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Line-of-sight shear in SLACS strong lenses I: shear and mass model parametrisations

This study utilizes the dolphin automated modelling pipeline to measure line-of-sight shear in 23 SLACS strong gravitational lenses, finding a mean magnitude of $0.056 \pm 0.013$ and demonstrating that neglecting post-Born corrections introduces degeneracies while adding octupole moments does not improve agreement with weak lensing expectations.

Original authors: Natalie B. Hogg, Daniel P. Johnson, Anowar J. Shajib, Julien Larena

Published 2026-07-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Natalie B. Hogg, Daniel P. Johnson, Anowar J. Shajib, Julien Larena

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: Looking Through a Distorted Window

Imagine you are looking at a beautiful, perfectly round balloon floating in the distance. Suddenly, you look at it through a thick, warped piece of glass (like a funhouse mirror or a heavy wine bottle). The balloon looks stretched, squashed, or twisted.

In astronomy, this "glass" is a massive galaxy sitting between us and a distant light source (like a quasar or another galaxy). This is called gravitational lensing. The gravity of the foreground galaxy bends the light, creating a distorted image of the background object.

Usually, astronomers use these distortions to learn about the foreground galaxy (the "glass"). But this paper asks a different question: Can we use the distortion to learn about the "air" between us and the glass?

The "air" in this analogy is the empty space of the universe, which isn't actually empty. It's filled with invisible clumps of dark matter and other galaxies. As light travels through this crowded universe, it gets nudged slightly by these clumps. This nudging is called shear.

The Goal: Measuring the "Nudge"

The authors wanted to measure this "nudge" (shear) for the first time in a specific set of 23 strong lenses (the SLACS catalogue).

Why does this matter?

Traditional method: Astronomers usually measure shear by looking at millions of faint, blurry galaxies and seeing how they are all slightly squashed in the same direction. This is called "cosmic shear."
This paper's method: They want to use the strong lenses (the ones with the big, clear rings or arcs) to measure the shear. If they can do this, it gives them a second, independent way to check the rules of the universe (cosmology), like a second opinion from a different doctor.

The Problem: The "Double-Decker" Confusion

Here is the tricky part. When you look at a distorted balloon through a warped window, you can't easily tell if the distortion came from:

The balloon being naturally oval-shaped.
The window being warped.
The wind (shear) blowing on the balloon.

In the past, when astronomers tried to measure the "wind" (shear) in these lenses, their math got stuck. The "wind" and the "shape of the balloon" (the lens galaxy's mass) were so mixed up in the equations that they couldn't separate them. It was like trying to figure out how much a car weighs while it's driving on a bumpy road; the bumps make the scale read the wrong weight.

The Solution: The "Minimal Model"

The authors used a special mathematical trick called the "minimal model."

Think of this like a gauge on a car. If you don't know where "zero" is, your speedometer is useless. But if you fix the definition of "zero" (the source position), you can finally read the speed accurately.

By using this "minimal model," the authors created a way to measure the shear that is mathematically "safe." It doesn't get confused with the shape of the galaxy. They proved this works on fake data (simulations), and now they are testing it on real data.

What They Did (The Experiment)

They took 23 real strong lenses and ran them through a super-computer pipeline (called dolphin, which uses a tool called lenstronomy). They tried two main things:

The "Clean" Model: They assumed the "wind" (foreground shear) might be messing with the main lens's gravity. They included this in their math.
The "Simplified" Model: They ignored the "wind" to see if it made the math faster and easier.
The "Boxy" Test: They wondered if the lenses looked weird because the galaxies themselves were shaped like boxes or disks (octupoles) rather than smooth ovals. They added "boxiness" to their models to see if that fixed the weird measurements.

The Results: What They Found

1. The Measurement Works (But is Big)
They successfully measured the shear for all 23 lenses. The average "nudge" they found was about 0.056.

The Catch: This number is surprisingly large. When they compared their results to what computer simulations of the universe predicted, their measurements were way too high. It's like measuring the wind speed and finding it's a hurricane, when the weather forecast said it should be a gentle breeze.

2. The "Boxy" Fix Didn't Work
They thought, "Maybe the galaxies are just weirdly shaped (boxy/disky), and that's why the shear looks so big."

The Result: Adding "boxiness" to the model didn't fix the problem. In most cases, the shear stayed just as large. It turns out, the galaxies aren't the only thing causing the confusion.

3. Don't Skip the "Wind" (Foreground Shear)
They tested if they could just ignore the "wind" (foreground shear) to make the math faster.

The Result: No. If they ignored the wind, the math gave them a slightly different answer for the galaxy's shape and the shear. It's like trying to weigh a car on a bumpy road by ignoring the bumps; you get a faster result, but it's the wrong weight. To get the right answer, you have to do the hard work of including the "wind" in your calculations.

The Conclusion

The authors conclude that:

They can measure the shear in strong lenses using this new "minimal model."
However, the shear they are measuring is larger than expected based on our current understanding of the universe.
Simply making the galaxy models more complex (adding "boxiness") doesn't solve the mystery.
To get accurate results for future cosmology, we must include the complex effects of the "wind" (foreground shear) in our models, even if it makes the math slower.

In short: They built a better ruler to measure the universe's "wind," but the wind turned out to be stronger than the weather forecast predicted. They still don't know exactly why, but they know they can't just ignore the wind to get a quick answer.

Technical Summary: Line-of-Sight Shear in SLACS Strong Lenses I: Shear and Mass Model Parametrisations

Problem Statement
Strong gravitational lensing occurs in an inhomogeneous Universe, where matter along the line of sight (LOS) distorts lensed images via shear. While traditionally treated as a nuisance parameter, measurable LOS shear offers a potential independent probe of cosmological parameters, complementary to cosmic shear. However, measuring this shear is complicated by degeneracies between the shear and the intrinsic ellipticity of the lens mass. Previous attempts to measure shear using strong lenses (e.g., Birrer et al. 2017) revealed strong degeneracies between shear parameters and lens mass ellipticity, rendering cosmological inferences unreliable. Furthermore, recent studies (Etherington et al. 2024) have found that external shear magnitudes measured in strong lenses are suspiciously large compared to weak lensing expectations, suggesting unmodelled complexity in the lens mass (such as higher-order multipoles) or systematic errors in the shear parametrization.

Methodology
The authors model 23 strong gravitational lenses from the Sloan Lens ACS (SLACS) catalogue using the dolphin automated modelling pipeline, which utilizes lenstronomy as its engine. The methodology involves:

Lens and Source Modelling:
- Mass: The main deflector is modelled using an Elliptical Power Law (EPL) profile.
- Lens Light: Modeled with two S'ersic profiles (indices $n_S=1$ and $n_S=4$ ) to account for exponential and de Vaucouleurs components, respectively.
- Source Light: Modeled using a combination of an elliptical S'ersic profile and Gaussian shapelets (Hermite polynomials) to reconstruct complex source morphologies.
- Einstein Radius: Fixed to values reported by Shajib et al. (2021) to improve computational efficiency.
Shear Parametrisations:
- Minimal LOS Shear Model: Based on Fleury et al. (2021), this model defines a "line-of-sight shear" ( $\gamma_{LOS}$ ) derived from a source-position transformation. It includes five parameters: foreground shear ( $\gamma_{od}$ ), LOS shear ( $\gamma_{LOS}$ ), and LOS rotation ( $\omega_{LOS}$ ). This formalism is theoretically free from degeneracies with lens mass ellipticity.
- No Foreground Shear Model: A variant where the foreground shear term ( $\gamma_{od}$ ) is fixed to zero, effectively neglecting post-Born corrections to the main deflector's potential.
- Octupole Extension: To test if unmodelled mass complexity drives large shear values, the authors re-fit the lenses adding an octupolar distortion ( $m=4$ multipole) to the EPL mass profile.
Inference:
- Parameter inference is performed using Markov Chain Monte Carlo (MCMC) with the emcee package.
- The sample is compared against expectations derived from the RayGalGroup suite of relativistic N-body simulations, which provide weak lensing maps including post-Born effects.

Key Contributions

First Measurement of LOS Shear in Real Data: This work presents the first measurement of the LOS shear ( $\gamma_{LOS}$ ) in a sample of 23 real strong lenses using the theoretically safe minimal model.
Systematic Investigation: The paper systematically tests two major sources of potential bias: (1) the neglect of foreground shear (post-Born corrections) and (2) the omission of octupolar mass distortions.
Validation of the Minimal Model: The study confirms that the minimal LOS shear model yields measurements consistent with previous "external shear" studies but provides a theoretically robust framework for cosmological inference.

Results

Shear Magnitude: Across the 23 lenses, the mean magnitude of the LOS shear is measured as $0.056 \pm 0.013$ .
Comparison with Simulations: The measured shear values are generally larger than expected from weak lensing simulations. The tension between measurements and simulation expectations reaches up to $7.9\sigma$ for the lens SDSSJ1531−0105. Seven lenses show tensions of $3\sigma$ or greater.
Impact of Neglecting Foreground Shear: Neglecting the foreground shear term (setting $\gamma_{od}=0$ ) leads to a propagation of degeneracies. While it artificially increases the precision of the lens mass ellipticity recovery, it shifts the inferred LOS shear values. The authors conclude that physical accuracy should not be traded for the marginal speed gain of removing these parameters.
Impact of Octupoles: Adding an octupole to the mass model does not systematically reduce the inferred LOS shear magnitude.
- In 14 of 21 lenses, the tension with simulations changed by less than $1.5\sigma$ .
- In most cases, the octupole model either increased the tension or provided no improvement.
- Only one lens (SDSSJ1531−0105) showed a better fit with the octupole model and a reduction in shear magnitude, but this was an exception rather than the rule.
- The recovered octupole strengths were often larger than observational constraints for early-type galaxies, suggesting the $m=4$ multipole alone does not capture the full complexity of the mass profiles.

Significance and Claims
The paper claims that the "minimal LOS shear model" is the necessary framework for attempting cosmological inference from strong lensing shear, as it avoids the degeneracies that plagued previous approaches. However, the authors are modest regarding the immediate cosmological utility of their results. They emphasize that:

The large shear values measured are not universally explained by unmodelled octupoles in the lens mass.
The agreement between their findings and previous "external shear" studies suggests the current lens models adequately capture the LOS shear contribution, but the discrepancy with weak lensing expectations remains unresolved.
Future progress requires not only better modelling techniques (e.g., accounting for higher-order multipoles, gradients, or flexion) but also higher-quality data (e.g., from JWST) to better separate lens and source light.
Currently, uniformly modelling large strong lens catalogues to obtain accurate shear measurements for cosmology is not achievable with existing data and techniques; the primary focus must shift to refining the physical complexity of the main deflector mass models.