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Imprints of Mass Accretion History on Galaxy Cluster Morphology

This study characterizes 305 massive galaxy clusters from The300 project to demonstrate that their mass accretion histories can be effectively constrained by correlating both dark matter dynamical state indicators and projected stellar morphological features with accretion rates at different cosmic epochs, utilizing Multivariable Conditional Abundance Matching to predict accretion histories and select specific cluster subsamples.

Original authors: Kabelo Tsiane, Camille Avestruz, Elena Rasia, Roan Haggar, Jesse B. Golden-Marx, Guillaume Mahler, Elizaveta Sazonova, James Taylor, Massimo Meneghetti

Published 2026-08-19

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CC BY 4.0

Original authors: Kabelo Tsiane, Camille Avestruz, Elena Rasia, Roan Haggar, Jesse B. Golden-Marx, Guillaume Mahler, Elizaveta Sazonova, James Taylor, Massimo Meneghetti

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

Galaxy clusters are the largest structures in the universe held together by gravity. They are not static collections of stars and gas, but rather dynamic systems that grow over billions of years by swallowing smaller galaxies and groups of stars. This process of growth, known as mass accretion, leaves a lasting mark on the cluster. Just as a tree's rings record its history of growth and drought, a galaxy cluster's current shape and internal motion record its history of collisions and mergers. Understanding this history is crucial for astronomers because the way these massive objects form influences how we measure the universe's expansion and the nature of dark matter. If a cluster is still settling down after a recent crash, its properties look different than if it has been quiet for a long time, and these differences can skew our calculations of the cosmos.

A team of researchers set out to decode these histories by looking at the shapes of galaxy clusters. They used a massive computer simulation called The300, which created 305 realistic galaxy clusters from scratch, allowing them to see the invisible dark matter and the visible stars in perfect detail. The scientists wanted to know if they could look at a cluster today and tell exactly when it had its last major meal. They focused on two types of clues: the internal movements of the invisible dark matter, which are hard to see in the real world, and the visible arrangement of stars, which can be photographed by telescopes. By comparing the visible shapes to the known history of the simulated clusters, they aimed to build a tool that could read the past of real clusters in the sky.

The researchers found that the visible arrangement of stars does indeed hold the key to a cluster's past, though the connection is not perfect. They discovered that the shape of the very center of a cluster is most sensitive to events that happened long ago. In contrast, the shape of the outer regions tells a story about more recent activity. When a cluster experiences a major merger, the stars in the outer regions get tossed around, creating a lopsided or disturbed appearance that fades over time. The team used a statistical method to link these shapes to the specific timeline of the cluster's growth. They found that by combining several different measurements of the star distribution, they could predict the cluster's growth history with reasonable accuracy, particularly for events that occurred within the last few billion years.

However, the study also revealed the limits of looking at light alone. The most accurate way to determine a cluster's history is to see the invisible dark matter and measure how fast its particles are moving relative to its center. The researchers found that these invisible measurements correlate much more strongly with the cluster's growth timeline than the visible star patterns do. When they tried to predict the history using only the visible stars, the accuracy dropped, and they lost some information about the earliest stages of the cluster's life. This suggests that while telescopes can see the scars of ancient collisions, the full story is often written in the dark matter that surrounds the stars, which remains invisible to our eyes.

Despite these limitations, the work offers a practical path forward for astronomers. The team developed a method that ranks clusters based on their shapes and uses that ranking to sort them into groups of "early formers" and "late formers." This approach does not require knowing the exact mass or distance of every star, only their relative order. This makes the technique potentially very useful for real-world observations, where data is often incomplete or noisy. By applying this ranking system, astronomers could select specific groups of clusters that have been quiet for a long time or those that are still chaotic, allowing for more precise studies of the universe's evolution. The study confirms that the shape of a galaxy cluster is a fossil record of its violent past, and with the right tools, we can begin to read it.

Technical Summary: Imprints of Mass Accretion History on Galaxy Cluster Morphology

Problem Statement
Galaxy clusters serve as critical cosmological probes, yet their utility is often compromised by biases and scatter in observable-mass scaling relations. These issues stem largely from the dynamical state of the clusters, which is an emergent feature of their mass accretion history (MAH). Mergers and accretion events drive systems out of hydrostatic equilibrium, introducing biases in mass estimates (e.g., a known ~20% bias in hydrostatic mass) and affecting intrinsic properties like triaxiality and thermodynamic profiles. While numerous proxies exist to quantify dynamical state—ranging from theoretical 3D parameters (e.g., substructure mass fraction, center-of-mass offset) to observable 2D morphological metrics (e.g., asymmetry, concentration)—there is no consensus on how to best link these indicators to specific epochs of a cluster's formation history. Furthermore, different metrics may be sensitive to different parts of the MAH, and the transition from "relaxed" to "disturbed" is a continuum rather than a dichotomy. This work seeks to quantify the connection between projected stellar morphological features and the full MAH of galaxy clusters, determining how well present-day observables can reconstruct past accretion events.

Methodology
The study utilizes a sample of 305 massive galaxy clusters from The300 project, a set of hydrodynamical re-simulations based on the MDPL2 dark-matter-only cosmology ( $\Omega_M=0.307, \sigma_8=0.823, H_0=67.8$ ).

Data Generation:
- Mass Accretion History (MAH): The MAH is parameterized as the normalized peak mass $m(a) = M_{peak}(a)/M_{peak}(a=1)$ , where $M_{peak}(a)$ is the maximum virial mass attained up to scale factor $a$ . This function is interpolated using piecewise cubic Hermite polynomials to ensure monotonicity across 128 snapshots ( $z=17$ to $z=0$ ).
- Theoretical Dynamical State (DS) Parameters: As a baseline, three 3D parameters are measured within $R_{200c}$ : substructure mass fraction ( $f_m$ ), center-of-mass offset ( $\Delta$ ), and virial ratio ( $\eta$ ).
- Morphological Measurements: Projected stellar density maps (generated at $z=0.06$ ) are analyzed using the statmorph Python library. Measurements include non-parametric statistics (Gini- $M_{20}$ , Concentration-Asymmetry-Smoothness) and Sérsic profile fits. Apertures are defined as a core region ( $r \le 30$ kpc) and a core-excised annulus ( $50 \text{ kpc} \le r \le 1 \text{ Mpc}$ ). The magnitude gap ( $m_{14}$ ) between the brightest and fourth brightest cluster members is also included.
Analytical Framework (MultiCAM):
The authors employ Multi-variable Conditional Abundance Matching (MultiCAM), a framework extending traditional abundance matching to multivariate predictions.
- The algorithm transforms feature vectors (morphological or DS parameters) and target vectors (MAH at various scale factors) into Gaussian space.
- A linear regression model is trained to predict the target distribution from the features.
- Inverse transformations map the predictions back to the original space, preserving the rank-ordering of the distributions.
- This approach allows the authors to predict the full MAH ( $m(a)$ ) from present-day ( $z=0$ ) observables without assuming a specific physical model for the relationship, making it potentially transferable to observational datasets.

Key Results

Correlation Strength and Time Lags:
- DS Parameters: There is a strong correlation ( $\rho_{sp} \gtrsim 0.5$ ) between present-day DS parameters and the MAH measured between $0.1 \lesssim z \lesssim 1$ . Specifically, the substructure mass fraction ( $f_m$ ) and center-of-mass offset ( $\Delta$ ) show the strongest anti-correlations with recent mass growth (indicating that high substructure/offset corresponds to a smaller $m(a)$ prior to a recent merger). The virial ratio ( $\eta$ ) shows weaker correlations.
- Morphological Parameters: Projected morphological features exhibit moderate correlations with MAH. Core-excised measurements ( $50 \text{ kpc} \le r \le 1 \text{ Mpc}$ ), particularly asymmetry and concentration, correlate better with late-time MAH ( $z \lesssim 0.5$ ). Core measurements ( $r \le 30$ kpc) show better correlation with early-time MAH ( $z \gtrsim 0.5$ ).
- Time Lag: The imprint of a merger is not instantaneous; it persists for several dynamical times ( $\sim 1.44$ Gyr). The study identifies a time lag where the strongest correlation between a present-day metric and the MAH occurs at a specific past epoch (e.g., $f_m$ at $z=0$ correlates most strongly with MAH at $z \approx 0.54$ ).
Predictive Power (MultiCAM):
- Using MultiCAM, the authors predict the MAH ( $m(a)$ ) from present-day features.
- Models trained on 3D DS parameters achieve peak prediction correlations of $\rho_{sp} \approx 0.7$ for the mass fraction between $1 \gtrsim z \gtrsim 0.1$ .
- Models trained on projected morphological features achieve lower but still reasonable performance, with peak correlations of $\rho_{sp} \approx 0.5$ in the same redshift range.
- Combining multiple features (both morphological and DS) generally improves predictive power over single-parameter models, with different features contributing information about different epochs of the accretion history.
- The magnitude gap ( $m_{14}$ ) provides weak correlation on its own but offers complementary late-time predictive power when combined with other morphological features.
Sample Selection Application:
The authors demonstrate a practical application by using MultiCAM coefficients to rank clusters by their predicted accretion history. By selecting the top and bottom quartiles of clusters based on these ranks, they successfully isolate subsamples with distinct formation histories (early vs. late forming), showing a clear separation in their actual MAHs. This validates the utility of these metrics for selecting specific dynamical subsamples for cosmological studies.

Significance and Claims
The paper claims to provide a quantitative link between the projected stellar morphology of galaxy clusters and their underlying mass accretion histories. Key contributions include:

Quantifying Imprints: Establishing that specific morphological features (core vs. core-excised) are sensitive to different epochs of the MAH, with core measurements tracing early assembly and outer regions tracing recent accretion.
Methodological Transferability: Demonstrating that MultiCAM, a rank-ordering based framework, can effectively translate simulation-based relationships to observational contexts. Because the method relies on rank ordering rather than absolute physical values, it is robust against discrepancies in subgrid physics or absolute calibration between simulations and observations.
Sample Selection: Providing a rigorous method to select "relaxed" or "disturbed" cluster subsamples based on their inferred accretion history, which is crucial for reducing biases in observable-mass scaling relations and improving cosmological parameter constraints (e.g., $\sigma_8$ and $\Omega_m$ ).

The authors remain modest regarding the limitations, noting that projected quantities inherently lose information compared to 3D data and that the predictive power drops significantly for very early accretion events ( $z > 1$ ) due to the finite lifetime of dynamical imprints. They emphasize that while the models are trained on simulations, the rank-ordering assumption allows for their application to real data, provided the relative ordering of the features is preserved.

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