The Three Hundred Project: Dynamical state of galaxy clusters and morphology from multi-wavelength synthetic maps

We study the connection between morphology and dynamical state of the simulated galaxy clusters in $z\in[0,1.031]$ from THE THREE HUNDRED Project. We quantify cluster dynamical state using a combination of dynamical indicators from theoretical measures and compare this combined parameter, $\chi$, with the results from morphological classifications. The dynamical state of the cluster sample shows a continuous distribution from dynamically relaxed, more abundant at lower redshift, to hybrid and disturbed. The dynamical state presents a clear dependence on the radius, with internal regions more relaxed than outskirts. The morphology from multi-wavelength mock observation of clusters in X-ray, optical, and Sunyaev-Zel'dovich (SZ) effect images, is quantified by $M$ -- a combination of six parameters for X-ray and SZ maps and the offsets between the optical position of the Brightest Central Galaxy (BCG) and the X-ray/SZ centroids. All the morphological parameters are highly correlated with each other, while they show a moderately strong correlation with the dynamical $\chi$ parameter. The X-ray or SZ peaks are less affected by the dynamical state than centroids, which results in reliable tracers of the cluster density peak. The principal source of contamination in the relaxed cluster fraction, inferred from morphological parameters, is due to dynamically hybrid clusters. Compared to individual parameters, which consider only one aspect of cluster property (e.g. only clumping or asymmetry), the combined morphological and dynamical parameters ($M$ and $\chi$) collect more information and provide a single and more accurate estimation of the cluster dynamical state.