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CHEX-MATE: Cluster Multi-Probes in Three Dimensions (CLUMP-3D) II. Combined Gas and Dark Matter Analysis from X-ray, SZE, and WL

This paper presents a multiprobe triaxial analysis methodology applied to the CHEX-MATE cluster Abell 1689, demonstrating that accounting for its line-of-sight elongation yields a significantly lower mass estimate than spherical models while confirming that its high concentration is intrinsic rather than an orientation artifact, and providing precise measurements of the non-thermal pressure fraction across its radius.

Original authors: Adriana Gavidia, Junhan Kim, Jack Sayers, Mauro Sereno, Loris Chappuis, Dominique Eckert, Keiichi Umetsu, Herve Bourdin, Federico De Luca, Stefano Ettori, Massimo Gaspari, Raphael Gavazzi, Scott Kay

Published 2026-06-03

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CC BY 4.0

Original authors: Adriana Gavidia, Junhan Kim, Jack Sayers, Mauro Sereno, Loris Chappuis, Dominique Eckert, Keiichi Umetsu, Herve Bourdin, Federico De Luca, Stefano Ettori, Massimo Gaspari, Raphael Gavazzi, Scott Kay, Lorenzo Lovisari, Pasquale Mazzotta, Gabriel Pratt, Elena Rasia, Mariachiara Rossetti

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 the universe as a giant, invisible web made of dark matter and hot gas. At the intersections of this web sit massive "cities" of galaxies called galaxy clusters. For a long time, astronomers have tried to measure the weight of these cities, but they've been making a big mistake: they've been assuming these cities are perfect spheres, like smooth beach balls.

This paper, titled CLUMP-3D, argues that galaxy clusters are actually more like squashed, stretched rugby balls or potatoes. They are "triaxial," meaning they have three different lengths (long, medium, and short) and are often stretched out in specific directions.

Here is a simple breakdown of what the researchers did and what they found, using everyday analogies:

1. The Problem: The "Spherical" Mistake

If you look at a rugby ball from the side, it looks long and oval. If you look at it from the end, it looks round. If you assume it's a perfect sphere, you will get the wrong measurements.

The Analogy: Imagine trying to guess the volume of a loaf of bread by measuring it as if it were a round meatball. You'd be way off.
The Consequence: When astronomers assumed galaxy clusters were spheres, their calculations for how heavy they are (their mass) were often too high. This is especially true for measurements taken using Weak Gravitational Lensing (WL). This technique looks at how the cluster's gravity bends the light of distant galaxies behind it, acting like a cosmic magnifying glass. If the "magnifying glass" is actually a stretched oval, the math changes.

2. The Solution: A 3D "Multi-Probe" Approach

To fix this, the team didn't just look at the cluster from one angle or with one tool. They combined three different "probes" (ways of seeing the cluster) to build a complete 3D picture:

X-rays: They looked at the hot gas inside the cluster (like seeing the steam inside a pressure cooker).
Sunyaev-Zel'dovich Effect (SZE): They looked at how the cluster distorts the background light of the universe (like seeing a heat haze).
Weak Lensing (WL): They looked at how the cluster bends light from galaxies behind it (like looking through a funhouse mirror).

By combining these three views, they could mathematically "de-project" the cluster, figuring out its true 3D shape rather than just guessing based on a 2D shadow.

3. The Test Case: Abell 1689

They tested their new method on a famous galaxy cluster called Abell 1689.

The Discovery: They found that Abell 1689 is indeed stretched out. It is about 27% longer along the line of sight (pointing toward Earth) than it is wide across the sky.
The Result: Because they corrected for this stretching, their new calculation for the cluster's mass is significantly lower than previous estimates.
- Old (Spherical) Estimate: ~17.77 units of mass.
- New (3D Rugby Ball) Estimate: ~13.69 units of mass.
- Takeaway: The cluster is lighter than we thought because we were previously overestimating its size by assuming it was a sphere.

4. The "Concentration" Mystery

Astronomers had noticed that Abell 1689 seemed to have an unusually high "concentration" (meaning its mass was packed very tightly in the center). Some thought this was a weird anomaly.

The Finding: The researchers found that even after correcting for the 3D shape, the cluster is still quite concentrated.
The Conclusion: The high concentration isn't just an optical illusion caused by the cluster's shape; it's a real physical feature. The cluster really is that dense in the middle.

5. The "Non-Thermal" Pressure

Finally, the team looked at the "pressure" inside the cluster.

The Analogy: Imagine a balloon. The air inside pushes out (thermal pressure). But if you shake the balloon, the air also moves chaotically (non-thermal pressure).
The Finding: They measured how much "shaking" (turbulence and motion) exists in the gas. They found that in the middle of the cluster, about 20% of the pressure comes from this "shaking" (non-thermal motion). At the very edges, this rises to nearly 30%.
Why it matters: This helps scientists understand how these clusters form and how they hold themselves together against gravity.

Summary

This paper is like upgrading from a 2D map to a 3D GPS. By realizing that galaxy clusters are stretched "rugby balls" rather than "beach balls," and by using three different telescopes to see them from all angles, the researchers were able to:

Correct the weight of a massive galaxy cluster (making it lighter).
Prove that its dense center is real, not just a trick of perspective.
Measure the "turbulence" inside the cluster's gas.

This method provides a much more accurate way to weigh the universe's largest structures.

Technical Summary: CHEX-MATE: CLUMP-3D II. Combined Gas and Dark Matter Analysis from X-ray, SZE, and WL

Problem Statement
Under the standard model of hierarchical structure formation, galaxy clusters are intrinsically triaxial rather than spherical. Applying spherically symmetric models to these structures introduces significant biases in derived properties, particularly mass estimates from weak gravitational lensing (WL), which are highly sensitive to the cluster's orientation and elongation along the line of sight (LOS). While triaxial models can mitigate these biases, they require deep multi-probe data and physically motivated models to constrain the three-dimensional geometry. Previous work (Paper I, Kim et al. 2024, hereafter K24) established a triaxial fitting formalism using only X-ray and Sunyaev-Zel'dovich (SZ) data to constrain gas geometry. However, this gas-only approach could not directly measure the total cluster mass or the non-thermal pressure support in the intracluster medium (ICM) without assumptions about the relationship between the gas and total mass distributions.

Methodology
This paper presents an extension of the K24 triaxial fitting pipeline by integrating weak lensing (WL) data with the existing X-ray and SZ analysis. The methodology involves:

Triaxial Geometry: The model assumes a triaxial ellipsoid for the ICM gas distribution and the gravitational potential. The intrinsic geometry is defined by axial ratios ( $q_1, q_2$ ) and Euler angles ( $\theta, \phi, \psi$ ) relative to the observer.
ICM Modeling: The electron density follows a modified $\beta$ -profile (Eq. 3), and the electron pressure follows a generalized Navarro-Frenk-White (gNFW) profile (Eq. 4). These profiles are projected along the LOS to generate model maps for X-ray surface brightness (SB), SZ Compton- $y$ parameter, and spectroscopic temperature.
Mass Reconstruction: Unlike previous approaches that assumed elliptical symmetry for the total density profile, this work assumes the gravitational potential follows the triaxial geometry of the ICM ( $q_{pot} = q_{ICM}$ ). This is motivated by simulations suggesting the potential is smoother than the total density. The total mass profile is constrained by the NFW form in a spherical basis, which is then numerically inverted via Poisson's equation onto the triaxial grid to generate the elliptical potential. This potential is projected to produce WL observables (reduced shear maps).
Fitting Framework: A Markov Chain Monte Carlo (MCMC) approach using emcee is employed to fit the combined dataset. The likelihood is defined by a total $\chi^2$ statistic combining SZ maps, X-ray SB (using a dual 2D/1D approach to mitigate clumping bias), X-ray temperature profiles, and 2D WL shear maps.
Non-Thermal Pressure: Once the total mass density and gas density profiles are constrained, the non-thermal pressure fraction ( $P_{nt}/P_{tot}$ ) is calculated by assuming a state of generalized hydrostatic equilibrium. The total pressure required to support the cluster against gravity is derived from the gravitational potential, and the non-thermal component is the difference between this total pressure and the thermal pressure derived from the gas temperature.

Key Contributions

Pipeline Integration: The paper successfully integrates WL data into the K24 gas-only triaxial pipeline, enabling the simultaneous measurement of cluster geometry, total mass, and concentration without relying on spherical symmetry assumptions.
Potential-Based Modeling: The authors introduce a novel approach where the triaxiality is applied to the gravitational potential rather than the total density profile, allowing for a smoother potential that aligns with ICM isodensity surfaces.
Validation: The methodology is validated using mock observations of clusters with known input parameters ( $M_{200c}$ , $c_{200c}$ , and geometry). The tests demonstrate that the pipeline can accurately recover input masses and geometries, with only minor biases in concentration when the input value deviates significantly from the prior distribution.

Results: Application to Abell 1689
The pipeline was applied to the CHEX-MATE cluster PSZ2 G313.33+61.13 (Abell 1689), utilizing XMM-Newton X-ray data, ACT/Planck SZ data, and Subaru WL data.

Geometry: The cluster is found to be elongated along the line of sight relative to the plane of the sky, with an elongation factor of $R_{LP} = 1.27 \pm 0.02$ .
Mass: Due to this elongation, the triaxial fit yields a total mass of $M_{200c} = (13.69^{+1.56}_{-1.41}) \times 10^{14} M_\odot$ . This is significantly lower than the value of $(17.77^{+2.00}_{-1.75}) \times 10^{14} M_\odot$ obtained from a spherically symmetric fit using the same methodology, highlighting the bias introduced by spherical assumptions.
Concentration: The triaxial fit yields a concentration of $c_{200c} = 8.55^{+2.20}_{-1.61}$ . This is consistent with the spherically symmetric value of $9.99^{+2.26}_{-1.78}$ , suggesting that the previously noted high concentration in Abell 1689 is not an artifact of triaxiality or orientation.
Non-Thermal Pressure: The non-thermal pressure fraction was measured in the radial range of 0.18–1.37 Mpc. The fraction exhibits a minimum of approximately 20% at intermediate radii, increasing to near 30% at both the smallest and largest radii, with a typical measurement precision of $\pm 5\%$ .

Significance
The paper demonstrates that combining X-ray, SZ, and WL data within a triaxial framework is essential for obtaining unbiased mass and concentration measurements for individual galaxy clusters. By explicitly modeling the 3D geometry, the study resolves the degeneracy between mass and elongation that plagues spherical analyses. Furthermore, the ability to reconstruct the total mass profile in a triaxial basis allows for a robust measurement of non-thermal pressure support in the cluster outskirts, providing observational constraints on the thermalization efficiency of accreting material that can be compared against hydrodynamical simulations. The results for Abell 1689 specifically indicate that its high concentration is an intrinsic property rather than a projection effect, and its mass is lower than previously estimated when spherical symmetry is assumed.