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Disentangling the dark and stellar mass through precise lens modelling of the JWST observation of lensed quasar WFI2033--4723

This study utilizes high-resolution JWST imaging and time-delay measurements of the lensed quasar WFI2033--4723 to construct a composite mass model that successfully disentangles stellar and dark matter components, revealing a stellar mass-to-light ratio between Chabrier and Salpeter expectations and a dark matter halo with an inner slope steeper than standard NFW, while demonstrating that cosmological priors are necessary to break degeneracies for robust standalone cosmological constraints.

Original authors: Tian Li, Thomas E. Collett, Coleman M. Krawczyk, Wolfgang J. R. Enzi, Aymeric Galan

Published 2026-07-10

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Tian Li, Thomas E. Collett, Coleman M. Krawczyk, Wolfgang J. R. Enzi, Aymeric Galan

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

Imagine a cosmic game of "Cosmic Cat and Mouse" played with light. In this game, a massive galaxy sits between us and a distant, flickering beacon called a quasar. The galaxy's gravity acts like a giant, invisible magnifying glass, bending the quasar's light into four separate images. But here's the tricky part: that galaxy isn't just one thing. It's a messy cocktail of two ingredients: a visible "stellar soup" made of billions of stars, and a hidden "dark matter ghost" that we can't see but feel through its gravity.

For years, astronomers have struggled to separate these two ingredients. It's like trying to figure out how much sugar and how much flour is in a cake just by looking at the final baked loaf. You know the total weight, but you don't know the recipe. This paper, led by Tian Li and team, uses a brand-new, super-sharp camera on the James Webb Space Telescope (JWST) to finally try and taste the ingredients separately.

The Great Cosmic Recipe Swap

The team looked at a specific cosmic lens called WFI2033–4723. They didn't just guess the recipe; they used a clever trick involving time. The four images of the quasar aren't just pictures; they are time-delayed echoes. Because the light takes different paths around the galaxy, the "blinks" of the quasar arrive at different times. It's like hearing an echo in a canyon: the sound that takes the long, winding path arrives later than the one that takes the shortcut.

The researchers used these time delays as a cosmic ruler. They said, "If we assume the universe is expanding at a certain speed (a known cosmological speed), then these time delays tell us exactly how much total mass is in the galaxy." Once they knew the total mass, they could swap their old, simple "total mass" model for a more complex "composite" model. This new model tries to split the mass into the visible stars and the invisible dark matter.

The Ingredients: Stars and Ghosts

When they ran the numbers, they found some fascinating things about the "recipe":

The Stars: The amount of starlight they saw suggested the galaxy has a stellar mass between $2.03^{+0.43}_{-0.62} \times 10^{11}$ and $2.30^{+0.38}_{-0.43} \times 10^{11}$ solar masses (depending on which cosmic speed they assumed). This puts the galaxy's "star density" right in the middle of two famous theories: the "Chabrier" recipe (which assumes fewer heavy stars) and the "Salpeter" recipe (which assumes more). It's not a pure Chabrier cake, but it's not a heavy Salpeter one either. It's a delicious middle-ground.
The Dark Matter Ghost: The invisible dark matter halo surrounding the stars turned out to be surprisingly "spiky." Instead of having a gentle, smooth center like a standard theory (called NFW) predicts, the data suggests the dark matter density gets steeper toward the center. The inner slope, a number called $\gamma_{in}$ , is about $1.32^{+0.12}_{-0.15}$ for one cosmic speed assumption and $1.30^{+0.16}_{-0.21}$ for the other. That is steeper than the standard "NFW cusp" we usually expect.

What They Ruled Out (The "No-Go" Zone)

The paper is very careful about what it didn't find. The authors explicitly tried to use this same model to figure out the speed of the universe's expansion (the Hubble constant, $H_0$ ) without any outside help. They asked, "Can we just look at the lens and the time delays and solve for the universe's speed?"

The answer was a firm no. When they tried to do this without an outside "cosmic speed" hint, the math got stuck in a loop. The model tried to cheat by shrinking the size of the dark matter halo to an impossibly small scale radius of about $2''$ (arcseconds). This tiny size forced the calculated speed of the universe to be huge and unrealistic. The paper argues that this isn't a discovery of a new universe speed; it's a sign that the model is missing something. Without extra information (like the speed of the stars moving inside the galaxy), the lens model can't distinguish between a small, fast halo and a big, slow one. So, the paper rules out the idea that this specific lens alone can solve the mystery of the universe's expansion speed.

How Sure Are They?

The team is quite confident in the separation of the ingredients, but they are humble about the limits.

The Separation: They are confident that the time-delay information successfully broke the "degeneracy" (the confusion) between the stars and the dark matter. They found that the results for the star mass and the dark matter shape were very similar whether they used one cosmic speed assumption or another. This suggests the JWST image data itself is doing the heavy lifting.
The Slope: They are confident the dark matter slope is steeper than standard ( $\gamma_{in} \approx 1.3$ ), but they note that this result is sensitive to how they model the stars.
The Gradient: They found a "mild" hint that the ratio of mass to light changes as you move away from the center (a positive gradient), but the data doesn't strongly demand it. It's a "maybe," not a "definitely."
The Cosmology: They are not confident that they can measure the universe's expansion speed with this lens alone. The paper explicitly states that the strong link between the Hubble constant and the halo size prevents a "robust standalone constraint."

The Bottom Line

This paper is a successful experiment in "cosmic dissection." By using the sharp eyes of JWST and the ticking clock of time delays, the team managed to separate the visible stars from the invisible dark matter in a way that previous models couldn't. They found a galaxy with a "medium-heavy" star population and a "spiky" dark matter core. However, they also proved that even with this powerful new tool, we still need outside help (like knowing how fast the universe is expanding) to get the full picture. The lens is a brilliant detective, but it still needs a partner to solve the biggest mystery of all.

Technical Summary: Disentangling the dark and stellar mass through precise lens modelling of the JWST observation of lensed quasar WFI2033–4723

Problem Statement
Strong gravitational lensing provides a precise measurement of the total mass enclosed within the Einstein radius of a galaxy, typically at the $\sim 1\%$ level. However, decomposing this total mass into its baryonic (stellar) and dark matter components is challenging due to the Mass-Sheet Transformation (MST) degeneracy. In composite models, variations in the stellar mass-to-light ratio ( $M/L$ ) and the dark matter halo profile can mimic one another, preserving the lensing observables while altering the physical interpretation. While stellar kinematics are commonly used to break this degeneracy, they introduce their own systematic uncertainties (e.g., anisotropy, projection effects). This paper investigates whether time-delay information, combined with high-resolution imaging and external cosmological priors, can effectively constrain the MST-like freedom in a composite stellar-plus-dark-matter model without relying primarily on kinematics.

Methodology
The authors model the quadruply imaged quasar WFI2033–4723 using high-resolution JWST/NIRCam imaging (specifically the F115W filter) and measured time delays from the COSMOGRAIL/H0LiCOW collaboration. The analysis employs the open-source code Herculens, which utilizes JAX for automatic differentiation and GPU acceleration.

The modelling strategy proceeds in two main stages:

EPL Baseline: An Elliptical Power-Law (EPL) mass model is first constructed to establish a reference solution and recover Fermat-potential differences (fpd). This serves as a benchmark for the total mass distribution.
Composite Star+gNFW Model: The total mass profile is replaced by a physically motivated decomposition:
- Stellar Mass: Modeled using a Multi-Gaussian Expansion (MGE) of the lens light, allowing for a free global normalization and a radial $M/L$ gradient.
- Dark Matter: Described by an elliptical generalized Navarro–Frenk–White (gNFW) halo with a free inner slope ( $\gamma_{in}$ ), scale radius ( $R_s$ ), and normalization.
- PSF Modelling: A rigorous Point Spread Function (PSF) correction is applied using field stars and on-the-fly corrections from the quasar images to mitigate residuals that could bias the mass reconstruction.
- Inference: The authors use Hamiltonian Monte Carlo (HMC) with a No-U-Turn Sampler (NUTS) and a Gibbs-like scheme to sample the high-dimensional posterior.

To constrain the MST degeneracy, the analysis incorporates the measured time delays under two distinct external cosmological priors in a flat $\Lambda$ CDM universe:

Pantheon+SH0ES: $H_0 = 73.50 \pm 1.07$ km s $^{-1}$ Mpc $^{-1}$ (local distance ladder).
Planck+DESI: $H_0 = 68.17 \pm 0.28$ km s $^{-1}$ Mpc $^{-1}$ (early Universe/large-scale structure).

Key Results

Baseline Consistency: The EPL baseline model recovers Fermat-potential differences consistent with previous HST-based (H0LiCOW) and JWST-based (TDCOSMO XX) analyses, validating the reference scale for the composite modelling.
Stellar Mass and IMF: Under both cosmological priors, the inferred stellar normalization lies between the expectations for Chabrier and Salpeter Initial Mass Functions (IMFs). The stellar mass is estimated at $M_\star \approx 2.03 \times 10^{11} M_\odot$ (Planck+DESI) and $2.30 \times 10^{11} M_\odot$ (Pantheon+SH0ES). The data show a mild preference for a positive radial $M/L$ gradient, though this parameter remains degenerate with the stellar normalization.
Dark Matter Halo: The dark matter halo exhibits an inner slope of $\gamma_{in} \simeq 1.3$ (specifically $1.32^{+0.12}_{-0.15}$ for Planck+DESI and $1.30^{+0.16}_{-0.21}$ for Pantheon+SH0ES). This is steeper than the standard NFW cusp ( $\gamma=1$ ) and steeper than results from the "Jackpot" lens analyzed with the same framework.
Cosmological Sensitivity: The main astrophysical conclusions regarding the stellar $M/L$ and the dark matter inner slope are largely insensitive to the choice of cosmological prior, suggesting the constraints are driven primarily by the JWST imaging and time-delay data.
Reverse Cosmology Test: When the authors attempted to infer $H_0$ directly from the composite model without an external prior, they found a strong degeneracy between $H_0$ and the halo scale radius $R_s$ . The model preferred an unphysically small $R_s$ ( $\sim 2''$ ), leading to an unreliable $H_0$ constraint. This indicates that time delays alone, without kinematic data or external priors, cannot robustly break the MST in this system.

Significance and Claims
The paper claims that composite time-delay lens modelling can effectively separate baryons from dark matter when constrained by external cosmological priors. The primary contribution is demonstrating that the combination of JWST imaging and time delays can constrain the MST-like freedom sufficiently to derive physical properties of the stellar population (IMF normalization) and the dark matter halo (inner slope) without relying on stellar kinematics.

The authors modestly conclude that while the star+gNFW framework successfully fits the data to the noise level and separates the mass components, the system WFI2033–4723 alone is insufficient for an independent, robust measurement of the Hubble constant due to the remaining degeneracy between the global halo scale radius and $H_0$ . They suggest that spatially resolved stellar kinematics will be necessary to fully constrain the inner mass profile and break the remaining degeneracies. The work highlights the utility of time delays as a complementary constraint to imaging in disentangling the mass components of strong lenses.

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