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arxiv: 2604.24908 · v1 · submitted 2026-04-27 · 🌌 astro-ph.CO · astro-ph.GA

TDCOSMO XXVI: Uniform lens modeling of eight doubly imaged quasars

Ryan Brady , Xiang-Yu Huang , Simon Birrer , Anowar J. Shajib , Nafis Sadik Nihal , Cameron Lemon , Martin Millon , Veronica Motta
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Dominique Sluse Frederic Courbin
This is my paper

Pith reviewed 2026-05-08 01:21 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords gravitational lensingtime-delay cosmographydoubly imaged quasarslens mass modelingFermat potentialsurface brightnessHubble Space TelescopeHubble constant
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The pith

Surface brightness of lensed host arcs sets the precision of mass models in doubly imaged quasars.

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

This paper applies a uniform Lenstronomy pipeline to eight doubly imaged quasars observed with the Hubble Space Telescope. The analysis reconstructs each system's lensing geometry and mass profile, then quantifies the uncertainty in the Fermat potential that enters time-delay cosmography. It finds a strong correlation showing that brighter extended host-galaxy arcs produce tighter constraints on the lens mass, while fainter arcs leave the models underconstrained. A separate conjugate-point test that ignores the arcs entirely reproduces broader posteriors and confirms the same brightness trend. The result identifies arc surface brightness as the dominant factor controlling model quality in doubles, which are far more numerous than quadruples.

Core claim

Uniform modeling of the eight systems yields Einstein radii consistent with literature values at 1.5 sigma and image separations matching Gaia DR2 to 3.6 mas rms. Full image reconstruction and a conjugate-point analysis that uses only the quasar positions demonstrate that Fermat-potential precision improves directly with the surface brightness of the spatially extended host arcs. An anti-correlation between mass-parameter hypervolume and arc magnitude further isolates arc brightness as the primary driver of how well the lens mass profile can be recovered in doubly imaged systems.

What carries the argument

Correlation between Fermat potential uncertainty and host-arc surface brightness, measured through full extended-image modeling versus a conjugate-point analysis restricted to quasar positions.

If this is right

  • Doubly imaged systems can now be ranked for cosmographic usefulness by a directly observable quantity: arc surface brightness.
  • The larger population of doubles can be incorporated into hierarchical H0 analyses once arc brightness is used to select or weight targets.
  • Uniform pipelines become feasible for the thousands of new lenses expected from LSST, Roman, and Euclid.
  • Model precision in doubles is shown to be limited by extended emission rather than by the mere number of point images.

Where Pith is reading between the lines

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

  • Survey strategies could prioritize follow-up of doubles that already show bright arcs in discovery imaging to maximize cosmographic return.
  • The same brightness trend may allow statistical marginalization over lens-model uncertainty when building large H0 samples.
  • Applying the conjugate-point test to triples or other configurations could reveal whether arc brightness remains the dominant constraint across image multiplicities.

Load-bearing premise

The tailored Lenstronomy pipeline accurately recovers the true lensing geometry and mass profiles of doubles without large biases from data heterogeneity or unmodeled systematics.

What would settle it

Finding no correlation between measured arc surface brightness and Fermat-potential uncertainty when the same eight systems are re-modeled with an independent code or additional high-resolution data.

read the original abstract

We present the first uniform gravitational lens modeling analysis of eight doubly imaged quasars from multi-band observations with the Hubble Space Telescope. Previous time-delay cosmography analyses by the TDCOSMO Collaboration have primarily relied on quadruply imaged quasars, while doubly imaged systems, despite being more abundant, remain underutilized due to their fewer geometric constraints. Using an open-source $\texttt{Lenstronomy}$ framework, we reconstruct the lensing systems with a pipeline tailored for doubles. Comparing our results to the literature, the modeled Einstein radii agree at an average of 1.5$\sigma$, which is expected given data and modeling heterogeneity, while modeled image separations differ from Gaia DR2 measurements with an r.m.s of only 3.6 mas. We find a strong correlation between Fermat potential precision and the surface brightness of the spatially extended host arcs, establishing that arc surface brightness is the primary driver of mass model precision in doubly imaged systems. To further quantify the information contributed by the lensed arcs, we performed a conjugate point analysis that uses only the quasar image positions to constrain the lens mass profiles. The resulting posteriors are substantially broader than those from full image modeling, and a strong anti-correlation between mass parameter hypervolume and arc magnitude additionally confirms that arc brightness determines the degree to which the lens mass profile can be constrained in doubles. A hierarchical cosmographic analysis incorporating time-delay measurements and stellar kinematics to infer $\text{H}_0$ will be presented in a subsequent publication. The uniform pipeline and arc surface brightness trends established here will significantly accelerate the construction of time-delay cosmography samples from the large lens populations expected from LSST, Roman, and Euclid.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents the first uniform gravitational lens modeling of eight doubly imaged quasars from HST multi-band data using a tailored open-source Lenstronomy pipeline. It reports 1.5σ average agreement on Einstein radii with literature values, 3.6 mas rms difference on image separations versus Gaia DR2, a strong correlation between Fermat potential precision and the surface brightness of the lensed host arcs, and an anti-correlation with mass-parameter hypervolume. A conjugate-point analysis using only quasar image positions yields substantially broader posteriors, confirming that the arcs provide the dominant constraints on the lens mass profiles. The work is positioned as preparation for a follow-up hierarchical cosmographic analysis to constrain H0.

Significance. If the reported correlation holds, the result is significant for time-delay cosmography because doubly imaged systems are far more abundant than quads yet have been underutilized due to fewer constraints. Demonstrating that arc surface brightness is the primary driver of Fermat-potential precision, backed by internal cross-checks (conjugate-point posteriors and hypervolume anti-correlation) and external consistency (Einstein radii and image positions), supplies a practical selection criterion for the large samples expected from LSST, Roman, and Euclid. The uniform, open-source pipeline is a clear strength that improves reproducibility across the TDCOSMO series.

major comments (2)
  1. [§4] §4 (correlation analysis): The central claim that arc surface brightness is the 'primary driver' of mass-model precision rests on a reported 'strong correlation,' yet no quantitative statistic (Spearman coefficient, Pearson r with uncertainty, or p-value) or explicit fit to the eight data points is provided; without this, it is impossible to judge whether the trend is statistically robust or dominated by outliers.
  2. [Conjugate-point analysis] Conjugate-point analysis section: The statement that posteriors are 'substantially broader' when only quasar positions are used is presented without a quantitative metric (e.g., ratio of credible-interval widths or hypervolume ratio) or the exact number and selection of conjugate points; this leaves the confirmation that arcs dominate the constraints qualitative rather than rigorous.
minor comments (2)
  1. [Abstract] Abstract: The phrase 'a subsequent publication' for the H0 analysis should include the planned paper number or title to aid readers following the TDCOSMO series.
  2. [Figure captions] Figure captions (e.g., those showing posterior contours): Captions should explicitly state the number of MCMC samples, burn-in length, and whether the displayed contours are 68 % and 95 % credible regions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation for minor revision. We address each major comment below and will incorporate the suggested quantitative improvements.

read point-by-point responses

  1. Referee: [§4] §4 (correlation analysis): The central claim that arc surface brightness is the 'primary driver' of mass-model precision rests on a reported 'strong correlation,' yet no quantitative statistic (Spearman coefficient, Pearson r with uncertainty, or p-value) or explicit fit to the eight data points is provided; without this, it is impossible to judge whether the trend is statistically robust or dominated by outliers.

    Authors: We agree that quantitative statistics are needed to substantiate the correlation claim. In the revised manuscript we will report the Spearman rank correlation coefficient with its p-value for Fermat potential precision versus arc surface brightness. We will also add a linear fit to the eight data points, including uncertainties on the slope and intercept, to allow evaluation of robustness and outlier influence. These results will be included in §4. revision: yes

  2. Referee: [Conjugate-point analysis] Conjugate-point analysis section: The statement that posteriors are 'substantially broader' when only quasar positions are used is presented without a quantitative metric (e.g., ratio of credible-interval widths or hypervolume ratio) or the exact number and selection of conjugate points; this leaves the confirmation that arcs dominate the constraints qualitative rather than rigorous.

    Authors: We agree that quantitative metrics would make this section more rigorous. In the revision we will state the exact number of conjugate points (the four quasar image positions) and their selection criteria. We will report the ratios of 68% credible-interval widths for key parameters (Einstein radius, power-law slope) between the full and conjugate-point-only models, and the posterior hypervolume ratio where relevant. These details will be added to the conjugate-point analysis section. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper performs uniform Lenstronomy modeling on HST imaging of eight doubly-imaged quasars and reports an empirical correlation between Fermat-potential precision and host-arc surface brightness. This correlation is obtained directly from the posterior widths of the full-image fits and is cross-checked by a conjugate-point analysis that deliberately omits the arcs and recovers substantially broader posteriors. External validation is provided by Gaia DR2 image separations (3.6 mas rms) and literature Einstein radii (1.5σ average agreement). No self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations appear in the derivation chain; the central claim rests on data-driven posteriors and independent external benchmarks rather than on any reduction to the paper's own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Central claims rest on standard gravitational lensing assumptions and the validity of the Lenstronomy implementation for double systems; no new entities introduced.

free parameters (1)
  • lens mass profile parameters
    Standard parameters (e.g., Einstein radius, ellipticity) fitted to image data in each system.
axioms (2)
  • standard math Standard general-relativity light deflection applies to these systems
    Foundation of all lens modeling in the pipeline.
  • domain assumption Chosen mass profiles adequately describe the foreground galaxies
    Implicit in the uniform pipeline for doubles.

pith-pipeline@v0.9.0 · 5646 in / 1302 out tokens · 44527 ms · 2026-05-08T01:21:29.635477+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

14 extracted references · 1 canonical work pages

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    Dashed blue lines at 30 degrees and 60 degrees delineate aligned, intermediate, and anti-aligned regimes

    Misalignment angle between the best-fit mass position angleϕ mass and external shear position angleϕ ext as a function of shear magnitudeγ ext, color-coded by mass axis ratioq mass. Dashed blue lines at 30 degrees and 60 degrees delineate aligned, intermediate, and anti-aligned regimes. Error bars reflect 1σposterior uncertainties from the full image mode...

    2024

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    J0602-5006.No previous works have performed lens modeling on this system

    ′′28, which may contribute to the observed difference inθ E. J0602-5006.No previous works have performed lens modeling on this system. Through ourLenstronomymulti- band HST modeling, we foundθ E = 0.′′914+0.014 −0.019, ∆θ= 1.′′826,q mass = 0.59+0.06 −0.05, andγ ext = 0.093+0.023 −0.029. J0806+2006.Our measured image separation, ∆θ=

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    (2008) from data obtained at the ESO Paranal Observatory and 84 mas larger than that of Inada et al

    ′′484, is 16 mas smaller than the value reported by Sluse et al. (2008) from data obtained at the ESO Paranal Observatory and 84 mas larger than that of Inada et al. (2006) with photometric data taken at the University of Hawaii 2.2m telescope and the W. M. Keck Observatory’s Keck I. Our measured value ofθ E is consistent within 1.2σwith the result of Ina...

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    (2016) may be consistent with solutions that move along this degeneracy

    The combination of high shear and a relatively round mass profile inferred by Rusu et al. (2016) may be consistent with solutions that move along this degeneracy. Our multi-band HST modeling, with improved resolution of the extended arcs, more effectively separates these contributions, yielding a lower shear and a correspondingly more elliptical mass dist...

    2016

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    (2014) and is in precise agreement with the value presented in Rusu et al

    ′′008, which differs by 19 mas from the value reported in Inada et al. (2014) and is in precise agreement with the value presented in Rusu et al. (2016). Additionally, our determination ofθ E is consistent at the 0.1σlevel with the value determined by Inada et al. (2014) via SIE mass modeling with photometric data from the University of Hawaii 2.2m telesc...

    2014

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    (2017) by 80 mas

    ′′82, which differs from the value measured in Ostrovski et al. (2017) by 80 mas. This is expected, as the aforementioned observations were obtained from the ground-based Dark Energy Survey, VISTA Hemisphere Survey, and WISE photometry. Given that our image separation agrees with Gaia DR2 at the 1 mas level, we do not consider this discrepancy to be cause...

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    (2017) likely reflects residual trade-offs between these components

    We infer a modestγ ext = 0.04±0.004, and the difference with Ostrovski et al. (2017) likely reflects residual trade-offs between these components. In their case, the absence of shear may lead to a more elliptical mass distribution, while our modeling supports a correspondingly rounder mass profile. In summary, we find no evidence for systematic discrepanc...

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    The associated uncertainties are statistical and were calculated using the 84th and 16th percentiles

    Best-fit source light model parameters. The associated uncertainties are statistical and were calculated using the 84th and 16th percentiles. We adopted a fiducial flat cosmology of H 0 = 70 km s −1 Mpc−1 and Ωm = 0.3 to calculate the angular diameter distance in the conversion ofR eff from angular size to physical size. The position angleϕ source is meas...

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    The degree of tightening varies across the sample in a manner that tracks arc brightness

    In every system, the full image modeling posteriors (green) appear as constrained regions fully within the much broader conjugate point distributions (blue), confirming that the arc surface brightness information systematically tightens the mass parameter constraints. The degree of tightening varies across the sample in a manner that tracks arc brightness...

    2006

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    Six of eight systems exhibit low S´ ersic indices, which align with disk-like morphologies commonly observed for lensed quasar hosts (Gabor et al. 2009). However, previous lens modeling studies have shown that S´ ersic indices can be biased toward lower values due to regularization and limited signal-to-noise, which tend to smooth centrally concentrated l...

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    In order to convert our modeled angular source size to physical size, we adopted a fiducial flat cosmology with H 0 = 70 km s −1 Mpc−1 and Ωm = 0.3

    The low-n S´ ersicmajority of our sample thus aligns with the disk-dominated character of AGN hosts at comparable redshifts. In order to convert our modeled angular source size to physical size, we adopted a fiducial flat cosmology with H 0 = 70 km s −1 Mpc−1 and Ωm = 0.3. Five of eight systems fall between 2 kpc< R eff <4 kpc, consistent with the expecta...

    2019

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    Contours reflect the 1- and 2σcredible regions, and the quoted parameter values correspond to the conjugate point posteriors

    Overlayed posterior probability distributions for the conjugate point model (blue) and the full image model (green) for the systems J0407-5006 (top left), J0602-4335 (top right), J0806+2006 (lower left), and J1001+5027 (lower right). Contours reflect the 1- and 2σcredible regions, and the quoted parameter values correspond to the conjugate point posterior...

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    At each dither position, both short and long exposures were taken to capture the large dynamic range between the bright AGN and its much fainter host galaxy

    HST GO-17199 (PI: Lemon) WFC3 observation details for each system presented in this study. At each dither position, both short and long exposures were taken to capture the large dynamic range between the bright AGN and its much fainter host galaxy. The Exposure Time therefore reflects the temporal combination of individual short and long exposure times. S...

    2024