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Constraints from the Giant Arc in Abell 370. A New Framework for Understanding Systematic Errors in Cluster Lens Modeling. IV. Constraints from the Giant Arc in Abell 370

T0 review · 4 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read This paper claims that fitting every pixel of the giant arc in Abell 370, rather than only point-like image positions, exposes local errors in all standard cluster mass models, and that retuning just the 11 galaxies near the arc reproduces

desk verdict Useful demonstration, but the headline residual improvement is confounded by mismatched noise and grid settings; the local corrections are credible, the quantitative claim is not. read the letter →

arxiv 2509.08227 v1 pith:ZOEW7F6X submitted 2025-09-10 astro-ph.CO

Lana Eid , Charles R. Keeton This is my paper
classification astro-ph.CO PACS 98.62.Sb
keywords gravitationallensinggalaxyclustersgiantarcspixel-basedsourcereconstructionAbell370HubbleFrontierFieldscriticalcurvesclustermassmodeling
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

Cluster lenses are usually calibrated with point-like image positions and bright clumps, but giant caustic-crossing arcs contain thousands of additional brightness constraints. This paper shows that when every pixel of the giant arc in Abell 370 is used to reconstruct the background source, every standard cluster mass model—parametric, nonparametric, and hybrid alike—de-lenses the arc into an implausible source, exposing systematic errors in the local cluster mass distribution. An optimized model that adjusts only the masses and truncation radii of eleven cluster galaxies projected near the arc, after separating two galaxies previously treated as one and correcting a misclassified morphology, reproduces the arc's brightness with residuals roughly an order of magnitude smaller. The changes shift the critical curves, and therefore the predicted high-magnification zones, only where the arc sits, leaving global cluster constraints essentially untouched. The conclusion is that any detailed study of a giant arc—its star formation, kinematics, transients, or microlensed stars—should refine the cluster model against the full arc before interpreting the lensing.

What carries the argument

The engine of the analysis is pixel-based source reconstruction: each image pixel is mapped back to the source plane under a trial lens model, the source is rebuilt on an adaptively spaced grid with a Laplacian regularization whose strength is set by Bayesian evidence, and the model is relensed pixel-by-pixel for comparison with the data. This turns the entire brightness distribution of the arc into a constraint on the mass model. The same code pipeline can consume any team's published deflection, convergence, and shear maps, which is what allows a uniform comparison across modeling approaches. The high-magnification regions are tracked through the lensing critical curves, and the optimized

What would settle it

Run the optimization jointly on the F435W, F606W, and F814W arc data with a single set of galaxy parameters; the F435W fit already misses the star-forming clumps, so if galaxies 43, 45, 46, and 128 drift between filters, the claimed corrections are filter-specific. Independently, compare the optimized model's critical curves with the JWST-observed positions of the arc's microlensed stars: if those stars still lie farther from the predicted critical curves than they did for the fiducial model, the improvement to high-magnification zones is not real.

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Extended reading notes

Core claim

Using pixel-based source reconstruction, which ray-traces every arc pixel back to the source plane and regularizes the source via Bayesian evidence, the authors model the full z=0.725 giant arc in Abell 370. The fiducial model and every public Hubble Frontier Fields model—parametric, nonparametric, hybrid—de-lens the arc into implausible sources. After validating a lightweight Python de-lensing prototype, they optimize the fiducial model by varying only the Einstein radii and truncation radii of eleven galaxies near the arc, first splitting a galaxy pair previously treated as one mass and reclassifying a misidentified member. The optimized model cuts arc residual RMS roughly tenfold (5e-3 to

Load-bearing premise

The analysis assumes that the pixel-by-pixel mismatch between the model and the arc is dominated by errors in the cluster mass model, not by the freedom in the source reconstruction (hand-set regularization strength, assumed noise level, grid resolution, and PSF); if the source model absorbs or distorts arc light, the corrected galaxy parameters and residual improvement do not measure lens-model quality.

Editorial extensions

If this is right

  • Models constrained only by point-like image positions and clumps fail to reproduce the full brightness distribution of the A370 giant arc; every HFF team model tested de-lenses the arc into an implausible source.
  • Full-arc pixel constraints can pinpoint which local mass components are wrong—an unresolved pair of galaxies, a misclassified morphology, a contaminated luminosity estimate—and correct them using the arc alone.
  • The optimized model changes the critical curves only locally, so all quantities derived from the highest-magnification zones (magnification factors, time delays, microlensing positions) are the most affected; global cluster mass conclusions remain unchanged.
  • Before interpreting a giant arc in terms of source physics or dark matter substructure, the cluster model should be refined against the full arc; otherwise systematic errors can masquerade as dark matter or stellar-population effects.
  • The Python de-lensing prototype reproduces the established code's results well enough to rank models, making full-arc refinement applicable to any cluster whose model is published as deflection, convergence, and shear maps.

Reading between the lines

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

  • Applied to the other HFF clusters with giant arcs, the same procedure could reveal a population of unresolved or misclassified cluster members near critical curves, which may explain the known model-to-model scatter in predicted magnifications and time delays.
  • Because the optimized galaxy parameters sit within the scatter of the luminosity–mass scaling relations, the method effectively recalibrates galaxy-scale priors in the regions the arc probes; full MCMC sampling would be needed to know whether the corrected values are unique or degenerate with source regularization.
  • The residual improvement is shown one filter at a time; a joint multi-filter reconstruction (which the paper names as future work) is the natural check that the corrected masses are astrophysical rather than artifacts of a single filter's noise.
  • If the local corrections are real, survey programs that search for giant arcs could use arc-pixel fitting as a cheap way to flag clusters whose mass models are unreliable in high-magnification regions before follow-up observations.
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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

4 major / 4 minor

Summary. The paper presents a pixel-based source reconstruction (PBSR) analysis of the giant arc in Abell 370, using HFF data and lens models. The authors (1) apply PBSR to the Keeton fiducial and range models, (2) introduce a prototype Python de-lensing code to evaluate other HFF team models, (3) optimize the Keeton fiducial model by varying the Einstein radii and truncation radii of 11 galaxies local to the arc, and (4) examine the effect on critical curves and source properties. They claim that the optimized model corrects resolution-limited assumptions in local cluster model inputs, yields significantly smaller arc residuals than standard HFF models, and changes critical curves most in regions local to the arc. The qualitative finding that existing models fail to reproduce the full arc brightness distribution is well illustrated, and the identification of the previously merged galaxies 45/46 and the morphology of galaxy 43 is credible. However, the headline quantitative residual comparison is confounded by non-matching reconstruction settings, and the optimized model is evaluated on the same data used to fit its parameters.

Significance. If the central claims hold, the paper offers a practical demonstration that full-arc PBSR can identify and correct local, resolution-limited errors in cluster lens models, which would be valuable for studies of high-magnification regions and for improving lens-model systematics. The Python de-lensing prototype is a useful contribution, and the paper explicitly connects its results to JWST observations of microlensed stars, giving the work broader relevance. The critical curve comparison and the confirmation of galaxy 45/46 separation by JWST are strengths. However, the main quantitative claim of significantly smaller residuals is not currently supported by the reported numbers, and the overfitting risk is not controlled. The paper's significance therefore hinges on whether the residual improvement survives a matched-settings comparison.

major comments (4)
  1. [§3.5, §4.1, §4.3.2, Figures 7, 8, 13] The headline residual comparison is not made under matched settings. The fiducial/range reconstructions in Figure 7 use noise=0.015, a 1/15 source grid, and no PSF, while the optimized model in Figure 13 uses noise=0.0045, a full grid, and the PSF. Figure 8 shows that the same lens model yields RMS=3.42e-03 with pixsrc (reduced settings) vs 5.51e-03 with the Python code (full grid), a factor of 1.6 due purely to reconstruction pipeline choices. The factor-14 improvement from 4.95e-03 to 3.53e-04 therefore cannot be attributed to the lens model changes. The authors should present the optimized model with the same noise, grid, and PSF settings as the fiducial/HFF comparisons, and also report the fiducial model at the optimized settings.
  2. [§4.3, §4.3.3] The optimized model is scored on the same arc data used to fit its 22 free parameters (Einstein radii and truncation radii of 11 galaxies), so the residual improvement is a training-set fit, not an out-of-sample validation. The only independent check reported in §4.3.3 is the point-image position RMS, which does not improve (0.71″ to 0.75″). This weakens the claim that the model is genuinely better rather than overfit. The authors should provide an out-of-sample test, for example fitting in one filter and testing in another, or fitting on part of the arc and testing on the remainder, and/or report the Bayesian evidence relative to the fiducial model to account for the increased parameter freedom.
  3. [§4.2, Figures 9–10] The abstract claims the optimized model has 'significantly smaller arc model residuals than results from the standard HFF models,' but the figures for the HFF team models do not report RMS values, and the text does not provide a quantitative comparison of those residuals with the optimized model. Without numbers for the other models' residuals under the same reconstruction settings, the claim is not substantiated. The authors should either add RMS (or similar) values to Figures 9–10 or state explicitly which models are being compared and provide the matched-set numbers.
  4. [§4.3, §4.3.1] The optimization procedure is not described in sufficient detail for reproducibility. The text says 'allowing pixsrc to vary the Einstein radii and truncation radii,' but does not specify the objective function, the optimization algorithm, whether the 22 parameters were varied jointly or sequentially, the number of iterations, or the convergence criteria. Section 3.6's noise-model procedure is also only used to assign error bars after optimization, not during it. Without this information, the risk of overfitting and the robustness of the inferred parameter changes cannot be assessed.
minor comments (4)
  1. [Abstract] There is a typo: 'and 4) and an investigation' should read 'and 4) an investigation.'
  2. [§2.4, Figure 8] The Python de-lensing code is compared to pixsrc on a single edited fiducial model. The text says ranking is consistent, but the quantitative RMS values differ by ~60%. A brief discussion of why the RMS differs (e.g., deconvolution versus forward modeling, interpolation regularization) would help the reader interpret the validation.
  3. [§3.5] The statement that the ranking of mass models by χ² was consistent for different source grids is important but unsupported by details. A supplementary figure or table showing the rankings for the seven models would strengthen this claim.
  4. [§3.6, Figure 12] The error bars on the fiducial model (from M/L scaling-relation scatter) and those on the optimized model (from the noise-model analysis) are not directly comparable, as they quantify different sources of uncertainty. This should be stated explicitly in the figure caption.

Circularity Check

1 steps flagged · score 6.0 of 10

Headline residual claim is an in-sample fit plus unmatched pipeline settings, not an out-of-sample prediction.

  1. fitted input called prediction [Section 4.3 and Section 4.3.2 (pp. 13–14)]
    "We then optimized the model by allowing pixsrc to vary the Einstein radii and truncation radii for the 11 galaxies near the arc that are shown in Figure 4. ... The final, optimized lens model in Figure 13 is better able to reproduce the input arc, as seen in both the improved residuals (especially near the aforementioned bend in the arc) as well as the lower rms value."

    The 11 local galaxy Einstein and truncation radii are optimized by fitting the same masked arc data that are later used to compute the residuals. The residual RMS=3.53e-4 in Figure 13 is therefore the minimized training objective, not an independent prediction. The fiducial/range comparisons in Figure 7 (RMS 4.95e-3–6.03e-3) used noise=0.015, a 1/15 source grid, and no PSF, while Figure 13 uses noise=0.0045, the full grid, and the PSF. Figure 8 shows that the same lens model gives RMS=3.42e-3 under pixsrc reduced settings versus RMS=5.51e-3 under the Python full-grid pipeline, so the residual difference is substantially affected by reconstruction hyperparameters. Thus the abstract claim of 'significantly smaller arc model residuals' reduces in part to the fitting procedure itself and in pa

full rationale

The paper contains a genuine partial circularity in its central quantitative claim. The optimized model's parameters are fitted to the arc, and the paper then presents the resulting residuals on that same arc as evidence that the model 'better reproduces the input arc' and as support for the abstract's claim of 'significantly smaller arc model residuals.' This is an in-sample comparison, and it is further confounded by the fact that the optimized model is evaluated with a different noise level, grid resolution, and PSF treatment than the fiducial/range or HFF-team comparisons. The paper itself demonstrates in Figure 8 that pipeline choices alone can change the RMS by more than 50%. The independent content is real: the splitting of galaxy 45/46 and the reclassification of galaxy 43 are confirmed by JWST data from Fudamoto et al. (2025), and the optimized F814W-based model partially reproduces the F606W and F435W arcs. The point-image residuals (0.71″→0.75″) provide a matched but non-improving independent check. Self-citations to Raney et al. (2020a) and Tagore & Keeton (2014) are normal methodological reuse and are not load-bearing in a circular way, since the paper also compares against other HFF teams. The score of 6 reflects that the headline residual claim reduces by construction to a fit plus unmatched settings, while the morphological corrections and cross-filter behavior retain independent content.

Assumptions & free parameters 6 free parameters · 9 assumptions · 0 invented entities

The central claim rests on the mass model parameterization and the source reconstruction regularization choices. The dominant free parameters are the 11 fitted local galaxy masses and truncation radii, plus hand-chosen noise values, regularization strengths, and grid resolutions. The axioms are mostly standard lensing theory and domain assumptions about the HFF mass models; the more fragile ones are the post-hoc mask choice and the noise-model substitution for a full MCMC.

free parameters (6)
  • Einstein radius of 11 local cluster galaxies = Figure 12 (optimized values)
    Varied together with truncation radii to minimize arc residuals in Section 4.3; the central claim that the optimized model fixes local mass errors rests on these fitted values.
  • Truncation radius of 11 local cluster galaxies = Figure 12 (optimized values)
    Same fit as above; truncation radii change the galaxy-scale lensing locally.
  • Assumed noise values = 0.015 (initial), 0.0045 (F814W/F606W optimized), 0.0030 (F435W optimized)
    Chosen by hand to regularize the PBSR; the residual comparison between fiducial and optimized models uses different noise values, confounding the RMS comparison (Sections 3.5, 4.3.2).
  • Regularization strength lambda = selected by Bayesian evidence per model
    Controls smoothness of the reconstructed source; affects the residuals and the ranking of models (Section 2.3).
  • Source grid resolution = 1/15 pixels used initially, full grid for optimized
    The reduced grid is used for model ranking, full grid for final results; differences in grid can change residuals independent of the lens model (Section 3.5).
  • Luminosity split for galaxies 45/46 = half the original luminosity each
    Chosen by hand before optimization; the split of the merged pair is a modeling decision, not a fit (Section 4.3).
assumptions (9)
  • standard math Gravitational lensing equations relating deflection, convergence, shear, magnification (Eqs. 1-6)
    Foundation of the analysis; standard theory cited to Narayan & Bartelmann 1996 and others.
  • standard math Surface brightness is conserved by lensing (Eq. 7)
    Basis of PBSR; the model and data are compared in surface brightness units.
  • domain assumption The cluster mass model parameterization (275 components: 4 dark matter halos, 256 galaxies, 15 line-of-sight galaxies) with M/L scaling relations is a valid representation of A370
    Taken from Raney et al. 2020a; the optimization only perturbs 11 of these components, so the overall mass model structure is assumed correct.
  • domain assumption Second-order (Laplacian) regularization is a suitable smoothness prior for the source
    Chosen in Section 2.3; the reconstructed source and the residuals depend on this choice.
  • domain assumption The ePSFs built from a limited star sample are accurate enough for deconvolution and model comparison
    Section 3.2; imperfect PSF subtraction can create residual features that may be mistaken for lens model error.
  • domain assumption The giant arc is a single background galaxy at z=0.725 lensed by A370 at z=0.375
    From the literature (Soucail et al. 1987; Richard et al. 2010); all scaling of lens models uses this redshift pair.
  • ad hoc to paper The 10 Gaussian noise maps span the model uncertainty space adequately
    Section 3.6; this substitutes for a full MCMC and is used to set the error bars on the optimized parameters.
  • ad hoc to paper The data mask that excludes the two galaxies at the bend improves the fit and does not bias the model comparison
    Sections 3.3-3.4; the authors state exclusion 'produced better results,' a post-hoc choice.
  • ad hoc to paper The M/L scatter priors (0.1 dex for Einstein radius, 0.03 dex for truncation radius) are appropriate for the optimization
    Section 4.3; these priors keep the optimized galaxies physical but are not derived within this paper.

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Cite this review

Pith. "Pith review of Constraints from the Giant Arc in Abell 370. A New Framework for Understanding Systematic Errors in Cluster Lens Modeling. IV. Constraints from the Giant Arc in Abell 370." pith.science (2026). https://pith.science/paper/ZOEW7F6X

@misc{pith2026250908227,
  author       = {Pith},
  title        = {Pith review of: Constraints from the Giant Arc in Abell 370. A New Framework for Understanding Systematic Errors in Cluster Lens Modeling. IV. Constraints from the Giant Arc in Abell 370},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZOEW7F6X}},
  note         = {Machine review of arXiv:2509.08227}
}
abstract

We aim to improve cluster lens modeling and source reconstruction by utilizing the full information in giant, caustic-crossing arcs lensed by galaxy clusters. Lens models are generally constrained using image positions and assuming point sources, but spatially extended giant arcs provide more constraints; however, they require a more complex model that accounts for the structure of the extended source. We seek to determine whether improvements to the lens model and reconstructed source merit the difficulty of handling the extra constraints. We choose the spatially extended $z=0.725$ giant arc in the $z=0.375$ Abell 370 galaxy cluster field for our study. We present 1) a series of pixel-based source reconstructions for cluster mass models exploring the range of uncertainties in our fiducial model, 2) a similar analysis done using a prototype \textit{python} de-lensing code for cluster mass models from each of the Hubble Frontier Fields modeling teams, 3) an optimized model with pixel-based source reconstructions, and 4) and an investigation of how our optimized model affects the cluster mass model locally and globally in the highest-magnification regions. We find that our optimized model 1) is able to correct resolution-limited assumptions in cluster model inputs local to the arc, 2) has significantly smaller arc model residuals than results from the standard Hubble Frontier Fields models, and 3) affects the critical curves and therefore the information derived from highest-magnification zones most significantly in regions local to the arc.

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Works this paper leans on

72 extracted references · 57 canonical work pages

  1. [1]

    2018, MNRAS, 479, 5184

    Atek, H., Richard, J., Kneib, J.-P., & Schaerer, D. 2018, MNRAS, 479, 5184

    2018

  2. [2]

    2015, ApJ, 814, 69

    Atek, H., Richard, J., Jauzac, M., et al. 2015, ApJ, 814, 69

    work page 2015

  3. [3]

    2024, MNRAS, 527, 3246

    Beauchesne, B., Clément, B., Hibon, P., et al. 2024, MNRAS, 527, 3246

    work page 2024

  4. [4]

    2023, A&A, 674, A79

    Bergamini, P., Grillo, C., Rosati, P., et al. 2023, A&A, 674, A79

    work page 2023

  5. [5]

    2018, PDU, 22, 189

    Birrer, S., & Amara, A. 2018, PDU, 22, 189

    work page 2018

  6. [6]

    2015, ApJ, 813, 102 Bradač, M., Schneider, P., Lombardi, M., & Erben, T

    Birrer, S., Amara, A., & Refregier, A. 2015, ApJ, 813, 102 Bradač, M., Schneider, P., Lombardi, M., & Erben, T. 2005, A&A, 437, 39 Bradač, M., Treu, T., Applegate, D., et al. 2009, ApJ, 706, 1201

    work page 2015

  7. [7]

    2022, astropy/photutils: v1.5.0, Zenodo, doi:10.5281/zenodo.6825092

    Bradley, L., Sipőcz, B., Robitaille, T., et al. 2022, astropy/photutils: v1.5.0, Zenodo, doi:10.5281/zenodo.6825092

    doi:10.5281/zenodo.6825092 2022

  8. [8]

    J., & Lewis, G

    Brewer, B. J., & Lewis, G. F. 2006, ApJ, 637, 608

    work page 2006

Show all 72 references
  1. [9]

    2013, MNRAS, 432, 1046

    Brimioulle, F., Seitz, S., Lerchster, M., Bender, R., & Snigula, J. 2013, MNRAS, 432, 1046

    2013

  2. [10]

    K., Alfred, A., et al

    Broadhurst, T., Li, S. K., Alfred, A., et al. 2025, ApJL, 978, L5

    2025

  3. [11]

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

    Caminha, G. B., Grillo, C., Rosati, P., et al. 2017, A&A, 600, A90

    2017

  4. [12]

    Coe, D., Benítez, N., Broadhurst, T., & Moustakas, L. A. 2010, ApJ, 723, 1678

    2010

  5. [13]

    A., & Miralda-Escud, J

    Dai, L., Venumadhav, T., Kaurov, A. A., & Miralda-Escud, J. 2018, ApJ, 867, 24

    2018

  6. [14]

    M., Tegmark, M., Protopapas, P., & Sandvik, H

    Diego, J. M., Tegmark, M., Protopapas, P., & Sandvik, H. B. 2007, MNRAS, 375, 958

    2007

  7. [15]

    M., Broadhurst, T., Benitez, N., et al

    Diego, J. M., Broadhurst, T., Benitez, N., et al. 2015, MNRAS, 446, 683

    2015

  8. [16]

    M., Broadhurst, T., Chen, C., et al

    Diego, J. M., Broadhurst, T., Chen, C., et al. 2016, MNRAS, 456, 356

    2016

  9. [17]

    M., Li, S

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

    2024

  10. [18]

    J., Sharon, K., Florian, M

    Dunham, S. J., Sharon, K., Florian, M. K., et al. 2019, ApJ, 875, 18

    2019

  11. [19]

    Dye, S., & Warren, S. J. 2005, ApJ, 623, 31

    2005

  12. [20]

    G., & Elmegreen, D

    Elmegreen, B. G., & Elmegreen, D. M. 2005, ApJ, 627, 632

    2005

  13. [21]

    2025, NatAs, 9, 428

    Fudamoto, Y., Sun, F., Diego, J.M., et al. 2025, NatAs, 9, 428

    2025

  14. [22]

    B., Knollmüller, J., Roth, J., & Suyu, S

    Galan, A., Caminha, G. B., Knollmüller, J., Roth, J., & Suyu, S. H. 2024, A&A, 689, A304

    2024

  15. [23]

    2015, ApJ, 799, 12

    Ishigaki, M., Kawamata, R., Ouchi, M., et al. 2015, ApJ, 799, 12

    2015

  16. [24]

    2012, MNRAS, 426, 3369

    Jauzac, M., Jullo, E., Kneib, J.-P., et al. 2012, MNRAS, 426, 3369

    2012

  17. [25]

    2014, MNRAS, 443, 1549

    Jauzac, M., Clément, B., Limousin, M., et al. 2014, MNRAS, 443, 1549

    2014

  18. [26]

    2025, ApJ, 980, 190

    Ji, L., & Dai, L. 2025, ApJ, 980, 190

    2025

  19. [27]

    L., Sharon, K., Bayliss, M

    Johnson, T. L., Sharon, K., Bayliss, M. B., et al. 2014, ApJ, 797, 48

    2014

  20. [28]

    A., & Mandel, E

    Joye, W. A., & Mandel, E. 2003, in ASP Conf. Ser. 295, Astronomical Data Analysis Software and Systems XII, ed. H. E. Payne, R. I. Jedrzejewski, & R. N. Hook (San Francisco, CA: ASP), 489

    2003

  21. [29]

    P., Limousin, M., et al

    Jullo, E., Kneib, J. P., Limousin, M., et al. 2007, NJPh, 9, 447

    2007

  22. [30]

    S., Frye, B

    Kamieneski, P. S., Frye, B. L., Pascale, M., et al. 2023, ApJ, 955, 91

    2023

  23. [31]

    2016, ApJ, 819, 114

    Kawamata, R., Oguri, M., Ishigaki, M., Shimasaku, K., & Ouchi, M. 2016, ApJ, 819, 114

    2016

  24. [32]

    2018, ApJ, 855, 4

    Kawamata, R., Ishigaki, M., Shimasaku, K., et al. 2018, ApJ, 855, 4

    2018

  25. [33]

    Keeton, C., 2025 PyGravLens: A Python Package for Gravitational Lensing, https://github.com/chuckkeeton/pygravlens

    2025

  26. [34]

    Keeton, C. R. 2001, arXiv:astro-ph/0102340

    2001 arXiv

  27. [35]

    R., 2011 GRAVLENS: Computational Methods for Gravitational

    Keeton, C. R., 2011 GRAVLENS: Computational Methods for Gravitational

    2011

  28. [36]

    R., Mao, S., & Witt, H

    Keeton, C. R., Mao, S., & Witt, H. J. 2000, ApJ, 537, 697

    2000

  29. [37]

    Kennicutt, R. C., Jr. 1989, ApJ, 344, 685

    1989

  30. [38]

    Kennicutt, R. C., Jr. 1998, ApJ, 498, 541

    1998

  31. [39]

    2011, A&ARv, 19, 47

    Kneib, J.-P., & Natarajan, P. 2011, A&ARv, 19, 47

    2011

  32. [40]

    Koopmans, L. V. E. 2005, MNRAS, 363, 1136

    2005

  33. [41]

    2007, MNRAS, 380, 1729

    Liesenborgs, J., de Rijcke, S., Dejonghe, H., & Bekaert, P. 2007, MNRAS, 380, 1729

    2007

  34. [42]

    2025, A&A, 693, A33

    Limousin, M., Beauchesne, B., Niemiec, A., et al. 2025, A&A, 693, A33

    2025

  35. [43]

    FRONTIER

    Lotz, J. 2013, HST Frontier Fields (“FRONTIER”), STScI/MAST, doi:10. 17909/T9KK5N

    2013

  36. [44]

    M., Koekemoer, A., Coe, D., et al

    Lotz, J. M., Koekemoer, A., Coe, D., et al. 2017, ApJ, 837, 97 LSST Science Collaboration, Abell, P. A., Allison, J., et al. 2009, arXiv:0912.0201

    2017 arXiv

  37. [45]

    1996, arXiv:astro-ph/9606001

    Narayan, R., & Bartelmann, M. 1996, arXiv:astro-ph/9606001

    1996 arXiv

  38. [46]

    2010, PASJ, 62, 1017 Patrício, V., Richard, J., Carton, D., et al

    Oguri, M. 2010, PASJ, 62, 1017 Patrício, V., Richard, J., Carton, D., et al. 2018, MNRAS, 477, 18

    2010

  39. [47]

    Perera, D., Williams, L. L. R., Liesenborgs, J., Ghosh, A., & Saha, P. 2024, MNRAS, 527, 2639

    2024

  40. [48]

    Pierel, J. D. R., Newman, A. B., Dhawan, S., et al. 2024, ApJ, 967, 37 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016, A&A, 594, A13

    2024

  41. [49]

    H., & Schechter, P

    Press, W. H., & Schechter, P. 1974, ApJ, 187, 425

    1974

  42. [50]

    P., Limousin, M., Edge, A., & Jullo, E

    Richard, J., Kneib, J. P., Limousin, M., Edge, A., & Jullo, E. 2010, MNRAS, 402, L44

    2010

  43. [51]

    2014, MNRAS, 444, 268

    Richard, J., Jauzac, M., Limousin, M., et al. 2014, MNRAS, 444, 268

    2014

  44. [52]

    A., et al

    Rivera, J., Baker, A., Gallardo, P. A., et al. 2019, ApJ, 879, 95

    2019

  45. [53]

    A., Brammer, G

    Rodney, S. A., Brammer, G. B., Pierel, J. D. R., et al. 2021, NatAs, 5, 1118

    2021

  46. [54]

    1959, ApJ, 129, 243

    Schmidt, M. 1959, ApJ, 129, 243

    1959

  47. [55]

    E., Tagore, A

    Sharon, C. E., Tagore, A. S., Baker, A. J., et al. 2019, ApJ, 879, 52

    2019

  48. [56]

    B., Dahle, H., et al

    Sharon, K., Bayliss, M. B., Dahle, H., et al. 2020, ApJS, 247, 12

    2020

  49. [57]

    1987, Msngr, 48, 43

    Soucail, G. 1987, Msngr, 48, 43

    1987

  50. [58]

    Soucail, G., Fort, B., Mellier, Y., & Picat, J. P. 1987, A&A, 172, L14

    1987

  51. [59]

    1988, A&A, 191, L19 18 The Astrophysical Journal, 990:196 (19pp), 2025 September 10 Eid & Keeton

    Soucail, G., Mellier, Y., Fort, B., Mathez, G., & Cailloux, M. 1988, A&A, 191, L19 18 The Astrophysical Journal, 990:196 (19pp), 2025 September 10 Eid & Keeton

    1988

  52. [60]

    H., Marshall, P

    Suyu, S. H., Marshall, P. J., Hobson, M. P., & Blandford, R. D. 2006, MNRAS, 371, 983

    2006

  53. [61]

    S., 2014 Lensing Code, https://github.com/tagoreas/Lensing-code

    Tagore, A. S., 2014 Lensing Code, https://github.com/tagoreas/Lensing-code

    2014

  54. [62]

    S., & Keeton, C

    Tagore, A. S., & Keeton, C. R. 2014, MNRAS, 445, 694

    2014

  55. [63]

    S., & Jackson, N

    Tagore, A. S., & Jackson, N. 2016, MNRAS, 457, 3066

    2016

  56. [64]

    M., & Bernstein, G

    Vega-Ferrero, J., Diego, J. M., & Bernstein, G. M. 2019, MNRAS, 486, 5414

    2019

  57. [65]

    Vegetti, S., & Koopmans, L. V. E. 2009, MNRAS, 392, 945

    2009

  58. [66]

    2024, SSRv, 220, 58

    Vegetti, S., Birrer, S., Despali, G., et al. 2024, SSRv, 220, 58

    2024

  59. [67]

    S., & Narayan, R

    Wallington, S., Kochanek, C. S., & Narayan, R. 1996, ApJ, 465, 64

    1996

  60. [68]

    1998, LRR, 1, 12

    Wambsganss, J. 1998, LRR, 1, 12

    1998

  61. [69]

    J., & Dye, S

    Warren, S. J., & Dye, S. 2003, ApJ, 590, 673

    2003

  62. [70]

    2023, ApJ, 943, 2

    Welch, B., Coe, D., Zitrin, A., et al. 2023, ApJ, 943, 2

    2023

  63. [71]

    2020, MNRAS, 496, 2648

    Yang, L., Birrer, S., & Treu, T. 2020, MNRAS, 496, 2648

    2020

  64. [72]

    J., Keeton, C

    Young, A. J., Keeton, C. R., & Baker, A. J. 2022, ApJ, 929, 6 19 The Astrophysical Journal, 990:196 (19pp), 2025 September 10 Eid & Keeton

    2022

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