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REVIEW 4 major objections 4 minor 1 cited by

Line-of-sight shear in SLACS strong lenses I: shear and mass model parametrisations

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Pith's one-line read The paper reports the first measurement of line-of-sight shear from real strong-lens images, with a mean magnitude of 0.056 across 23 SLACS lenses.

desk verdict First real-data measurement of the minimal-model LOS shear, done carefully and honestly, but the main-deflector model is the acknowledged unknown and the headline uncertainty has a fixable inconsistency. read the letter →

arxiv 2501.16292 v3 pith:YCZGIDFL submitted 2025-01-27 astro-ph.CO astro-ph.GA

classification astro-ph.COastro-ph.GA PACS 98.62.Sb
keywords stronggravitationallensingline-of-sightshearminimalmodelSLACSellipticalpower-lawprofileoctupolemultipolepost-Borncorrectionscosmic
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

This paper attempts the first measurement of line-of-sight (LOS) shear in real strong gravitational lens images, using the 'minimal model' designed to be free from the degeneracy between shear and the lens galaxy's mass ellipticity. Fitting 23 lenses from the SLACS catalogue with an automated modelling pipeline, it reports a mean LOS shear magnitude of $0.056 \pm 0.013$, a value larger than what N-body simulations of the cosmic web predict for the same lines of sight. The paper also shows that dropping the foreground shear — the post-Born correction to the deflector's potential — biases the inferred shear, and that adding an octupole term to the lens mass does not systematically bring measurements into agreement with simulations. If the result holds, strong-lens images carry a measurable weak-lensing signal that could complement cosmic shear as a cosmological probe, with the modelling of the lens galaxy itself now the dominant systematic.

What carries the argument

The central object is the minimal LOS shear model. It begins with three separate tidal shears acting on the light path — between observer and source, deflector and source, and observer and deflector — and multiplies the lens equation by $A_{\rm od} A_{\rm ds}^{-1}$, a source-position transformation that absorbs the individually unmeasurable shears into a single LOS amplification matrix. What survives in the model is the combination $\gamma_{\rm LOS} \equiv \gamma_{\rm od} + \gamma_{\rm os} - \gamma_{\rm ds}$, argued to be free of degeneracy with the lens mass ellipticity at leading order, alongside a foreground shear $\gamma_{\rm od}$ acting through the effective deflector potential $\psi_{\rm eff}(\theta) = \psi(A_{\rm od}\theta)$ and a LOS rotation $\omega_{\rm LOS}$. The pipeline fits each lens with an elliptical power-law mass profile, two Sérsic profiles for the deflector light, and a Sérsic-plus-shapelet source model, sampling the posterior with MCMC and reading $\gamma_{\rm LOS}$ off the recovered shear components.

What would settle it

Measure the fourth-order isophotal distortions of the 23 lens galaxies from their own images: the fits recover octupole strengths of 2% or more in a third of the sample, whereas observational studies of early-type galaxies find roughly 1% distortions, and a mismatch would show the mass model is absorbing non-octupolar complexity rather than real boxiness. A complementary check is to compare each measured $\gamma_{\rm LOS}$ against shear reconstructed from background galaxy shapes along the same sightline, since a systematic excess in the lens-based values would signal leakage from the deflector model.

Watch

Extended reading notes

Core claim

The central claim is that the line-of-sight shear of the minimal model, $\gamma_{\rm LOS} \equiv \gamma_{\rm od} + \gamma_{\rm os} - \gamma_{\rm ds}$, can be recovered from real strong-lens images, and the paper reports the first such measurement: across 23 SLACS lenses the mean magnitude is $0.056 \pm 0.013$. The individual measurements are said to be consistent with the external shears fitted to the same lenses in earlier work, but the sample mean sits well above the expectations drawn from N-body simulation light cones, with several lenses in tension at more than $3\sigma$. The paper further claims that fixing the foreground shear to zero (the no-foreground-shear model) propagates degeneracies and shifts the inferred LOS shear, so the full minimal model must be kept for shear science, and that including an octupole ($m=4$) term in the lens mass profile rarely lowers the shear — only SDSSJ1531-0105 is better fit by the octupole model, which reduces its shear by just over $1\sigma$. Its stated conclusion is that the line-of-sight contribution is adequately captured by the model, and that attention must now shift to the mass model of the main deflector.

Load-bearing premise

The load-bearing assumption is that the smooth elliptical power-law mass profile — and, in the extended model, a single octupole term — describes each lens galaxy well enough that any unmodelled complexity in the deflector, such as ellipticity gradients, isophotal twists, other multipoles, or substructure, does not mimic shear and leak into the measured $\gamma_{\rm LOS}$.

Editorial extensions

If this is right

  • If the measurement is right, strong-lens images can be used to measure weak-lensing shear along individual lines of sight, and the mean $|\gamma_{\rm LOS}| \approx 0.056$ becomes the first observational anchor for the signal.
  • The measured shear being larger than cosmic-web simulations predict independently confirms, for the LOS formalism, the known discrepancy between strong-lens external shear and weak-lensing expectations.
  • Pipelines that aim to measure shear must keep the foreground shear parameters: fixing $\gamma_{\rm od} = 0$ trades a small speed gain for a biased LOS shear and artificially tightens the recovered lens ellipticity.
  • Because octupole flexibility does not systematically reduce the shear, the explanation for large shear values must lie elsewhere in the mass model, so adding boxiness and diskyness is not a cure.
  • The result lays the groundwork for using strong-lens shear as a cosmological probe, but only after the mass-model systematics are controlled.

Reading between the lines

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

  • A direct cleanliness test that the paper does not run: compare each measured $\gamma_{\rm LOS}$ with shear reconstructed from galaxy shapes (cosmic shear) in the same sky patch; a systematic excess in the lens-based values would show that part of the 'LOS' signal is still mass-model leakage.
  • The recovered octupole strengths could be checked against independent isophotal measurements of the same galaxies; a mismatch would indicate that the mass model is absorbing something other than true boxiness or diskyness, with the same leakage possibly contaminating $\gamma_{\rm LOS}$.
  • Extending the minimal-model pipeline to the full 50-lens SLACS sample, or beyond, would turn the mean $|\gamma_{\rm LOS}|$ into a distribution-wide comparison with simulations and would clarify whether the high-shear tail (for example SDSSJ1112+0826 at about 0.23) is physical or pathological.
  • If later, more flexible mass models bring the mean shear down toward the roughly 0.01–0.02 level predicted by simulations, the excess reported here would itself become a diagnostic of how much complexity the elliptical power-law fits miss.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. This paper presents the first application of the 'minimal' line-of-sight (LOS) shear model of Fleury et al. (2021) to real strong-lens imaging, modelling 23 SLACS lenses with the dolphin/lenstronomy pipeline using an elliptical power-law (EPL) main deflector, two Sérsic profiles for deflector light, and a Sérsic plus shapelets model for source light. The authors report per-lens LOS shear magnitudes, a sample mean |γ_LOS| = 0.056 (quoted as ±0.016 in §4.2 and ±0.013 in the abstract), compare these values with RayGalGroup N-body weak-lensing expectations, and examine two systematic variations: setting the foreground shear γ_od to zero and adding an m=4 octupole to the mass profile. They conclude that the minimal model should be used, that the octupole does not generally reduce the inferred shear, and that future effort should focus on main-deflector modelling.

Significance. If the measurement is robust, this is a genuinely new probe: strong-lens image shapes would constrain a shear quantity that is theoretically free of the ellipticity degeneracy that plagues conventional external shear, and the comparison with N-body predictions would establish a new test of large-scale structure. The paper is exemplary in reproducibility: the pipeline, inputs, MCMC chains, and figure scripts are publicly released, and the comparison to RayGalGroup simulations is an independent, falsifiable check. The authors are also candid about the main limitation — the simplicity of the EPL deflector — and their negative octupole result is a useful data point for the field. However, the headline value is only interpretable as a LOS shear if unmodelled deflector complexity does not leak into the five shear parameters; this condition is not yet established by the tests in the paper.

major comments (4)
  1. [Abstract and §4.2] The abstract states a mean LOS shear of 0.056 ± 0.013, while Section 4.2 states 0.056 ± 0.016; these are different statements about the same quantity and must be reconciled. Please specify how the mean and its uncertainty are computed (e.g., sample mean of per-lens posterior medians, standard error, or inverse-variance weighted mean including asymmetric errors) and correct the inconsistent value.
  2. [§3.2] The Einstein radius θ_E is fixed to the best-fit value from Shajib et al. (2021) and is not sampled, so the reported per-lens shear uncertainties do not include uncertainty in θ_E. Because θ_E is tightly constrained, the effect may be small, but this is an assumption rather than a demonstrated result; please quantify the effect by re-fitting at least a subset with θ_E free or by marginalizing over the Shajib et al. posterior.
  3. [§4.3] The octupole test is inconclusive as a control for deflector complexity. The recovered |a_4| values are larger than the ~1% level observed in early-type isophotes (35% of lenses at or above 2%, with a further 45% above 5%), which is itself a red flag that the m=4 term is absorbing something else; for SDSSJ1204+0358 the octupole model finds a different solution with |a_4| consistent with zero but χ² increases from 0.68 to 1.08, indicating model instability rather than a clean null test. The m=4 multipole is also only one of several plausible complexities (m=1, m=3, ellipticity gradients, twists, substructure), so the conclusion that 'shear does not compensate for unmodelled octupoles' does not establish that the reported mean is free of deflector systematics. Please add recovery tests on mock images with realistic deflector complexity (not just EPL+octupole) and report the induced bias in γ_LOS.
  4. [§4.2 and Fig. 6] The comparison with RayGalGroup simulations uses the mean expected |γ_LOS| for each (z_d, z_s) pair, but the distribution of |γ_LOS| is positive-definite and likely non-Gaussian, so the tension statistic in Eq. (14) may overstate the significance of a 7.9σ outlier; please report the full simulated distribution of |γ_LOS| and the percentile of each measurement. In addition, the simulation expectation does not condition on the SLACS selection function (e.g., group environments), which is relevant to the claim that measured values are larger than expected.
minor comments (4)
  1. [Table 1 and Figs. 1–4] The per-lens |γ_LOS| values in Table 1 disagree with those printed in the corresponding figure panels for several lenses: for example, SDSSJ0029-0055 is 0.029+0.009−0.013 in Table 1 but 0.034+0.012−0.013 in Fig. 1, SDSSJ0330-0020 is 0.049+0.013−0.012 in the table but 0.059+0.012−0.014 in Fig. 1, and SDSSJ0728+3835 is 0.042+0.017−0.013 in the table but 0.028+0.013−0.011 in Fig. 1. These inconsistencies must be resolved or explained.
  2. [§4.3] The text refers to 'SDSSJ1204+0385' in three places; the correct name is SDSSJ1204+0358.
  3. [§4.3] For SDSSJ1204+0358 the paper reports '|a_4| = −0.02 +0.07 −0.04', which is impossible for a magnitude; please clarify whether a_4 is a signed amplitude and whether the reported quantity is a_4 or |a_4|.
  4. [Footnote 4] The footnote acknowledges that ordinary least squares is inaccurate when the independent variable has significant uncertainties, but the linear fit in Fig. 10 is still presented without an errors-in-variables treatment; please either use a suitable regression method or label the fit as illustrative only.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the LOS shear measurement is a model fit to real data, anchored by external N-body predictions, not a re-statement of its inputs.

full rationale

The paper's central result is a fitted parameter from real HST imaging using an openly specified model: an EPL main deflector, two Sersic lens-light profiles, a Sersic-plus-shapelet source, and the minimal LOS shear parametrisation. The minimal model is constructed explicitly in Section 2, Eqs. (5)-(8), through a source-position transformation; the measured combination gamma_LOS = gamma_od + gamma_os - gamma_ds is a definition of the parametrisation, not a consequence of the measurement. No equation in the paper reduces the reported mean |gamma_LOS| = 0.056 to a fitted input or a prior. The mock-data confirmation cited from Hogg et al. (2023) involves the same authors and the same model family, but the paper itself states the limiting condition: gamma_LOS is recoverable 'provided the lens mass model has a complexity equivalent to that with which the mock images were generated.' That is a bounded internal-consistency check, not the derivation of the current measurement. The real-data result is independently anchored by comparison with RayGalGroup N-body simulations, which provide external predictions of the expected LOS shear for each (z_d, z_s) pair, and by consistency with the separately fitted external shear values of Shajib et al. (2021). The authors also acknowledge the open question of whether the inferred shear is truly line-of-sight, concluding that 'It is the modelling of the main deflector to which attention must now be devoted.' Such a stated limitation is a correctness risk, not circularity: the claimed measurement is not equivalent by construction to its assumptions. I find no specific reduction of a prediction to an input, no fitted parameter renamed as a prediction, and no load-bearing self-citation chain that forces the result.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The LOS shear measurement is a fitted quantity, not a derivation. The central free parameters are the shear components and the mass model parameters; the Einstein radius is taken from a previous fit, the mask radii and shapelet orders are chosen by hand, and the octupole strength is fitted in the extended model. The interpretation rests on literature assumptions: the tidal approximation, the source-position transformation gauge choice, the sufficiency of the EPL profile, and the unbiasedness of the RayGalGroup expectations. No new physical entities are introduced.

free parameters (8)
  • γ_LOS^1, γ_LOS^2 (per lens) = mean |γ_LOS| = 0.056; per-lens values in Table 1
    The two LOS shear components are the target measurement, fitted by MCMC for each lens; the headline magnitude is derived from their posteriors.
  • γ_od^1, γ_od^2 (foreground shear per lens)
    Fitted in the minimal model; fixed to zero in the no-foreground-shear model. The foreground shear enters the effective potential and its post-Born correction.
  • ω_LOS (LOS rotation)
    Fitted as part of the minimal five-parameter shear model.
  • EPL slope γ_EPL and ellipticity (e1,e2) per lens
    Mass model parameters fitted jointly; the ellipticity is degenerate with foreground shear in the minimal model, so priors linking mass and light ellipticity are deliberately not used.
  • Einstein radius θ_E per lens = fixed to Shajib et al. (2021) best-fit values
    Not sampled in MCMC to save computation; uncertainty in θ_E is therefore not propagated into the shear measurement.
  • Source light parameters (Sersic + shapelet coefficients, β, n_max per lens) = n_max listed in Table 1
    Shapelet order was set by trial and error; the scale β and coefficients are fitted. These degrees of freedom absorb part of the source structure and can trade off against shear.
  • Octupole strength a4 and orientation φ4 per lens
    Added in the octupole model; recovered strengths are larger than observed 1% isophotal distortions in 45% of lenses.
  • Annular mask inner and outer radii per lens = typically 0.4 arcsec and 3.0 arcsec
    Chosen manually per lens; the sensitivity of the shear measurement to this choice is not tested.
assumptions (6)
  • domain assumption Tidal approximation: LOS perturbations are described by constant amplification matrices A_ab (Eqs 5-7), excluding non-tidal effects such as flexion and double-plane lensing.
    Used throughout Section 2 to define the minimal model; references Fleury et al. (2021).
  • domain assumption Source-position transformation: up to a linear transformation of the source, image positions are preserved (Schneider and Sluse 2014), so ψ_eff(θ)=ψ(A_od θ) represents the physical lens.
    Invoked in Section 2 to justify the minimal model's gauge choice.
  • domain assumption EPL profile is a sufficient description of the main deflector mass for unbiased shear recovery; known systematics are acknowledged.
    Section 3.2; the key premise that unmodelled mass complexity does not bias γ_LOS, acknowledged as the main open issue in Section 5.
  • domain assumption RayGalGroup N-body maps, interpolated between redshifts following Johnson et al. (2025), give an unbiased expected |γ_LOS| for each (z_d,z_s).
    Section 4.2; used to claim measured shear exceeds weak-lensing expectations, with tensions up to 7.9σ.
  • ad hoc to paper In the no-foreground-shear model, post-Born corrections to the deflector potential are degenerate enough with main-lens parameters to be absorbed.
    Section 3.3; the authors state they do not assume the post-Born corrections are physically negligible, only that fixing γ_od=0 is testable; the test then argues against this parametrisation.
  • domain assumption Uniform priors in Table 2, without mass-light alignment priors, are appropriate for LOS shear inference.
    Section 3.4; standard physical priors are deliberately omitted because foreground shear can misalign mass and light.

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Cite this review

Pith. "Pith review of Line-of-sight shear in SLACS strong lenses I: shear and mass model parametrisations." pith.science (2026). https://pith.science/paper/YCZGIDFL

@misc{pith2026250116292,
  author       = {Pith},
  title        = {Pith review of: Line-of-sight shear in SLACS strong lenses I: shear and mass model parametrisations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YCZGIDFL}},
  note         = {Machine review of arXiv:2501.16292}
}
abstract

Inhomogeneities along the line of sight in strong gravitational lensing distort the images produced, in an effect called shear. If measurable, this shear may provide independent constraints on cosmological parameters, complementary to traditional cosmic shear. We model 23 strong gravitational lenses from the Sloan Lens ACS (SLACS) catalogue with the aim of measuring the line-of-sight (LOS) shear for the first time. We use the 'minimal model' for the LOS shear, which has been shown to be theoretically safe from degeneracies with lens model parameters, a finding which has been confirmed using mock data. We use the dolphin automated modelling pipeline, which uses the lenstronomy software as a modelling engine, to model our selected lenses. Across the 23 lenses, we measure the LOS shear with a mean magnitude of $0.056 \pm 0.013$. Neglecting the post-Born correction to the potential of the main deflector due to foreground shear leads to a propagation of degeneracies in the LOS shear measurement with other lens model parameters, and the inclusion of an octupole moment in the lens mass profile does not lead to shear measurements that are in better agreement with the expectations from weak lensing.

Figures

Figures reproduced from arXiv: 2501.16292 by the authors.

Figure 1
Figure 1. — The first six lenses fit with the minimal model. From left to right, the panels show the single-band image data for each lens, our reconstruction of the image along with the reduced χ 2 of the model, the residual difference between the image and the reconstruction, the reconstructed source and the one dimensional marginalised posterior distribution of the LOS shear magnitude, |γLOS|. The shaded area is the 1σ conf… view at source ↗
Figure 2
Figure 2. — The next six lenses fit with the minimal model. The panels show the same information as in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. — The next six lenses fit with the minimal model. The panels show the same information as in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: — The final five lenses fit successfully with the minimal model. The panels show the same information as in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: — This figure shows the histograms of the |γLOS| values measured in this work (solid blue) and the external shear values measured in Shajib et al. (2021) (unfilled black). 2019; Rasera et al. 2022). The maps provide convergence and shear measurements at a given set of …
Figure 6
Figure 6. Figure 6: — This figure shows the measured value of |γLOS| and the 1σ error bars for each lens in our sample. The black dotted line shows the mean expected value of |γLOS| for that system’s lens and source redshift, computed from the RayGalGroup simulations, as described in the …
Figure 7
Figure 7. Figure 7: — This figure shows the measured value of |γLOS| with the m4 multipole included in the lens mass model. The black dotted line shows the overall mean expected value of |γLOS|, computed from the RayGalGroup simulations, as described in the main text, with the associated …
Figure 8
Figure 8. Figure 8: — This figure shows the residual difference between model and data when modelling SDSSJ1204+0358, SDSS0737+3216 and SDSSJ1531-0105 using the minimal model (left panel) and with the inclusion of an octupole (middle panel). The right-hand panel shows the 1D marginalised …
Figure 9
Figure 9. Figure 9: — The one and two-dimensional joint marginalised posterior distributions for the lens mass ellipticity, foreground shear and LOS shear in lens SDSSJ1630+4520. The posteriors recovered in the minimal model are shown in blue and those recovered in the no foreground shear…
Figure 10
Figure 10. Figure 10: — Left: |γLOS| measurements in the minimal model versus the no foreground shear model. Right: the same but restricted to show only |γLOS| < 0.1. The black solid line represents a linear ordinary least squares fit to the measurements, with the 1σ uncertainty shown by t…

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Line-of-sight shear in SLACS strong lenses II: validation tests with an extended sample

    astro-ph.CO 2025-12 conditional novelty 4.0 of 10

    Line-of-sight shear in 45 SLACS lenses is often larger than N-body expectations (mean |γ_LOS| ≈ 0.085–0.11), and adding mass octupoles or checking image properties does not remove the excess.

Reference graph

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.