Merger-induced disturbance and temporal signatures in galaxy clusters: a combined phase space and photometric analysis

Abstract

We present a physically interpretable framework to quantify dynamical disturbances in galaxy clusters using projected two-dimensional phase-space information. Based on the TNG-Cluster simulation, we construct a disturbance score that captures merger-driven asymmetries through features such as velocity dispersion and Gaussian Mixture Model (GMM) peak fitting, which captures asymmetries indicative of dynamical disturbance. All features are derived from observable quantities and are intended to be measurable in future surveys. To enable observational application, we adopt a simplified estimator using aperture mass map statistics as a mass ratio proxy in TNG300-1, and validate its performance with weak lensing data from The Local Volume Complete Cluster Survey (LoVoCCS). While phase-space diagnostics reveal merger-driven asymmetries, they are not sensitive to whether the secondary progenitor is infalling or receding, and thus cannot distinguish future mergers from past mergers. To address this, we incorporate the star formation rate (SFR) from TNG-Cluster and propose the blue galaxy fraction as a promising observational tracer of merger timing. Finally, we construct mock Chandra X-ray images of TNG-Cluster halos at redshift $z=0.2$, and find that the offset between the X-ray peak and the position of the most massive black hole (used as a proxy for the Brightest Cluster Galaxy, BCG) correlates with our disturbance score, serving as a consistency check. We also perform case studies using LoVoCCS observational data, correlating the blue galaxy fraction with disturbance scores derived from the eROSITA morphology catalog.

Figures (18)

• Figure 1: Mock X-ray images of FOF halo 0 from three projections (X, Y, Z), centered on the group position and smoothed to a $\sim$10 kpc resolution. Black dots mark the centers used for cropping. A 1000 kpc scale bar is shown in each panel. The color indicates the photon counts, normalized using logarithmic scaling.
• Figure 2: Example mock observation from the TNG300-1 simulation. A 500 kpc scale bar is shown in each panel. Left: Simulated aperture mass map (S/N) of FOF halo 142, with $R_{200c} \sim 750$kpc, incorporating shape noise consistent with observational weak lensing data. For visualization, the maps are Gaussian-smoothed with a kernel scale of $\sim$ 60 kpc; this smoothing is applied for display purposes only. Right: Surface mass density map (dark matter + gas) in units of $\log\,M_\odot$/pixel. The positions of the central and the most massive satellite subhalos are marked for reference.
• Figure 3: Model performance as a function of $\tau$, evaluated using three target score definitions: past-merger (left), future-merger (middle), and full-merger (right). Orange lines show the $R^2$ on the training set, and blue lines show the $R^2$ on the test set. All results are based on the rotated projection configuration described in Section \ref{['sec: Decay Timescale Selection']}.
• Figure 4: Test $R^2$ as a function of the time window $\tau$ for the past-, future-, and full-merger scores, under matched time window conditions. The right panel summarizes the phase-space input features used in the model.
• Figure 5: Comparison of permutation feature importance rankings for models using the three merger score definitions: past-merger (left), future-merger (middle), and full-merger (right). Bars indicate the mean importance of each feature, with error bars representing the standard deviation over 10 independent permutations. The red dashed line marks the 0.01 threshold used for feature selection. Features are labeled F1–F17, ranked by importance within each model. Their definitions are as follows: F1: $\Delta R$, F2: $v_1$, F3: $v_2$, F4: $\Delta v$, F5: $\sigma_{r,1}$, F6: $\sigma_{r,2}$, F7: $\sigma_{v,1}$, F8: $\sigma_{v,2}$, F9: $f_n$, F10: bic1, F11: bic2, F12: $\Delta\mathrm{bic}$, F13: $\lambda_2/\lambda_1$, F14: $z$, F15: $f_m$, F16: $\sigma_r$, F17: $\sigma_v$.