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arxiv: 2605.20352 · v1 · pith:YXYP2WN3new · submitted 2026-05-19 · 🌌 astro-ph.GA · astro-ph.CO

On the correlation between globular clusters and the distribution of dark matter in galaxy clusters: the case of Abell 2744

Marta Reina-Campos , Joshua S. Speagle , William E. Harris This is my paper

Pith reviewed 2026-05-21 07:29 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords globular clustersgalaxy clustersdark matterweak lensingAbell 2744spatial distributionPoisson point process
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The pith

Bright globular clusters trace the mass distribution in Abell 2744 more closely than other galactic components.

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

This paper develops a statistical method assuming that globular cluster locations follow an inhomogeneous spatial Poisson point process, then uses it to test which mass map the clusters best match. Applied to the merging galaxy cluster Abell 2744, the analysis shows that bright globular clusters trace the three main interacting clumps and correlate more strongly with predicted mass maps than galaxies or other components, reaching Spearman rank coefficients above 0.7. Bright blue globular clusters in particular align with the mass map derived only from weak lensing data. A sympathetic reader would care because the result suggests globular clusters can serve as an independent, observable tracer of dark matter that works across different cosmic epochs.

Core claim

The spatial distribution of bright globular clusters roughly traces the three main interacting clumps in Abell 2744 alongside galaxies with large globular cluster populations. The globular cluster populations correlate more closely with the predicted mass maps than any other galactic component, with Spearman rank coefficients exceeding 0.7. Bright blue globular clusters prove compatible with the mass map derived solely from weak lensing, indicating they supply complementary and independent information on the mass distribution at a level of detail comparable to weak lensing.

What carries the argument

inhomogeneous spatial Poisson point process model for globular cluster locations, used to identify the closest-matching mass map

If this is right

  • Globular clusters can provide complementary information on mass distribution in galaxy clusters with detail similar to weak lensing.
  • The method distinguishes which mass map the globular cluster distribution agrees with most closely.
  • Catalogs of globular clusters at different cosmic epochs can be combined with this approach to study mass distributions independently.

Where Pith is reading between the lines

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

  • If the correlation holds in other clusters, globular cluster catalogs could map dark matter where weak lensing coverage is incomplete.
  • Testing the same method on non-merging clusters would show whether bright blue globular clusters consistently trace weak lensing maps across environments.
  • The approach might be applied to other potential tracers such as intracluster light to check for similar correlations.

Load-bearing premise

Globular cluster locations around a galaxy cluster follow an inhomogeneous spatial Poisson point process that lets the method distinguish which mass map they agree with most closely.

What would settle it

Repeating the analysis on Abell 2744 or a similar cluster and finding Spearman rank coefficients below 0.7 for globular clusters versus the mass maps, or finding that bright blue globular clusters no longer match the weak lensing mass map.

Figures

Figures reproduced from arXiv: 2605.20352 by Joshua S. Speagle, Marta Reina-Campos, William E. Harris.

Figure 1
Figure 1. Figure 1: Visual schematic of the cross-map comparison described in Sect. 2.3: after introducing the observational selection into the map λ1 and spawning coordinates for N points, we calculate the log-likehood against a map λ2. We repeat the process to obtain a distribution of log-likelihoods. X-ray emission to trace the mass distribution. By com￾paring these cross-map distributions against the empir￾ical log-likeli… view at source ↗
Figure 3
Figure 3. Figure 3: Overlapping spatial distributions of bright blue and red GCs. The filled contours correspond to log10{n/[arcsec−2 ]} = −1.9, 1.4, −1.2, −0.9, −0.4. Blue bright star clusters are more extended around galaxies and into the intercluster medium than red ones. 95th and 99th percentiles of the distribution of num￾ber densities in the smoothed map of blue GCs. These contours allow us to visually identify structur… view at source ↗
Figure 2
Figure 2. Figure 2: Spatial distributions of GCs brighter than F150W < 29.5 in Abell 2744: all GCs (top panel), com￾plete GCs (second panel), as well as blue and red GCs (third and fourth panels, respectively). The number density maps include the observational bias, and are smoothed by a bi-di￾mensional Gaussian kernel of size 20 kpc. Bright clusters are concentrated in three large structures that correspond to the main inter… view at source ↗
Figure 4
Figure 4. Figure 4: Multi-component view of Abell 2744. (Top row) Predicted mass distributions from strong and weak lens￾ing analysis (P. Bergamini et al. 2023; S. H. Price et al. 2025; S. Cha et al. 2024, respectively). Contours are drawn at log10(Σ/[M⊙/kpc2 ]) = 8.3, 8.5, 8.7, and 9.1, and the colourbar is logarithmically normalized between 108 –1010 M⊙/kpc2 . (Bot￾tom left and middle panels) Original and modelled stellar l… view at source ↗
Figure 5
Figure 5. Figure 5: Spatial distribution of bright GCs (grey contours) overlaid over the projected total mass distributions (left-hand panel), the modelled stellar light mosaic from UNCOVER (middle panel) and the X-ray emission (right-hand panel) in Abell 2744. The grey contours in every panel represent the number density of GCs, weighted by their probability of recovery and smoothed by a Gaussian kernel. All panels are shown… view at source ↗
Figure 6
Figure 6. Figure 6: Pixel-by-pixel comparison between the smoothed spatial distribution of Bright GCs and different galactic com￾ponents: the predicted mass maps from S. H. Price et al. (2025) and S. Cha et al. (2024) (top row), the modeled stel￾lar light, and the X-ray emission. The Spearman rank coeffi￾cients are listed in the top-left corner of every panel. Bright GCs correlate more strongly with the mass maps than any oth… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the Z–scores between our samples of GCs and maps of different galactic components. This score is anchored by the mean and standard deviation, E[ln P] and σ, of the expected distribution of probability densities of a given map (ln P{(Bi) λeff |λeff }, violin plots around 0). Vertical lines show the Z–score of the GC sample against a galactic component, and the violin plots correspond to the bo… view at source ↗
Figure 8
Figure 8. Figure 8: Cross comparison among some of the galactic components of Abell 2744 considered in this work. The colorbar corresponds to the median Z-score of the log-likelihoods: spawning datapoints from the tracer map λ1 (vertical axis) and calculating the log-likelihood against λ2 (horizontal axis), ln P{(xi, yi, θi) λ1 |λ2}. Darker colors indicate a closer agreement between the maps, and masked cells correspond to as… view at source ↗
read the original abstract

Globular clusters (GCs) lie scattered around the inner $40\%$ of the virial radius of galaxy clusters, potentially being excellent tracers of the underlying mass distribution. In this paper, we present a statistical method based on assuming that the location of GCs around a galaxy cluster follows an inhomogenous spatial Poisson point process, and we use this method to assess to which galactic component GCs are better tracers of. We apply the method to the galaxy cluster Abell 2744, and we find that the spatial distribution of bright GCs roughly traces the three main interacting clumps in the galaxy cluster, alongside other galaxies with sizeable GC populations. The GC populations are more closely correlated to the predicted mass maps than any other galactic component (Spearman rank coefficients $>0.7$). A perk of this statistical method is that it allows us to distinguish to which map the agreement is closest to. In particular, we find that the Bright Blue GCs are compatible with the mass map solely derived from weak lensing, suggesting that they can provide complementary and independent information on the mass distribution in galaxy clusters with a similar level of detail to that of weak lensing. This statistical method is available in a public repository, and combined with catalogs of GCs in galaxy clusters at different cosmic epochs, it provides an independent method for investigating the mass distribution in these galactic environments.

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 introduces a statistical method that models the positions of globular clusters (GCs) around galaxy clusters as an inhomogeneous spatial Poisson point process. Applied to Abell 2744, the method is used to compare the spatial distribution of bright GCs (and subsets such as bright blue GCs) against mass maps derived from different galactic components and weak-lensing data. The central claims are that bright GCs trace the three main interacting clumps similarly to other GC-rich galaxies, that GC populations show Spearman rank correlations >0.7 with the predicted mass maps (higher than other components), and that bright blue GCs are compatible with the weak-lensing-only mass map, providing complementary information on the cluster mass distribution.

Significance. If the quantitative results hold after addressing the modeling assumptions, the work provides a new, publicly available statistical tool for using GCs as mass tracers in clusters at various redshifts, independent of weak lensing. The finding that GCs correlate more strongly with mass maps than other galactic components, together with the specific compatibility of blue GCs with the lensing map, could offer an additional probe of dark-matter distribution in merging systems.

major comments (2)
  1. [Statistical method (abstract and methods description)] The core method assumes GC locations follow an inhomogeneous spatial Poisson point process whose intensity is proportional to a chosen mass map. In Abell 2744, however, GCs are physically tied to member galaxies that themselves trace the three merging clumps; this induces positive spatial correlations on galaxy scales that violate the independence assumption of the Poisson process. If the likelihood or Spearman comparison is performed under this misspecification, the reported preference for the weak-lensing map may be an artifact of how galaxy positions align with that map rather than a genuine tracer property of the GCs themselves.
  2. [Abstract and results] The abstract states Spearman rank coefficients above 0.7 and compatibility of bright blue GCs with the weak-lensing map, yet provides no details on GC sample selection criteria, error estimation on the coefficients, or the explicit construction of the Poisson intensity function from each mass map. These omissions make the central quantitative claims difficult to evaluate or reproduce.
minor comments (2)
  1. [Data and sample] Clarify the exact definition of 'bright' and 'blue' GCs (magnitude and color cuts) and state how many objects fall into each category for Abell 2744.
  2. [Abstract] The public repository is mentioned; include a direct link or DOI in the manuscript for immediate access.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We have addressed each major point below, proposing revisions to improve clarity and acknowledge modeling assumptions where appropriate.

read point-by-point responses

  1. Referee: [Statistical method (abstract and methods description)] The core method assumes GC locations follow an inhomogeneous spatial Poisson point process whose intensity is proportional to a chosen mass map. In Abell 2744, however, GCs are physically tied to member galaxies that themselves trace the three merging clumps; this induces positive spatial correlations on galaxy scales that violate the independence assumption of the Poisson process. If the likelihood or Spearman comparison is performed under this misspecification, the reported preference for the weak-lensing map may be an artifact of how galaxy positions align with that map rather than a genuine tracer property of the GCs themselves.

    Authors: We agree that GCs are hosted within galaxies and that this introduces spatial correlations at galaxy scales, which formally violates the strict independence assumption of the Poisson point process. Our model uses the inhomogeneous Poisson process as an approximation focused on cluster-scale intensity variations driven by the mass maps. The Spearman rank correlations are calculated directly between the binned GC counts and the mass maps and do not rely on the Poisson likelihood. We will add a dedicated paragraph in the Methods section discussing this approximation, its limitations, and why the large-scale tracing results remain informative despite small-scale galaxy clustering. revision: partial

  2. Referee: [Abstract and results] The abstract states Spearman rank coefficients above 0.7 and compatibility of bright blue GCs with the weak-lensing map, yet provides no details on GC sample selection criteria, error estimation on the coefficients, or the explicit construction of the Poisson intensity function from each mass map. These omissions make the central quantitative claims difficult to evaluate or reproduce.

    Authors: The abstract is kept concise by design, but the Methods section details the GC sample (bright GCs selected by magnitude and color cuts), the construction of the Poisson intensity (normalized mass map values used as the intensity function), and error estimation on the Spearman coefficients (via resampling). We will revise the abstract to include a short reference to the sample selection and direct readers to the Methods for the model construction and statistical details, improving reproducibility without lengthening the abstract excessively. revision: yes

Circularity Check

0 steps flagged

No significant circularity: GC positions tested against independent lensing mass maps via Poisson model

full rationale

The paper's core method assumes GC locations follow an inhomogeneous spatial Poisson point process whose intensity is taken proportional to a chosen mass map, then computes Spearman rank correlations and compatibility metrics to identify which map (including a weak-lensing-only map) the observed bright blue GCs best trace. The mass maps are derived independently from weak lensing and other data; GC positions are observed catalog data. No parameter is fitted to the final claim, no self-citation supplies a load-bearing uniqueness theorem, and the output (GCs trace the lensing map at Spearman >0.7) is not equivalent to the input by construction. The Poisson assumption is a modeling choice whose validity can be checked externally, but it does not create definitional circularity within the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the modeling assumption that GC positions are realizations of an inhomogeneous Poisson point process and on the availability of independent mass maps for comparison. No explicit free parameters or new physical entities are named in the abstract.

axioms (1)
  • domain assumption The locations of globular clusters follow an inhomogeneous spatial Poisson point process
    Explicitly stated as the basis of the statistical method in the abstract.

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Works this paper leans on

70 extracted references · 70 canonical work pages

  1. [1]

    2023, https://github.com/marimo-team/marimo Alamo-Mart´ ınez, K

    Agrawal, A., & Scolnick, M. 2023, https://github.com/marimo-team/marimo Alamo-Mart´ ınez, K. A., Blakeslee, J. P., Jee, M. J., et al. 2013, ApJ, 775, 20, doi: 10.1088/0004-637X/775/1/20

    work page doi:10.1088/0004-637x/775/1/20 2023

  2. [2]

    Allen, S. W. 1998, MNRAS, 296, 392, doi: 10.1046/j.1365-8711.1998.01358.x

    work page doi:10.1046/j.1365-8711.1998.01358.x 1998

  3. [3]

    Allingham, J. F. V., Zitrin, A., Kokorev, V., et al. 2026, arXiv e-prints, arXiv:2602.14074, doi: 10.48550/arXiv.2602.14074

    work page doi:10.48550/arxiv.2602.14074 2026

  4. [4]

    2021, MNRAS, 500, 5249, doi: 10.1093/mnras/staa3441 Astropy Collaboration, Robitaille, T

    Asencio, E., Banik, I., & Kroupa, P. 2021, MNRAS, 500, 5249, doi: 10.1093/mnras/staa3441 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: 10.3847/1538-3881/aabc4f Astropy Collaboration, Price-W...

    work page doi:10.1093/mnras/staa3441 2021

  5. [5]

    2020, JCAP, 2020, 024, doi: 10.1088/1475-7516/2020/02/024

    Banerjee, A., Adhikari, S., Dalal, N., More, S., & Kravtsov, A. 2020, JCAP, 2020, 024, doi: 10.1088/1475-7516/2020/02/024

    work page doi:10.1088/1475-7516/2020/02/024 2020

  6. [6]

    C., Eadie, G

    Berek, S. C., Eadie, G. M., Speagle, J. S., & Wang, S. Y. 2024, ApJ, 972, 104, doi: 10.3847/1538-4357/ad6147

    work page doi:10.3847/1538-4357/ad6147 2024

  7. [7]

    2023, ApJ, 952, 84, doi: 10.3847/1538-4357/acd643

    Bergamini, P., Acebron, A., Grillo, C., et al. 2023, ApJ, 952, 84, doi: 10.3847/1538-4357/acd643

    work page doi:10.3847/1538-4357/acd643 2023

  8. [8]

    M., Windhorst, R

    Berkheimer, J. M., Windhorst, R. A., Harris, W. E., et al. 2026, AJ, 171, 48, doi: 10.3847/1538-3881/ae209a

    work page doi:10.3847/1538-3881/ae209a 2026

  9. [9]

    E., et al

    Bezanson, R., Labbe, I., Whitaker, K. E., et al. 2024, ApJ, 974, 92, doi: 10.3847/1538-4357/ad66cf

    work page doi:10.3847/1538-4357/ad66cf 2024

  10. [10]

    2026, ApJ, 1001, 60, doi: 10.3847/1538-4357/ae41b0

    Cerny, C., Mahler, G., Sharon, K., et al. 2026, ApJ, 1001, 60, doi: 10.3847/1538-4357/ae41b0

    work page doi:10.3847/1538-4357/ae41b0 2026

  11. [11]

    Y., Joo, H., et al

    Cha, S., Cho, B. Y., Joo, H., et al. 2025, ApJL, 987, L15, doi: 10.3847/2041-8213/add2f0

    work page doi:10.3847/2041-8213/add2f0 2025

  12. [12]

    P., Joo, H., & Jee, M

    Cha, S., HyeongHan, K., Scofield, Z. P., Joo, H., & Jee, M. J. 2024, ApJ, 961, 186, doi: 10.3847/1538-4357/ad0cbf

    work page doi:10.3847/1538-4357/ad0cbf 2024

  13. [13]

    Y., Jee, M

    Cho, B. Y., Jee, M. J., Joo, H., Cha, S., & HyeongHan, K. 2025, arXiv e-prints, arXiv:2512.03150, doi: 10.48550/arXiv.2512.03150

    work page doi:10.48550/arxiv.2512.03150 2025

  14. [14]

    2004, ApJ, 604, 596, doi: 10.1086/381970

    Clowe, D., Gonzalez, A., & Markevitch, M. 2004, ApJ, 604, 596, doi: 10.1086/381970

    work page doi:10.1086/381970 2004

  15. [15]

    Diego, J. M. 2026, arXiv e-prints, arXiv:2602.15940, doi: 10.48550/arXiv.2602.15940

    work page doi:10.48550/arxiv.2602.15940 2026

  16. [16]

    M., Broadhurst, T., Wong, J., et al

    Diego, J. M., Broadhurst, T., Wong, J., et al. 2016, MNRAS, 459, 3447, doi: 10.1093/mnras/stw865 15

    work page doi:10.1093/mnras/stw865 2016

  17. [17]

    M., Goolsby, C., Conselice, C

    Diego, J. M., Goolsby, C., Conselice, C. J., & Palencia, J. M. 2026, arXiv e-prints, arXiv:2602.12332, doi: 10.48550/arXiv.2602.12332

    work page doi:10.48550/arxiv.2602.12332 2026

  18. [18]

    M., Pascale, M., Frye, B., et al

    Diego, J. M., Pascale, M., Frye, B., et al. 2023a, A&A, 679, A159, doi: 10.1051/0004-6361/202345868

    work page doi:10.1051/0004-6361/202345868

  19. [19]

    M., Meena, A

    Diego, J. M., Meena, A. K., Adams, N. J., et al. 2023b, A&A, 672, A3, doi: 10.1051/0004-6361/202245238

    work page doi:10.1051/0004-6361/202245238

  20. [20]

    M., Adams, N

    Diego, J. M., Adams, N. J., Willner, S. P., et al. 2024, A&A, 690, A114, doi: 10.1051/0004-6361/202349119

    work page doi:10.1051/0004-6361/202349119 2024

  21. [21]

    M., Sun, F., Palencia, J

    Diego, J. M., Sun, F., Palencia, J. M., et al. 2025, A&A, 703, A207, doi: 10.1051/0004-6361/202556062

    work page doi:10.1051/0004-6361/202556062 2025

  22. [22]

    1998, ApJ, 502, 141, doi: 10.1086/305901

    Dubinski, J. 1998, ApJ, 502, 141, doi: 10.1086/305901

    work page doi:10.1086/305901 1998

  23. [23]

    Bisterzo, R

    Ebeling, H., Edge, A. C., Mantz, A., et al. 2010, MNRAS, 407, 83, doi: 10.1111/j.1365-2966.2010.16920.x

    work page doi:10.1111/j.1365-2966.2010.16920.x 2010

  24. [24]

    L., Chary, R

    Faisst, A. L., Chary, R. R., Brammer, G., & Toft, S. 2022, ApJL, 941, L11, doi: 10.3847/2041-8213/aca1bf

    work page doi:10.3847/2041-8213/aca1bf 2022

  25. [25]

    J., Zitrin, A., Weaver, J

    Furtak, L. J., Zitrin, A., Weaver, J. R., et al. 2023, MNRAS, 523, 4568, doi: 10.1093/mnras/stad1627

    work page doi:10.1093/mnras/stad1627 2023

  26. [26]

    2024, ApJ, 973, 77, doi: 10.3847/1538-4357/ad684a

    Gledhill, R., Strait, V., Desprez, G., et al. 2024, ApJ, 973, 77, doi: 10.3847/1538-4357/ad684a

    work page doi:10.3847/1538-4357/ad684a 2024

  27. [27]

    H., Rosati, P., et al

    Grillo, C., Suyu, S. H., Rosati, P., et al. 2015, ApJ, 800, 38, doi: 10.1088/0004-637X/800/1/38

    work page doi:10.1088/0004-637x/800/1/38 2015

  28. [28]

    Harris and 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

  29. [29]

    E., & Reina-Campos, M

    Harris, W. E., & Reina-Campos, M. 2023, MNRAS, 526, 2696, doi: 10.1093/mnras/stad2903

    work page doi:10.1093/mnras/stad2903 2023

  30. [30]

    E., & Reina-Campos, M

    Harris, W. E., & Reina-Campos, M. 2024, ApJ, 971, 155, doi: 10.3847/1538-4357/ad583c

    work page doi:10.3847/1538-4357/ad583c 2024

  31. [31]

    E., & Speagle, J

    Harris, W. E., & Speagle, J. S. 2024, AJ, 168, 38, doi: 10.3847/1538-3881/ad4a76

    work page doi:10.3847/1538-3881/ad4a76 2024

  32. [32]

    E., Brown, R

    Harris, W. E., Brown, R. A., Durrell, P. R., et al. 2020, ApJ, 890, 105, doi: 10.3847/1538-4357/ab6992

    work page doi:10.3847/1538-4357/ab6992 2020

  33. [33]

    E., Reina-Campos, M., Keatley, K

    Harris, W. E., Reina-Campos, M., Keatley, K. E., et al. 2025, ApJ, 993, 210, doi: 10.3847/1538-4357/ae073f

    work page doi:10.3847/1538-4357/ae073f 2025

  34. [34]

    R., Kamieneski, P

    Hinrichs, T. R., Kamieneski, P. S., Windhorst, R. A., et al. 2026, ApJ, 1001, 91, doi: 10.3847/1538-4357/ae50ee

    work page doi:10.3847/1538-4357/ae50ee 2026

  35. [35]

    2013, SSRv, 177, 75, doi: 10.1007/s11214-013-9978-5

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

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

  36. [36]

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

    work page doi:10.1109/mcse.2007.55 2007

  37. [37]

    2015, MNRAS, 452, 1437, doi: 10.1093/mnras/stv1402

    Jauzac, M., Richard, J., Jullo, E., et al. 2015, MNRAS, 452, 1437, doi: 10.1093/mnras/stv1402

    work page doi:10.1093/mnras/stv1402 2015

  38. [38]

    2001, http://www.scipy.org/

    Jones, E., Oliphant, T., Peterson, P., et al. 2001, http://www.scipy.org/

    work page 2001

  39. [39]

    2016, ApJ, 819, 114, doi: 10.3847/0004-637X/819/2/114

    Ouchi, M. 2016, ApJ, 819, 114, doi: 10.3847/0004-637X/819/2/114

    work page doi:10.3847/0004-637x/819/2/114 2016

  40. [40]

    E., & Harris, W

    Keatley, K. E., & Harris, W. E. 2025, ApJ, 990, 67, doi: 10.3847/1538-4357/adf5c4

    work page doi:10.3847/1538-4357/adf5c4 2025

  41. [41]

    A., Montes, M., et al

    Kluge, M., Hatch, N. A., Montes, M., et al. 2025, A&A, 697, A13, doi: 10.1051/0004-6361/202450772

    work page doi:10.1051/0004-6361/202450772 2025

  42. [42]

    2011, A&A Rv, 19, 47, doi: 10.1007/s00159-011-0047-3

    Kneib, J.-P., & Natarajan, P. 2011, A&A Rv, 19, 47, doi: 10.1007/s00159-011-0047-3

    work page doi:10.1007/s00159-011-0047-3 2011

  43. [43]

    G., Bae, J

    Lee, M. G., Bae, J. H., & Jang, I. S. 2022, ApJL, 940, L19, doi: 10.3847/2041-8213/ac990b

    work page doi:10.3847/2041-8213/ac990b 2022

  44. [44]

    G., & Jang, I

    Lee, M. G., & Jang, I. S. 2016, ApJ, 831, 108, doi: 10.3847/0004-637X/831/1/108

    work page doi:10.3847/0004-637x/831/1/108 2016

  45. [45]

    D., Eadie, G

    Li, D. D., Eadie, G. M., Brown, P. E., et al. 2025, ApJ, 984, 147, doi: 10.3847/1538-4357/adc71f

    work page doi:10.3847/1538-4357/adc71f 2025

  46. [46]

    H., Clowe, D., et al

    Markevitch, M., Gonzalez, A. H., Clowe, D., et al. 2004, ApJ, 606, 819, doi: 10.1086/383178

    work page doi:10.1086/383178 2004

  47. [47]

    S., Sarrouh, G

    Martis, N. S., Sarrouh, G. T. E., Willott, C. J., et al. 2024, ApJ, 975, 76, doi: 10.3847/1538-4357/ad7735

    work page doi:10.3847/1538-4357/ad7735 2024

  48. [48]

    2016, ApJ, 817, 24, doi: 10.3847/0004-637X/817/1/24

    Medezinski, E., Umetsu, K., Okabe, N., et al. 2016, ApJ, 817, 24, doi: 10.3847/0004-637X/817/1/24

    work page doi:10.3847/0004-637x/817/1/24 2016

  49. [49]

    Thirty systems with space-based light curves

    Merten, J., Coe, D., Dupke, R., et al. 2011, MNRAS, 417, 333, doi: 10.1111/j.1365-2966.2011.19266.x

    work page doi:10.1111/j.1365-2966.2011.19266.x 2011

  50. [50]

    Mihos, J. C. 2016, in IAU Symposium, Vol. 317, The General Assembly of Galaxy Halos: Structure, Origin and Evolution, ed. A. Bragaglia, M. Arnaboldi, M. Rejkuba, & D. Romano, 27–34, doi: 10.1017/S1743921315006857

    work page doi:10.1017/s1743921315006857 2016

  51. [51]

    2022, Nature Astronomy, 6, 308, doi: 10.1038/s41550-022-01616-z

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

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

  52. [52]

    2014, ApJ, 794, 137, doi: 10.1088/0004-637X/794/2/137

    Montes, M., & Trujillo, I. 2014, ApJ, 794, 137, doi: 10.1088/0004-637X/794/2/137

    work page doi:10.1088/0004-637x/794/2/137 2014

  53. [53]

    2019, MNRAS, 482, 2838, doi: 10.1093/mnras/sty2858

    Montes, M., & Trujillo, I. 2019, MNRAS, 482, 2838, doi: 10.1093/mnras/sty2858

    work page doi:10.1093/mnras/sty2858 2019

  54. [54]

    2022, ApJL, 940, L51, doi: 10.3847/2041-8213/ac98c5

    Montes, M., & Trujillo, I. 2022, ApJL, 940, L51, doi: 10.3847/2041-8213/ac98c5

    work page doi:10.3847/2041-8213/ac98c5 2022

  55. [55]

    S., Randall, S

    Owers, M. S., Randall, S. W., Nulsen, P. E. J., et al. 2011, ApJ, 728, 27, doi: 10.1088/0004-637X/728/1/27 Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6, doi: 10.1051/0004-6361/201833910

    work page doi:10.1088/0004-637x/728/1/27 2011

  56. [56]

    H., Bezanson, R., Labbe, I., et al

    Price, S. H., Bezanson, R., Labbe, I., et al. 2025, ApJ, 982, 51, doi: 10.3847/1538-4357/adaec1

    work page doi:10.3847/1538-4357/adaec1 2025

  57. [57]

    J., et al

    Rajpurohit, K., Vazza, F., van Weeren, R. J., et al. 2021, A&A, 654, A41, doi: 10.1051/0004-6361/202141060

    work page doi:10.1051/0004-6361/202141060 2021

  58. [58]

    2020, doi: 10.5281/zenodo.3509134

    Reback, J., McKinney, W., jbrockmendel, et al. 2020, doi: 10.5281/zenodo.3509134

    work page doi:10.5281/zenodo.3509134 2020

  59. [59]

    Reina-Campos, M., & Harris, W. E. 2024, MNRAS, 531, 4099, doi: 10.1093/mnras/stae1414

    work page doi:10.1093/mnras/stae1414 2024

  60. [60]

    J., et al

    Reina-Campos, M., Trujillo-Gomez, S., Deason, A. J., et al. 2022, MNRAS, 513, 3925, doi: 10.1093/mnras/stac1126

    work page doi:10.1093/mnras/stac1126 2022

  61. [61]

    L., et al

    Reina-Campos, M., Trujillo-Gomez, S., Pfeffer, J. L., et al. 2023, MNRAS, 521, 6368, doi: 10.1093/mnras/stad920

    work page doi:10.1093/mnras/stad920 2023

  62. [62]

    2014, MNRAS, 444, 268, doi: 10.1093/mnras/stu1395

    Richard, J., Jauzac, M., Limousin, M., et al. 2014, MNRAS, 444, 268, doi: 10.1093/mnras/stu1395 Rihtarˇ siˇ c, G., Bradaˇ c, M., Desprez, G., et al. 2025, A&A, 696, A15, doi: 10.1051/0004-6361/202451117 16

    work page doi:10.1093/mnras/stu1395 2014

  63. [63]

    V., Lange-Vagle, D., Marchesini, D., et al

    Shipley, H. V., Lange-Vagle, D., Marchesini, D., et al. 2018, The Astrophysical Journal Supplement Series, 235, 14, doi: 10.3847/1538-4365/aaacce

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

  64. [64]

    L., Jauzac, M., Acebron, A., et al

    Steinhardt, C. L., Jauzac, M., Acebron, A., et al. 2020, ApJS, 247, 64, doi: 10.3847/1538-4365/ab75ed

    work page doi:10.3847/1538-4365/ab75ed 2020

  65. [65]

    A., Weaver, J

    Suess, K. A., Weaver, J. R., Price, S. H., et al. 2024, ApJ, 976, 101, doi: 10.3847/1538-4357/ad75fe

    work page doi:10.3847/1538-4357/ad75fe 2024

  66. [66]

    2010, ARA&A, 48, 87, doi: 10.1146/annurev-astro-081309-130924

    Treu, T. 2010, ARA&A, 48, 87, doi: 10.1146/annurev-astro-081309-130924

    work page doi:10.1146/annurev-astro-081309-130924 2010

  67. [67]

    2015, ApJ, 811, 29, doi: 10.1088/0004-637X/811/1/29

    Wang, X., Hoag, A., Huang, K.-H., et al. 2015, ApJ, 811, 29, doi: 10.1088/0004-637X/811/1/29

    work page doi:10.1088/0004-637x/811/1/29 2015

  68. [68]

    Waskom, M. L. 2021, Journal of Open Source Software, 6, 3021, doi: 10.21105/joss.03021

    work page doi:10.21105/joss.03021 2021

  69. [69]

    R., Cutler, S

    Weaver, J. R., Cutler, S. E., Pan, R., et al. 2024, ApJS, 270, 7, doi: 10.3847/1538-4365/ad07e0

    work page doi:10.3847/1538-4365/ad07e0 2024

  70. [70]

    2015, ApJ, 801, 44, doi: 10.1088/0004-637X/801/1/44

    Zitrin, A., Fabris, A., Merten, J., et al. 2015, ApJ, 801, 44, doi: 10.1088/0004-637X/801/1/44

    work page doi:10.1088/0004-637x/801/1/44 2015