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Three quadruply lensed quasars observed with HST and JWST are compact subarcsecond lenses whose galaxies are likely early-type systems at redshifts 0.4 to 1.5.

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2026-08-02 22:21 UTC pith:66EM2WPC

load-bearing objection Useful new measurements of three quads, but the claim that they occupy an unexplored high-z/low-theta_E corner is only secure for one of the three and depends on template-based photometric redshifts. the 3 major comments →

arxiv 2602.16995 v2 pith:66EM2WPC submitted 2026-02-19 astro-ph.GA

Varstrometry for Off-nucleus and Dual Subkiloparsec AGN (VODKA): Three Quadruply Lensed Quasars at Cosmic Noon in HST and JWST

Mingrui Liu , Yu-Ching Chen , Nadia L. Zakamska , Xin Liu , Yue Shen , Xuheng Ding , Arran Gross , Hsiang-Chih Hwang
show 2 more authors
Yuzo Ishikawa Kedar A. Phadke
This is my paper
classification astro-ph.GA
keywords quadruply lensed quasarsstrong gravitational lensingearly-type galaxiesEinstein radiuslens redshiftSersic profileJWST NIRCamsubarcsecond imaging
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.

This paper reports detailed imaging models of three quadruply lensed quasars at source redshifts 2.55, 2.98, and 1.50, using HST for one system and JWST/NIRCam for the other two. From fits assuming a singular isothermal ellipsoid mass distribution, the authors measure Einstein radii of 0.44, 0.58, and 0.49 arcseconds, all below one arcsecond. Since no spectroscopic lens redshifts exist, they constrain the lenses photometrically by comparing enclosed mass-to-light ratios and synthetic colors from galaxy templates, obtaining redshift ranges 0.5–1.2, 1.0–1.5, and 0.4–0.9. They conclude that all three lenses are likely early-type galaxies with Sersic indices near 4 and effective radii of a few kiloparsecs. The significance is that these systems occupy an under-explored corner of the quad-lens population — small Einstein radii combined with relatively high lens redshifts — which upcoming high-resolution surveys will target.

Core claim

The central discovery is that the three quads J2218-3322, J0803+3908, and J0813+2545 constitute a population of single-galaxy strong lenses with unusually compact Einstein radii (0.44, 0.58, and 0.49 arcseconds) and lens redshifts between 0.4 and 1.5, as inferred from photometric SED modeling. Using a singular isothermal ellipsoid mass model, the authors convert the measured Einstein radii into enclosed masses and, using ten galaxy spectral templates, determine the redshifts at which the enclosed mass-to-light ratio and the template colors are simultaneously plausible. The derived lens properties — Sersic index near 4, effective radius of 1.5–3.5 kpc, and consistency with the mass-size plane

What carries the argument

The argument is carried by the Einstein radius: for a singular isothermal ellipsoid mass profile — a 3D density falling as r^-2 with elliptical symmetry — the measured Einstein radius fixes the enclosed total mass via M_Ein = (c^2/4G)(D_L D_S/D_LS) theta_E^2. Because the angular diameter distances D_L, D_S, and D_LS all depend on lens redshift, the same measured theta_E gives a redshift-dependent mass. The authors combine this with the lens's fitted Sersic light profile to obtain an enclosed mass-to-light ratio as a function of redshift, and compare synthetic colors from ten galaxy spectral templates (elliptical, spiral, starburst) with the observed lens colors. The reported lens redshift ra

Load-bearing premise

The load-bearing assumption is that each lens galaxy's spectrum is well described by one of the ten adopted galaxy templates and that known dynamical mass-to-light ratios measured within about one effective radius apply to the ~1–3.5 kpc Einstein-radius apertures; a different template set or mass-to-light prior would shift the redshift ranges and could change the early-type classification.

What would settle it

A single spectroscopic redshift for any of the three lens galaxies — for example, measuring J2218-3322's lens redshift with JWST/NIRSpec and finding it outside 0.5–1.2 — would directly falsify the photometric constraints; likewise, a stellar velocity dispersion measurement yielding a mass-to-light ratio incompatible with an old, passively evolving stellar population would undercut the early-type classification.

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

If this is right

  • If these lenses are indeed early-type galaxies, they extend the known galaxy-scale strong-lens population to smaller Einstein radii and higher lens redshifts, testing whether the roughly isothermal density profile holds for compact massive galaxies at z ≈ 0.5–1.5.
  • The measured enclosed masses (on the order of one to ten times 10^10 – 10^11 solar masses, depending on template and redshift) within 1–3.5 kpc can be combined with future stellar kinematics to constrain dark matter fractions in these galaxies.
  • The demonstration that photometric SED methods can constrain lens redshifts for subarcsecond quads will help pre-screen the thousands of small-separation lenses expected from upcoming high-resolution surveys.
  • The flagged PSF mismatches and flux-ratio anomalies in the JWST data imply that accurate PSF subtraction is a prerequisite for using such quads in dark matter substructure studies or time-delay cosmography.
  • The three lenses being early-type supports the selection-effect picture that compact, massive old galaxies dominate strong-lens production even at intermediate redshifts.

Where Pith is reading between the lines

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

  • If the photometric redshift ranges are approximately correct, these systems could be valuable for time-delay cosmography; their small Einstein radii correspond to short time delays (days to weeks), which reduce the influence of line-of-sight structure but require rapid cadence monitoring.
  • The flux-ratio anomalies (for example, in J2218-3322 the predicted brightest image is observed as the dimmest) hint that small-separation quads at higher lens redshift may be especially sensitive to dark matter substructure or microlensing; a systematic study of flux ratios across this new quadrant could probe subhalo abundance at z ~ 1.
  • The three lenses span a wide range in luminosity and color (J0813+2545 is roughly two magnitudes brighter than J0803+3908), suggesting that the early-type classification covers diverse formation histories; spectroscopy could reveal recent mergers or dust differences.
  • Because the lens galaxies are compact and at intermediate redshift, they may strongly magnify the background quasars; JWST observations of the quasar host galaxies, which the paper notes may be offset from the quasar, could test recoiling black hole scenarios.

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 / 4 minor

Summary. The paper presents HST/WFC3 and JWST/NIRCam imaging of three quadruply lensed quasars (J2218-3322, J0803+3908, J0813+2545). Using Lenstronomy with a singular isothermal ellipsoid mass profile and an elliptical Sérsic light profile, the authors reconstruct the lens geometry and report Einstein radii of 0.44", 0.58", and 0.49". Since no spectroscopic lens redshifts are available, they use template SED fits, mass-to-light ratios, and colors to constrain the lens redshifts to 0.5<z<1.2, 1.0<z<1.5, and 0.4<z<0.9, respectively. They classify the lenses as likely early-type galaxies based on n_Sérsic~4 and R_e~1.5–3.5 kpc, and argue that these objects occupy a previously unexplored low-Einstein-radius, high-lens-redshift quadrant of the known quad-lens population.

Significance. If the lens-redshift and structural classifications are secure, these three quads are valuable additions to the small-separation lens population and natural targets for Euclid/Roman and JWST follow-up. The paper has several strengths: it uses public HST/JWST data, provides a useful compilation of known quadruply lensed quasars with lens redshifts (Appendix), openly discusses PSF mismatch and model degeneracy, and compares Lenstronomy results with an independent analytical lens model. However, the headline population claim rests on photometric redshifts and on Sérsic indices derived from fits with large PSF residuals; these pillars need strengthening or the claims need to be softened.

major comments (3)
  1. [§4.2, Figs. 7–9, Section 5.4] The lens-redshift intervals are the main support for the claim that these lenses occupy a low-θ_E, high-z_L quadrant. The method selects, for each of ten SWIRE templates, redshifts where (i) M_Ein/L_B from Eq. (3) falls inside literature dynamical M/L boxes measured within ~1 R_e and (ii) one model color overlaps the observed two-filter color. This is a thresholded envelope over templates with no stated likelihood or template ranking, and the boxes are broad. A different SED library or M/L prior could plausibly shift the ranges by several tenths in z. Only J0803+3908 has a lower bound clearly above the known quad-lens mean z≈0.59; the ranges for J2218-3322 and J0813+2545 overlap the bulk of the known population. Please quantify the dependence on template choice and M/L priors, or soften the 'high-redshift quadrant' conclusion accordingly.
  2. [Table 1; Figs. 5–6; §5.1] The two JWST fits have χ²_ν=3.87 and 4.56 and show ≥6σ PSF residuals around each lensed image. The derived n_Sérsic and R_e therefore carry systematic errors not captured by the quoted uncertainties. In particular, for J0813+2545 the best-fit n=3.37^{+0.18}_{-0.09} excludes n=4, so the statement in §5.1 that all three lenses are consistent with a de Vaucouleurs n=4 profile is not supported by Table 1. The alternative Witt/Wynne model (§4.3) gives structural parameters inconsistent with Lenstronomy, which is additional evidence that the light-profile parameters should not be used as secure early-type classifications. Please re-fit with better PSF characterization or explicitly report these values as tentative and remove them from the classification argument.
  3. [§5.1, §5.4, Conclusion] The early-type classification and the 'upper end of lens redshift' assertion are overstated for the sample as a whole. The JWST lenses have bluer colors than typical early-types (§5.1), the Sérsic indices come from poor fits, and the photometric redshifts of J2218-3322 and J0813-2545 are consistent with the bulk of the known population. The paper should present the classification and population placement as preliminary, with only J0803+3908 securely in the high-redshift tail, unless independent data (spectroscopic lens redshifts or redder photometry) are obtained.
minor comments (4)
  1. [Abstract] The abstract contains a LaTeX corruption of 'Sérsic' ('S\A\c{opyright}rsic'); the rendered text should be corrected.
  2. [Table 1] The uncertainties for θ_E, lens centroid offsets, and image offsets are all printed as ±0.00, which is uninformative. Please report these quantities with a meaningful number of significant digits.
  3. [§3.1] Eq. (1) uses the symbol P for surface mass density, which is typically denoted Σ to avoid confusion with pressure; please adopt standard notation.
  4. [§4.2] The M*_B(z) relation from Gabasch et al. (2004) is shown as a reference line in Figs. 7–9, but the text does not specify how it is used. It should be stated that this is illustrative, not a constraint.

Circularity Check

0 steps flagged

No significant circularity: the lens redshift ranges are photometric, template- and M/L-prior-dependent estimates, but they are not defined to equal the population claim and the central result is an observational characterization.

full rationale

The paper's central output is an observational characterization: it fits SIE+Sersic models to HST/JWST images of three known quads (theta_E, R_e, n), derives photometric lens redshift ranges by requiring the enclosed mass-to-light ratio M_Ein/L_B(z_L) from Eq. (3) and SWIRE-template colors to fall in literature ranges, and compares the resulting systems with a catalog of known quads. No step reduces to its own inputs by construction. In particular, the lens redshift intervals are not defined to equal the population claim; they are produced by an independent two-filter SED/M-L threshold and could in principle have excluded the 'high-z, small-theta_E' quadrant. The early-type classification is an interpretation of fitted Sersic indices and R_e, not a fitted parameter relabeled as a prediction. Self-citations (Chen et al. 2022, 2025; Gross et al. 2025; VODKA papers) are contextual: they provide target identification and one spectroscopic source redshift, and the source redshift is an externally falsifiable measurement, not the result being derived. The paper explicitly discloses limitations: no spectroscopic lens redshifts, chi2_nu = 3.87/4.56 PSF residuals, and inconsistency between Lenstronomy and the Witt/Wynne model. Those are robustness/correctness concerns, not circularity. The photometric redshift ranges are assumption-dependent (template library, M/L priors measured within 1 R_e), but that is model dependence inherent to any photometric estimate, not a self-justifying derivation. Score 0.

Axiom & Free-Parameter Ledger

5 free parameters · 7 axioms · 0 invented entities

All listed free parameters are fitted to the imaging data; the redshift constraints additionally rely on template SEDs and M/L priors from the literature. No new physical entities are introduced.

free parameters (5)
  • Einstein radius theta_E = 0.44, 0.58, 0.49 arcsec
    Fitted per system with Lenstronomy SIE model; central to the claim that these are compact subarcsecond lenses.
  • Sersic index n_Sersic = 4.24, 4.10, 3.37
    Fitted light-profile parameter; drives the early-type classification via n~4.
  • Effective radius R_e = 0.30, 0.35, 0.45 arcsec
    Fitted light-profile parameter; converted to physical kpc using the photometric redshift ranges.
  • Axis ratio q and position angle phi = q=0.61,0.77,0.91; phi=42.61,-22.54,13.28 deg
    Fitted geometry parameters; the paper notes these are the least robust, with run-to-run variability exceeding reported uncertainties.
  • Lens and image centroid offsets = Delta x/y values in Table 1
    Fitted positions used for the lensing geometry and for comparison against the alternative Witt/Wynne model.
axioms (7)
  • domain assumption Singular isothermal ellipsoid mass profile with gamma=2 describes the total mass distribution of each lens galaxy.
    Invoked in Eq. 1 and Section 3.1; the fits and Einstein radii depend on this profile choice.
  • domain assumption The lens and source light distributions follow elliptical/spherical Sersic profiles.
    Adopted in Section 3.2; the recovered n_Sersic and R_e values depend on this parametric form.
  • domain assumption The PSF extracted from a field star (or archival WFC3 star) accurately represents the target PSF.
    Used in Section 3.3; the paper itself attributes the large JWST residuals to this assumption being imperfect.
  • domain assumption The SWIRE SED templates and literature mass-to-light ratio priors are representative of the lens galaxies at z~0.4-1.5.
    Used in Section 4.2 to convert fitted fluxes and masses into redshift constraints; different templates or M/L priors would change the quoted ranges.
  • domain assumption Flat LambdaCDM cosmology with Omega_Lambda=0.7, Omega_M=0.3, H0=70 km/s/Mpc.
    Adopted in Section 1; used to compute angular diameter distances and physical sizes.
  • domain assumption External shear and line-of-sight perturbers are negligible for these systems.
    Stated in Section 3.1 after testing a shear term; the reported parameters are from shear-free fits.
  • standard math Standard gravitational lens equations (deflection, convergence, Einstein radius formula) are valid.
    Used throughout Sections 3 and 4.2; these are well-established results in the lensing literature.

pith-pipeline@v1.3.0-alltime-deepseek · 26595 in / 9471 out tokens · 92531 ms · 2026-08-02T22:21:20.164523+00:00 · methodology

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read the original abstract

We present results from imaging observations of three quadruply lensed quasars by Hubble Space Telescope (HST) and James Webb Space Telescope (JWST) at redshifts $z = 2.550$, 2.975, and 1.500. We model our targets assuming a singular isothermal ellipsoid mass profile and an elliptical S\~A\c{opyright}rsic profile for the lensing galaxies, and reconstruct the geometric configuration of each system with measured Einstein radii of 0.44$'$, 0.58$'$, and 0.49$'$. While no spectroscopic measurements are available for the lenses, we constrain the redshift of each lens to $0.5 < z < 1.2$, $1.0 < z < 1.5$, and $0.4 < z < 0.9$. For all three lenses, the best-fit light model yield a typical de Vaucouleurs $n_{\rm S\acute{e}rsic} \sim 4$ profile and an effective radius $R_e$ around $\sim 1.5 - 3.5$ kpc. We accordingly classify the three lenses as early-type galaxies at an intermediate to high redshift, a common type for strong lensing galaxies. Compared to other known quadruple lenses, the lensing galaxies in this work are at the lower end of the distribution of Einstein radii and upper end of the distribution of the lens redshifts. They represent an interesting quadrant of subarcsecond-separation lenses in the population of single-galaxy strong lensing which have been largely unexplored yet and will be great targets of interest in upcoming high-resolution lensing surveys.

Figures

Figures reproduced from arXiv: 2602.16995 by Arran Gross, Hsiang-Chih Hwang, Kedar A. Phadke, Mingrui Liu, Nadia L. Zakamska, Xin Liu, Xuheng Ding, Yu-Ching Chen, Yue Shen, Yuzo Ishikawa.

Figure 1
Figure 1. Figure 1: Images of J2218-3322 in the HST WFC3 F475W and F814W band. often combined with stellar kinematics and photome￾try, probes mass structures of lensing galaxies, capable of decomposing them into stellar and dark matter con￾stituents (Dutton & Treu 2014; Cappellari et al. 2015). It provides unique constraints on the mass distribu￾tion of galaxies at intermediate to high redshifts (Koop￾mans et al. 2006; Shajib… view at source ↗
Figure 2
Figure 2. Figure 2: Images of J0803+3908 in the JWST NIRCam F115W, F200W, F277W, and F356W band [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Images of J0813+2545 in the JWST NIRCam F115W, F200W, F277W, and F356W band. Voids in the two long filters are saturated pixels blanked out during data reduction. Cycle 2 program GO-4204 (PI: Chen) to investi￾gate small-separation dual quasars and lensed quasars. J0803+3908 is a confirmed lensed quasar in Gaia DR2 found by the dedicated survey for gravitationally lensed quasars in the Gaia catalog first co… view at source ↗
Figure 4
Figure 4. Figure 4: Best-fit models for J2218-3322 with Lenstronomy in the F814W band. Each panel from left to right presents the observed image, the reconstructed image, the normalized residual map, and the magnification map. Parameter J2218-3322 J0803+3908 J0813+2545 θE ( ′′) 0.44+0.00 −0.00 0.58+0.00 −0.00 0.49+0.00 −0.00 Re ( ′′) 0.30+0.02 −0.02 0.35+0.07 −0.03 0.45+0.01 −0.01 nS´ersic 4.24+0.30 −0.18 4.10+0.08 −0.12 3.37… view at source ↗
Figure 5
Figure 5. Figure 5: Best-fit models for J0803+3908 with Lenstronomy in the F200W band. Panels are arranged in the same convention as in [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Best-fit models for J0813+2545 with Lenstronomy in the F200W band. Panels are arranged in the same convention as in [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Photometry analysis of J2218-3322’s lens. Left to right: rest-frame B-band luminosity (in AB mag), B-band mass-to￾light ratio, and WFC3 [F475W - F814W] color. Black dotted line lays out B-band characteristic luminosity of early-type galaxies at intermediate redshifts reproduced from Gabasch et al. (2004). Shaded regions near each curve indicates the relative size of associated uncertainty. Vertical dotted … view at source ↗
Figure 8
Figure 8. Figure 8: Photometry analysis of J0803+3908’s lens. Panels are arranged in the same convention as in [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Photometry analysis of J0813+2545’s lens. Panels are arranged in the same convention as in [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Fitting result for the three lensing systems in this work with the alternative model. Blue dots represent the lensed quasar images. Cyan crosses represent the fitted source position. Purple stars represent the fitted position of the center of the lensing potential. report the constrained redshift range for each lens to be: J2218-3322: 0.5 < z < 1.2; J0803+3908: 1.0 < z < 1.5; J0813+2545: 0.4 < z < 0.9. Im… view at source ↗
Figure 11
Figure 11. Figure 11: Lens redshifts and Einstein radii θE of lensing galaxies of known quadruply lensed quasars. Previously discovered objects are plotted with dots and squares. The three targets in this work are plotted with barred colored horizontal lines. See Appendix for a complete list of objects shown and corresponding reference. seem to often have bottom-heavy initial mass functions dominated by low-mass stars (Conroy … view at source ↗

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