For a complete picture of galaxy cluster formation, it is important that we start probing the early epoch of z~2-7 during which clusters and their galaxies first began to form. Because the study of these so-called “proto-clusters” is currently limited by small number statistics, widely varying selection techniques and assumptions, we have performed a systematic study of cluster formation utilizing cosmological simulations. We use the Millennium Simulations to track the evolution of dark matter and galaxies in ~3,000 clusters from the earliest times to z=0. We define an effective radius R_e for proto-clusters and characterize their growth in size and mass. We show that the progenitor regions of galaxy clusters (M>10^14 M_sun/h) can already be identified at least up to z~5, provided that the galaxy overdensities, delta_gal, are measured on a sufficiently large scale (R_e~5-10 cMpc). We present the overdensities in matter, DM halos, and galaxies as functions of present-day cluster mass, redshift, bias, and window size that can be used to interpret the structures found in real surveys. We derive the probability that a structure having a delta_gal, defined by a set of observational selection criteria, is indeed a proto-cluster, and show how their z=0 masses can already be estimated long before virialization. Galaxy overdensity profiles as a function of radius are presented. We further show how their projected surface overdensities decrease as the uncertainties in redshift measurements increase. We provide a table of proto-cluster candidates selected from the literature, and discuss their properties in the light of our simulations predictions. This work provides the general framework that will allow us to extend the study of cluster formation out to much higher redshifts using the large number of proto-clusters that are expected to be discovered in, e.g., the upcoming HETDEX and HSC surveys.
Date added: Mon, 14 Oct 13