On the choice of the most suitable indicator for the assembly state of dark matter haloes through cosmic time

The dynamical state and morphological features of galaxies and galaxy clusters, and their high-redshift precursors, are tightly connected with their assembly history, encoding crucial information about the formation and evolution of such cosmic structures. As a first step towards finding an optimal indicator of the assembly state of observed structures, we use a cosmological simulation of a moderate volume to critically examine the best definition of an indicator that is able to discriminate dark matter haloes undergoing mergers and/or strong accretion from haloes experimenting a relaxed evolution. Using a combination of centre offset, virial ratio, mean radial velocity, sparsity and ellipticity of the dark matter halo, we study how the thresholds on these parameters, as well as their relative weights, should evolve with redshift to provide the best classification possible. This allows us to split a sample of haloes in a totally relaxed, a marginally relaxed and an unrelaxed subsamples. The resulting classification strongly correlates with the merging activity obtained from the analysis of complete merger trees extracted from whole simulation data. The results on how the different indicators depend on redshift and halo mass, and their optimal combination to better match the true assembly history of haloes, could constitute relevant hints to find a suitable set of indicators applicable to observational data.