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 simulated clusters in $z\in[0,1.031]$ from THE THREE HUNDRED Project cluster sample. We evaluate the dynamical state using a combination of dynamical parameters -- $\chi$ from theoretical measures and compare the results with other two relaxation criteria that come from observation measures: the morphology in mock X-ray and Sunyaev-Zeldovich (SZ) effect images of galaxy clusters -- the $M$ indicator which is a combination of seven morphological parameters, and the offsets $\Delta$ between the peaks or centroids of X-ray and SZ maps and the Brightest Central Galaxy (BCG) position estimated from optical maps. We study the efficiency of morphological indicators and the correlations with the dynamical state of the combined $M$ and dynamical $\chi$ parameters, that have the advantage of proving and collecting different aspects of the cluster structures than single parameters. An evolution with the redshift of the dynamical state is present, but the populations of the dynamical state classes differ when different radii are used. The main source of contamination in relaxed fraction inferred from morphological parameters is constituted by hybrid clusters. $M$ combined parameter describes with the same efficiency the morphology in X-ray and SZ maps, with a correlation coefficient of $\rho=0.81$. A moderately strong correlation between $M$ and $\chi$ is present, with a coefficient of $\rho=-0.66$. The offset parameters based on centroids are more sensitive to dynamical state than peaks positions offsets. The correlation with $\chi$ for centroids is of the same order of $M$, with $\rho=-(0.63$-$0.67)$ if SZ or X-ray centroids are respectively used.