Estimating the triaxiality of massive clusters from 2D observables in MillenniumTNG with machine learning

TL;DR

The paper tackles the problem of recovering the 3D triaxial geometry and orientation of massive galaxy clusters from 2D observables by introducing a fusion CNN-GNN network trained on high-fidelity MillenniumTNG simulations. It leverages 2D multi-wavelength images (soft, medium, hard X-ray, and tSZ) and graph representations of line-of-sight velocities, projected positions, and V-band luminosities to infer intrinsic shape and orientation, outperforming spherical-model baselines by about 30%. The authors report an $R^2=0.85$ for predicting the major-axis length and a $71 ext{\%}$ success rate in identifying prolate clusters aligned along the line of sight, demonstrating the viability of learning complex 3D cluster structure from 2D data. This approach advances precision cosmology by reducing biases from spherical assumptions in cluster analyses and enabling more accurate mass and morphology inferences from multi-wavelength surveys.

Abstract

Properties of massive galaxy clusters, such as mass abundance and concentration, are sensitive to cosmology, making cluster statistics a powerful tool for cosmological studies. However, favoring a more simplified, spherically symmetric model for galaxy clusters can lead to biases in the estimates of cluster properties. In this work, we present a deep-learning approach for estimating the triaxiality and orientations of massive galaxy clusters (those with masses $\gtrsim 10^{14}\,M_\odot h^{-1}$) from 2D observables. We utilize the flagship hydrodynamical volume of the suite of cosmological-hydrodynamical MillenniumTNG (MTNG) simulations as our ground truth. Our model combines the feature extracting power of a convolutional neural network (CNN) and the message passing power of a graph neural network (GNN) in a multi-modal, fusion network. Our model is able to extract 3D geometry information from 2D idealized cluster multi-wavelength images (soft X-ray, medium X-ray, hard X-ray and tSZ effect) and mathematical graph representations of 2D cluster member observables (line-of-sight radial velocities, 2D projected positions and V-band luminosities). Our network improves cluster geometry estimation in MTNG by $30\%$ compared to assuming spherical symmetry. We report an $R^2 = 0.85$ regression score for estimating the major axis length of triaxial clusters and correctly classifying $71\%$ of prolate clusters with elongated orientations along our line-of-sight.

Figures (2)

• Figure 1: Histogram of MTNG cluster mass. We define massive clusters as those having of ${\rm M_{200}} > 10^{14}$$\mathrm{M}_{\odot}$ , yielding 4,117 massive clusters in MTNG. Most cluster masses fall between ${\rm log_{10} (14.0-14.5)}$$\mathrm{M}_{\odot}$. For machine learning applications, we must ensure that low-frequency clusters are properly distributed across train/validation/test splits.
• Figure 2: Visualization of massive MTNG clusters. In each panel, dark matter particles (sampled at 1-in-100) are shown in blue, gas particles (sampled at 1-in-100) are shown in magenta, and subhalos are shown in orange. Corresponding ellipses are drawn for the $\epsilon_{+}$ of the positions. Blue ellipses correspond to $\epsilon_{+}$ measured from the dark matter positions weighted by particle mass, magenta ellipses correspond to that of gas particle positions weighted by particle mass and the orange ellipses correspond to that of V-band luminosity weighted subhalo positions. We additionally show green ellipses which correspond to the $\epsilon_{+}$ measured using all subhalos given equal weighting. The the black dashed circle shows where $\rm R_{200}$ lies from the center of the cluster. For this work, we utilize $\epsilon_{+}$ of all subhalo positions as shown in the green ellipses.