pith. sign in

arxiv: 2606.23808 · v1 · pith:PLFHQTRKnew · submitted 2026-06-22 · 🌌 astro-ph.GA · astro-ph.CO

First measurement of narrow-line flux ratios for a lensed quasar with JWST/NIRSpec IFS

Hadrien Paugnat , Tommaso Treu , Anna M. Nierenberg , Anowar J. Shajib , Shawn Knabel , Daniel Gilman This is my paper

Pith reviewed 2026-06-26 07:41 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords gravitational lensingflux ratiosnarrow-line emissiondark matter substructureJWSTintegral field spectroscopylensed quasarRXJ1131-1231
0
0 comments X

The pith

JWST/NIRSpec IFS yields first narrow-line flux ratios for lensed quasar RXJ1131-1231 at 5% precision and detects cusp anomaly.

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

The paper establishes that integral field spectroscopy with JWST can extract narrow-line flux ratios from the [S III] doublet in a quadruply imaged quasar by using full lens modeling to separate extended emission from the nuclear source. This produces measurements with roughly five percent uncertainties that are insensitive to stellar microlensing, directly addressing the need for clean probes of low-mass dark matter halos through flux-ratio anomalies. The results for RXJ1131-1231 show a clear deviation in the cusp images from a smooth lens model prediction while remaining consistent with earlier narrow-line and mid-infrared dust measurements. The approach is presented as generalizable to other systems and as a way to combine emission regions of different sizes for tighter substructure constraints.

Core claim

Using JWST/NIRSpec IFS data on RXJ1131-1231, flux ratios are measured from the [S III] 9071/9533 Å narrow-line doublet for the first time in a lensed quasar by performing a full lens model reconstruction that isolates unresolved nuclear emission from extended narrow-line emission. Joint spectral fitting with the introduced lensqso-specfit package achieves approximately five percent uncertainties on the flux ratios. These ratios exhibit a clear anomaly in the cusp images relative to a standard smooth lens model, agree with previous narrow-line results, and show only marginal two-to-three sigma deviations from JWST/MIRI warm dust ratios.

What carries the argument

The [S III] narrow-line doublet isolated via full lens model reconstruction and joint spectral fitting with lensqso-specfit to separate extended emission from the nuclear source for microlensing-insensitive flux ratios.

If this is right

  • Flux ratio uncertainties reach five percent, matching the precision of JWST/MIRI warm dust measurements.
  • A clear anomaly appears in the cusp images compared to predictions from a standard smooth lens model.
  • Results remain in good agreement with prior narrow-line measurements and show only marginal deviations from MIRI warm dust ratios.
  • The method applies to other lensed quasars that have or will have IFS observations.
  • Pairing narrow-line ratios with warm dust ratios supplies a new route to stronger dark matter substructure constraints.

Where Pith is reading between the lines

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

  • Differences between flux ratios from differently sized emission regions can be amplified by spatial offsets as small as ten parsecs between the narrow-line and dust-emitting zones.
  • The public lensqso-specfit package allows the same joint fitting approach to be applied to additional quadruply imaged systems.
  • Comparing multiple narrow lines within the same IFS data set could test whether the assumption of negligible microlensing holds across different physical scales.
  • Larger samples built with this technique would improve the statistical power of flux-ratio anomaly studies for constraining the low-mass end of the dark matter halo mass function.

Load-bearing premise

The [S III] narrow-line emission originates from an extended region insensitive to stellar microlensing and the lens model reconstruction accurately isolates it from the unresolved nuclear emission.

What would settle it

Time-series observations showing significant variability in the [S III] line fluxes across images that matches the pattern expected from stellar microlensing rather than remaining constant.

Figures

Figures reproduced from arXiv: 2606.23808 by Anna M. Nierenberg, Anowar J. Shajib, Daniel Gilman, Hadrien Paugnat, Shawn Knabel, Tommaso Treu.

Figure 1
Figure 1. Figure 1: Left panel: “White-light” image of RXJ1131−1231 from the JWST/NIRSpec datacube, summed over the entire wavelength range. The four quasar images (A, B, C, and D) are labeled following the convention from previous studies of the same system (Sluse et al. 2007; Sugai et al. 2007; Keeley et al. 2025; Gilman et al. 2025; Shajib et al. 2026), for direct comparison of the flux ratios. The main deflector and its n… view at source ↗
Figure 2
Figure 2. Figure 2: Image model for the PSF reconstruction step. Top row: (Left) White-light image summed over the 9320 − 9420 Å wavelength range (in green in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Image model for the detailed lens modeling step. Top row, from left to right: white-light image summed over the 8900 − 9650 Å wavelength range (in gray in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Best-fit joint model for the four extracted quasar spectra at images A, B, C, and D. The observed data points are shown in black, with errorbars representing the estimated ±1𝜎 uncertainties, forwarding the PSF and lens modeling uncertainties. Each spectral feature used in the model is displayed separately, with the total model flux in red. The absolute residuals are shown at the bottom of each panel. ampli… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between the flux ratios measured in this work (for the narrow [S iii] doublet, the broad Pa 𝜀 line, and the continuum over the 8900−9650Å range), the magnification ratios predicted by the lens model predicted in Section 3.1.2 (displayed as filled bands representing 95% credible intervals), and some flux-ratio values found in the literature. The narrow [O iii] doublet measurements are taken from … view at source ↗
Figure 6
Figure 6. Figure 6: Relative magnification 𝜇NLR/𝜇wd between the NLR and the warm dust, as a function of the offset of both emission regions relative to the center of a perturbing NFW halo. We assume Gaussian light distribution for the profiles of both regions, with a FHWM of 5 pc for the warm dust (Keeley et al. 2025). In order to illustrate the impact of the other parameters, we vary the FHWM of the NLR (20 pc or 50 pc, Müll… view at source ↗
read the original abstract

Strong gravitational lensing is a powerful probe of dark matter (DM) structure on subgalactic scales: in particular, statistics of flux-ratio anomalies (discrepancies between mass model predictions and observed flux ratios) in quadruply imaged quasars are sensitive to perturbations by low-mass DM halos down to $\sim 10^6 M_\odot$. Studies leveraging these anomalies require high-quality flux-ratio measurements from an emission region insensitive to stellar microlensing. In this paper, we present the first measurement of narrow-line flux ratios for a gravitationally lensed quasar using JWST/NIRSpec with Integral Field Spectroscopy (IFS), targeting the well-studied system RXJ1131$-$1231. Flux ratios are extracted from the [S III] 9071/9533 $\r{A}$ narrow-line doublet - the first use of this doublet for substructure studies - by performing a full lens model reconstruction to isolate the unresolved nuclear emission from extended narrow-line emission. The resulting spectra are jointly modeled using $\texttt{lensqso-specfit}$, a publicly available software package introduced in this work for the simultaneous spectral fitting of multiple lensed quasar images. We achieve $\sim$ 5% uncertainties on the flux ratios, comparable to the precision of JWST/MIRI warm dust measurements, and detect a clear anomaly in the cusp images relative to a standard smooth lens model. Our results are in good agreement with previous narrow-line measurements and broadly consistent with JWST/MIRI warm dust flux ratios, with marginal ($\sim 2-3\sigma$) deviations. We demonstrate how such shifts between differently sized emission regions may be enhanced by small ($\sim 10$ pc) spatial offsets. Our method is generalizable to other systems with existing or future IFS observations, and the combination of narrow-line and warm dust flux ratios offers a new avenue for improving DM constraints with flux-ratio anomaly statistics.

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 paper claims to present the first measurement of narrow-line flux ratios for the lensed quasar RXJ1131-1231 using JWST/NIRSpec IFS observations of the [S III] 9071/9533 Å doublet. Flux ratios are extracted via full lens model reconstruction to separate unresolved nuclear emission from extended narrow-line emission, using the new publicly available lensqso-specfit package for joint spectral fitting of multiple images. The work reports ~5% uncertainties on the ratios (comparable to MIRI warm dust), detects a clear anomaly in the cusp images relative to a smooth lens model, finds good agreement with prior narrow-line results and broad consistency with MIRI (with marginal 2-3σ deviations), and discusses how small spatial offsets can enhance shifts between emission regions of different sizes. The method is presented as generalizable to other lensed systems.

Significance. If the lens-model separation holds at the claimed precision, this introduces a new narrow-line tracer for flux-ratio anomaly statistics that is insensitive to stellar microlensing, enabling improved constraints on low-mass dark matter substructure down to ~10^6 M_⊙. The public release of lensqso-specfit for simultaneous fitting of lensed quasar spectra and the explicit discussion of combining narrow-line and warm-dust ratios are concrete strengths that enhance reproducibility and future applicability.

major comments (2)
  1. [Methods (lens model reconstruction and spectral fitting)] The headline result of ~5% flux-ratio precision and anomaly detection depends on the lens-model reconstruction cleanly isolating extended [S III] emission from unresolved nuclear continuum. The methods description provides no quantitative validation such as mock-data recovery tests or runs with alternative surface-brightness profiles/regularization to demonstrate robustness at the few-percent level; this is load-bearing for the central claims of anomaly detection and cross-comparison with MIRI.
  2. [Abstract and Results] Abstract and §3 (results): the reported ~5% uncertainties and consistency statements are presented without accompanying error budgets, covariance matrices, or tabulated flux values and model parameters, preventing direct assessment of whether post-hoc modeling choices affect the cusp anomaly at the stated significance.
minor comments (1)
  1. [Abstract] The wavelength notation "9071/9533 \r{A}" in the abstract should be written explicitly as Ångstroms for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments, which have helped us identify areas for improvement. We address each major comment point by point below and will revise the manuscript accordingly where the suggestions strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Methods (lens model reconstruction and spectral fitting)] The headline result of ~5% flux-ratio precision and anomaly detection depends on the lens-model reconstruction cleanly isolating extended [S III] emission from unresolved nuclear continuum. The methods description provides no quantitative validation such as mock-data recovery tests or runs with alternative surface-brightness profiles/regularization to demonstrate robustness at the few-percent level; this is load-bearing for the central claims of anomaly detection and cross-comparison with MIRI.

    Authors: We agree that explicit quantitative validation of the lens-model reconstruction at the few-percent level is important for supporting the central claims. The current manuscript describes the lensqso-specfit package and the reconstruction process but does not include mock recovery tests or systematic checks with alternative profiles. We will add a dedicated subsection to the methods with mock-data tests and regularization variations to demonstrate robustness, along with quantitative metrics on recovered flux ratios. revision: yes

  2. Referee: [Abstract and Results] Abstract and §3 (results): the reported ~5% uncertainties and consistency statements are presented without accompanying error budgets, covariance matrices, or tabulated flux values and model parameters, preventing direct assessment of whether post-hoc modeling choices affect the cusp anomaly at the stated significance.

    Authors: We acknowledge that the abstract and main results section would benefit from more explicit presentation of error budgets and covariances to allow readers to evaluate the impact of modeling choices. While tabulated flux values and model parameters appear in the full manuscript (including appendices), we will revise §3 to include a summary table of flux ratios with uncertainties and covariances, and update the abstract to reference these supporting materials for improved transparency. revision: yes

Circularity Check

0 steps flagged

No significant circularity: direct observational measurement from JWST data

full rationale

The paper reports an empirical measurement of [S III] narrow-line flux ratios extracted via lens-model reconstruction and spectral fitting of JWST/NIRSpec IFS data on RXJ1131-1231. The central result (∼5% flux-ratio values and cusp anomaly) is obtained from observed spectra rather than from any self-referential definition, fitted parameter renamed as prediction, or load-bearing self-citation chain. The introduced lensqso-specfit package is a tool for performing the fit; it does not make the output quantities equivalent to the inputs by construction. No uniqueness theorem, ansatz smuggling, or renaming of known results is invoked to force the reported numbers. The derivation chain is therefore self-contained against external data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

As an observational measurement report, the claim rests on standard domain assumptions in gravitational lensing and spectroscopy rather than new free parameters or invented entities. The lens modeling and spectral isolation steps invoke typical assumptions about emission region sizes and smoothness of the macro lens model.

axioms (1)
  • domain assumption The [S III] narrow-line region is spatially extended relative to the stellar microlensing scale
    This premise underpins the claim that the measured flux ratios are insensitive to microlensing and can probe DM substructure.

pith-pipeline@v0.9.1-grok · 5912 in / 1378 out tokens · 24907 ms · 2026-06-26T07:41:21.464003+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

160 extracted references · 135 canonical work pages · 6 internal anchors

  1. [8]

    , keywords =

    Predicted Fe II Emission-Line Strengths from Active Galactic Nuclei. , keywords =. astro-ph/0206096 , primaryClass =

    Pith/arXiv arXiv

  2. [25]

    Space Science Reviews , volume=

    Strong gravitational lensing as a probe of dark matter , author=. Space Science Reviews , volume=. 2024 , publisher=

    2024

  3. [46]

    , volume =

    Constraining resonant dark matter self-interactions with strong gravitational lenses , author =. , volume =. 2023 , month =. doi:10.1103/PhysRevD.107.103008 , url =

    work page doi:10.1103/physrevd.107.103008 2023

  4. [47]

    , keywords =

    Strong lensing signatures of self-interacting dark matter in low-mass haloes. , keywords =. doi:10.1093/mnras/stab2335 , primaryClass =

    work page doi:10.1093/mnras/stab2335

  5. [70]

    2007 , isbn =

    Table of Integrals, Series, and Products , author =. 2007 , isbn =

    2007

  6. [79]

    Nature Astronomy , volume=

    A fast-rotator post-starburst galaxy quenched by supermassive black-hole feedback at z= 3 , author=. Nature Astronomy , volume=. 2024 , publisher=

    2024

  7. [84]

    Space Science Reviews , volume=

    Strong lensing by galaxies , author=. Space Science Reviews , volume=. 2024 , publisher=

    2024

  8. [85]

    Boletin de la Asociacion Argentina de Astronomia , year = 1963, month = feb, volume =

    Influence of the atmospheric and instrumental dispersion on the brightness distribution in a galaxy. Boletin de la Asociacion Argentina de Astronomia , year = 1963, month = feb, volume =

    1963

  9. [86]

    Atlas de Galaxias Australes

  10. [96]

    1202.3665 , doi =

    emcee: The MCMC Hammer , journal =. 1202.3665 , doi =

    Pith/arXiv arXiv

  11. [97]

    Hunter, J. D. , Title =. Computing in Science & Engineering , Volume =

  12. [98]

    Positioning and Power in Academic Publishing: Players, Agents and Agendas , title =

    Thomas Kluyver and Benjamin Ragan-Kelley and Fernando P. Positioning and Power in Academic Publishing: Players, Agents and Agendas , title =. 2016 , pages =

    2016

  13. [100]

    and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and

    Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and. Nature Methods , year =

  14. [101]

    pandas-dev/pandas: Pandas , month = dec, year = 2023, publisher =

    2023

  15. [103]

    Model-Based Derivative-Free Optimization Methods and Software , author =

  16. [104]

    Ragonneau, T. M. and Zhang, Z. , title =

  17. [106]

    Strong lensing with ALMA: resolving the nature of high-redshift galaxies

  18. [146]

    A., Popovi \'c L

    Abajas C., Mediavilla E., Mu \ n oz J. A., Popovi \'c L. C ., Oscoz A., 2002, @doi [ ] 10.1086/341793 , https://ui.adsabs.harvard.edu/abs/2002ApJ...576..640A 576, 640

    work page doi:10.1086/341793 2002

  19. [147]

    Detection of a dark matter subhalo in the strongly lensed system PJ011646

    Amvrosiadis A., et al., 2026, @doi [arXiv e-prints] 10.48550/arXiv.2605.21212 , https://ui.adsabs.harvard.edu/abs/2026arXiv260521212A p. arXiv:2605.21212

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2605.21212 2026

  20. [148]

    Anguita T., Faure C., Yonehara A., Wambsganss J., Kneib J.-P., Covone G., Alloin D., 2008, @doi [ ] 10.1051/0004-6361:20077306 , https://ui.adsabs.harvard.edu/abs/2008A&A...481..615A 481, 615

    work page doi:10.1051/0004-6361:20077306 2008

  21. [149]

    Astropy Collaboration et al., 2013, @doi [ ] 10.1051/0004-6361/201322068 , http://adsabs.harvard.edu/abs/2013A

    work page doi:10.1051/0004-6361/201322068 2013

  22. [150]

    Astropy Collaboration et al., 2018, @doi [ ] 10.3847/1538-3881/aabc4f , https://ui.adsabs.harvard.edu/abs/2018AJ....156..123A 156, 123

    work page doi:10.3847/1538-3881/aabc4f 2018

  23. [151]

    Astropy Collaboration et al., 2022, @doi [ ] 10.3847/1538-4357/ac7c74 , https://ui.adsabs.harvard.edu/abs/2022ApJ...935..167A 935, 167

    work page internal anchor Pith review doi:10.3847/1538-4357/ac7c74 2022

  24. [152]

    J., Enzi W

    Ballard D. J., Enzi W. J. R., Collett T. E., Turner H. C., Smith R. J., 2024, @doi [ ] 10.1093/mnras/stae514 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.528.7564B 528, 7564

    work page doi:10.1093/mnras/stae514 2024

  25. [153]

    F., et al., 2018, @doi [ ] 10.1093/mnras/sty1793 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.479.4796B 479, 4796

    Bate N. F., et al., 2018, @doi [ ] 10.1093/mnras/sty1793 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.479.4796B 479, 4796

    work page doi:10.1093/mnras/sty1793 2018

  26. [154]

    S., Wills B

    Bennert N., Falcke H., Schulz H., Wilson A. S., Wills B. J., 2002, @doi [ ] 10.1086/342420 , https://ui.adsabs.harvard.edu/abs/2002ApJ...574L.105B 574, L105

    work page doi:10.1086/342420 2002

  27. [155]

    Bennert N., Jungwiert B., Komossa S., Haas M., Chini R., 2006, @doi [ ] 10.1051/0004-6361:20065319 , https://ui.adsabs.harvard.edu/abs/2006A&A...456..953B 456, 953

    work page doi:10.1051/0004-6361:20065319 2006

  28. [156]

    Birrer S., Amara A., 2018, @doi [Physics of the Dark Universe] 10.1016/j.dark.2018.11.002 , https://ui.adsabs.harvard.edu/abs/2018PDU....22..189B 22, 189

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

  29. [157]

    Birrer S., Amara A., Refregier A., 2015, @doi [ ] 10.1088/0004-637X/813/2/102 , https://ui.adsabs.harvard.edu/abs/2015ApJ...813..102B 813, 102

    work page doi:10.1088/0004-637x/813/2/102 2015

  30. [158]

    Birrer S., Amara A., Refregier A., 2016, @doi [ ] 10.1088/1475-7516/2016/08/020 , https://ui.adsabs.harvard.edu/abs/2016JCAP...08..020B 2016, 020

    work page doi:10.1088/1475-7516/2016/08/020 2016

  31. [159]

    Birrer S., et al., 2021, @doi [The Journal of Open Source Software] 10.21105/joss.03283 , https://ui.adsabs.harvard.edu/abs/2021JOSS....6.3283B 6, 3283

    work page doi:10.21105/joss.03283 2021

  32. [160]

    Birrer S., et al., 2024, @doi [ ] 10.1007/s11214-024-01079-w , https://ui.adsabs.harvard.edu/abs/2024SSRv..220...48B 220, 48

    work page doi:10.1007/s11214-024-01079-w 2024

  33. [161]

    A., Pooley D., Rappaport S., Schechter P

    Blackburne J. A., Pooley D., Rappaport S., Schechter P. L., 2011, @doi [ ] 10.1088/0004-637X/729/1/34 , https://ui.adsabs.harvard.edu/abs/2011ApJ...729...34B 729, 34

    work page doi:10.1088/0004-637x/729/1/34 2011

  34. [162]

    P., Turok N., 2001, @doi [ ] 10.1086/321541 , https://ui.adsabs.harvard.edu/abs/2001ApJ...556...93B 556, 93

    Bode P., Ostriker J. P., Turok N., 2001, @doi [ ] 10.1086/321541 , https://ui.adsabs.harvard.edu/abs/2001ApJ...556...93B 556, 93

    work page doi:10.1086/321541 2001

  35. [163]

    B \"o ker T., et al., 2022, @doi [ ] 10.1051/0004-6361/202142589 , https://ui.adsabs.harvard.edu/abs/2022A&A...661A..82B 661, A82

    work page doi:10.1051/0004-6361/202142589 2022

  36. [164]

    S., & Boylan-Kolchin, M

    Bullock J. S., Boylan-Kolchin M., 2017, @doi [ ] 10.1146/annurev-astro-091916-055313 , https://ui.adsabs.harvard.edu/abs/2017ARA&A..55..343B 55, 343

    work page doi:10.1146/annurev-astro-091916-055313 2017

  37. [165]

    Burtscher L., et al., 2013, @doi [ ] 10.1051/0004-6361/201321890 , https://ui.adsabs.harvard.edu/abs/2013A&A...558A.149B 558, A149

    work page doi:10.1051/0004-6361/201321890 2013

  38. [166]

    Cappellari M., Emsellem E., 2004, @doi [ ] 10.1086/381875 , https://ui.adsabs.harvard.edu/abs/2004PASP..116..138C 116, 138

    work page internal anchor Pith review doi:10.1086/381875 2004

  39. [167]

    S., Dai X., Moore D., Mosquera A

    Chartas G., Kochanek C. S., Dai X., Moore D., Mosquera A. M., Blackburne J. A., 2012, @doi [ ] 10.1088/0004-637X/757/2/137 , https://ui.adsabs.harvard.edu/abs/2012ApJ...757..137C 757, 137

    work page doi:10.1088/0004-637x/757/2/137 2012

  40. [168]

    C.-F., et al., 2016, @doi [ ] 10.1093/mnras/stw991 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.462.3457C 462, 3457

    Chen G. C.-F., et al., 2016, @doi [ ] 10.1093/mnras/stw991 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.462.3457C 462, 3457

    work page doi:10.1093/mnras/stw991 2016

  41. [169]

    Chen J., et al., 2019, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stz2183 , 489, 855

    work page doi:10.1093/mnras/stz2183 2019

  42. [170]

    C.-F., Treu T., Fassnacht C

    Chen G. C.-F., Treu T., Fassnacht C. D., Ragland S., Schmidt T., Suyu S. H., 2021, @doi [ ] 10.1093/mnras/stab2587 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.508..755C 508, 755

    work page doi:10.1093/mnras/stab2587 2021

  43. [171]

    T., 2005, @doi [ ] 10.1086/430403 , https://ui.adsabs.harvard.edu/abs/2005ApJ...627...53C 627, 53

    Chiba M., Minezaki T., Kashikawa N., Kataza H., Inoue K. T., 2005, @doi [ ] 10.1086/430403 , https://ui.adsabs.harvard.edu/abs/2005ApJ...627...53C 627, 53

    work page doi:10.1086/430403 2005

  44. [172]

    Claeskens J.-F., Sluse D., Riaud P., Surdej J., 2006, @doi [ ] 10.1051/0004-6361:20054352 , https://ui.adsabs.harvard.edu/abs/2006A&A...451..865C 451, 865

    work page doi:10.1051/0004-6361:20054352 2006

  45. [173]

    2005 , keywords =

    Congdon A. B., Keeton C. R., 2005, @doi [ ] 10.1111/j.1365-2966.2005.09699.x , https://ui.adsabs.harvard.edu/abs/2005MNRAS.364.1459C 364, 1459

    work page doi:10.1111/j.1365-2966.2005.09699.x 2005

  46. [174]

    S., 2002, @doi [ ] 10.1086/340303 , https://ui.adsabs.harvard.edu/abs/2002ApJ...572...25D 572, 25

    Dalal N., Kochanek C. S., 2002, @doi [ ] 10.1086/340303 , https://ui.adsabs.harvard.edu/abs/2002ApJ...572...25D 572, 25

    work page doi:10.1086/340303 2002

  47. [175]

    M., Fassnacht C

    Despali G., Heinze F. M., Fassnacht C. D., Vegetti S., Spingola C., Klessen R., Tajalli M., 2025, @doi [ ] 10.1051/0004-6361/202451546 , https://ui.adsabs.harvard.edu/abs/2025A&A...699A.222D 699, A222

    work page doi:10.1051/0004-6361/202451546 2025

  48. [176]

    Diemer B., Joyce M., 2019, @doi [ ] 10.3847/1538-4357/aafad6 , https://ui.adsabs.harvard.edu/abs/2019ApJ...871..168D 871, 168

    work page doi:10.3847/1538-4357/aafad6 2019

  49. [177]

    Du X., et al., 2024, @doi [ ] 10.1103/PhysRevD.110.023019 , https://ui.adsabs.harvard.edu/abs/2024PhRvD.110b3019D 110, 023019

    work page doi:10.1103/physrevd.110.023019 2024

  50. [178]

    Du X., Gilman D., Treu T., Benson A., Gannon C., 2025, @doi [Phys. Rev. D] 10.1103/6tbt-w3nv , 112, 023009

    work page doi:10.1103/6tbt-w3nv 2025

  51. [179]

    Dumont A., et al., 2025, @doi [ ] 10.1051/0004-6361/202554494 , https://ui.adsabs.harvard.edu/abs/2025A&A...703A..54D 703, A54

    work page doi:10.1051/0004-6361/202554494 2025

  52. [180]

    D’Eugenio F., et al., 2024, Nature Astronomy, 8, 1443

    2024

  53. [181]

    C ., Dvorkin C., 2025, @doi [ ] 10.1093/mnras/staf1366 , https://ui.adsabs.harvard.edu/abs/2025MNRAS.542.2610E 542, 2610

    Ephremidze N., Chandrashekar C., S eng \"u l A. C ., Dvorkin C., 2025, @doi [ ] 10.1093/mnras/staf1366 , https://ui.adsabs.harvard.edu/abs/2025MNRAS.542.2610E 542, 2610

    work page doi:10.1093/mnras/staf1366 2025

  54. [182]

    Nature Astronomy 2:652–655

    Evans N. W., Witt H. J., 2003, @doi [ ] 10.1046/j.1365-2966.2003.07057.x , https://ui.adsabs.harvard.edu/abs/2003MNRAS.345.1351E 345, 1351

    work page doi:10.1046/j.1365-2966.2003.07057.x 2003

  55. [183]

    A., Falco E

    Fian C., Guerras E., Mediavilla E., Jim \'e nez-Vicente J., Mu \ n oz J. A., Falco E. E., Motta V., Hanslmeier A., 2018, @doi [ ] 10.3847/1538-4357/aabc0d , https://ui.adsabs.harvard.edu/abs/2018ApJ...859...50F 859, 50

    work page doi:10.3847/1538-4357/aabc0d 2018

  56. [184]

    A., For \'e s-Toribio R., Mediavilla E., Jim \'e nez-Vicente J., Chelouche D., Kaspi S., Richards G

    Fian C., Mu \ n oz J. A., For \'e s-Toribio R., Mediavilla E., Jim \'e nez-Vicente J., Chelouche D., Kaspi S., Richards G. T., 2024, @doi [ ] 10.1051/0004-6361/202347382 , https://ui.adsabs.harvard.edu/abs/2024A&A...682A..57F 682, A57

    work page doi:10.1051/0004-6361/202347382 2024

  57. [185]

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

    Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, @doi [ ] 10.1086/670067 , 125, 306

    work page doi:10.1086/670067 2013

  58. [186]

    Garcia-Rissmann A., Rodr \' guez-Ardila A., Sigut T. A. A., Pradhan A. K., 2012, @doi [ ] 10.1088/0004-637X/751/1/7 , https://ui.adsabs.harvard.edu/abs/2012ApJ...751....7G 751, 7

    work page doi:10.1088/0004-637x/751/1/7 2012

  59. [187]

    E., 1993, @doi [ ] 10.1093/mnras/265.1.213 , https://ui.adsabs.harvard.edu/abs/1993MNRAS.265..213G 265, 213

    Gerhard O. E., 1993, @doi [ ] 10.1093/mnras/265.1.213 , https://ui.adsabs.harvard.edu/abs/1993MNRAS.265..213G 265, 213

    work page doi:10.1093/mnras/265.1.213 1993

  60. [188]

    Gilman D., Birrer S., Treu T., Nierenberg A., Benson A., 2019, @doi [ ] 10.1093/mnras/stz1593 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.5721G 487, 5721

    work page doi:10.1093/mnras/stz1593 2019

  61. [189]

    Gilman D., Birrer S., Nierenberg A., Treu T., Du X., Benson A., 2020, @doi [ ] 10.1093/mnras/stz3480 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.491.6077G 491, 6077

    work page doi:10.1093/mnras/stz3480 2020

  62. [190]

    Gilman D., Birrer S., Nierenberg A., Oh M. S. H., 2024, @doi [ ] 10.1093/mnras/stae1810 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.533.1687G 533, 1687

    work page doi:10.1093/mnras/stae1810 2024

  63. [191]

    JWST lensed quasar dark matter survey IV: Stringent warm dark matter constraints from the joint reconstruction of extended lensed arcs and quasar flux ratios

    Gilman D., et al., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2511.07513 , https://ui.adsabs.harvard.edu/abs/2025arXiv251107513G p. arXiv:2511.07513

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2511.07513 2025

  64. [192]

    Academic Press, @doi 10.1016/B978-0-08-047111-2.50015-7

    Gradshteyn I., Ryzhik I., 2007, Table of Integrals, Series, and Products, 7th edn. Academic Press, @doi 10.1016/B978-0-08-047111-2.50015-7

    work page doi:10.1016/b978-0-08-047111-2.50015-7 2007

  65. [193]

    Harris and K

    Harris C. R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , 585, 357

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

  66. [194]

    Hern \'a n-Caballero A., Hatziminaoglou E., Alonso-Herrero A., Mateos S., 2016, @doi [ ] 10.1093/mnras/stw2107 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.463.2064H 463, 2064

    work page doi:10.1093/mnras/stw2107 2016

  67. [195]

    D., et al., 2016, @doi [ ] 10.3847/0004-637X/823/1/37 , https://ui.adsabs.harvard.edu/abs/2016ApJ...823...37H 823, 37

    Hezaveh Y. D., et al., 2016, @doi [ ] 10.3847/0004-637X/823/1/37 , https://ui.adsabs.harvard.edu/abs/2016ApJ...823...37H 823, 37

    work page doi:10.3847/0004-637x/823/1/37 2016

  68. [196]

    W., Enzi W., Vegetti S., Auger M

    Hsueh J. W., Enzi W., Vegetti S., Auger M. W., Fassnacht C. D., Despali G., Koopmans L. V. E., McKean J. P., 2020, @doi [ ] 10.1093/mnras/stz3177 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.492.3047H 492, 3047

    work page doi:10.1093/mnras/stz3177 2020

  69. [197]

    Hui L., 2021, @doi [ ] 10.1146/annurev-astro-120920-010024 , https://ui.adsabs.harvard.edu/abs/2021ARA&A..59..247H 59, 247

    work page doi:10.1146/annurev-astro-120920-010024 2021

  70. [198]

    Computing in Science and Engineering , keywords =

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

    work page doi:10.1109/mcse.2007.55 2007

  71. [199]

    Hutsem \'e kers D., Sluse D., Savi \'c ., 2024, @doi [ ] 10.1051/0004-6361/202452240 , https://ui.adsabs.harvard.edu/abs/2024A&A...691A.292H 691, A292

    work page doi:10.1051/0004-6361/202452240 2024

  72. [200]

    Ir s s i c c V., et al., 2024, @doi [ ] 10.1103/PhysRevD.109.043511 , 109, 043511

    work page doi:10.1103/physrevd.109.043511 2024

  73. [201]

    J., Williams L

    Jones T. J., Williams L. L. R., Ertel S., Hinz P. M., Vaz A., Walsh S., Webster R., 2019, @doi [ ] 10.3847/1538-3881/ab5108 , https://ui.adsabs.harvard.edu/abs/2019AJ....158..237J 158, 237

    work page doi:10.3847/1538-3881/ab5108 2019

  74. [202]

    E., et al., 2024, @doi [ ] 10.1093/mnras/stae2458 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.535.1652K 535, 1652

    Keeley R. E., et al., 2024, @doi [ ] 10.1093/mnras/stae2458 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.535.1652K 535, 1652

    work page doi:10.1093/mnras/stae2458 2024

  75. [203]

    E., et al., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2511.07765 , https://ui.adsabs.harvard.edu/abs/2025arXiv251107765K p

    Keeley R. E., et al., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2511.07765 , https://ui.adsabs.harvard.edu/abs/2025arXiv251107765K p. arXiv:2511.07765

    work page doi:10.48550/arxiv.2511.07765 2025

  76. [204]

    R., Kochanek C

    Keeton C. R., Kochanek C. S., Seljak U., 1997, @doi [ ] 10.1086/304172 , https://ui.adsabs.harvard.edu/abs/1997ApJ...482..604K 482, 604

    work page doi:10.1086/304172 1997

  77. [205]

    R., Burles S., Schechter P

    Keeton C. R., Burles S., Schechter P. L., Wambsganss J., 2006, @doi [The Astrophysical Journal] 10.1086/499264 , 639, 1

    work page doi:10.1086/499264 2006

  78. [206]

    Kim S.-H., et al., 2022, @doi [ ] 10.1093/mnras/stab3473 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.510..815K 510, 815

    work page doi:10.1093/mnras/stab3473 2022

  79. [207]

    IOS Press, pp 87--90, https://eprints.soton.ac.uk/403913/

    Kluyver T., et al., 2016, in Positioning and Power in Academic Publishing: Players, Agents and Agendas. IOS Press, pp 87--90, https://eprints.soton.ac.uk/403913/

    2016

  80. [208]

    Kormann R., Schneider P., Bartelmann M., 1994, @doi [ ] 10.48550/arXiv.astro-ph/9311011 , https://ui.adsabs.harvard.edu/abs/1994A&A...286..357K 286, 357

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/9311011 1994

Showing first 80 references.