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REVIEW 3 major objections 5 minor 64 references

This paper claims that the line-of-sight shear measured in 45 strong gravitational lenses is systematically larger than N-body simulations predict, and that no tested observational feature explains the excess.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-03 18:25 UTC pith:WDZPJXCI

load-bearing objection Useful extension of the LOS-shear sample to 45 lenses, but the central 'large shears survive octupole' claim is undercut because the octupole fits only succeed for low-to-moderate shear systems, not the ones driving the mean. the 3 major comments →

arxiv 2512.05050 v2 pith:WDZPJXCI submitted 2025-12-04 astro-ph.CO astro-ph.GA

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

Natalie B. Hogg , Daniel P. Johnson , Anowar J. Shajib , Julien Larena This is my paper
classification astro-ph.CO astro-ph.GA
keywords line-of-sight shearstrong gravitational lensingSLACS lenseselliptical power lawminimal LOS shear modeloctupole distortionN-body simulationsshear correlations
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The authors are trying to establish that the line-of-sight (LOS) shear inferred from strong-lens images is genuinely larger than structure-formation simulations predict. Modelling 22 additional lenses from the SLACS sample with a minimal shear parameterisation, they find a mean shear magnitude of 0.11 ± 0.024, and 12 of the 22 lenses exceed |γ_LOS| > 0.1. Adding an octupolar distortion to the lens mass does not systematically reduce the inferred shear, and tests against lens/source redshift, sky location, filter, PSF, flux, and signal-to-noise find no statistically robust observational driver. The authors conclude that the cause must lie in the lens and source model, while explicitly leaving isophotal twist and other angular complexity as open possibilities. A sympathetic reader would care because the excess, if real, changes what we expect from line-of-sight structure and how usable strong-lens shear is as a cosmological probe.

Core claim

The central claim is that the combination γ_LOS = γ_od + γ_os − γ_ds, as defined by the minimal model, is measurable in individual strong lenses and comes out with magnitudes larger than expected from N-body ray-tracing simulations, with a mean of 0.11 ± 0.024 for the 22 lenses newly modelled here. The paper reports that 12 of these 22 lenses have |γ_LOS| > 0.1, versus only 2 of 23 in the companion paper, and that including an octupole in the lens mass model changes the tension with simulation expectations in only one system (a 7σ decrease there, but the shear remains above the 5σ simulation envelope). Correlations with redshift, sky position, filter, PSF, flux, and SNR are tested; only the

What carries the argument

The minimal line-of-sight shear model, which re-parameterises the lensed source position so that the only shear contribution free of the source-position-transform degeneracy is the combination γ_LOS = γ_od + γ_os − γ_ds. The paper uses this with an elliptical power-law mass profile and a double Sérsic light profile for each lens, then repeats the fit with an octupolar ('boxy'/'disky') distortion added to the mass to test whether unmodelled angular structure is inflating the shear. The octupole test is the central mechanism for ruling out one class of mass-model complexity.

Load-bearing premise

The load-bearing premise is that the fitted |γ_LOS| is a true line-of-sight shear and not a fudge factor absorbing unmodelled angular structure in the main lens; the paper tests one such structure (an octupole) but explicitly leaves other angular complexity, such as isophotal twist, unexplored.

What would settle it

Measure the isophotal position-angle twist of the 22 newly modelled lens galaxies and re-fit each image with a mass model that includes twist as a free parameter. If the large |γ_LOS| values drop below 0.1 while the residuals remain at the noise level, the excess is a mass-model artifact; if they persist, the case for genuinely large line-of-sight shear is strengthened.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the excess is real, line-of-sight structure along these sightlines is more abundant or more massive than current N-body simulations encode, which would change predictions for strong-lens shear and for time-delay cosmography.
  • The minimal LOS shear parameterisation can be applied semi-automatically to a large fraction (45 of 50, or 90%) of selected galaxy-scale strong lenses, so the statistic is not restricted to a handful of systems.
  • Since the octupole does not explain the large shears, future lens models must either include additional angular degrees of freedom (isophotal twist, higher multipoles) or accept that the excess is a cosmological signal.
  • The absence of correlations with flux, SNR, redshift, and sky location means the excess is unlikely to be a simple observational selection effect, guiding the search toward the mass model.
  • The mean shear magnitude across 45 lenses, 0.085 ± 0.019, provides a reference value that any future model or simulation should reproduce.

Where Pith is reading between the lines

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

  • A testable extension would be to re-fit the same lenses with an isophotal-twist or higher-multipole mass model; if the large |γ_LOS| values collapse to the simulation expectation while image residuals stay at the noise level, the excess is a mass-model artifact rather than a cosmological signal.
  • If the excess survives such tests, stacking the lenses by line-of-sight galaxy counts or convergence maps from wide surveys should reveal an environmental correlation, since the minimal model's shear is tied to actual line-of-sight structures.
  • The marginal F606W-filter correlation (p = 0.042) suggests that even if the PSF comparison shows no difference, resolving power and source-lens separation may mediate how much angular freedom the shear parameter absorbs; a controlled test varying the effective resolution of mock images could settle this.
  • The paper's 90% successful-modelling rate implies that the minimal model is not the bottleneck; the bottleneck is deciding how much complexity the data justify, which bears directly on systematic errors in H0 measurements from strong lenses.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper extends the authors' previous study of line-of-sight (LOS) shear in SLACS strong lenses by modelling 27 additional systems, successfully fitting 22 with the minimal LOS-shear parameterisation of Fleury et al. (2021). Combining with Paper I, the sample grows to 45 lenses. The headline result is a mean |gamma_LOS| = 0.11 ± 0.024, with a significant fraction of lenses having |gamma_LOS| > 0.1, which the authors argue is unexpectedly large compared to N-body simulation expectations. They test whether an octupolar distortion in the deflector mass reduces the shears, finding no systematic reduction in the eight lenses for which such fits converge. They also investigate correlations with redshift, sky location, filter, PSF, flux, and signal-to-noise ratio, concluding that no observational feature robustly explains the large shears.

Significance. If correct, the result would indicate a genuine discrepancy between measured LOS shears in strong lenses and the predictions of current N-body simulations, with implications for the interpretation of external shear in strong-lens modelling and for using LOS shear as a cosmological probe. The paper is commendable for using a consistent, semi-automated forward-modelling pipeline, making data and code public, and showing posterior distributions and chi-square statistics. However, the central claim is not yet fully supported: the octupole test is only successful for a subset of lenses that excludes the most extreme shears, and the reported mean shear may be affected by the positive-definite nature of |gamma| combined with measurement noise. These issues need to be addressed before the main conclusion can be accepted.

major comments (3)
  1. [§3.1, Fig. 7, Table 1] The octupole test is only successful for 8 of the 22 lenses, and these are predominantly the low-to-moderate shear systems. The five largest measured shears—SDSSJ0008−0004 (|gamma|=0.295), SDSSJ0044+0113 (0.273), SDSSJ1134+6027 (0.183), SDSSJ1142+1001 (0.184), and SDSSJ1614+4522 (0.199)—are not included in Figure 7. The text states that the octupole inclusion 'often results in pathological problems' for these lenses. Therefore the abstract's claim that large shears persist 'even when an octupolar distortion is included in the lens mass' is not demonstrated for the very systems that drive the mean. Since the LOS shear term can absorb unmodelled angular structure, this is a load-bearing, unresolved degeneracy.
  2. [§3, mean shear magnitude] The mean |gamma_LOS| = 0.11 ± 0.024 is computed by averaging posterior means of a positive-definite quantity. For low-SNR lenses, the posterior mean of |gamma| is biased high (noise bias), and no null test (e.g., injecting zero-shear images with the same pipeline) or correction for this bias is presented. The mock tests in §3.2.2 compare PSFs only, not the zero-shear recovery distribution. Without such a test, the comparison of the observed mean to N-body expectations is not apples-to-apples, and the 'unexpectedly large' conclusion could be at least partly a measurement artifact.
  3. [Appendix Table 1 vs. §3] Table 1 lists SDSSJ1538+5817 with |gamma_LOS| = 0.042 ± 0.016 and SDSSJ2347−0005 with 0.146 ± 0.011, but the text in §3 explicitly excludes both lenses from the successful sample ('poor source reconstruction' and 'forward modelling did not produce a convincing source reconstruction'). This is an internal contradiction that affects the sample size and potentially the summary statistics. The table or the text must be corrected.
minor comments (5)
  1. [§3.2.2 and Abstract] The abstract states that 'none of these features play a statistically significant role', but the text reports a p-value of 0.042 for the filter correlation, which is significant at the 95% level. The authors interpret this as non-physical, but the wording of the abstract is too strong and should be qualified.
  2. [Fig. 7 caption] The caption says each point shows |gamma_LOS| with the m=4 multipole included, but the colour encodes Δσ. Consider also plotting the minimal-model values for direct comparison, and make the colour scale more explicit.
  3. [Eq. (7) and Eq. (10)] The sign convention for Im(gamma) in the Jacobian in Eq. (7) appears different from the convention in Eq. (10). Please check that the sign convention is consistent throughout.
  4. [Table 2] The prior ranges for gamma_od and gamma_LOS are [-0.2,0.2] and [-0.5,0.5] respectively. Since both are shear components, the asymmetry deserves a justification.
  5. [§1.3] The phrase 'final inmate in the nomenclature zoo' is informal; consider rewording for a journal audience.

Circularity Check

0 steps flagged

No circular derivation: fitted shear values are compared against an external N-body benchmark, not reconstructed from the fitted values; acknowledged internal-vs-LOS degeneracy is a robustness limitation, not a definitional reduction.

full rationale

The paper's central claim is empirical: the minimal-LOS-shear parameter gamma_LOS is fitted to each lens image, and the resulting values are compared with expectations from the RayGalGroupSims N-body simulations processed in Paper I and Johnson et al. (2025). The expected distribution is not constructed from the same fitted values, so the comparison is not circular in the definitional sense. The minimal-model formalism is derived in Eqs. (9)-(11) within the paper and originates from the externally published Fleury et al. (2021) derivation; no uniqueness theorem from the authors is invoked to exclude alternatives. The octupole test is a model comparison, not a tautology: it fits an additional m=4 multipole and examines whether the inferred shear tension decreases. The incompleteness of this test (only 8 of 22 lenses could be modelled with the octupole, and several of the highest-shear systems, e.g., SDSSJ0008-0004 at gamma=0.295, do not appear in Fig. 7) is a real evidential weakness in the abstract's claim that the excess persists 'even when an octupolar distortion is included.' However, that is a robustness gap, not a circular reduction. The paper itself flags the key degeneracy in Sec. 1.3: 'in practice this might not always be distinguishable from internal contributions,' and in Sec. 3.1 says 'Other types of angular complexity, such as isophotal twistyness, remain as avenues for future exploration.' These passages acknowledge that fitted gamma_LOS may absorb unmodelled angular structure, but they do not make the N-body comparison an identity or rename a fitted parameter as a prediction. Self-citations to Paper I and Hogg et al. (2023) provide external mock and simulation validation; they are not used to define the measured values. The score is therefore 0: the derivation chain, as presented, is self-contained against external benchmarks, with the caveat that the physical interpretation of large fitted shears remains uncertain.

Axiom & Free-Parameter Ledger

8 free parameters · 7 axioms · 0 invented entities

The analysis relies on ~8 groups of fitted model parameters plus several domain assumptions carried from prior work. No new particles, forces, or physical entities are introduced. The most consequential input is the N-body expected-shear calibration, which is external but built by the same group's pipeline.

free parameters (8)
  • γ_LOS1, γ_LOS2 (per-lens line-of-sight shear components) = posterior means per lens; |γ_LOS| values listed in Appendix Table 1
    The measured line-of-sight shear is the central fitted quantity; it is a model parameter inferred from the images, not independently derived.
  • γ_od1, γ_od2 (observer–deflector shear components) = not tabulated
    Free shear components in the minimal model; fitted and marginalised over, with priors [−0.2, 0.2].
  • ω_LOS (rotation term from lens–lens coupling) = not tabulated
    Part of the minimal LOS model (Eq. 10); fitted with prior [−0.2, 0.2].
  • γ_EPL (power-law slope of the deflector mass) = prior [1.3, 2.8]
    Fitted for each lens; the slope affects how much freedom remains in the mass model and can trade against shear.
  • e1, e2 (deflector ellipticity) = not tabulated
    Lens mass ellipticity components, priors [−0.5, 0.5]; partially degenerate with shear.
  • Lens-light parameters (Reff, e1, e2, x, y) = not tabulated
    Double Sersic lens-light model; fitted and marginalised over.
  • Source-light parameters (Reff, nS, e1, e2, x, y, shapelet coefficients) = not tabulated
    Elliptical Sersic plus Gaussian shapelets; fitted and marginalised over; source-position transforms are part of the minimal-model degeneracy structure.
  • a4, φ4 (octupole strength and orientation) = e.g. a4 = −0.047 ± 0.019 for SDSSJ2341+0000
    Fitted only when the boxy/disky octupole is included; successfully fitted for 8 of 22 lenses in this work.
axioms (7)
  • domain assumption Minimal LOS-shear reparameterisation (Eqs. 9–11) correctly captures line-of-sight effects and leaves γ_LOS free of degeneracies
    The paper assumes the Fleury et al. (2021) model maps LOS perturbations into a single effective plane with amplification matrix A_LOS; if this formalism is incomplete, the inferred γ_LOS is not equivalent to the physical line-of-sight shear.
  • standard math Reduced shear g = γ/(1−κ) can be approximated by γ
    Stated in the introduction (footnote 1): both κ and γ are small for these LOS perturbations, so g ≈ γ.
  • domain assumption The expected |γ_LOS| distribution from the RayGalGroupSims N-body simulations is the correct benchmark
    The 'unexpectedly large shear' claim is defined relative to this simulation-based expectation, which is described in Paper I and Johnson et al. (2025) rather than derived in this paper.
  • domain assumption Elliptical power-law (EPL) mass profile and Sersic light profiles are adequate descriptions of the lenses
    The whole fitting procedure uses these parametric choices; unmodelled angular complexity is the main alternative explanation for large shears.
  • domain assumption TinyTim PSF models accurately represent the HST PSFs
    PSF errors can distort the inferred shear; the paper relies on TinyTim PSFs and tests only F555W vs F606W differences.
  • domain assumption Uniform priors and MCMC convergence imply unbiased posterior estimates
    The paper uses uniform priors listed in Table 2 and removes burn-in before summarizing posteriors; no convergence diagnostics are shown in the text.
  • domain assumption Gaussian shapelets provide a sufficiently flexible source model
    Source surface brightness is modelled with shapelets; if the basis is too restrictive or too flexible, source-position transforms and shear can trade off.

pith-pipeline@v1.3.0-alltime-deepseek · 18662 in / 12176 out tokens · 122463 ms · 2026-08-03T18:25:52.045336+00:00 · methodology

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read the original abstract

Strong gravitational lensing images are subject to shape distortions due to inhomogeneities along the line of sight. The leading order shape distortion is shear, which, if measurable, will be a complementary cosmological probe to traditional cosmic shear. In Hogg et al. (2025a), we modelled 23 of the SLACS strong lenses, studying the line-of-sight (LOS) shear under a variety of shear and mass model parametrisations. In this work, we successfully model 22 of an additional 27 lenses, extending our sample of LOS shear constraints to 45 in total. We find a mean shear magnitude of $0.11\pm 0.024$, showing that a significant fraction of the lenses modelled in this work possess LOS shears with unexpectedly large magnitudes, $|\gamma_{\rm LOS}| > 0.1$, even when an octupolar distortion is included in the lens mass. We further investigate if factors such as lens and source redshift, filter and PSF, or flux and signal-to-noise ratio in the lensed arcs correlate with shear. We find that none of these features play a statistically significant role in the production of unusually large shear magnitudes.

Figures

Figures reproduced from arXiv: 2512.05050 by Anowar J. Shajib, Daniel P. Johnson, Julien Larena, Natalie B. Hogg.

Figure 1
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 t… view at source ↗
Figure 2
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_p005_2.png] view at source ↗
Figure 3
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_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: — The final four lenses fit with the minimal model. The panels show the same information as in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: — The lenses in our sample for which we consider the modelling using the baseline EPL + minimal LOS shear model to be a failure. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 |γLOS| 0 2 4 6 8 Count Paper I This work [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: — Histograms of the |γLOS| values measured from the lenses presented in Paper I (solid blue) and in this work (unfilled black). SDSSJ2343−0030 and SDSSJ2341+0000, are 0.71◦ apart. There is no significant clustering of large shear and small shear lenses in a given area of the sky. 3.2.2. Filters and PSF After detection in SDSS, the lens candidates were fol￾lowed up with HST. The photometry available to us i… view at source ↗
Figure 7
Figure 7. Figure 7: — Each point in 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 median expected value of |γLOS| from an N-body simulation, with the associated 1, 3 and 5σ uncertainties around this median given by the grey shaded bands. The measured values are coloured by the change in the tension between the minimal model and the… view at source ↗
Figure 9
Figure 9. Figure 9: — Violin plots showing the distribution of the difference between the value of |γ| recovered after fitting the mock lenses and the value input to create the mocks, split by filter. 4. CONCLUSIONS In this work, a companion to our Paper I (Hogg et al. 2025a), we modelled 27 strong gravitational lenses from the SLACS catalogue, achieving successful lens models for 22 of these systems. Added to the sample of 2… view at source ↗
Figure 8
Figure 8. Figure 8: — The point spread functions (PSFs) associated with the two HST filters in which the lenses studied in this work were observed. The colour bar indicates the flux in a given pixel of the PSF kernel, normalised so the maximum flux is one. F555W F606W Filter −0.04 −0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 |γfit| − | γtrue| [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗

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