On the evolution of clustering and the biased galaxy formation scenario

Using a large N-body simulation, we investigate the evolution of clustering of mass particles and individual dark matter halos in a standard cold dark matter (CDM) universe. The two-point correlation function, ξ(r), is computed at several epochs in the simulation corresponding to redshifts, z, between 5 and 0, where z = 0 corresponds to a bias parameter, b, of 1. Previous studies of the evolution of clustering in CDM universes have investigated a much smaller range of redshifts. Two classes of halos are considered: high overdensity (~2000) and moderate overdensity (~250). The evolution of ξ(r) as a function of halo mass is also investigated. The two-point correlation function evolves differently from the prediction of linear theory, both in the case of the mass particles and the individual halos. The amplitude of ξ(r) for the mass grows continuously over the course of the simulation, but from z = 1.5 to z = 0, it grows more slowly than linear theory on large scales (r 9h^-1^ Mpc) and more quickly than linear theory on small scales (r~1h^-1^ Mpc). The two-point correlation functions of the various catalogs of halos exhibit evolution that is strikingly different from linear theory. The details of the evolution of ξ(r) for the halos are a function of both the overdensity and mass of the halos, but four general patterns emerge: (1) a decrease in the amplitude of ξ(r) from z = 5 to z~2, followed by an increase in the amplitude of ξ(r) from z~2 to z = 0 (small, moderate-overdensity halos), (2) a decrease in the amplitude of ξ(r) from z = 5 to z~1, after which the amplitude of ξ(r) remains approximately constant (large, moderate-overdensity halos), (3) little evolution from z = 5 to z~1, followed by obvious small-scale evolution from z~1 to z~0 (small, high-overdensity halos), and (4) no noticeable evolution in ξ(r) over the course of the simulation (large, high- overdensity halos). Each catalog of halos is strongly clustered at early epochs in the simulation, implying that if the universe is dominated by CDM and b~1 today, high-redshift galaxies should be strongly clustered. The redshift at which the observed galaxy correlation amplitude is at a minimum can be used to infer the current value of b.