The eventful life journey of galaxy clusters. I. Impact of DM halo and ICM properties on their full assembly histories

Context. Galaxy clusters assemble over gigayears in a very anisotropic environment, which causes a remarkable diversity in their mass assembly histories (MAH). Aims. In this work, we have aimed to understand how the present-day properties of the dark matter halo and the intracluster medium are related to the whole evolution of these structures. Methods. To this end, we analysed a $\Lambda$CDM hydrodynamical+$N$-Body simulation of a $(100 \, h^{-1} \mathrm{Mpc})^3$ volume, containing over 30 clusters and 300 groups, and looked at the individual and the stacked MAHs (determined from complete merger trees) in relation to properties of the DM haloes and the ICM at fixed cosmic time (indicators of assembly state). Results. The ensemble MAHs are well separated when stacked in bins of these indicators, yielding clear dependencies of evolutionary properties (such as formation redshift) on fix-time halo properties. Additionally, we find that different indicators are informative about distinct epochs of accretion. Finally, by summarising the complex MAH diversity with two parameters, we describe how different indicators bring complementary information in different directions of this biparametric space. Overall, halo spin and a combined indicator appear to be the ones encoding the most information about the MAH. Conclusions. The results shown here add up to the idea that the dynamical state of cosmic structures is a multifaceted concept, and warn that single indicators are incapable of capturing the whole complexity of the process. This work sheds light on the nature of this characterisation by untangling precisely when and how several indicators are informative about. In turn, this can provide clues to better constrain the MAH of observed structures.