| Abstract
| - A classification of the galaxy cluster’s dynamical state is crucial when dealing with large samples. The identification of the most relaxed and most disturbed objects is necessary for both cosmological analysis, focused on spherical and virialised systems, and astrophysical studies, centred around all those micro-physical processes that take place in disturbed clusters (such as particle acceleration or turbulence). Among the most powerful tools for the identification of the dynamical state of clusters is the analysis of their intracluster medium (ICM) distribution. In this work, we performed an analysis of the X-ray morphology of the 118 (Cluster HEritage project with XMM-Newton - Mass Assembly and Thermodynamics at the Endpoint of structure formation) CHEX-MATE clusters, with the aim of providing a classification of their dynamical state. To investigate the link between the X-ray appearance and the dynamical state, we considered four morphological parameters: the surface brightness concentration, the centroid shift, and the second- and third-order power ratios. These indicators result to be strongly correlated with each other, powerful in identifying the disturbed and relaxed population, characterised by a unimodal distribution, and not strongly influenced by systematic uncertainties. In order to obtain a continuous classification of the CHEX-MATE objects, we combined these four parameters in a single quantity, M, which represents the grade of relaxation of a system. On the basis of the M value, we identified the most extreme systems of the sample, finding 15 very relaxed and 27 very disturbed galaxy clusters. From a comparison with previous analysis on X-ray selected samples, we confirmed that the Sunyaev-Zeldovich (SZ) clusters tend to be more disturbed. Finally, by applying our analysis to a simulated sample, we found a general agreement between the observed and simulated results, with the only exception being the concentration. This latter behaviour is partially related to the presence of particles with a high smoothed-particle-hydrodynamics density in the central regions of the simulated clusters due to the action of the idealised isotropic thermal active galactic nucleus (AGN) feedback.
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