Estimating the Triaxiality of Massive Clusters from 2D Observables in MillenniumTNG with Machine Learning

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 ≳10 ^14 M _⊙ 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 and the message passing power of a graph neural network in a multimodal, fusion network. Our model is able to extract 3D geometry information from 2D idealized cluster multiwavelength 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.