we have the axis rat… view at source ↗
read the original abstract

The 3D mass distributions of galaxy clusters are generally triaxial, a geometry that is difficult to constrain from projected observations. In this work, we measure the projected halo shapes of clusters from their weak lensing signatures using the triaxiality functionality in the Cluster Lensing Mass Modeling software, a tool developed by the Dark Energy Science Collaboration to analyze data from NSF-DOE Rubin Observatory's Legacy Survey of Space and Time (LSST). We measure ensemble halo ellipticity on the plane of the sky via axis-aligned stacking and multipole expansion of the weak lensing data. We study a precursor dataset -- the redMaPPer cluster catalog, the metacalibration shape catalog, and the Directional Neighborhood Fitting photometric redshift catalog from the Dark Energy Survey Year 3 public data release. We select clusters that have a high centering probability (>90%) of the identified central galaxy, and use the satellite galaxy distribution to determine the major-axis orientation for stacking. We extend the analysis to the second order of ellipticity in the monopole and quadrupole measurement. The projected ellipticity of the cluster sample is found to be $0.310^{+0.017}_{-0.016}$ (axis ratio $0.527^{+0.018}_{-0.019}$). The projected cluster ellipticity shows no statistically significant dependence on mass and redshift. We further verify the accuracy of the cluster shape measurement using mock catalogs. This analysis is applicable to datasets from upcoming wide-area cosmic surveys such as LSST, Euclid, and the Roman Space Telescope, where larger sample sizes will lead to tighter constraints on the cluster ellipticities.

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. The paper measures the projected ellipticity of galaxy clusters from DES Y3 weak-lensing data by selecting clusters with >90% centering probability, aligning stacks using the major axis inferred from satellite galaxy positions, and extracting ellipticity from the monopole and quadrupole of the lensing signal extended to second order. Using the CLMM triaxiality module, they report a sample ellipticity of 0.310^{+0.017}_{-0.016} (axis ratio 0.527^{+0.018}_{-0.019}) with no statistically significant mass or redshift dependence, validate the pipeline on mocks, and frame the work as preparation for LSST/Rubin data.

Significance. If the alignment and centering assumptions hold without substantial bias, the result supplies a useful benchmark for cluster shapes ahead of larger LSST samples and demonstrates the practical extension of multipole analysis beyond leading order. The absence of mass/redshift trends is a clear, falsifiable outcome that could constrain formation models. The use of public DES catalogs and open CLMM software is a strength for reproducibility.

major comments (2)
  1. [Methodology and mock verification] The axis-aligned stacking procedure (described in the methodology) assumes satellite galaxies accurately trace the halo major axis. Simulations and observations indicate typical misalignments of 20-40 degrees, which would dilute the quadrupole amplitude and bias the reported ellipticity low. The mock verification tests the pipeline only under the assumed perfect-alignment model and does not quantify or correct for this effect, making the central numerical claim (0.310^{+0.017}_{-0.016}) dependent on an untested assumption.
  2. [Data selection and results] The >90% centering-probability cut is applied to select the sample, yet no robustness test varying the threshold (e.g., 80% or 95%) is shown to assess possible selection bias toward more relaxed, better-aligned systems. This directly affects the measured ellipticity and its claimed lack of mass/redshift dependence.
minor comments (2)
  1. [Abstract and Results] The abstract and results section would benefit from explicit statement of the covariance estimation method and any systematic error budget (e.g., photo-z, shape calibration, or mask effects) to support the quoted uncertainties.
  2. [Methodology] Notation for the second-order ellipticity terms in the monopole/quadrupole expansion should be cross-referenced to the relevant CLMM equations for readers unfamiliar with the software.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's careful review and insightful comments on our manuscript. The suggestions highlight important aspects of the methodology and data selection that we will address in the revision. Below, we provide point-by-point responses to the major comments.

read point-by-point responses

  1. Referee: [Methodology and mock verification] The axis-aligned stacking procedure (described in the methodology) assumes satellite galaxies accurately trace the halo major axis. Simulations and observations indicate typical misalignments of 20-40 degrees, which would dilute the quadrupole amplitude and bias the reported ellipticity low. The mock verification tests the pipeline only under the assumed perfect-alignment model and does not quantify or correct for this effect, making the central numerical claim (0.310^{+0.017}_{-0.016}) dependent on an untested assumption.

    Authors: We thank the referee for pointing out this potential source of bias. Indeed, the misalignment between satellite galaxies and the underlying halo major axis is a known effect in the literature. Our mock verification was designed to test the recovery of the input ellipticity under the assumption of perfect alignment, as stated in the paper, to validate the pipeline implementation. However, we agree that quantifying the impact of realistic misalignments is necessary. In the revised version, we will add a section discussing this effect and present results from mocks incorporating misalignment angles of 20-40 degrees, showing the expected dilution and any necessary corrections or caveats to the reported ellipticity value. revision: yes

  2. Referee: [Data selection and results] The >90% centering-probability cut is applied to select the sample, yet no robustness test varying the threshold (e.g., 80% or 95%) is shown to assess possible selection bias toward more relaxed, better-aligned systems. This directly affects the measured ellipticity and its claimed lack of mass/redshift dependence.

    Authors: We acknowledge the importance of testing the sensitivity to the centering probability threshold. The >90% cut was chosen to ensure reliable central galaxy identification and minimize miscentering effects on the lensing signal. To address the referee's concern, we will include in the revised manuscript additional measurements using alternative thresholds (80% and 95%) and demonstrate that the ensemble ellipticity and its lack of dependence on mass and redshift remain consistent within uncertainties. revision: yes

Circularity Check

0 steps flagged

Direct data-driven measurement via stacking and multipole expansion; no reduction to inputs by construction

full rationale

The paper's central result is an observational extraction of projected ellipticity (0.310^{+0.017}_{-0.016}) from DES Year 3 weak-lensing data. Clusters are selected by centering probability, oriented using the observed satellite galaxy distribution, stacked axis-aligned, and analyzed via monopole/quadrupole multipoles extended to second order in ellipticity. This chain operates directly on external survey data using the described pipeline; the output ellipticity is not a fitted parameter renamed as a prediction, nor does any step invoke a self-citation whose content is required to justify the numerical result. Mock verification tests the pipeline under the alignment assumption but does not substitute for the data measurement itself. The derivation is therefore self-contained against external benchmarks with no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper is an observational measurement that relies on standard weak-lensing assumptions rather than new theoretical constructs or fitted parameters beyond the reported data product.

axioms (2)
  • domain assumption Weak lensing shear traces the projected mass distribution of the cluster
    Invoked implicitly when converting lensing signal to ellipticity; standard in the field.
  • domain assumption Satellite galaxy distribution traces the major axis of the dark matter halo
    Used to orient the stacks; appears in the sample selection description.

pith-pipeline@v0.9.0 · 5670 in / 1390 out tokens · 90216 ms · 2026-05-08T05:27:47.762932+00:00 · methodology

discussion (0)

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