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Lensing-Reconstructed Dark Matter-Intracluster Medium Coherence as a Probe of Cluster Dynamical State: Application to HSTFF, RELICS, and CLASH Clusters

This paper introduces a Fourier-space coherence analysis between lensing-reconstructed dark matter and X-ray intracluster gas as a new diagnostic for cluster dynamical states, revealing that most of the 49 studied clusters are dynamically disturbed and demonstrating the method's complementarity to traditional classification techniques.

Original authors: Giulia Cerini (Jet Propulsion Laboratory California Institute of Technology), Sayan Saha (Northeastern University), Jacqueline McCleary (Northeastern University), Eric Habjan (Northeastern University)

Published 2026-07-03

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CC BY 4.0

Original authors: Giulia Cerini (Jet Propulsion Laboratory California Institute of Technology), Sayan Saha (Northeastern University), Jacqueline McCleary (Northeastern University), Eric Habjan (Northeastern University), Nico Cappelluti (Department of Physics University of Miami), Priyamvada Natarajan (Department of Astronomy Yale University, Department of Physics Yale University, Black Hole Initiative Harvard University), Sabina Khizroev (Duke University), Jason Rhodes (Jet Propulsion Laboratory California Institute of Technology), Eric Huff (Jet Propulsion Laboratory California Institute of Technology), Nicole Chidester (Northeastern University), Maya Amit (New York University), Andrew Robertson (Carnegie Observatories), Bryanne McDonough (Adelphi University), Elena Bellomi (Center for Astrophysics Harvard & Smithsonian), Erwin T. Lau (Nara Womens University), John ZuHone (Center for Astrophysics Harvard & Smithsonian)

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 galaxy cluster as a giant, cosmic city. This city isn't made of buildings, but of two main things: a massive, invisible "scaffolding" made of Dark Matter (which holds everything together with gravity) and a hot, glowing "fog" of gas called the Intracluster Medium (which shines in X-rays).

Usually, in a calm, settled city, the scaffolding and the fog are perfectly aligned. They move together, breathe together, and look like they belong to the same neighborhood. But when the city is in chaos—perhaps two cities are crashing into each other—the invisible scaffolding might keep moving in one direction while the hot gas gets sloshed around in another, creating a messy mismatch.

This paper is like a new way of checking the "vibe" of these cosmic cities to see if they are calm or chaotic.

The New Detective Tool: "Coherence"

The authors, led by Giulia Cerini, developed a mathematical tool to measure how well the invisible scaffolding (Dark Matter) and the hot gas (ICM) are dancing together. They call this "coherence."

Think of it like listening to a duet:

High Coherence: The two singers are perfectly in sync, hitting the same notes at the same time. This means the cluster is relaxed and calm.
Low Coherence: One singer is off-key or lagging behind. This means the cluster is disturbed, likely because it's in the middle of a violent crash or merger.

They measure a specific number called the "Coherence Length" ( $\ell_{CR}$ ).

Small Coherence Length: The singers stay in sync even when they get very close together. The city is very calm.
Large Coherence Length: The singers only stay in sync when they are far apart; as soon as they get close, they start fighting. The city is chaotic.

What They Did

The team looked at 49 galaxy clusters from three major space surveys (HST Frontier Fields, CLASH, and RELICS). They used two powerful telescopes:

Hubble Space Telescope: To map the invisible Dark Matter (by seeing how it bends light from background stars).
Chandra X-ray Observatory: To map the hot gas.

They compared these two maps for every cluster to see how well they matched up.

The Big Findings

The "Relaxed" Minority: When they set a strict rule for what counts as "calm" (a small coherence length), they found that only about 16% of the 49 clusters were truly relaxed. If they were a bit more lenient, about 41% were considered calm.
The "Chaos" Surprise: This method found more chaotic clusters than previous methods did. About 24% of the time, their new tool said a cluster was "messy," while older methods (which mostly looked at the shape of the X-ray gas) said it was "calm."
- Why? The new tool is like a high-definition microscope. It can see small-scale mismatches between the Dark Matter and the gas that older, blurrier methods missed. It's sensitive to the fact that even if the gas looks round, the invisible Dark Matter underneath might be shifting around.
The "Map" Problem: The authors admitted their tool has a quirk. To measure the "dance," they needed a map of the Dark Matter. Some of these maps were made using different mathematical guesses (models).
- Sometimes, changing the math model changed the result. About half the time, the "coherence length" varied depending on which map you used.
- Also, some maps were "cropped" (cut off at the edges). If you cut off the edge of a chaotic city, it might look calmer than it really is. The authors found that smaller maps tended to make clusters look more relaxed than they actually were.

The Conclusion

This paper introduces a new, powerful way to diagnose the health of galaxy clusters. It acts like a "stress test" that checks if the invisible gravity holding the cluster together is still in sync with the hot gas inside.

While it confirms that many clusters are indeed chaotic (more so than we thought), the authors warn that to get the perfect diagnosis, we need better, more uniform maps of the invisible Dark Matter. They are currently working on using new balloon-borne telescopes and future space missions to get these clearer maps, which will help them understand the universe's structure even better.

In short: They built a new ruler to measure how "together" the invisible and visible parts of galaxy clusters are. They found that many clusters are more "out of sync" than we realized, but they also realized their ruler needs to be calibrated with better maps to be perfectly accurate.

Technical Summary: Lensing-Reconstructed Dark Matter-Intracluster Medium Coherence as a Probe of Cluster Dynamical State

Problem Statement
Galaxy clusters are critical laboratories for cosmology and the study of dark matter (DM), yet their utility is limited by uncertainties in mass estimation and dynamical state classification. Current methods for inferring cluster mass often assume hydrostatic or virial equilibrium, an assumption that breaks down in merging or accreting systems, leading to mass underestimates of up to ~20%. Furthermore, existing dynamical state indicators—primarily based on X-ray morphology (e.g., centroid shifts, power ratios) or optical offsets—often fail to capture the full complexity of multi-scale misalignments between the collisionless dark matter and the collisional intracluster medium (ICM). There is a need for a robust, scale-resolved diagnostic that directly couples the dominant gravitational component (DM) with the baryonic gas to identify departures from equilibrium without relying on equilibrium assumptions.

Methodology
This study applies a Fourier-space coherence analysis to a sample of 49 observed galaxy clusters from the Hubble Frontier Fields (HSTFF), Cluster Lensing And Supernova Survey with Hubble (CLASH), and Reionization Lensing Cluster Survey (RELICS). The methodology involves:

Data Integration: The authors combine publicly available gravitational lensing convergence maps ( $\kappa$ ), reconstructed from HST strong and weak lensing data, with Chandra X-ray imaging (0.5–7 keV) of the ICM.
Signal Processing: To isolate intrinsic fluctuations, the X-ray data is processed using the $A-B$ method (splitting observations into two interleaved subsets) to generate noise maps ( $\frac{1}{2}(A-B)$ ) and signal maps ( $\frac{1}{2}(A+B)$ ). Point sources are masked using $r_{90}$ radii. Similarly, uncertainty maps for the lensing convergence are utilized.
Fourier Analysis: The authors compute the 1D auto-power spectra for the mass ( $P_m$ ) and X-ray ( $P_X$ ) fields, subtracting noise contributions to obtain clean spectra. They then calculate the cross-power spectrum ( $P_{mX}$ ) between the lensing mass and X-ray gas.
Coherence Metric: The coherence $C(q)$ is defined as the normalized cross-power spectrum: $C(q) = (P_{mX})^2 / (P_m P_X)$ . This quantifies the correlation between DM and gas as a function of spatial scale.
Dynamical Indicator: The primary diagnostic is the coherence length ( $\ell_{CR}$ ), defined as the smallest scale at which the coherence drops below $C = 0.9$ . Relaxed systems are expected to exhibit high coherence across all scales (small $\ell_{CR}$ ), while disturbed systems show decorrelation at small and intermediate scales (large $\ell_{CR}$ ).
Systematic Controls: The analysis accounts for lensing model dependence by comparing multiple reconstructions (e.g., Zitrin, CATS, Lenstool) per cluster and investigates map-size effects by testing the stability of $\ell_{CR}$ against truncated fields of view.

Key Contributions

First Observational Application: This paper presents the first application of the DM-ICM coherence framework to a representative sample of 49 observed galaxy clusters, moving beyond previous validation on single systems or simulations.
Scale-Resolved Diagnostic: It introduces $\ell_{CR}$ as a quantitative, scale-dependent measure of dynamical state that directly probes the alignment between the total mass distribution and the hot gas.
Public Code: The authors announce the release of accompanying public code designed for coherence-based dynamical state assessment, intended for broad applicability to future datasets.
Systematic Characterization: The work explicitly quantifies the sensitivity of coherence measurements to lensing model assumptions and the heterogeneous extent of available convergence maps.

Results

Dynamical Classification: Using a conservative threshold of $\ell_{CR}/r_{500} < 0.2$ , only ~16% (9/49) of the sample is classified as dynamically relaxed. A more permissive threshold ( $\ell_{CR}/r_{500} < 0.4$ ) increases this fraction to ~41% (20/49).
Comparison with Previous Classifications: The coherence method identifies a ~24% disagreement (12 out of 49 clusters) with previous classifications based on X-ray morphology or cool-core status. In these cases, the coherence method classifies systems as more disturbed than traditional X-ray or optical indicators suggest. For example, several CLASH clusters, selected for regular X-ray morphologies, exhibit large coherence lengths ( $\ell_{CR}/r_{500} > 0.4$ ), indicating significant DM-ICM decorrelation.
Model Dependence: Approximately 52% of the sample shows non-negligible scatter in $\ell_{CR}$ across different lensing models. This indicates that the coherence signal is sensitive to the specific assumptions and constraints (particularly strong-lensing constraints) used in mass reconstruction.
Map Size Effects: Tests on clusters with large map extents reveal that reducing the field of view can artificially lower the inferred coherence length, making disturbed systems appear more relaxed. This highlights the need for homogeneous, wide-field maps.
Physical Interpretation: The results confirm that relaxed systems (e.g., Abell 2261) maintain high coherence down to small scales, while merging systems (e.g., MACS J0717+3745, Abell 2744) show a rapid drop in coherence, consistent with merger-induced displacements between collisionless DM and collisional gas.

Significance
The paper claims that lensing-X-ray coherence provides a complementary and physically interpretable probe of cluster dynamical state. Its primary significance lies in its ability to directly combine the two dominant mass components (DM and ICM) to reveal multi-scale misalignments that are often missed by real-space morphological estimators. The authors argue that this method offers a more stringent test of equilibrium, potentially identifying a larger population of dynamically unrelaxed systems than previously recognized.

However, the authors are modest regarding the immediate universality of the results. They emphasize that the current application is limited by the heterogeneity of existing lensing maps (both in methodology and field of view) and the dependence on specific mass models. Consequently, the paper positions this work as a foundational step, arguing that future applications to homogeneous, model-independent weak-lensing datasets (such as those from SuperBIT, Euclid, or Roman) are necessary to fully control reconstruction systematics and realize the method's potential for precision cosmology and dark matter physics.

The New Detective Tool: "Coherence"

What They Did

The Big Findings

The Conclusion

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