2010MNRAS.405..995P

We show that, observationally, the projected local density distribution in high-z clusters is shifted towards higher values compared to clusters at lower redshift. To search for the origin of this evolution, we analyse a sample of haloes selected from the Millennium simulation and populated using semi-analytic models, investigating the relation between observed projected density and physical three-dimensional (3D) density, using densities computed from the 10 and three closest neighbours. Both observationally and in the simulations, we study the relation between number of cluster members and cluster mass, and the number of members per unit of cluster mass. We find that the observed evolution of projected densities reflects a shift to higher values of the physical 3D density distribution. In turn, this must be related with the globally higher number of galaxies per unit of cluster volume N/V in the past. We show that the evolution of N/V is due to a combination of two effects: (i) distant clusters were denser in dark matter (DM) simply because the DM density within R₂₀₀(∼ the cluster virial radius) is defined to be a fixed multiple of the critical density of the Universe, and (ii) the number of galaxies per unit of cluster DM mass is remarkably constant both with redshift and cluster mass if counting galaxies brighter than a passively evolving magnitude limit. Our results highlight that distant clusters were much denser environments than today's clusters, both in galaxy number and mass, and that the density conditions felt by galaxies in virialized systems do not depend on the system mass.