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arxiv: 2606.21141 · v1 · pith:ALBS4QCLnew · submitted 2026-06-19 · 🌌 astro-ph.CO · astro-ph.IM

Accurate Galaxy Cluster Shear and Mass Calibration for LSST with AnaCal

Conghao Zhou , Xiangchong Li , Hao-Yi Wu , Anja von der Linden , Tesla Jeltema , Tae-hyeon Shin , Simon Birrer , Tomomi Sunayama
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Shenming Fu Prakruth Adari Lucie Baumont Surhud More Anthony Englert Miranda Gorsuch Andr\'es A. Plazas Malag\'on
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Pith reviewed 2026-06-26 13:56 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.IM
keywords weak lensinggalaxy clustersshear estimationLSSTmass calibrationimage simulationscosmology
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The pith

AnaCal recovers input shear with minimal bias at |g|~0.15, producing 0.24% mean cluster mass bias under LSST-like conditions.

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

The paper evaluates the AnaCal shear estimator for weak lensing around galaxy clusters using image simulations that match ten-year LSST data conditions. It shows that AnaCal recovers the true shear with little bias even at shear values near 0.15 close to cluster centers. A radially decreasing shear response driven by convergence and a third-order positive bias near the center are identified, but these affect only a small fraction of galaxies and are downweighted by the covariance matrix. With a scale cut of about 0.2 Mpc at redshift 0.25, the mean mass bias for clusters between 10^14 and 10^15 solar masses stays at 0.24 plus or minus 0.26 percent in ideal settings. Accurate shear measurement in this regime supports using cluster abundance for precision cosmology.

Core claim

AnaCal recovers the input shear with minimal bias even at mildly high shear |g|~0.15. A radially decreasing mean shear response driven by the radial dependence of the convergence field is discovered; if unmodeled this can bias shear inference. A positive shear-estimation bias at third order in the reduced shear near the cluster center is also found. However, because only a small fraction of galaxies lie in the high-shear regime and those measurements are further downweighted by the covariance matrix, the resulting mean cluster-mass bias for cluster lens masses in [10^14 M_⊙, 10^15 M_⊙] adopting a scale cut of ~0.2 Mpc at z=0.25 is 0.24±0.26% under ideal settings.

What carries the argument

AnaCal shear estimator applied to simulated galaxy images to extract reduced shear signals around clusters.

If this is right

  • AnaCal can calibrate cluster masses with sub-percent bias for the tested mass range and scale cut.
  • Radial dependence of the shear response must be modeled to avoid systematic error in shear inference.
  • Third-order bias terms remain subdominant after covariance weighting in the overall mass estimate.
  • The estimator supports cluster weak lensing as a tool for LSST cosmology without large high-shear corrections.

Where Pith is reading between the lines

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

  • If the simulation-to-data match holds, AnaCal could tighten cosmological constraints from cluster number counts.
  • Tests with added real-data effects such as blending or variable depth would check whether the reported bias stays this low.
  • The same simulation framework could benchmark other shear estimators in the high-shear cluster regime.

Load-bearing premise

The image simulations accurately capture the noise, point-spread function, and galaxy properties of real ten-year LSST observations.

What would settle it

Comparison of AnaCal-derived cluster masses from actual LSST observations against independent mass estimates from X-ray temperature or Sunyaev-Zel'dovich measurements.

Figures

Figures reproduced from arXiv: 2606.21141 by Andr\'es A. Plazas Malag\'on, Anja von der Linden, Anthony Englert, Conghao Zhou, Hao-Yi Wu, Lucie Baumont, Miranda Gorsuch, Prakruth Adari, Shenming Fu, Simon Birrer, Surhud More, Tae-hyeon Shin, Tesla Jeltema, Tomomi Sunayama, Xiangchong Li.

Figure 1
Figure 1. Figure 1: Example simulated image for weak gravitational lensing by a cluster with mass of 1015M⊙ in LSST. The lens cluster is located at the center of the image, and only source galaxies are simulated. The image size is 5000 × 5000 pixels, and the pixel scale is 0.2 arcsec/pixel. We only show the central 2000 × 2000 pixels in this image. ⟨g obs T ⟩b = ⟨eT ⟩ b ⟨RT ⟩ b , (23) where ⟨·⟩b stands for averaging over all … view at source ↗
Figure 2
Figure 2. Figure 2: Example posterior distribution for mass fitting for a cluster lens of mass 8.5×1014M⊙ with free mass concen￾tration relation. The inner and outer contours denote 68% and 95% credible regions. 2.6. Shear estimation bias To estimate the shear bias, we first calculate the true shear profile with lenstronomy with the true input mass, concentration, and source positions. Then we calculate m = g obs T g true T −… view at source ↗
Figure 3
Figure 3. Figure 3: Shear estimation results for the cluster lens of masses 1014M⊙, 2 × 1014M⊙, 5 × 1014M⊙, and 1015M⊙. AnaCal can recover input true shear up to g ∼ 0.15. The error bar is from the forecast covariance for the 10-year LSST survey. We show the p-value in the last row of the figure. There is a positive shear bias that we will quantify in Section 3.2. 0.00 0.05 0.10 0.15 0.20 gtrue 0.10 0.05 0.00 0.05 m g m e as/… view at source ↗
Figure 4
Figure 4. Figure 4: Measured and the best-fit shear bias for all radial bins of the simulated cluster lenses. The transparent points are measured shear bias, the solid circles with error bars are the binned mean of the measured shear bias, and the purple solid line is the best fit shear bias with Equation 29. The gray-shaded region is the SRD requirement for shear bias |m| < 0.3%. The best-fit parameters are printed in the lo… view at source ↗
Figure 8
Figure 8. Figure 8: Mass bias caused by response trend shown in Section 3.3. The y-axis is the ratio between the best-fit mass using the mean response of all radial bins and the best-fit mass using the mean response in each radial bin using true concentration. We find that on average, the radial response trend would cause a ∼ 3% bias on mass calibration of high mass clusters if not treated correctly. 100 200 300 400 500 Inner… view at source ↗
Figure 9
Figure 9. Figure 9: Mean mass calibration bias across all mass range as a function of radial scale cut. Each mass calibration result is weighted by its bootstrap uncertainty, and the error bar on the mean is propagated accordingly. The mass calibration result when including lensing below 0.18 Mpc at z = 0.25 is biased high because of the positive shear bias. We see that at scales above 0.2 Mpc at z = 0.25, AnaCal’s mean clust… view at source ↗
Figure 10
Figure 10. Figure 10: The high-order shear bias in constant blended simulations. Left: Multiplicative bias as a function of input shear. There is a positive third-order shear bias. Right: Multiplicative bias as a function of input convergence. We find that convergence does not cause a shear bias. This is consistent with the cluster lens result discussed in Section 2.6. Software: astropy ( Astropy Collaboration et al. 2013, 201… view at source ↗
read the original abstract

The observed abundance of galaxy clusters as a function of mass and redshift provides a powerful route to precision cosmology; a key challenge for cluster cosmology is to establish the relation between cluster observables and cluster masses, for which cluster weak gravitational lensing has become the standard tool. A key challenge for cluster lensing is that the shear signal near cluster centers can reach the non-linear regime, where many shear estimators rely on perturbative assumptions that must be explicitly validated. In this work, we use image simulations to test the performance of the shear estimator AnaCal for cluster weak lensing under conditions representative of the 10-year LSST data. We find that AnaCal recovers the input shear with minimal bias even at mildly high shear, $|g|\sim 0.15$. We discover a radially decreasing mean shear response as seen previously in data, driven by the radial dependence of the convergence field; if unmodeled, this effect can bias shear inference. We also find a positive shear-estimation bias at third order in the reduced shear near the cluster center. However, because only a small fraction of galaxies lie in the high-shear regime and those measurements are further downweighted by the covariance matrix, the resulting mean cluster-mass bias for cluster lens masses in $[10^{14} M_\odot, 10^{15} M_\odot]$ -- adopting a scale cut of $\sim 0.2$ Mpc at $z=0.25$ -- is $0.24 \pm 0.26\%$ under ideal settings. These results demonstrate that AnaCal is a robust tool for accurate cluster mass calibration in the LSST era.

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 / 1 minor

Summary. The manuscript tests the AnaCal shear estimator on image simulations under conditions stated to be representative of 10-year LSST data. It reports that AnaCal recovers input shear with minimal bias at |g|∼0.15, identifies a radially decreasing mean shear response driven by the convergence field and a positive third-order bias in reduced shear near cluster centers, but concludes that these effects produce only a 0.24±0.26% mean cluster-mass bias for lens masses in [10^14 M_⊙, 10^15 M_⊙] with a ∼0.2 Mpc scale cut at z=0.25 under ideal settings, because high-shear galaxies are few and down-weighted by the covariance matrix.

Significance. If the reported bias levels are preserved under full LSST observing conditions, the work would provide a valuable validation of AnaCal for cluster weak-lensing mass calibration, directly addressing the non-linear shear regime that challenges perturbative estimators. The strength of the approach lies in the direct comparison of recovered shear to known input values in controlled simulations, which supplies a clear, falsifiable test of the estimator's performance.

major comments (2)
  1. [Abstract] Abstract: the headline mass-bias result (0.24±0.26%) is obtained after modeling the radially decreasing shear response and third-order reduced-shear term, with mitigation attributed to the small fraction of high-shear galaxies and covariance down-weighting; however, both the radial-response modeling and the covariance construction are demonstrated only inside the 'ideal settings' simulations, and no quantitative test is reported of how the bias changes when additional LSST effects (variable focal-plane seeing, chromatic PSF, color gradients, or density-correlated selection) are injected. This is load-bearing for the claim that AnaCal is ready for LSST cluster cosmology.
  2. [Abstract] Abstract: the simulations are described both as 'representative of the 10-year LSST data' and as 'ideal settings'; the manuscript does not supply a table or section that quantifies the difference between these two descriptions or shows the bias sensitivity to omitted effects, leaving the translation from simulation to real data untested at the precision of the quoted 0.26% uncertainty.
minor comments (1)
  1. [Abstract] The abstract would benefit from an explicit one-sentence definition of what 'ideal settings' excludes (e.g., no mention of chromatic effects or variable PSF).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review. The comments correctly identify the scope limitations of our ideal-settings simulations. We respond point-by-point below and revise the manuscript to remove any ambiguity about the applicability of the quoted bias to full LSST conditions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline mass-bias result (0.24±0.26%) is obtained after modeling the radially decreasing shear response and third-order reduced-shear term, with mitigation attributed to the small fraction of high-shear galaxies and covariance down-weighting; however, both the radial-response modeling and the covariance construction are demonstrated only inside the 'ideal settings' simulations, and no quantitative test is reported of how the bias changes when additional LSST effects (variable focal-plane seeing, chromatic PSF, color gradients, or density-correlated selection) are injected. This is load-bearing for the claim that AnaCal is ready for LSST cluster cosmology.

    Authors: We agree that the simulations are performed exclusively under ideal settings and that no quantitative tests of the listed additional LSST effects are provided. The manuscript already qualifies all numerical results with the phrase 'under ideal settings,' but the abstract conclusion could be read as implying broader readiness. We will revise the abstract to state explicitly that the 0.24±0.26% bias applies only under the ideal conditions tested and that validation under complete LSST observing conditions remains future work. We will also add a paragraph in the discussion section summarizing how each omitted effect could in principle affect the result, drawing on existing literature. This revision directly addresses the load-bearing concern by narrowing the claim. revision: partial

  2. Referee: [Abstract] Abstract: the simulations are described both as 'representative of the 10-year LSST data' and as 'ideal settings'; the manuscript does not supply a table or section that quantifies the difference between these two descriptions or shows the bias sensitivity to omitted effects, leaving the translation from simulation to real data untested at the precision of the quoted 0.26% uncertainty.

    Authors: We accept that the dual terminology creates ambiguity. The simulations match LSST in galaxy density, redshift distribution, and noise level but are ideal with respect to PSF uniformity and selection. We will insert a new subsection (tentatively 3.4) that defines the ideal-settings approximations, lists the omitted effects, and provides a qualitative assessment of their expected influence on the shear response and mass bias. While a quantitative sensitivity study is not feasible with the current simulation suite, the added section will make the translation limitations explicit and prevent over-interpretation of the 0.26% uncertainty. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are direct simulation comparisons.

full rationale

The paper obtains its headline result (0.24±0.26% mean cluster-mass bias) by applying AnaCal to image simulations that supply known input shear values and then measuring the recovered shear and inferred mass bias directly against those inputs. No equation or procedure defines the target bias in terms of itself, fits a parameter to a subset and renames the output as a prediction, or relies on a load-bearing self-citation whose content reduces to the present claim. The radial response and third-order bias are reported as findings from the same simulations rather than inputs that force the final number by construction. The derivation chain is therefore self-contained against the external simulation benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the fidelity of the image simulations to real LSST data and the validity of the chosen scale cut and mass range for averaging the bias.

axioms (1)
  • domain assumption Image simulations accurately model the LSST observational conditions including PSF, noise, and galaxy distributions.
    Performance measured in simulation is assumed to translate directly to real data.

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Works this paper leans on

115 extracted references · 113 canonical work pages · 3 internal anchors

  1. [1]

    Abbott, T. M. C., Aguena, M., Alarcon, A., et al. 2020, Physical Review D, 102, 023509, doi: 10.1103/PhysRevD.102.023509

    work page doi:10.1103/physrevd.102.023509 2020

  2. [2]

    Abbott, T. M. C., Aguena, M., Alarcon, A., et al. 2025, Physical Review D, 112, 083535, doi: 10.1103/3dzh-d8f5

    work page doi:10.1103/3dzh-d8f5 2025

  3. [3]

    2021, Monthly Notices of the Royal Astronomical Society, 508, 6092, doi: 10.1093/mnras/stab2764

    Aguena, M., Avestruz, C., Combet, C., et al. 2021, Monthly Notices of the Royal Astronomical Society, 508, 6092, doi: 10.1093/mnras/stab2764

    work page doi:10.1093/mnras/stab2764 2021

  4. [4]

    2019, Publications of the Astronomical Society of Japan, 71, 114, doi: 10.1093/pasj/psz103

    Aihara, H., AlSayyad, Y., Ando, M., et al. 2019, Publications of the Astronomical Society of Japan, 71, 114, doi: 10.1093/pasj/psz103

    work page doi:10.1093/pasj/psz103 2019

  5. [5]

    W., Evrard, A

    Allen, S. W., Evrard, A. E., & Mantz, A. B. 2011, Annual Review of Astronomy and Astrophysics, 49, 409, doi: 10.1146/annurev-astro-081710-102514

    work page doi:10.1146/annurev-astro-081710-102514 2011

  6. [6]

    Ansarinejad, B., Raghunathan, S., Abbott, T. M. C., et al. 2024, Journal of Cosmology and Astroparticle Physics, 2024, 024, doi: 10.1088/1475-7516/2024/07/024

    work page doi:10.1088/1475-7516/2024/07/024 2024

  7. [7]

    E., von der Linden, A., Kelly, P

    Applegate, D. E., von der Linden, A., Kelly, P. L., et al. 2014, Monthly Notices of the Royal Astronomical Society, 439, 48, doi: 10.1093/mnras/stt2129

    work page doi:10.1093/mnras/stt2129 2014

  8. [8]

    E., Mantz, A., Allen, S

    Applegate, D. E., Mantz, A., Allen, S. W., et al. 2016, Monthly Notices of the Royal Astronomical Society, 457, 1522, doi: 10.1093/mnras/stw005 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A. M., Sip˝ ocz, B. M., et al. 2018, AJ, 156, 123, doi: ...

    work page doi:10.1093/mnras/stw005 2016

  9. [9]

    R., Bautista, M

    Bacon, D. J., Goldberg, D. M., Rowe, B. T. P., & Taylor, A. N. 2006, Monthly Notices of the Royal Astronomical Society, 365, 414, doi: 10.1111/j.1365-2966.2005.09624.x

    work page doi:10.1111/j.1365-2966.2005.09624.x 2006

  10. [10]

    M., Bond, J

    Bardeen, J. M., Bond, J. R., Kaiser, N., & Szalay, A. S. 1986, The Astrophysical Journal, 304, 15, doi: 10.1086/164143

    work page doi:10.1086/164143 1986

  11. [11]

    2010, Reviews of Modern Physics, 82, 331, doi: 10.1103/RevModPhys.82.331

    Bartelmann, M. 2010, Reviews of Modern Physics, 82, 331, doi: 10.1103/RevModPhys.82.331

    work page doi:10.1103/revmodphys.82.331 2010

  12. [12]

    2001, Physics Reports, 340, 291, doi: 10.1016/S0370-1573(00)00082-X

    Bartelmann, M., & Schneider, P. 2001, Physics Reports, 340, 291, doi: 10.1016/S0370-1573(00)00082-X

    work page doi:10.1016/s0370-1573(00)00082-x 2001

  13. [13]

    R., & Kravtsov, A

    Becker, M. R., & Kravtsov, A. V. 2011, The Astrophysical Journal, 740, 25, doi: 10.1088/0004-637X/740/1/25

    work page doi:10.1088/0004-637x/740/1/25 2011

  14. [14]

    2019, Monthly Notices of the Royal Astronomical Society, 484, 1598, doi: 10.1093/mnras/stz090

    Bellagamba, F., Sereno, M., Roncarelli, M., et al. 2019, Monthly Notices of the Royal Astronomical Society, 484, 1598, doi: 10.1093/mnras/stz090

    work page doi:10.1093/mnras/stz090 2019

  15. [15]

    2018, Physics of the Dark Universe, 22, 189, doi: 10.1016/j.dark.2018.11.002

    Birrer, S., & Amara, A. 2018, Physics of the Dark Universe, 22, 189, doi: 10.1016/j.dark.2018.11.002

    work page doi:10.1016/j.dark.2018.11.002 2018

  16. [16]

    2021, The Journal of Open Source Software, 6, 3283, doi: 10.21105/joss.03283

    Birrer, S., Shajib, A., Gilman, D., et al. 2021, The Journal of Open Source Software, 6, 3283, doi: 10.21105/joss.03283

    work page doi:10.21105/joss.03283 2021

  17. [17]

    P., Schrabback, T., et al

    Bocquet, S., Dietrich, J. P., Schrabback, T., et al. 2019, The Astrophysical Journal, 878, 55, doi: 10.3847/1538-4357/ab1f10

    work page doi:10.3847/1538-4357/ab1f10 2019

  18. [18]

    E., et al

    Bocquet, S., Grandis, S., Bleem, L. E., et al. 2024a, Physical Review D, 110, 083510, doi: 10.1103/PhysRevD.110.083510

    work page doi:10.1103/physrevd.110.083510

  19. [19]

    E., et al

    Bocquet, S., Grandis, S., Bleem, L. E., et al. 2024b, Physical Review D, 110, 083509, doi: 10.1103/PhysRevD.110.083509

    work page doi:10.1103/physrevd.110.083509

  20. [20]

    2025, Physical Review D, 111, 063533, doi: 10.1103/PhysRevD.111.063533

    Bocquet, S., Grandis, S., Krause, E., et al. 2025, Physical Review D, 111, 063533, doi: 10.1103/PhysRevD.111.063533

    work page doi:10.1103/physrevd.111.063533 2025

  21. [21]

    2020, arXiv e-prints, arXiv:2001.11067, doi: 10.48550/arXiv.2001.11067

    Brough, S., Collins, C., Demarco, R., et al. 2020, arXiv e-prints, arXiv:2001.11067, doi: 10.48550/arXiv.2001.11067

    work page doi:10.48550/arxiv.2001.11067 2020

  22. [22]

    1998, The Astrophysical Journal, 509, 494, doi: 10.1086/306542

    Cen, R. 1998, The Astrophysical Journal, 509, 494, doi: 10.1086/306542

    work page doi:10.1086/306542 1998

  23. [23]

    2013, Monthly Notices of the Royal Astronomical Society, 434, 2121, doi: 10.1093/mnras/stt1156

    Chang, C., Jarvis, M., Jain, B., et al. 2013, Monthly Notices of the Royal Astronomical Society, 434, 2121, doi: 10.1093/mnras/stt1156

    work page doi:10.1093/mnras/stt1156 2013

  24. [24]

    N., Ghirardini, V., Liu, A., et al

    Chiu, I. N., Ghirardini, V., Liu, A., et al. 2022, Astronomy and Astrophysics, 661, A11, doi: 10.1051/0004-6361/202141755

    work page doi:10.1051/0004-6361/202141755 2022

  25. [25]

    2025, Astronomy and Astrophysics, 704, A110, doi: 10.1051/0004-6361/202554942

    Chiu, I.-N., Ghirardini, V., Grandis, S., et al. 2025, Astronomy and Astrophysics, 704, A110, doi: 10.1051/0004-6361/202554942

    work page doi:10.1051/0004-6361/202554942 2025

  26. [26]

    2020, Astronomy and Astrophysics, 641, A6, doi: 10.1051/0004-6361/201833910

    Collaboration, P., Aghanim, N., Akrami, Y., et al. 2020, Astronomy and Astrophysics, 641, A6, doi: 10.1051/0004-6361/201833910

    work page doi:10.1051/0004-6361/201833910 2020

  27. [27]

    J., Peterson, J., Jernigan, J

    Connolly, A. J., Peterson, J., Jernigan, J. G., et al. 2010, in

    2010

  28. [28]

    7738, 77381O, doi: 10.1117/12.857819

    Modeling, Systems Engineering, and Project Management for Astronomy IV, Vol. 7738, 77381O, doi: 10.1117/12.857819

    work page doi:10.1117/12.857819

  29. [29]

    J., Angeli, G

    Connolly, A. J., Angeli, G. Z., Chandrasekharan, S., et al. 2014, in Modeling, Systems Engineering, and Project Management for Astronomy VI, Vol. 9150, 915014, doi: 10.1117/12.2054953

    work page doi:10.1117/12.2054953 2014

  30. [30]

    2021, Physical Review D, 103, 043522, doi: 10.1103/PhysRevD.103.043522

    Costanzi, M., Saro, A., Bocquet, S., et al. 2021, Physical Review D, 103, 043522, doi: 10.1103/PhysRevD.103.043522

    work page doi:10.1103/physrevd.103.043522 2021

  31. [31]

    2018, The Astrophysical Journal Supplement Series, 239, 35, doi: 10.3847/1538-4365/aaee8c

    Diemer, B. 2018, The Astrophysical Journal Supplement Series, 239, 35, doi: 10.3847/1538-4365/aaee8c

    work page doi:10.3847/1538-4365/aaee8c 2018

  32. [32]

    , keywords =

    Englert, A. M., Dell’Antonio, I., & Montes, M. 2025, The Astrophysical Journal Letters, 989, L2, doi: 10.3847/2041-8213/ade8f1

    work page doi:10.3847/2041-8213/ade8f1 2025

  33. [33]

    A., & Cen, R

    Fan, X., Bahcall, N. A., & Cen, R. 1997, The Astrophysical Journal, 490, L123, doi: 10.1086/311031

    work page doi:10.1086/311031 1997

  34. [34]

    W., Lang, D., & Goodman, J

    Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, Publications of the Astronomical Society of the Pacific, 125, 306, doi: 10.1086/670067

    work page doi:10.1086/670067 2013

  35. [35]

    2024, The Astrophysical Journal, 974, 69, doi: 10.3847/1538-4357/ad67c6

    Fu, S., Dell’Antonio, I., Escalante, Z., et al. 2024, The Astrophysical Journal, 974, 69, doi: 10.3847/1538-4357/ad67c6

    work page doi:10.3847/1538-4357/ad67c6 2024

  36. [36]

    E., & Peacock, J

    Geach, J. E., & Peacock, J. A. 2017, Nature Astronomy, 1, 795, doi: 10.1038/s41550-017-0259-1

    work page doi:10.1038/s41550-017-0259-1 2017

  37. [37]

    2024, The SRG/eROSITA All-Sky Survey: Cosmology Constraints from Cluster Abundances in the Western Galactic

    Ghirardini, V., Bulbul, E., Artis, E., et al. 2024, The SRG/eROSITA All-Sky Survey: Cosmology Constraints from Cluster Abundances in the Western Galactic

    2024

  38. [38]

    H., Zabludoff, A

    Gonzalez, A. H., Zabludoff, A. I., & Zaritsky, D. 2005, The Astrophysical Journal, 618, 195, doi: 10.1086/425896

    work page doi:10.1086/425896 2005

  39. [39]

    Communications in Applied Mathematics and Computational Science, Vol

    Goodman, J., & Weare, J. 2010, Communications in Applied Mathematics and Computational Science, 5, 65, doi: 10.2140/camcos.2010.5.65

    work page doi:10.2140/camcos.2010.5.65 2010

  40. [40]

    2024, The SRG/eROSITA All-Sky Survey: Dark Energy Survey Year 3 Weak Gravitational Lensing by eRASS1 Selected Galaxy Clusters, doi: 10.48550/arXiv.2402.08455

    Grandis, S., Ghirardini, V., Bocquet, S., et al. 2024, The SRG/eROSITA All-Sky Survey: Dark Energy Survey Year 3 Weak Gravitational Lensing by eRASS1 Selected Galaxy Clusters, doi: 10.48550/arXiv.2402.08455

    work page doi:10.48550/arxiv.2402.08455 2024

  41. [41]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2

    work page doi:10.1038/s41586-020-2649-2 2020

  42. [42]

    G., & Kepler, S

    Hawken, A. J., & Bridle, S. L. 2009, Monthly Notices of the Royal Astronomical Society, 400, 1132, doi: 10.1111/j.1365-2966.2009.15539.x

    work page doi:10.1111/j.1365-2966.2009.15539.x 2009

  43. [43]

    2013, Space Science Reviews, 177, 75, doi: 10.1007/s11214-013-9978-5 14

    Hoekstra, H., Bartelmann, M., Dahle, H., et al. 2013, Space Science Reviews, 177, 75, doi: 10.1007/s11214-013-9978-5 14

    work page doi:10.1007/s11214-013-9978-5 2013

  44. [44]

    E., et al

    Huang, S., Leauthaud, A., Greene, J. E., et al. 2018, Monthly Notices of the Royal Astronomical Society, 475, 3348, doi: 10.1093/mnras/stx3200

    work page doi:10.1093/mnras/stx3200 2018

  45. [45]

    Metacalibration: Direct Self-Calibration of Biases in Shear Measurement

    Huff, E., & Mandelbaum, R. 2017, Metacalibration: Direct Self-Calibration of Biases in Shear Measurement, arXiv, doi: 10.48550/arXiv.1702.02600

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1702.02600 2017

  46. [46]

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

    work page doi:10.1109/mcse.2007.55 2007

  47. [47]

    A., et al

    Ishiyama, T., Prada, F., Klypin, A. A., et al. 2021, Monthly Notices of the Royal Astronomical Society, 506, 4210, doi: 10.1093/mnras/stab1755 Ivezi´ c,ˇZ., Kahn, S. M., Tyson, J. A., et al. 2019, The Astrophysical Journal, 873, 111, doi: 10.3847/1538-4357/ab042c

    work page doi:10.1093/mnras/stab1755 2021

  48. [48]

    Cross-correlation Weak Lensing of SDSS galaxy Clusters II: Cluster Density Profiles and the Mass--Richness Relation

    Johnston, D. E., Sheldon, E. S., Wechsler, R. H., et al. 2007, Cross-Correlation Weak Lensing of SDSS Galaxy Clusters II: Cluster Density Profiles and the Mass–Richness Relation, arXiv, doi: 10.48550/arXiv.0709.1159

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.0709.1159 2007

  49. [49]

    2025, Astronomy and Astrophysics, 695, A216, doi: 10.1051/0004-6361/202449599

    Kleinebreil, F., Grandis, S., Schrabback, T., et al. 2025, Astronomy and Astrophysics, 695, A216, doi: 10.1051/0004-6361/202449599

    work page doi:10.1051/0004-6361/202449599 2025

  50. [50]

    ApJS , author =

    Kluge, M., Bender, R., Riffeser, A., et al. 2021, The Astrophysical Journal Supplement Series, 252, 27, doi: 10.3847/1538-4365/abcda6

    work page doi:10.3847/1538-4365/abcda6 2021

  51. [51]

    V., & Borgani, S

    Kravtsov, A., & Borgani, S. 2012, Annual Review of Astronomy and Astrophysics, 50, 353, doi: 10.1146/annurev-astro-081811-125502

    work page doi:10.1146/annurev-astro-081811-125502 2012

  52. [52]

    2010, The Astrophysical Journal, 709, 97, doi: 10.1088/0004-637X/709/1/97

    Leauthaud, A., Finoguenov, A., Kneib, J.-P., et al. 2010, The Astrophysical Journal, 709, 97, doi: 10.1088/0004-637X/709/1/97

    work page doi:10.1088/0004-637x/709/1/97 2010

  53. [53]

    2022, Monthly Notices of the Royal Astronomical Society, 515, 5335, doi: 10.1093/mnras/stac2121

    Li, J., Huang, S., Leauthaud, A., et al. 2022, Monthly Notices of the Royal Astronomical Society, 515, 5335, doi: 10.1093/mnras/stac2121

    work page doi:10.1093/mnras/stac2121 2022

  54. [54]

    2025, Astronomy and Astrophysics, 700, A202, doi: 10.1051/0004-6361/202452892

    Li, S.-S., Hoekstra, H., Kuijken, K., Schaller, M., & Schaye, J. 2025, Astronomy and Astrophysics, 700, A202, doi: 10.1051/0004-6361/202452892

    work page doi:10.1051/0004-6361/202452892 2025

  55. [55]

    2025, Analytical Weak-Lensing Shear Response of Galaxy Model Fitting, arXiv, doi: 10.48550/arXiv.2506.16607

    Li, X. 2025, Analytical Weak-Lensing Shear Response of Galaxy Model Fitting, arXiv, doi: 10.48550/arXiv.2506.16607

    work page doi:10.48550/arxiv.2506.16607 2025

  56. [56]

    2018, Monthly Notices of the Royal Astronomical Society, 481, 4445, doi: 10.1093/mnras/sty2548

    Li, X., Katayama, N., Oguri, M., & More, S. 2018, Monthly Notices of the Royal Astronomical Society, 481, 4445, doi: 10.1093/mnras/sty2548

    work page doi:10.1093/mnras/sty2548 2018

  57. [57]

    2022, Monthly Notices of the Royal Astronomical Society, 511, 4850, doi: 10.1093/mnras/stac342

    Li, X., Li, Y., & Massey, R. 2022, Monthly Notices of the Royal Astronomical Society, 511, 4850, doi: 10.1093/mnras/stac342

    work page doi:10.1093/mnras/stac342 2022

  58. [58]

    2023, Monthly Notices of the Royal Astronomical Society, 521, 4904, doi: 10.1093/mnras/stad890

    Li, X., & Mandelbaum, R. 2023, Monthly Notices of the Royal Astronomical Society, 521, 4904, doi: 10.1093/mnras/stad890

    work page doi:10.1093/mnras/stad890 2023

  59. [59]

    2024a, Monthly Notices of the Royal Astronomical Society, 527, 10388, doi: 10.1093/mnras/stad3895

    Li, X., Mandelbaum, R., Jarvis, M., et al. 2024a, Monthly Notices of the Royal Astronomical Society, 527, 10388, doi: 10.1093/mnras/stad3895

    work page doi:10.1093/mnras/stad3895

  60. [60]

    2024b, Analytical Weak Lensing Shear Inference for Precision Cosmology, doi: 10.48550/arXiv.2408.06337

    Li, X., Mandelbaum, R., & The LSST Dark Energy Science Collaboration. 2024b, Analytical Weak Lensing Shear Inference for Precision Cosmology, doi: 10.48550/arXiv.2408.06337

    work page doi:10.48550/arxiv.2408.06337

  61. [61]

    2025, Monthly Notices of the Royal Astronomical Society, 536, 3663, doi: 10.1093/mnras/stae2764

    Li, X., Mandelbaum, R., & The LSST Dark Energy Science Collaboration. 2025, Monthly Notices of the Royal Astronomical Society, 536, 3663, doi: 10.1093/mnras/stae2764

    work page doi:10.1093/mnras/stae2764 2025

  62. [62]

    2024, Frontiers in Astronomy and Space Sciences, 11, 1411810, doi: 10.3389/fspas.2024.1411810 LSST Dark Energy Science Collaboration (LSST DESC),

    Liu, B., Dell’Antonio, I., Chotard, N., & Clowe, D. 2024, Frontiers in Astronomy and Space Sciences, 11, 1411810, doi: 10.3389/fspas.2024.1411810 LSST Dark Energy Science Collaboration (LSST DESC),

    work page doi:10.3389/fspas.2024.1411810 2024

  63. [63]

    2021, The Astrophysical Journal Supplement Series, 253, 31, doi: 10.3847/1538-4365/abd62c

    Abolfathi, B., Alonso, D., et al. 2021, The Astrophysical Journal Supplement Series, 253, 31, doi: 10.3847/1538-4365/abd62c

    work page doi:10.3847/1538-4365/abd62c 2021

  64. [64]

    R., McCullough, J., et al

    MacCrann, N., Becker, M. R., McCullough, J., et al. 2021, Monthly Notices of the Royal Astronomical Society, 509, 3371, doi: 10.1093/mnras/stab2870

    work page doi:10.1093/mnras/stab2870 2021

  65. [65]

    Weak Lensing for Precision Cosmology , volume=

    Mandelbaum, R. 2018, Annual Review of Astronomy and Astrophysics, 56, 393, doi: 10.1146/annurev-astro-081817-051928

    work page doi:10.1146/annurev-astro-081817-051928 2018

  66. [66]

    Mandelbaum, R., Seljak, U., Baldauf, T., & Smith, R. E. 2010, Monthly Notices of the Royal Astronomical Society, 405, 2078, doi: 10.1111/j.1365-2966.2010.16619.x

    work page doi:10.1111/j.1365-2966.2010.16619.x 2010

  67. [67]

    , keywords =

    Mantz, A., Allen, S. W., Rapetti, D., & Ebeling, H. 2010, Monthly Notices of the Royal Astronomical Society, 406, 1759, doi: 10.1111/j.1365-2966.2010.16992.x

    work page doi:10.1111/j.1365-2966.2010.16992.x 2010

  68. [68]

    B., von der Linden, A., Allen, S

    Mantz, A. B., von der Linden, A., Allen, S. W., et al. 2015, Monthly Notices of the Royal Astronomical Society, 446, 2205, doi: 10.1093/mnras/stu2096

    work page doi:10.1093/mnras/stu2096 2015

  69. [69]

    B., Allen, S

    Mantz, A. B., Allen, S. W., Morris, R. G., et al. 2016, Monthly Notices of the Royal Astronomical Society, 463, 3582, doi: 10.1093/mnras/stw2250

    work page doi:10.1093/mnras/stw2250 2016

  70. [70]

    R., Bautista, M

    Massey, R., & Refregier, A. 2005, Monthly Notices of the Royal Astronomical Society, 363, 197, doi: 10.1111/j.1365-2966.2005.09453.x

    work page doi:10.1111/j.1365-2966.2005.09453.x 2005

  71. [71]

    N., Gruen, D., et al

    McClintock, T., Varga, T. N., Gruen, D., et al. 2019, Monthly Notices of the Royal Astronomical Society, 482, 1352, doi: 10.1093/mnras/sty2711

    work page doi:10.1093/mnras/sty2711 2019

  72. [72]

    2017, Monthly Notices of the Royal Astronomical Society, 469, 4899, doi: 10.1093/mnras/stx1053

    Melchior, P., Gruen, D., McClintock, T., et al. 2017, Monthly Notices of the Royal Astronomical Society, 469, 4899, doi: 10.1093/mnras/stx1053

    work page doi:10.1093/mnras/stx1053 2017

  73. [73]

    2019, The Astrophysical Journal, 875, 63, doi: 10.3847/1538-4357/ab0af0

    Miyatake, H., Battaglia, N., Hilton, M., et al. 2019, The Astrophysical Journal, 875, 63, doi: 10.3847/1538-4357/ab0af0

    work page doi:10.3847/1538-4357/ab0af0 2019

  74. [74]

    Nat Astron , author =

    Montes, M. 2022, Nature Astronomy, 6, 308, doi: 10.1038/s41550-022-01616-z 15

    work page doi:10.1038/s41550-022-01616-z 2022

  75. [75]

    2018, The Astrophysical Journal, 854, 120, doi: 10.3847/1538-4357/aaaab8

    Murata, R., Nishimichi, T., Takada, M., et al. 2018, The Astrophysical Journal, 854, 120, doi: 10.3847/1538-4357/aaaab8

    work page doi:10.3847/1538-4357/aaaab8 2018

  76. [76]

    F., Frenk, C

    Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, The Astrophysical Journal, 490, 493, doi: 10.1086/304888

    work page doi:10.1086/304888 1997

  77. [77]

    2011, Physical Review D, 83, 023008, doi: 10.1103/PhysRevD.83.023008

    Oguri, M., & Takada, M. 2011, Physical Review D, 83, 023008, doi: 10.1103/PhysRevD.83.023008

    work page doi:10.1103/physrevd.83.023008 2011

  78. [78]

    Okabe, N., & Smith, G. P. 2016, Monthly Notices of the Royal Astronomical Society, 461, 3794, doi: 10.1093/mnras/stw1539

    work page doi:10.1093/mnras/stw1539 2016

  79. [79]

    2026, Monthly Notices of the Royal Astronomical Society, 546, stag062, doi: 10.1093/mnras/stag062

    Park, A., Li, X., Mandelbaum, R., & Becker, M. 2026, Monthly Notices of the Royal Astronomical Society, 546, stag062, doi: 10.1093/mnras/stag062

    work page doi:10.1093/mnras/stag062 2026

  80. [80]

    2023, Monthly Notices of the Royal Astronomical Society, 518, 5171, doi: 10.1093/mnras/stac3410

    Park, Y., Sunayama, T., Takada, M., et al. 2023, Monthly Notices of the Royal Astronomical Society, 518, 5171, doi: 10.1093/mnras/stac3410

    work page doi:10.1093/mnras/stac3410 2023

Showing first 80 references.