Imprints of Mass Accretion History on Galaxy Cluster Morphology

Abstract: Variations in dynamical states of galaxy clusters can introduce biases and scatter in observable-mass relations. The dynamical state of a cluster is an emergent feature of its mass accretion history (MAH), it is therefore useful to constrain the MAH of the cluster. In this work, we characterize 305 massive clusters from The300 project by connecting features from their projected stellar distributions to their mass accretion histories (MAH). As a baseline, we first correlate host dark matter halo dynamical state indicators at $z=0$ with their MAH via the Spearman rank correlation coefficient $ρ<em>{\mathrm{sp}}$. Both substructure mass fraction and center-of-mass offset measurements correlate strongly with the MAH measured between $0.1\lesssim z\lesssim 1$. We repeat this exercise with morphological measurements of projected stellar density maps, many of which exhibit moderate correlation strength with different times in the MAH. Broadly, core morphological measurements ($r \leq 30\,\mathrm{kpc}$) correlate better with early-time MAH. Core-excised ($50\,\mathrm{kpc} \leq r \leq 1\,\mathrm{Mpc}$) morphological measurements correlate better with late-time MAH. We further quantify the MAH prediction power of both traditional dynamical state indicators and morphological parameters using Multivariable Conditional Abundance Matching (MultiCAM). MultiCAM employs simple rank-ordering operations, making it straightforward to translate to observed datasets. We find reasonable ($ρ</em>{\mathrm{sp}} \geq 0.6$) performance for predictions of the mass fraction between $1\lesssim z\lesssim 0.1$, though with notable information loss when using projected quantities. In one example application of our methodology, we use the coefficients of the MultiCAM models to select subsamples of galaxy clusters that have accreted more (or less) of their $z = 0$ mass budget over a given time frame.

• The paper quantifies how present-day cluster properties encode mass accretion history using 305 massive clusters from The Three Hundred hydrodynamical simulations and MultiCAM rank-order regression.
• Three-dimensional dynamical indicators predict late-time accretion most effectively, with substructure fraction reaching Spearman correlations near 0.75, while projected morphology provides complementary information across earlier and later epochs.
• Core concentration traces earlier growth and core-excised asymmetry traces more recent accretion, allowing observable-based ranking of fast- and slow-growing clusters despite limitations from idealized simulated images.

Overview

This paper quantifies how a galaxy cluster's mass accretion history (MAH) is encoded in its present-day observable and theoretical properties. Using 305 massive clusters from The Three Hundred hydrodynamical simulation suite, the authors connect features of projected stellar density maps — measured with non-parametric morphology statistics — to the normalized peak mass history $m(a) = M_{\mathrm{peak}}(a)/M_{\mathrm{peak}}(a=1)$ of the main progenitor halo. As a benchmark, they compare against standard three-dimensional dark matter dynamical state (DS) parameters, and they use MultiCAM, a multivariable conditional abundance matching framework built on rank-ordering assumptions, to assess how well present-day properties predict the full accretion history (2608.18031).

The motivation is practical: merger-driven departures from equilibrium introduce bias and scatter in observable–mass scaling relations and in hydrostatic mass estimates, propagating into cosmological constraints on $\sigma_8$ and $\Omega_m$. Because different dynamical state metrics are sensitive to different portions of the MAH, the authors treat dynamical state as a continuum rather than a relaxed/disturbed dichotomy.

Data and methodology

The sample is drawn from The Three Hundred project: 324 regions re-simulated from MDPL2 with GADGET-X including AGN and stellar feedback, yielding clusters with $M_{200c} > 6.42\times10^{14}\,h^{-1}M_\odot$. Stellar density maps ($5\times5$ Mpc field, 10 Mpc line-of-sight depth) are produced at $a=0.94$ for 305 clusters along three orthogonal projections. Morphological diagnostics are computed with statmorph, using a simplified circular/annular segmentation appropriate to noiseless, foreground-free simulation images. Features include half-light radius, concentration $C = 5\log_{10}(r_{80}/r_{20})$, the asymmetry index $A$, S\'ersic amplitude, and the projected magnitude gap $m_{14}$ measured between the BCG (within 30 kpc) and the fourth brightest member within $0.5R_{200c}$. Apertures were selected empirically: core-excised annuli ($\sigma_8$0) and core apertures ($\sigma_8$1).

The benchmark DS parameters are the substructure mass fraction $\sigma_8$2, center-of-mass offset $\sigma_8$3, and virial ratio $\sigma_8$4, computed at $\sigma_8$5 (and $\sigma_8$6). MultiCAM Gaussianizes feature and target marginals via quantile transforms, fits linear regression in that space, then inverts the transforms; because it relies only on rank ordering, the authors argue it should transfer more readily from simulations to observations than flexible nonlinear models.

Imprints of MAH on dynamical state parameters

Cross-correlation heatmaps of $\sigma_8$7 against each DS parameter's time evolution show that accretion imprints persist over several dynamical times ($\sigma_8$8 Gyr). Mass accretion at any epoch correlates tightly ($\sigma_8$9) with accretion within $\Omega_m$0 in scale factor, establishing the timescale on which imprints remain detectable. At $\Omega_m$1, the substructure mass fraction carries the strongest imprint, anti-correlated at $\Omega_m$2 with mass accreted as early as $\Omega_m$3 ($\Omega_m$4); $\Omega_m$5 shows a weaker but systematic correlation ($\Omega_m$6), and $\Omega_m$7 weaker still, peaking near $\Omega_m$8.

A key finding is that the time lag of the imprint is not constant across epochs: measurements made at earlier times ($\Omega_m$9) trace accretion further back in time with shorter-lived peak signals. This implies that dynamical state metrics calibrated at $M_{200c} > 6.42\times10^{14}\,h^{-1}M_\odot$0 are less suitable for characterizing higher-redshift cluster samples — an increasingly relevant concern as high-$M_{200c} > 6.42\times10^{14}\,h^{-1}M_\odot$1 cluster catalogs grow. Measurements at $M_{200c} > 6.42\times10^{14}\,h^{-1}M_\odot$2 show broadly similar but weaker and shorter-lived correlations, suggesting the outskirts retain more MAH information. The authors also note an unexplained blue arc in the correlation maps (a delayed anti-correlation whose longest lags cluster around $M_{200c} > 6.42\times10^{14}\,h^{-1}M_\odot$3, near the end of matter domination), which they flag as unresolved.

Predictive power for the full MAH

Using only present-day DS parameters, MultiCAM achieves its best performance at late epochs: the model trained on all DS features predicts $M_{200c} > 6.42\times10^{14}\,h^{-1}M_\odot$4 with $M_{200c} > 6.42\times10^{14}\,h^{-1}M_\odot$5 for $M_{200c} > 6.42\times10^{14}\,h^{-1}M_\odot$6, peaking near $M_{200c} > 6.42\times10^{14}\,h^{-1}M_\odot$7 at $M_{200c} > 6.42\times10^{14}\,h^{-1}M_\odot$8. Substructure fraction dominates the constraining power, with minor mergers contributing meaningfully through the distinction between total and most-massive-substructure fractions. The magnitude gap adds little information in this high-mass regime ($M_{200c} > 6.42\times10^{14}\,h^{-1}M_\odot$9), consistent with expectations that $5\times5$0 correlates most strongly with assembly history in lower-mass systems; restricting to clusters with large $5\times5$1 recovers moderate late-time correlations ($5\times5$2 at $5\times5$3).

Projected morphological features perform more weakly but still usefully. Core-excised asymmetry reaches moderate correlation ($5\times5$4) over $5\times5$5, while core concentration traces early-time accretion ($5\times5$6, $5\times5$7). Combining all morphologies plus $5\times5$8 yields predictions correlated with truth at $5\times5$9 over $a=0.94$0, peaking slightly above 0.7. The aperture-dependent behavior — core morphology encoding early growth, core-excised morphology encoding recent growth — motivates multi-aperture feature vectors, and the paper demonstrates complementary early/late information content when combining features.

For the alternative parameterization $a=0.94$1 (the epoch at which a mass fraction is first reached), the full DS-feature model attains $a=0.94$2 for $a=0.94$3, comparable to the $a=0.94$4 results. For formation time specifically, the DS model explains $a=0.94$5 of variance versus $a=0.94$6 for morphologies alone. Notably, an XGBoost comparison performs no better on DS features ($a=0.94$7) while producing physically implausible residual-feature correlations, whereas MultiCAM residuals are largely uncorrelated with features — supporting the claim that rank-ordering models extract interpretable information comparably to nonlinear learners.

Sample selection application

As a demonstration, the authors weight present-day features by MultiCAM regression coefficients evaluated at $a=0.94$8 ($a=0.94$9) to score clusters, then compare upper- and lower-quartile splits of the resulting ranked MAH distributions. The median separation in $C = 5\log_{10}(r_{80}/r_{20})$0 is 0.484 for DS-trained weights and 0.353 for morphology-trained weights, closely matching separations obtained from raw Spearman coefficients (0.480 and 0.353). This confirms that rank ordering by present-day observables can isolate fast- versus slow-accreting subsamples without requiring accurate absolute $C = 5\log_{10}(r_{80}/r_{20})$1 recovery — a property the authors emphasize as central to observational applicability.

Limitations and open questions

Several caveats bear directly on the results. The analysis uses noiseless, PSF-free stellar density maps with idealized segmentation; real observations require masking non-member contaminants via photometric or spectroscopic redshifts, which would unpredictably perturb feature ranks. The transferability of MultiCAM to data rests on the assumption that feature rank orderings are preserved across simulations and observations despite differing baryonic feedback prescriptions. The physical interpretation of the unexplained anti-correlation arc in the DS–MAH cross-correlations remains open, as does the apparent coincidence of maximal lags with the end of the matter-dominated era. The projected-information penalty is significant ($C = 5\log_{10}(r_{80}/r_{20})$2 for 3D inputs versus $C = 5\log_{10}(r_{80}/r_{20})$3 for projected ones at matched epochs), so whether multi-wavelength observables can close this gap is explicitly deferred to future work. Finally, all conclusions rest on one simulation suite and one baryonic physics model at fixed cosmology.

Conclusion

This work establishes quantitative, epoch-dependent links between galaxy cluster morphology and mass accretion history, demonstrating that (i) substructure fraction is the strongest single tracer among 3D dynamical indicators, (ii) core and core-excised optical morphology encode early- and late-time accretion respectively, and (iii) simple rank-ordering regression combines these into useful predictive models of the full MAH, reaching $C = 5\log_{10}(r_{80}/r_{20})$4 (3D) and $C = 5\log_{10}(r_{80}/r_{20})$5–$C = 5\log_{10}(r_{80}/r_{20})$6 (projected) at intermediate redshifts. By framing prediction as a rank-ordering problem, the approach offers a direct path toward selecting dynamically characterized cluster subsamples in upcoming wide-field surveys, with the principal open challenge being robust morphological measurement in realistic, contaminated imaging data.