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A Constraint on Dark Matter Self-Interaction from Combined Strong Lensing and Stellar Kinematics in MACS J0138-2155

By combining strong gravitational lensing and spatially resolved stellar kinematics in the galaxy cluster MACS J0138-2155, this study establishes a competitive 95% confidence upper limit on the dark matter self-interaction cross section of $\sigma/m < 0.613$ cm $^2$ /g and predicts the earlier reappearance of the lensed supernova Requiem.

Original authors: Jackson H. O'Donnell, Tesla E. Jeltema, M. Grant Roberts, James Nightingale, Abigail Flowers, Dhruv Aldas

Published 2026-02-25

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CC BY 4.0

Original authors: Jackson H. O'Donnell, Tesla E. Jeltema, M. Grant Roberts, James Nightingale, Abigail Flowers, Dhruv Aldas

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: What is the Mystery?

Imagine the universe is a giant, invisible ocean. We can't see the water (Dark Matter), but we can see the ships (galaxies) floating on it and how they move. For decades, scientists have assumed this "water" is like a ghost: it has mass, it pulls on things with gravity, but it never bumps into itself or anything else. It just passes right through. This is called Collisionless Dark Matter.

However, some scientists suspect the "water" might actually be a bit sticky. They call this Self-Interacting Dark Matter (SIDM). If dark matter particles are sticky, they might bump into each other, bounce around, and even form a fluffy, spread-out cloud in the center of galaxies instead of a tight, dense knot.

This paper is like a detective story where the authors try to figure out: Is the dark matter in a specific galaxy cluster "ghostly" or "sticky"?

The Crime Scene: MACS J0138

The authors chose a specific galaxy cluster named MACS J0138 as their crime scene. Think of this cluster as a massive, natural magnifying glass made of gravity. Because it is so heavy, it bends the light from galaxies behind it, creating distorted, stretched-out images (like looking through a funhouse mirror).

This cluster is special for two reasons:

It's a "Super-Lens": It creates multiple images of the same background galaxy, allowing scientists to map out the invisible mass inside the cluster with incredible precision.
It's a Time Machine: It has captured two exploding stars (supernovae), named Requiem and Encore. Because the light takes different paths to get to us, these explosions appear at different times. It's like seeing the same movie scene played on five different screens, but each screen is delayed by a few years.

The Investigation: Two Different Clues

To solve the mystery of the dark matter, the team didn't just look at the lens; they used two different types of clues that had to agree with each other.

Clue 1: The Gravitational Lens (The "Shadow")
Imagine shining a flashlight through a foggy window. The way the light bends tells you how thick the fog is. The team used the distorted images of the background galaxies to map the "shadow" of the dark matter. This tells them how the mass is distributed far out from the center of the cluster.

Clue 2: The Stellar Kinematics (The "Dance")
This is the new, fancy part of the investigation. The team looked at the central galaxy in the cluster (the "Brightest Cluster Galaxy"). They used a special instrument (MUSE) to measure how fast the stars inside that galaxy are moving.

The Analogy: Imagine a spinning carousel. If the horses (stars) are moving very fast, the carousel must be heavy to keep them from flying off. If they are moving slowly, it's lighter. By measuring the speed of the stars in different spots, the team could weigh the dark matter right in the very center of the cluster.

The Method: Putting the Puzzle Together

In the past, scientists usually looked at just the "Shadow" (lensing) OR just the "Dance" (stars). But this paper is special because they combined both.

Think of it like trying to guess the shape of a hidden object in a box.

Lensing tells you the shape of the box from the outside.
Kinematics tells you how heavy the object is in the middle.

By combining these two, the team built a 3D model of the dark matter halo. They tested two theories:

The Ghost Theory: Dark matter doesn't interact (standard Cold Dark Matter).
The Sticky Theory: Dark matter bumps into itself (SIDM).

The Verdict: How Sticky is it?

The team ran their models and found that the "Sticky" theory could work, but only if the particles aren't too sticky.

The Result: They put a strict limit on how "sticky" the dark matter can be. They found that if dark matter particles do interact, they do so very rarely.
The Limit: They calculated that for every gram of dark matter, the chance of it bumping into another particle is less than 0.613 square centimeters. (Imagine a tiny speck of dust; that's how small the interaction area is).

This is a huge improvement because it's the most detailed study of a single system ever done. Previous studies looked at many clusters at once, but this one looked deep into just one, giving a much sharper picture.

The Bonus Prediction: When Will the Stars Explode Again?

Because they built such a precise map of the gravity in this cluster, they could predict the future of the supernovae.

The Old Prediction: Previous models said the next image of the "Requiem" supernova wouldn't appear until the mid-2030s (about 20 years after the first one).
The New Prediction: Because their map is more accurate, they realized the light paths are slightly different. They predict the next "Requiem" explosion will actually appear sooner, likely between January 2027 and November 2028.

Why Does This Matter?

Refining the Rules of the Universe: By proving that dark matter is likely "mostly ghostly" but with a tiny bit of stickiness, we get closer to understanding what the universe is actually made of.
Better Time Machines: This study improves our ability to use these cosmic lenses to measure the expansion rate of the universe (the Hubble Constant).
A Race Against Time: The prediction that the supernova will return in 2027-2028 means astronomers need to get their telescopes ready now. If they catch it, it will be a massive victory for cosmology.

In summary: This paper is a masterclass in cosmic detective work. By combining the bending of light and the movement of stars, the authors have put a very tight leash on how "sticky" dark matter can be, and they've given us a head-start on when to look for the next cosmic fireworks show.

1. Problem Statement

The nature of dark matter remains a fundamental unsolved problem in physics. While the Cold Dark Matter (CDM) model successfully explains large-scale structure, it faces potential tensions at smaller scales (e.g., the "core-cusp" problem in dwarf galaxies). Self-Interacting Dark Matter (SIDM) is a leading alternative where dark matter particles interact via a new force, potentially flattening density profiles (creating "cores") or leading to gravothermal collapse.

Previous constraints on the SIDM cross-section ( $\sigma/m$ ) have been derived from:

Dwarf galaxies: Suggesting high cross-sections ( $\sim 1-10$ cm $^2$ /g) to explain rotation curves.
Galaxy clusters: Suggesting much lower cross-sections ( $\lesssim 0.1$ cm $^2$ /g) based on strong lensing.

This discrepancy implies that if SIDM exists, the interaction must be velocity-dependent. However, previous cluster-scale studies often relied on simplified models, lacked spatially resolved kinematic data for the central galaxy, or treated SIDM constraints as post-hoc derivations rather than integral parts of the mass modeling. The authors aim to provide the most rigorous, self-consistent constraint on SIDM in a single cluster system by combining two complementary probes: strong gravitational lensing (SL) and spatially resolved stellar kinematics.

2. Methodology

The study focuses on the galaxy cluster MACS J0138-2155, a relaxed system hosting two strongly lensed supernovae (SN Requiem and SN Encore). The analysis combines data from HST, JWST, and VLT/MUSE.

A. Data Sources

Imaging: High-resolution JWST NIRCam and HST WFC3/ACS imaging to map lensed arcs and the Brightest Cluster Galaxy (BCG).
Spectroscopy: VLT/MUSE Integral Field Unit (IFU) data to measure spatially resolved stellar velocity dispersions of the central BCG.

B. Modeling Framework

The authors developed a unified, self-consistent mass model that simultaneously fits lensing and kinematic data.

SIDM Mass Profile:
- Instead of fitting a parametric cored profile and converting to SIDM later, they solve the isothermal Jeans equation at every step of the Markov Chain Monte Carlo (MCMC) sampling.
- The model assumes a standard NFW profile at large radii, transitioning to an isothermal core within a radius $r_1$ where self-interactions occur.
- The transition radius $r_1$ is defined by the condition that particles have experienced one scattering event over the halo's lifetime.
- The model includes a 3D prolate ellipticity (axis ratio $q_{3d}$ , inclination $i$ , position angle $\phi$ ) to account for triaxiality, avoiding biases inherent in 2D projections.
Baryonic Component:
- The stellar mass of the BCG is modeled using a Multi-Gaussian Expansion (MGE) derived from HST imaging.
- A stellar mass-to-light ratio ( $\Upsilon_*$ ) is treated as a free parameter with a wide prior to account for IMF uncertainties.
Strong Lensing Constraints:
- Utilized the PyAutoLens package.
- Modeled the cluster halo using a sum of Cored Steep Ellipsoids (CSEs) to approximate the SIDM profile.
- Included member galaxies modeled as dPIE (double Power-law Isothermal Ellipsoid) profiles, scaled via the Faber-Jackson relation (calibrated specifically for MACS J0138 using MUSE data).
- Constraints were applied to 29 observed positions of lensed features (including SN Requiem and Encore images) using a conjugate point likelihood method.
Stellar Kinematics Constraints:
- Used vorbin to create Voronoi bins with constant signal-to-noise (S/N) across the BCG.
- Extracted stellar velocity dispersions ( $\sigma_{LOS}$ ) using pPXF with the X-Shooter Spectral Library (XSL) templates.
- Modeled the kinematics using the JAM (Jeans Anisotropic Modeling) code, which forward-models the observed velocity dispersion based on the 3D mass distribution and anisotropy parameter ( $\beta_{sph}$ ).
- Constructed a likelihood function comparing the model to the 25 measured spatial bins, including a full covariance matrix derived from systematic tests (varying wavelength ranges, template libraries, and dust extinction).

3. Key Contributions

Methodological Advancement: This is the first study to perform a joint, self-consistent fit of strong lensing and spatially resolved stellar kinematics for a cluster-scale SIDM constraint. Unlike previous works, the SIDM profile is computed dynamically during the sampling process rather than as a post-processing step.
High-Resolution Kinematics: The use of MUSE IFU data allows for 25 spatial bins in the central galaxy, providing a much tighter constraint on the inner mass profile ( $\sim 1-20$ kpc) than previous 1D slit studies.
3D Triaxiality: The model explicitly accounts for the 3D prolate shape of the dark matter halo, correcting for biases that typically inflate apparent concentrations in lensing-only studies.
Supernova Time Delays: The model provides updated predictions for the time delays and magnifications of the lensed supernovae, crucial for future cosmography.

4. Results

A. SIDM Constraints

The joint analysis yields a 95% confidence upper limit on the SIDM cross-section:
$\sigma/m < 0.613 \text{ cm}^2/\text{g}$
at an interaction velocity of $\langle v_{pair} \rangle < 2090$ km/s.

Consistency: The lensing-only and kinematics-only results are highly consistent, validating the model.
Degeneracy: A strong degeneracy exists between the stellar mass-to-light ratio ( $\Upsilon_*$ ) and the SIDM cross-section ( $\sigma/m$ ). High stellar mass can mimic a cored dark matter profile. However, the joint model suppresses the high-cross-section mode seen in lensing-only analyses.
Concentration: The derived halo concentration ( $c_{200m} \approx 10$ ) is $\sim 2\sigma$ higher than standard $\Lambda$ CDM predictions (L16 relation). The authors attribute this to the selection bias of strong lensing (which favors concentrated, elongated halos) and the relaxed state of MACS J0138.

B. System Parameters

Halo Mass: $\log_{10}(M_{200m}/M_\odot) = 14.81 \pm 0.12$ .
Stellar Mass-to-Light Ratio: $\log_{10} \Upsilon_* = 0.47^{+0.19}_{-0.35}$ .
Isothermal Radius: $\log_{10}(r_1/\text{kpc}) = 1.58^{+0.69}_{-0.99}$ .

C. Supernova Predictions

The updated mass model significantly alters predictions for the reappearance of the lensed supernovae:

SN Requiem: The next image (feature 'd') is predicted to appear between January 2027 and November 2028 (assuming $H_0 = 67.7$ km s $^{-1}$ Mpc $^{-1}$ ). This is roughly 12 years after the first appearance, significantly sooner than the previously predicted ~20-year delay (mid-2030s).
SN Encore: The next image is predicted for 2033–2034.

5. Significance

Tightening SIDM Limits: This result provides one of the most stringent constraints on SIDM at cluster scales to date, derived from a single system with unprecedented detail. It supports the hypothesis that SIDM cross-sections are velocity-dependent, as the cluster limit is lower than dwarf galaxy limits.
Cosmography: The refined time-delay predictions for SN Requiem and Encore are critical for upcoming observations. Measuring these delays will allow for a high-precision determination of the Hubble constant ( $H_0$ ) from a single system, helping to resolve the Hubble Tension.
Modeling Benchmark: The methodology demonstrates the power of combining complementary gravitational probes (lensing + kinematics) to break degeneracies in mass modeling. This approach sets a new standard for future studies of dark matter physics and time-delay cosmography in strong lensing systems.

In conclusion, the paper establishes that MACS J0138-2155 is consistent with CDM or SIDM with a low cross-section, while providing a robust framework for future precision cosmology using multi-messenger strong lensing systems.