What to expect from dynamical modelling of cluster haloes II. Investigating dynamical state indicators with Random Forest

TL;DR

This study uses Random Forest machine learning to identify key dynamical features, especially the virial ratio, that predict the dynamical state of galaxy clusters from simulations and mock observations, aiding observational analysis.

Contribution

It introduces a robust method for feature importance evaluation using out-of-bag scores and highlights the most informative features for dynamical state prediction, including the virial ratio.

Findings

Virial ratio ($$) is the most important single feature.

Simulation-based features outperform mock map features in predicting DS.

A combination of three diverse features saturates prediction accuracy.

Abstract

We investigate the importances of various dynamical features in predicting the dynamical state (DS) of galaxy clusters, based on the Random Forest (RF) machine learning approach. We use a large sample of galaxy clusters from the Three Hundred Project of hydrodynamical zoomed-in simulations, and construct dynamical features from the raw data as well as from the corresponding mock maps in the optical, X-ray, and Sunyaev-Zel'dovich (SZ) channels. Instead of relying on the impurity based feature importance of the RF algorithm, we directly use the out-of-bag (OOB) scores to evaluate the importances of individual features and different feature combinations. Among all the features studied, we find the virial ratio, $\eta$, to be the most important single feature. The features calculated directly from the simulations and in 3-dimensions carry more information on the DS than those constructed from the mock maps. Compared with the features based on X-ray or SZ maps, features related to the centroid positions are more important. Despite the large number of investigated features, a combination of up to three features of different types can already saturate the score of the prediction. Lastly, we show that the most sensitive feature $\eta$ is strongly correlated with the well-known half-mass bias in dynamical modelling. Without a selection in DS, cluster halos have an asymmetric distribution in $\eta$, corresponding to an overall positive half-mass bias. Our work provides a quantitative reference for selecting the best features to discriminate the DS of galaxy clusters in both simulations and observations.