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TDCOSMO XXVI: Uniform lens modeling of eight doubly imaged quasars

This paper presents the first uniform gravitational lens modeling analysis of eight doubly imaged quasars using the Lenstronomy framework, demonstrating that the surface brightness of lensed host arcs is the primary factor determining mass model precision and establishing a pipeline to accelerate future time-delay cosmography samples from upcoming large-scale surveys.

Original authors: Ryan Brady, Xiang-Yu Huang, Simon Birrer, Anowar J. Shajib, Nafis Sadik Nihal, Cameron Lemon, Martin Millon, Veronica Motta, Dominique Sluse, Frederic Courbin

Published 2026-04-29

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CC BY 4.0

Original authors: Ryan Brady, Xiang-Yu Huang, Simon Birrer, Anowar J. Shajib, Nafis Sadik Nihal, Cameron Lemon, Martin Millon, Veronica Motta, Dominique Sluse, Frederic Courbin

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Measuring the Universe's Speed

Imagine the universe is a giant balloon being blown up. Scientists want to know exactly how fast it is expanding right now. This speed is called the Hubble Constant ( $H_0$ ).

Currently, there is a massive disagreement in the scientific community. Some measurements (looking at the "baby pictures" of the universe) say the balloon is expanding at one speed, while others (looking at the "adult" universe nearby) say it's expanding faster. This is known as the "Hubble Tension."

To solve this mystery, scientists use gravitational lensing. Think of a massive galaxy in space as a giant, curved glass lens. When light from a distant, bright star (a quasar) passes behind this galaxy, the gravity bends the light, creating multiple images of that single star.

The Problem: Too Many Glasses, Not Enough Clues

For years, scientists have mostly studied systems where the lens creates four images of the quasar (like a four-way mirror). These are great because they give lots of clues to calculate the expansion speed.

However, there are actually four times as many systems that only create two images (doubles). The problem is that with only two images, it's much harder to figure out the shape of the "glass lens" (the galaxy). It's like trying to guess the shape of a hidden object by only seeing two reflections instead of four. Because it's so tricky, scientists have mostly ignored these "double" systems, even though there are so many of them.

What This Paper Did: Building a Better Map

This paper is the first time a team of scientists has built a standardized, uniform map for eight of these "double" systems using high-resolution photos from the Hubble Space Telescope.

They used a sophisticated software tool called Lenstronomy (think of it as a digital GPS for gravity) to reconstruct exactly what the lensing galaxies look like. Their goal wasn't to solve the Hubble Tension in this specific paper, but to build a reliable, repeatable method for measuring these double systems so they can be used in future studies.

Key Findings in Simple Terms

1. The "Double" Systems Are Reliable
The team checked their new maps against old data and measurements from the Gaia satellite (which maps star positions).

The Result: Their measurements of the distance between the two images matched the satellite data almost perfectly (within the width of a human hair from a mile away).
The Takeaway: They proved that you can trust these difficult "double" systems if you use the right tools.

2. The Brighter the "Arc," the Better the Map
When light bends around a galaxy, it often forms a curved streak of light called an arc (the host galaxy of the quasar).

The Discovery: They found a strong link between how bright these arcs are and how precise their gravity map is.
The Analogy: Imagine trying to figure out the shape of a foggy window. If the fog is thick and bright (high surface brightness), you can see the patterns clearly and guess the shape easily. If the fog is faint and dim, you can barely see anything, and your guess will be a wild shot in the dark.
The Result: The brighter the arc, the tighter and more accurate their calculation of the galaxy's mass.

3. Why "Full Pictures" Beat "Just Dots"
To prove the importance of seeing the whole picture, they ran a second test.

Test A (Full Modeling): They used the entire image, including the bright arcs and the galaxy's glow.
Test B (Conjugate Point): They used only the positions of the two bright dots (the quasar images), ignoring the arcs.
The Result: Test B was wildly uncertain. The range of possible answers was 109 times larger than Test A.
The Takeaway: Just knowing where the two dots are isn't enough. You need the detailed shape and brightness of the surrounding arcs to pin down the answer. Without the arcs, the "double" systems are too ambiguous to be useful for precise cosmology.

The Bottom Line

This paper is a "how-to" guide for the future. It shows that:

We can model "double" quasar systems reliably.
We need high-quality, deep images to see the faint arcs around them.
The brightness of those arcs is the secret sauce that turns a vague guess into a precise measurement.

By creating this uniform pipeline, the team has paved the way to use thousands of these "double" systems (which will be found by future telescopes like LSST and Euclid) to finally solve the mystery of how fast the universe is expanding.

1. Problem Statement

Time-delay cosmography (TDC) is a primary method for measuring the Hubble constant ( $H_0$ ) to resolve the "Hubble tension" between early-universe (CMB) and late-universe (distance ladder) measurements. While quadruply imaged quasars ("quads") have been the standard for TDC due to their rich geometric constraints, doubly imaged quasars ("doubles") are approximately four times more abundant in the universe. However, doubles have historically been underutilized because they offer fewer observables (only two image positions), making them more susceptible to the Mass-Sheet Degeneracy (MSD) and mass-sheet transform (MST).

The core challenge addressed in this paper is the lack of a uniform, scalable modeling framework specifically designed for doubly imaged systems. Previous analyses often relied on heterogeneous datasets and modeling techniques, preventing the construction of large, statistically robust samples necessary for hierarchical Bayesian cosmographic inference. Furthermore, the specific contribution of extended host galaxy arcs (surface brightness) to breaking degeneracies in doubles had not been systematically quantified.

2. Methodology

The authors utilized the Lenstronomy open-source software framework to develop a uniform modeling pipeline for eight doubly imaged quasars observed by the Hubble Space Telescope (HST) as part of program GO-17199.

Data: Multi-band observations using WFC3 filters: F160W (IR), F814W, and F475X (UVIS).
Mass Modeling:
- The main deflector galaxies were modeled as Singular Isothermal Ellipsoids (SIE).
- External shear ( $\gamma_{ext}$ ) was included to account for line-of-sight perturbations, with a conservative prior ( $\gamma_{ext} \leq 0.15$ ).
- For systems with nearby perturbers (e.g., J1001+5027), additional SIE components were added.
Light Modeling:
- Lens Light: Modeled using elliptical Sérsic profiles. Complex systems (e.g., edge-on galaxies like J0602-4335) utilized double Sérsic components.
- Source Light: The quasar host galaxy was modeled as an elliptical Sérsic profile. For J2325-5229, Shapelets (Gauss-Hermite polynomials) were added to the IR band to capture complex arc structures.
- PSF Handling: Point Spread Functions were reconstructed using STARRED from isolated stars. An iterative process was employed where lens light was subtracted to refine the PSF based on quasar residuals. A PSF variance map was generated to downweight pixels where PSF uncertainty was high.
Fitting Sequence:
1. Initial Particle Swarm Optimization (PSO) on F160W.
2. Iterative PSF reconstruction and refinement.
3. Joint optimization across all three bands (F160W, F814W, F475X).
4. Markov Chain Monte Carlo (MCMC) sampling using emcee to fully marginalize uncertainties.
Conjugate Point Analysis: To isolate the value of surface brightness data, the authors performed a "conjugate point" analysis. This method used only the quasar image positions (treating them as observational truths) to constrain the mass model, excluding all extended arc information. This was compared against the full image modeling results.

3. Key Contributions

Uniform Pipeline: Established the first standardized, open-source pipeline tailored specifically for modeling doubly imaged quasars, enabling the processing of large samples from future surveys (LSST, Roman, Euclid).
Quantification of Arc Information: Systematically demonstrated that the surface brightness of the lensed host arcs is the primary driver of mass model precision in doubles, rather than just the point-source positions.
Conjugate Point Benchmarking: Provided a rigorous comparison between point-source-only constraints and full surface brightness modeling, quantifying the "information gain" provided by high-resolution imaging.
New Measurements: Provided the first uniform Einstein radius and image separation measurements for the entire sample, including the first measurements for J0602-4335.

4. Key Results

Model Accuracy:
- Modeled Einstein radii ( $\theta_E$ ) agree with previous literature at an average of 1.5 $\sigma$ . The largest discrepancy (4.5 $\sigma$ ) occurred in J0407-5006, attributed to the small separation of Image B from the lens centroid, which challenges ground-based deblending.
- Modeled image separations differ from Gaia DR2 measurements by an RMS of only 3.6 mas (excluding the J0407-5006 outlier), validating the astrometric precision of the pipeline.
Arc Brightness vs. Precision:
- A strong positive correlation (Pearson $r = 0.97$ ) was found between the surface brightness of the lensed arc and the precision of the Fermat potential ( $\Delta\Phi$ ).
- Brighter arcs (e.g., J1001+5027, $m_{arc} \approx 18.96$ ) yield Fermat potential precisions of $\sim0.87\%$ , while fainter arcs (e.g., J1515+1511, $m_{arc} \approx 21.6$ ) result in $\sim2.89\%$ uncertainty.
Conjugate Point vs. Full Modeling:
- The posterior hypervolume (uncertainty space) of the mass parameters in the conjugate point analysis was, on average, 109 times larger than in the full image modeling.
- A strong anti-correlation ( $r = -0.87$ ) exists between arc magnitude and the mass parameter hypervolume, confirming that brighter arcs significantly break the mass-shear degeneracy.
Mass-Light Alignment:
- In the high-S/N F160W band, mass and light position angles are generally well-aligned (within the 10 $^\circ$ prior), though deviations in some systems suggest the influence of nearby perturbers not included in the simple SIE+shear model.

5. Significance and Future Outlook

This work establishes that doubly imaged quasars are viable candidates for precision cosmography, provided that high-resolution imaging can resolve the extended host galaxy arcs. The study proves that:

Scalability: A uniform pipeline can handle the heterogeneity of doubles, preparing the field for the thousands of lenses expected from upcoming surveys.
Observational Strategy: The strong dependence of Fermat potential precision on arc brightness dictates that future cosmographic samples must prioritize deep, high-resolution follow-up to detect extended arcs. Without this, the mass-sheet degeneracy cannot be sufficiently broken using point-source data alone.
Cosmographic Pathway: The uniform outputs (Einstein radii, Fermat potentials, and uncertainties) generated here serve as the foundational inputs for a subsequent hierarchical Bayesian analysis (to be presented in a future paper) that will combine time delays and stellar kinematics to infer $H_0$ with improved precision and reduced systematics.

In summary, this paper bridges the gap between the abundance of double lenses and their utility in cosmology, demonstrating that with modern modeling and deep imaging, doubles can complement quads in resolving the Hubble tension.