Mind the Information Gap: Unveiling Detailed Morphologies of z 0.5-1.0 Galaxies with SLACS Strong Lenses and Data-Driven Analysis

TL;DR

This work addresses the challenge of accurately modeling strong gravitational lensing by introducing data-driven priors, learned via score-based diffusion, into a Bayesian, pixellated framework that jointly infers lens mass, lens light, and background source while marginalizing PSF uncertainties. Applied to 30 SLACS lenses, the method achieves high-resolution reconstructions and produces posterior samples for all major components, with background sources resolved to ~200 pc at $z \in [0.5,1.0]$. Comparisons with prior lens-modeling studies show reduced residuals and highlight how prior choices influence inferred mass parameters, underscoring the value of flexible, data-driven priors over traditional parametric forms. The approach paves the way for robust, high-fidelity strong-lensing analyses in future surveys (e.g., LSST, Euclid) by enabling principled uncertainty quantification and mitigating biases from conventional priors.

Abstract

We present new state-of-the-art lens models for strong gravitational lensing systems from the Sloan Lens ACS (SLACS) survey, developed within a Bayesian framework that employs high-dimensional (pixellated), data-driven priors for the background source, foreground lens light, and point-spread function (PSF). Unlike conventional methods, our approach delivers high-resolution reconstructions of all major physical components of the lensing system and substantially reduces model-data residuals compared to previous work. For the majority of 30 lensing systems analyzed, we also provide posterior samples capturing the full uncertainty of each physical model parameter. The reconstructions of the background sources reveal high significance morphological structures as small as 200 parsecs in galaxies at redshifts of z 0.5-1.0, demonstrating the power of strong lensing and the analysis method to be used as a cosmic telescope to study the high redshift universe. This study marks the first application of data-driven generative priors to modeling real strong-lensing data and establishes a new benchmark for strong lensing precision modeling in the era of large-scale imaging surveys.

Figures (37)

• Figure 1: Lens model of SDSSJ1430+4105. From top to bottom: the four dithered FLT frame data cutouts (log-scaled) with the applied data-quality DQ mask; the residuals between the data and the lens model normalized by the pixel-wise likelihood standard deviation, $\sigma = \texttt{ERR}$, with colormap centered and clipped at $\pm 5$ ($5\sigma$); and a summary of the lens model. The bottom row shows, from left to right, the full lens model, the lens model without lens light, the isolated lens light model, and the reconstructed background source (all in log-scale). The red curve indicates the lensing caustic overlaid on the source model: source features inside the caustic are lensed into four observable images.
• Figure 2: Joint posterior distribution for SDSSJ1430+4105. The corner plot shows posterior samples (light blue) of the foreground mass parameters $\mathbf{M}$, with contours (dark blue) marking the 1$\sigma$ and 2$\sigma$ regions. The 1-D corner plot marginals display the posterior median of the foreground mass parameters $\mathbf{M}$ with 16th–84th percentile uncertainties, indicated by dashed vertical lines and reported above each panel. Posterior samples and uncertainties for the source $\mathbf{S}$, lens light $\mathbf{L}$, and PSF model $\mathbf{P}_0$ (frame 0 of 4) are also shown. The upper-right panels display, from top to bottom, two posterior samples, the median model, and the relative 68% credible interval (interval width divided by the median). All results are based on 300 posterior samples and are marginalized over alignment parameters $\boldsymbol{\delta}$.
• Figure 3: Example high-resolution ($512 \times 512$) sample of the background source for representative lensing systems. Each panel shows the reconstructed source with the lensing caustic overlaid, along with the name of the lensing system, source redshift and a physical reference scale in kiloparsecs (kpc). The physical scale is computed assuming a flat $\Lambda$CDM cosmology with $\Omega_{\mathrm{m}} = 0.3$, $\Omega_{\Lambda} = 0.7$, and $H_{0} = 70~\mathrm{km,s^{-1},Mpc^{-1}}$. Full lens model reconstructions and data–model residuals based on these source models are presented in Appendix \ref{['sec:appendix_results']}.
• Figure 4: Comparison of inferred foreground mass parameter values between this work and Etherington2022 (obtained from Table B1 of their supplementary material) for the Einstein radius $R_{\mathrm{E}}$, EPL slope $t$ and external shear magnitude $\gamma_{\mathrm{ext}}$ with error bars signifying the $68\%$ credible-interval widths. Only lenses modeled in both studies are shown; systems for which our inference did not converge or yield stable posterior sampling are excluded. Because Etherington2022 did not include multipole terms in the foreground mass model, exact agreement with our results—which do include third- and fourth-order multipoles—is not expected. Note that Etherington2022 report $68\%$ credible intervals on the Cartesian components of the external shear $(\gamma_{1,\mathrm{ext}}, \gamma_{2,\mathrm{ext}})$. The uncertainties we report on their magnitude $\gamma_{\mathrm{ext}}$ are approximate: we draw bootstrap samples of $(\gamma_{1,\mathrm{ext}}, \gamma_{2,\mathrm{ext}})$ from independent Gaussian distributions with $\sigma$ set by their reported $68\%$ credible widths, transform the samples to the shear magnitude, and take the resulting $68\%$ credible width.
• Figure 5: Same as Figure \ref{['fig:etherington_milex']}, but comparing our results with those of Tan2024 taken from https://www.projectdinos.com/dinos-i. Their foreground mass model adopts a power-law profile with external shear but no multipoles. Therefore, exact one-to-one agreement is not guaranteed.