Pith. sign in

REVIEW 3 major objections 5 minor 69 references

A compact group lens modeled with GIGA-Lens: Enhanced inference for complex systems

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read An upgraded lens-modeling pipeline fits a 29-parameter model of the compact group DES J0248-3955 in minutes, finding a 690 km/s halo and a candidate second source plane.

desk verdict The inference engine is a real step forward; the claimed z~2.7 third source is an in-sample fit, not a prediction, and the paper needs a double-plane refit before that claim stands. read the letter →

arxiv 2412.04567 v1 pith:34BQBKFI submitted 2024-12-05 astro-ph.CO astro-ph.GAastro-ph.IM

F. Urcelay , E. Jullo , L. F. Barrientos , X. Huang , J. Hernandez This is my paper · ORCID
classification astro-ph.COastro-ph.GAastro-ph.IM
keywords stronggravitationallensinggalaxygroupsGIGA-LensBayesianinferencesequentialMonteCarloGPUaccelerationdoublesourceplaneDESJ0248-3955
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

The paper extends the GIGA-Lens code so that group- and cluster-scale strong lenses with many free parameters can be modeled quickly from ground-based images, and it demonstrates the upgrade on the compact group DES J0248-3955. New VLT/X-shooter spectra place the group at $z=0.69\pm0.04$ and the bright arc S1a at $z=1.2722\pm0.0005$. The central result is that a 29-parameter lens model with broad priors is fully constrained in about 4.5 minutes of sequential Monte Carlo sampling, yielding a single isothermal dark-matter halo with $\sigma_v = (690\pm30)\,\mathrm{km\,s^{-1}}$. The model also predicts two additional lensed sources, one at the same redshift as S1a and one at $z\sim2.7$, making DES J0248-3955 a candidate double-source-plane lens. If these results hold, the pipeline opens a route to automated modeling of the large group-lens samples expected from LSST and similar surveys.

What carries the argument

The load-bearing mechanism is a two-stage annealed posterior, $P_{\lambda_1,\lambda_2}(\Theta;D) = \pi(\Theta) L_\beta^{\lambda_1} L_{\mathrm{pix}}^{\lambda_2}$, in which $L_\beta$ is a source-plane image-position likelihood and $L_{\mathrm{pix}}$ is a pixelated surface-brightness likelihood. The sampler first turns on $L_\beta$ to shrink the prior volume, then gradually swaps weight to $L_{\mathrm{pix}}$ in a simulated-annealing schedule, using sequential Monte Carlo with Hamiltonian Monte Carlo transitions and automatic differentiation throughout. The distance ratio $\eta = \alpha_2/\alpha_1$ rescales the deflection between source planes and is the single fitted parameter that carries the double-source-plane interpretation.

What would settle it

A spectroscopic redshift for source S2 that falls outside the range implied by the prior on the distance ratio (about $z=2.1$ to $3.2$), or a double-lens-plane model in which the distance ratio becomes consistent with unity, would overturn the second-source-plane interpretation; so would high-resolution imaging showing that S2.1-4 are unrelated galaxies rather than a single quadruply imaged source.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the compact group lens DES J0248-3955 can be modeled with a single singular isothermal ellipsoid halo plus external shear and three Sérsic sources, a total of 29 free parameters, using only ground-based g-band pixels and image positions. The fitted Einstein radius is $\theta_E = 5.052'' \pm 0.005''$ for the source at $z=1.2722$, and through the isothermal velocity-dispersion relation this yields $\sigma_v = (690 \pm 30)\,\mathrm{km\,s^{-1}}$ for the group. The distance ratio between the two source planes comes out at $\eta = 0.626 \pm 0.001$, more than $5\sigma$ away from unity, which the authors read as strong evidence that the third source is a separate, more distant plane near $z \sim 2.7$ rather than a second image of the first source. The authors are explicit that this $z \sim 2.7$ value is an upper limit from a single-lens-plane model, and that the mass of source S1a shifts the S2 images by about $0.12''$, so a double-lens-plane model is needed to firm up the distance claim.

Load-bearing premise

The double-source-plane result rests on the assumption that the image families assigned to S1b and S2 are genuine multiple images of single background galaxies, and that the fitted distance ratio has not absorbed the single-lens-plane approximation that the paper shows is violated by the mass of S1a.

Editorial extensions

If this is right

  • Group-scale lenses can be modeled from ground-based, lower-resolution data in minutes, which is the speed regime needed to handle LSST/Euclid samples without per-object expert tuning.
  • The SMC annealing schedule reaches a lower reduced $\chi^2_{\nu,\mathrm{pix}}$ than the multi-start gradient descent used by the original galaxy-scale pipeline, so broad priors and high-dimensional spaces remain tractable.
  • DES J0248-3955 is a double-source-plane lens candidate whose fitted distance ratio $\eta=0.626\pm0.001$ deviates from unity by more than $5\sigma$, so a spectroscopic redshift for S2 could turn this system into a probe of $\Omega_m$ and $w$.
  • The single-plane value $z_{\mathrm{S2}} \leq 2.7$ is only an upper limit; incorporating the $0.12''$ deflection by S1a in a multiplane model is a required next step before the source distance is trusted.

Reading between the lines

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

  • If the same annealing strategy is combined with the scaling relations the paper proposes for cluster members, the method could plausibly move from one-off group lenses to automated cluster samples; the unresolved question is whether automated image-family identification can be made as reliable as the sampling itself.
  • The quoted uncertainty on $\theta_E$ is about 0.1%, which is unusually small for low-signal ground-based data; a plausible reading is that the rigid SIE plus Sérsic model confines the posterior to a narrow slice of parameter space, and allowing a free power-law slope would probably widen the errors and could shift $\sigma_v$.
  • A direct observational test follows from the model's own geometry: S1b should show the same emission lines as S1a at $z=1.2722$, and S2 should show lines near $z\sim2.7$; either spectrum would confirm or break the image-family assignment.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper presents an enhanced version of the GIGA-Lens strong-lensing inference code, combining source-plane image-position likelihoods with pixel-level surface-brightness likelihoods in a two-stage simulated-annealing SMC sampler, implemented in JAX on GPUs. The method is applied to the compact group lens DES J0248-3955 using ground-based DES/legacy-survey imaging and new VLT/X-shooter spectroscopy. The authors report a group redshift z_L = 0.69 ± 0.04, a source redshift z_S1 = 1.2722 ± 0.0005 for the arc S1a, a 29-parameter lens model constrained in about 4.5 minutes, a velocity dispersion σ_v = (690 ± 30) km/s for the group, and the presence of a second source at z = 1.2722 and a third source at z ≈ 2.7. They argue that the system is a double-source-plane lens that could constrain cosmology. The methodological contribution is a faster, memory-efficient sampling scheme for high-dimensional group/cluster lens models with broad priors.

Significance. If the claims hold, the methodological advance is significant: extending GPU-accelerated Bayesian lens modeling from galaxy-scale to group-scale systems with ~29 free parameters in minutes would be valuable for upcoming surveys like LSST. The paper includes concrete timing measurements, a comparison with multi-start gradient descent showing the SMC approach reaches lower χ², and residual maps. The combination of position and pixel likelihoods with annealing is a reasonable and potentially generalizable strategy. However, the headline astrophysical claims — the second source plane and z_S2 ≈ 2.7 — currently rest on a circular image-family assignment, a prior on the distance ratio that excludes unity, and a single-lens-plane approximation that the authors themselves show is violated. The method may be sound, but the evidence presented does not yet support the double-source-plane interpretation or the quoted z_S2.

major comments (3)
  1. [Section 4] The image-family assignments for S1b and S2 are determined using the lens model itself: the text states that the authors 'employed the model to predict the image families' and 'explored various models considering a single source and different image combinations until we obtained a model that successfully reproduces images S1a.1-4', then used that model to predict the counterimages of S1b and S2. Because the same model is then fit to these assigned families, the constraints from S1b and S2 are not independent. The paper should provide an independent justification for the image pairing (e.g., colors, morphologies, or spectra of S1b and S2) or explicitly re-frame the S1b/S2 identification as a model-dependent hypothesis rather than a prediction.
  2. [Section 5.2, Table 2] The posterior distance ratio η = 0.626 ± 0.001 is obtained with a prior η ~ U(0.6, 0.7), which by construction excludes η = 1 and maps to z_S2 in (2.1, 3.2). The statement that the distance ratio 'deviates from unity with a discrepancy greater than 5σ' is therefore a prior-induced result, not evidence for two distinct source planes. The authors should re-fit the model with a prior that includes unity, e.g., a uniform prior on η that contains η = 1 or a uniform prior on z_S2 covering the full plausible range, and report how the posterior changes. The current >5σ claim is not meaningful when the prior excludes the null value.
  3. [Sections 5.2 and 5.3] The paper itself demonstrates that the single-lens-plane approximation is violated: adding a plausible S1a mass with σ_v ≈ 100 km/s shifts the S2 images by about 0.12 arcsec at 5σ significance (Fig. 5). Yet the quoted z_S2 ≈ 2.7 and the 'prediction' of a third source are derived from the single-plane model. Section 5.2 correctly states that 'the model estimates an upper limit for the redshift of S2 to be z_S2 ≤ 2.7', but the abstract and conclusions present z ≈ 2.7 as a definite prediction. The paper must either (a) perform a double-lens-plane refit and derive z_S2 from that model, or (b) revise the abstract and conclusions to state that z_S2 is only an upper limit under a known-to-be-invalid approximation. As written, the central astrophysical claim is not supported by the analysis presented.
minor comments (5)
  1. [Section 5.2] The text says the model 'predicts the presence of a second source at the same redshift', but S1b's redshift is fixed to z = 1.2722 during modeling, so this is an assumption, not a prediction; please clarify.
  2. [Abstract and Section 5.2] The abstract states 'a third source at approximately z ~ 2.7' without the qualification that the single-plane model gives only an upper limit; the wording should be adjusted to avoid overstating the result.
  3. [Table 2 and Figure 4] There are typos: 'suqared arcsecond' appears in the Table 2 notes and Figure 4 caption, and 'asumming' in Section 5.3; please correct these.
  4. [Section 4] The prior for S2's ellipticity is given in parentheses in Table 2 but is not explained clearly in the table notes; please state explicitly that the narrower ellipticity prior is applied to S2.
  5. [Figure 3] The caption refers to 'the tangential critical lines ... for the source plane S1 (inner) and S2 (outer)', but the model is single-plane; please clarify that the outer line is obtained by rescaling to the S2 redshift via η, not from a true multi-plane calculation.

Circularity Check

3 steps flagged · score 7.0 of 10

The claimed 'prediction' of a third source at z≈2.7 is an in-sample value of the fitted distance-ratio parameter η, whose prior excludes unity; the 'second source at the same redshift' has its redshift fixed as an input, so the double-source-plane evidence is prior- and input-driven rather than predicted.

  1. fitted input called prediction [Abstract; Section 4 'Lens Model'; Table 2; Section 5.2; Eq. (4)]
    "The conclusive model incorporates all three aforementioned sources and introduces an additional parameter η that accounts for the distance to source S2 (see equation (4)). ... Source distance: η ∼U (0.6, 0.7) ... The source distance prior limits zS 2 to (2.1, 3.2)."

    The abstract's headline claim that the model 'predicts the presence of ... a third source at approximately z∼2.7' is not an out-of-sample prediction. The final model fits η as a free parameter (Table 3: η=0.626±0.001), and Eq. (4) converts that fitted η into a distance ratio and hence, under the assumed cosmology, a redshift. Table 2 restricts η to the narrow interval [0.6,0.7], which maps to zS2∈(2.1,3.2), so z≈2.7 lies in the prior by construction. Section 5.2's 'deviates from unity with discrepancy greater than 5σ' is forced by the prior support excluding η=1; a posterior that cannot reach unity cannot be evidence for a second plane independent of that prior.

  2. fitted input called prediction [Section 5.2 'Lens and Sources Analysis'; Abstract]
    "There are two sources in the left panel: S1a, which has a spectroscopic redshift of z = 1.2722, and S1b, which the model predicts to be at a similar redshift, and we fix its redshift to z = 1.2722 during modeling."

    The abstract says the model 'predicts the presence of a second source at the same redshift', but S1b's redshift is not measured or predicted by the model; it is fixed to z=1.2722 as a modeling input. The derivation chain is therefore inverted: the model was given z=1.2722 and returns it, and this input is then relabeled as a prediction. No independent spectrum of S1b is presented, and the color difference g−r=0.19 vs 0.31 is only suggestive. The claim of a second source at the same redshift is thus an assumption restated as a result.

1 more flagged steps
  1. self definitional [Section 4 'Lens Model']
    "Due to large errors in the colors, which hindered an accurate match of the multiple images, we employed the model to predict the image families. For this, we explored various models considering a single source and different image combinations until we obtained a model that successfully reproduces images S1a.1-4, from a single source, denoted S1a... We then employ this model to predict the counterimages of the remaining 1 to 2 image systems..."

    The image-family assignments that are later presented as model predictions were themselves produced by the model: the authors tried different image combinations until a model reproduced S1a.1-4, and then used that model to assign the counterimages that became S1b and S2. The final 'successful' reproduction of S1a.1-4, S1b.1-2, and S2.1-4 is therefore a fit to image groupings that the same model defined. This is a self-definitional loop for the double-source-plane evidence: the data partitioning was not fixed a priori, so the model's agreement with the assigned families is partly by construction. It does not invalidate the fast-inference methodology, but it weakens the claim that the model independently 'predicts' the presence of multiple source planes.

full rationale

The methodological contribution of the paper, namely the GIGA-Lens extension with hybrid position-plus-pixel likelihoods, SMC annealing, and sparse-mask GPU inference, appears technically self-contained and is not circular: the speed and convergence behavior can be checked against the stated equations and runtime without invoking the astrophysical conclusions. The velocity dispersion σv=(690±30) km/s is a standard transformation of the fitted Einstein radius through Eq. (12) and is not by itself a circular claim. However, the headline astrophysical claims are different. The 'third source at approximately z∼2.7' is not an independent prediction: it is obtained by inserting the fitted parameter η into Eq. (4) under an assumed cosmology, with η's prior U(0.6,0.7) mapping directly to zS2∈(2.1,3.2). The '>5σ deviation from unity' quoted in Section 5.2 is partly a prior artifact because η=1 lies outside the prior support. The 'second source at the same redshift' has its redshift fixed to z=1.2722 during modeling, so the abstract's word 'predicts' rewrites an input as an output. Finally, Section 4 shows that image families S1b and S2 were assigned by the model itself after iterative exploration, so the subsequent agreement is partially self-definitional. The paper's own Section 5.3 shows that a single-plane model is violated at the 0.12 arcsec level by S1a's mass, and Section 5.2 concedes that the quoted zS2≤2.7 is an upper limit under that approximation. For these reasons the fast-inference result is credible, but the double-source-plane result and zS2≈2.7 reduce to fitted and prior-constrained inputs rather than to independent predictions.

Assumptions & free parameters 5 free parameters · 7 assumptions · 2 invented entities

The central claims rest on standard lensing theory plus several domain assumptions: a fixed flat ΛCDM cosmology, the adequacy of the SIE+shear mass model, the correctness of model-derived image-family assignments, the representativeness of the BGG redshift, and convergence of the SMC sampler. The model also carries fitted parameters (θE, ellipticity, shear, η, source shapes) that are not independently measured; in particular, η is a prior-constrained fitted quantity converted into the claimed S2 redshift.

free parameters (5)
  • Einstein radius θE = 5.052 ± 0.005 arcsec
    Scale radius of the SIE mass profile; strongly constrained by image positions and pixels. Prior U(3,8) arcsec.
  • Halo ellipticity ϵ and position angle ϕ = ϵ = 0.203 ± 0.002, ϕ = 12.1 deg
    Quadrupole shape of the group halo; high ellipticity drives the image configuration and the difference from earlier position-only models.
  • External shear γ1, γ2 = γ1 = 0.003 ± 0.001, γ2 = -0.015 ± 0.001
    Accounts for the influence of nearby group members and a rich group to the south.
  • Source distance ratio η = 0.626 ± 0.001
    Fitted free parameter with prior U(0.6,0.7); converts to the claimed z_S2 ≈ 2.7 through Eq. (4). This parameter is the entire basis of the double-source-plane claim.
  • Source Sérsic parameters (R, n, I, x, y, e1, e2) for S1a, S1b, S2 = not tabulated; priors in Table 2
    21 parameters describing the surface brightness of the three sources; values are not reported individually, only shown as reconstructed images in Fig. 4.
assumptions (7)
  • standard math Standard gravitational lensing equations: lens equation, deflection integral, and critical density (Eqs. 1-3).
    Background theory used throughout the paper; not derived or verified here.
  • domain assumption Flat ΛCDM with Ωm,0 = 0.3 and H0 = 70 km/s/Mpc.
    Stated in Sect. 1; used to convert distances and to translate η into the claimed z_S2 ≈ 2.7.
  • domain assumption The lens mass is well described by a single SIE plus external shear, without member-galaxy halos.
    Sect. 4 model definition; Sect. 5.1 admits model rigidity likely underestimates uncertainties and subhalos may explain S1b residuals.
  • ad hoc to paper The image-family assignments (S1a, S1b, S2) and the interpretation of S1b and S2 as lensed background sources are correct.
    Sect. 4: families were predicted by the model and combinations were tried until the data were reproduced; S1b and S2 lack spectroscopic confirmation.
  • domain assumption The BGG spectroscopic redshift is representative of the group redshift, with uncertainty taken from photometric redshifts.
    Sect. 2: z_L = 0.69 ± 0.04 is based on one galaxy; authors note additional observations are needed.
  • domain assumption A single-lens-plane model is sufficient for S2 in the main inference, with S1a's mass neglected.
    Sect. 5.3: a two-plane check shows S1a shifts S2 images by about 0.12 arcsec, so the inferred z_S2 is an upper limit under this assumption.
  • domain assumption The SMC annealed sampler with 1000 particles and 100 steps converges to the posterior.
    Sects. 3 and 6 report consistency across runs but provide no convergence proof or blind validation on simulated systems with known truth.
invented entities (2)
  • Source S2 (claimed lensed background source at z ≈ 2.7)
    purpose: Explains the observed S2.1-4 four-image configuration and provides the double-source-plane signal via η ≈ 0.63.
    No spectrum is presented for S2; its redshift is derived from the fitted η under a single-plane approximation, and the image family was assigned using the model itself. It is a falsifiable prediction for future spectroscopy, but not an independent detection.
  • Source S1b (claimed second source at z = 1.2722)
    purpose: Accounts for the S1b.1-2 arc; its redshift is fixed to the S1a spectroscopic redshift during modeling.
    The g-r color of S1b differs from S1a, so it may be a separate galaxy, but no spectrum exists and the paper states that spectra and higher-quality imaging would be needed to confirm it.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A compact group lens modeled with GIGA-Lens: Enhanced inference for complex systems." pith.science (2026). https://pith.science/paper/34BQBKFI

@misc{pith2026241204567,
  author       = {Pith},
  title        = {Pith review of: A compact group lens modeled with GIGA-Lens: Enhanced inference for complex systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/34BQBKFI}},
  note         = {Machine review of arXiv:2412.04567}
}
abstract

In the era of large-scale astronomical surveys, fast modeling of strong lens systems has become increasingly vital. While significant progress has been made for galaxy-scale lenses, the development of automated methods for modeling larger systems, such as groups and clusters, is not as extensive. Our study aims to extend the capabilities of the GIGA-Lens code, enhancing its efficiency in modeling multi-galaxy strong lens systems. We focus on demonstrating the potential of GPU-accelerated Bayesian inference in handling complex lensing scenarios with a high number of free parameters. We employ an improved inference approach that combines image position and pixelated data with an annealing sampling technique to obtain the posterior distribution of complex models. This method allows us to overcome the challenge of limited prior information, a high number of parameters, and memory usage. Our process is exemplified through the analysis of the compact group lens system DES J0248-3955, for which we present VLT/X-shooter spectra. We measure a redshift of $z = 0.69 \pm 0.04$ for the group, and $z = 1.2722 \pm 0.0005$ for one of the extended arcs. Our enhanced method successfully constrained a lens model with 29 free parameters and lax priors in a remarkably short time. The mass of the lens is well described by a single dark-matter halo with a velocity dispersion of $\sigma_v = (690 \pm 30) \, km \, s^{-1}$. The model predicts the presence of a second source at the same redshift and a third source at approximately $z \sim 2.7$. Our study demonstrates the effectiveness of our lens modeling technique for dealing with a complex system in a short time using ground-based data. This presents considerable potential within the context of large surveys such as LSST.

Figures

Figures reproduced from arXiv: 2412.04567 by the authors.

Figure 1
Figure 1. Top panels: X-Shooter 1D spectrum of the BGG at redshift z = 0.685 ± 0.002. The redshift is driven by the K and H absorption lines (right panel), as well as the shape of the continuum. The red shaded region around the K and H lines represents the associated uncertainty. Second-row panels: 2D spectrum of the source S1a.1 at redshift z = 1.2722 ± 0.0005 without sky subtraction, centered around the [O II] (left) and Hα… view at source ↗
Figure 2
Figure 2. (a): Color composite of the system, the red labels indi￾cate possible group members and the white box represents the X-shooter slit passing through image S1a.1 and between mem￾bers g2 and g3. (b): g-band image with Sérsic surface brightness model of g1 to g5 subtracted, overlaid with the segmentation of the multiple images labeled in black [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Left panel: g-band image with g1-g5 foreground-light subtracted. The green regions show the pixels included in the sim￾ulation. Image systems are labeled as S1a.1-4, S1b.1-2, and S2.1-4. Middle panel: Model reproduction of the image based on the median of the marginalized parameters. The tangential critical lines are shown in cyan for the source plane S1 (inner) and S2 (outer). Right panel: Normalized residual betwe… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Surface brightness model for the sources S1a and S1b [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Left: The model consists of two lens planes. The plane at zL has the same mass model as the one shown in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Evolution of the reduced χ 2 pix along multi-start gradient descent steps. The regions account for the 1σ, 2σ, and 3σ per￾centiles. The dashed line shows the χ 2 ν,pix achieved with SMC for comparison. 7. Conclusions We present a novel lens modeling software, which is …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

69 extracted references · 46 canonical work pages

  1. [1]

    2023, A&A, 680, L9

    Acebron, A., Schuldt, S., Grillo, C., et al. 2023, A&A, 680, L9

    work page 2023

  2. [2]

    2023, ApJ, 951, 6

    Adam, A., Perreault-Levasseur, L., Hezaveh, Y ., & Welling, M. 2023, ApJ, 951, 6

    work page 2023

  3. [3]

    2015, ApJ, 814, 69

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

    2015

  4. [4]

    W., Treu, T., Bolton, A

    Auger, M. W., Treu, T., Bolton, A. S., et al. 2010, ApJ, 724, 511

    2010

  5. [5]

    2023, ApJ, 952, 84

    Bergamini, P., Acebron, A., Grillo, C., et al. 2023, ApJ, 952, 84

    2023

  6. [6]

    2022, A&A, 675, A125

    Biggio, L., Vernardos, G., Galan, A., & Peel, A. 2022, A&A, 675, A125

    work page 2022

  7. [7]

    & Amara, A

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

    work page 2018

  8. [8]

    2015, ApJ, 813, 102

    Birrer, S., Amara, A., & Refregier, A. 2015, ApJ, 813, 102

    2015

Show all 69 references
  1. [9]

    2021, JOSS, 6, 3283

    Birrer, S., Shajib, A., Gilman, D., et al. 2021, JOSS, 6, 3283

    2021

  2. [10]

    2018, JAX: composable transforma- tions of Python+NumPy programs

    Bradbury, J., Frostig, R., Hawkins, P., et al. 2018, JAX: composable transforma- tions of Python+NumPy programs

    2018

  3. [11]

    2023, astropy/photutils: 1.8.0

    Bradley, L., Sip˝ocz, B., Robitaille, T., et al. 2023, astropy/photutils: 1.8.0

    2023

  4. [12]

    G., Blandford, R

    Brainerd, T. G., Blandford, R. D., & Smail, I. 1996, ApJ, 466, 623

    1996

  5. [13]

    B., Suyu, S

    Caminha, G. B., Suyu, S. H., Grillo, C., & Rosati, P. 2022, A&A, 657, A83

    2022

  6. [14]

    2018, ApJ, 859, 159

    Cerny, C., Sharon, K., Andrade-Santos, F., et al. 2018, ApJ, 859, 159

    2018

  7. [15]

    2020, MNRAS, 496, 381

    Chianese, M., Coogan, A., Hofma, P., Otten, S., & Weniger, C. 2020, MNRAS, 496, 381

    2020

  8. [16]

    T., Huang, X., et al

    Cikota, A., Bertolla, I. T., Huang, X., et al. 2023, ApJ, 953, L5

    2023

  9. [17]

    Collett, T. E. 2015, ApJ, 811, 20

    2015

  10. [18]

    Collett, T. E. & Auger, M. W. 2014, MNRAS, 443, 969

    2014

  11. [19]

    E., Auger, M

    Collett, T. E., Auger, M. W., Belokurov, V ., Marshall, P. J., & Hall, A. C. 2012, MNRAS, 424, 2864

    2012

  12. [20]

    & Kochanek, C

    Dalal, N. & Kochanek, C. S. 2002, ApJ, 572, 25 Del Moral, P., Doucet, A., & Jasra, A. 2012, Statistics and Computing, 22, 1009

    2002

  13. [21]

    J., Lang, D., et al

    Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168 Article number, page 9 of 10 A&A proofs: manuscript no. main

    2019

  14. [22]

    V ., Langmore, I., Tran, D., et al

    Dillon, J. V ., Langmore, I., Tran, D., et al. 2017, arXiv

    2017

  15. [23]

    2022, ApJ, 935, 17

    Gu, A., Huang, X., Sheu, W., et al. 2022, ApJ, 935, 17

    2022

  16. [24]

    P., & McCarthy, I

    Harvey, D., Courbin, F., Kneib, J. P., & McCarthy, I. G. 2017, MNRAS, 472, 1972

    2017

  17. [25]

    D., Levasseur, L

    Hezaveh, Y . D., Levasseur, L. P., & Marshall, P. J. 2017, Nature, 548, 555

    2017

  18. [26]

    2021, ApJ, 909, 27

    Huang, X., Storfer, C., Gu, A., et al. 2021, ApJ, 909, 27

    2021

  19. [27]

    2019, ApJS, 243, 17

    Jacobs, C., Collett, T., Glazebrook, K., et al. 2019, ApJS, 243, 17

    2019

  20. [28]

    2016, MNRAS, 463, 3876

    Jauzac, M., Eckert, D., Schwinn, J., et al. 2016, MNRAS, 463, 3876

    2016

  21. [29]

    2007, New Journal of Physics, 9, 447

    Jullo, E., Kneib, J.-P., Limousin, M., et al. 2007, New Journal of Physics, 9, 447

    2007

  22. [30]

    2010, Sci, 329, 924

    Jullo, E., Natarajan, P., Kneib, J.-P., et al. 2010, Sci, 329, 924

    2010

  23. [31]

    L., Rodney, S., Treu, T., et al

    Kelly, P. L., Rodney, S., Treu, T., et al. 2023, Sci, 380, abh1322

    2023

  24. [32]

    W., Nightingale, J., et al

    Knabel, S., Holwerda, B. W., Nightingale, J., et al. 2023, MNRAS, 520, 804

    2023

  25. [33]

    Kochanek, C. S. 1991, ApJ, 373, 354

    1991

  26. [34]

    Koopmans, L. V . E., Bolton, A., Treu, T., et al. 2009, ApJ, 703, L51

    2009

  27. [35]

    2022, A&A, 664, A90

    Limousin, M., Beauchesne, B., & Jullo, E. 2022, A&A, 664, A90

    2022

  28. [36]

    2012, A&A, 544, A71

    Limousin, M., Ebeling, H., Richard, J., et al. 2012, A&A, 544, A71

    2012

  29. [37]

    P., & Natarajan, P

    Limousin, M., Kneib, J. P., & Natarajan, P. 2005, MNRAS, 356, 309

    2005

  30. [38]

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

    Lotz, J. M., Koekemoer, A., Coe, D., et al. 2017, ApJ, 837, 97

    2017

  31. [39]

    2021, MN- RAS, 505, 6155

    Magro, D., Zarb Adami, K., DeMarco, A., Riggi, S., & Sciacca, E. 2021, MN- RAS, 505, 6155

    2021

  32. [40]

    2023, ApJ, 945, 49

    Mahler, G., Jauzac, M., Richard, J., et al. 2023, ApJ, 945, 49

    2023

  33. [41]

    1993, ApJ, 407, 33

    Mellier, Y ., Fort, B., & Kneib, J.-P. 1993, ApJ, 407, 33

    1993

  34. [42]

    2007, A&A, 461, 25

    Meneghetti, M., Argazzi, R., Pace, F., et al. 2007, A&A, 461, 25

    2007

  35. [43]

    2011, MNRAS, 417, 333

    Merten, J., Coe, D., Dupke, R., et al. 2011, MNRAS, 417, 333

    2011

  36. [44]

    R., Levasseur, L

    Morningstar, W. R., Levasseur, L. P., Hezaveh, Y . D., et al. 2019, ApJ, 883, 14

    2019

  37. [45]

    B., Treu, T., Ellis, R

    Newman, A. B., Treu, T., Ellis, R. S., & Sand, D. J. 2013, ApJ, 765, 25

    2013

  38. [46]

    W., Dye, S., & Massey, R

    Nightingale, J. W., Dye, S., & Massey, R. J. 2018, MNRAS, 478, 4738 O’Donnell, J. H., Wilkinson, R. D., Diehl, H. T., et al. 2022, ApJS, 259, 27

    2018

  39. [47]

    2006, Monthly Notices of the Royal Astronomical Society, 367, 1241

    Oguri, M. 2006, Monthly Notices of the Royal Astronomical Society, 367, 1241

    2006

  40. [48]

    L., Pierel, J

    Pascale, M., Frye, B. L., Pierel, J. D. R., et al. 2024, arXiv e-prints, arXiv:2403.18902

    2024 arXiv

  41. [49]

    2019, MNRAS, 488, 991

    Pearson, J., Li, N., & Dye, S. 2019, MNRAS, 488, 991

    2019

  42. [50]

    2021, MNRAS, 505, 4362

    Pearson, J., Maresca, J., Li, N., & Dye, S. 2021, MNRAS, 505, 4362

    2021

  43. [51]

    1964, MNRAS, 128, 307

    Refsdal, S. 1964, MNRAS, 128, 307

    1964

  44. [52]

    2024, The Open Journal of Astro- physics, 7, 65

    Roche, C., McDonald, M., Borrow, J., et al. 2024, The Open Journal of Astro- physics, 7, 65

    2024

  45. [53]

    2022, A&A, 668, A73

    Rojas, K., Savary, E., Clément, B., et al. 2022, A&A, 668, A73

    2022

  46. [54]

    P., Turner, E

    Schneider, D. P., Turner, E. L., Gunn, J. E., et al. 1988, AJ, 95, 1619

    1988

  47. [55]

    Schneider, P., Ehlers, J., & Falco, E. E. 1992, Gravitational Lenses, Astronomy and Astrophysics Library (Berlin, Heidelberg: Springer Berlin Heidelberg)

    1992

  48. [56]

    2023, A&A, 671, A147

    Schuldt, S., Cañameras, R., Shu, Y ., et al. 2023, A&A, 671, A147

    2023

  49. [57]

    H., Meinhardt, T., et al

    Schuldt, S., Suyu, S. H., Meinhardt, T., et al. 2021, A&A, 646, A126

    2021

  50. [58]

    E., & Linder, E

    Sharma, D., Collett, T. E., & Linder, E. V . 2023, JCAP, 2023, 001

    2023

  51. [59]

    B., Dahle, H., et al

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

    2020

  52. [60]

    2022, A&A, 662, A4

    Shu, Y ., Cañameras, R., Schuldt, S., et al. 2022, A&A, 662, A4

    2022

  53. [61]

    2004, in American Institute of Physics Conference Series, V ol

    Skilling, J. 2004, in American Institute of Physics Conference Series, V ol. 735, Bayesian Inference and Maximum Entropy Methods in Science and Engi- neering: 24th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. R. Fisch...

    2004

  54. [62]

    2019, Monthly Notices of the Royal Astronomical Society, 482, 1824

    Stapelberg, S., Carrasco, M., & Maturi, M. 2019, Monthly Notices of the Royal Astronomical Society, 482, 1824

    2019

  55. [63]

    2022, arXiv e-prints, arXiv:2206.02764 van de Sande, J., Kriek, M., Franx, M., Bezanson, R., & van Dokkum, P

    Storfer, C., Huang, X., Gu, A., et al. 2022, arXiv e-prints, arXiv:2206.02764 van de Sande, J., Kriek, M., Franx, M., Bezanson, R., & van Dokkum, P. G. 2015, ApJ, 799, 125

    2022 arXiv

  56. [64]

    2023, arXiv, arXiv:2306.11781

    Vegetti, S., Birrer, S., Despali, G., et al. 2023, arXiv, arXiv:2306.11781

    2023 arXiv

  57. [65]

    2011, A&A, 536, A105

    Vernet, J., Dekker, H., D’Odorico, S., et al. 2011, A&A, 536, A105

    2011

  58. [66]

    C., Suyu, S

    Wong, K. C., Suyu, S. H., Chen, G. C. F., et al. 2020, MNRAS, 498, 1420

    2020

  59. [67]

    A., Drlica-Wagner, A., Ashmead, F., et al

    Zaborowski, E. A., Drlica-Wagner, A., Ashmead, F., et al. 2023, ApJ, 954, 68

    2023

  60. [68]

    A., Mao, Y .-Y ., et al

    Zhou, R., Newman, J. A., Mao, Y .-Y ., et al. 2021, MNRAS, 501, 3309

    2021

  61. [69]

    2012, Monthly Notices of the Royal Astronomical Society, 423, 2308 Article number, page 10 of 10

    Zitrin, A., Broadhurst, T., Bartelmann, M., et al. 2012, Monthly Notices of the Royal Astronomical Society, 423, 2308 Article number, page 10 of 10

    2012

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.