Context. Galaxy clusters assemble over gigayears in a very anisotropic environment, leading to a remarkable diversity in their mass assembly histories (MAHs). Aims. In this work, we aim to understand how the present-day properties of the dark matter (DM) halo and the intracluster medium (ICM) are related to the whole evolution of these structures. Methods. To this end, we analysed a ΛCDM hydrodynamical + N-Body simulation of a (100 h−1 Mpc)3 volume, containing over 30 clusters and 300 groups. We looked at the individual and the stacked MAHs (determined from complete merger trees) in relation to the properties of the DM halos and the ICM at a fixed cosmic time (i.e. indicators of assembly state). Results. The ensemble MAHs are well separated when stacked in bins of these indicators, yielding clear dependencies of the evolutionary properties (e.g. formation redshift) on the fixed-time halo properties. Additionally, we find that different indicators offer a varying range of information on distinct epochs of accretion. Finally, by summarising the complex MAH diversity with two parameters, we have described how different indicators bring in complementary information in different directions of this biparametric space. Overall, the 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, with a warning 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 a number of these indicators provide information about. In turn, these results offer clues that can help to better constrain the MAH of observed structures.
Vallés-Pérez et al. (2025) studied this question.