Time Evolution of Galaxy Formation and Bias in Cosmological Simulations

The clustering of galaxies relative to the underlying mass distribution declines with cosmic time for three reasons. First, nonlinear peaks become less rare events as the density field evolves. Second, the densest regions stop forming new galaxies because their gas becomes too hot to cool and collapse. Third, after galaxies form, they are subject to the same gravitational forces as the dark matter, and thus they tend to trace the dark matter distibution more closely with time; in this sense, they are gravitationally “debiased.” In order to illustrate these effects, we perform a large-scale hydrodynamic cosmological simulation of a ΛCDM model with Ω0 = 0.37 and examine the statistics of δ∗(r, z), the density field of recently formed galaxies at position r and redshift z. We find that the bias of recently formed galaxies b∗ ≡ 〈δ 2 ∗〉 1/2 /〈δ〉 1/2 , where δ is the mass overdensity, evolves from b∗ ∼ 4.5 at z = 3 to b∗ ∼ 1 at z = 0, on 8 h −1 Mpc comoving scales. The correlation coefficient r∗ ≡ 〈δδ∗〉/〈δ 〉 1/2 〈δ ∗〉 1/2 evolves from r∗ ∼ 0.9 at z = 3 to r∗ ∼ 0.25 at z = 0. That is, as gas in the universe heats up and prevents star formation, the star-forming galaxies become poorer tracers of the mass density field. We show that the linear continuity equation is a good approximation for describing the gravitational debiasing, even on nonlinear scales. The most interesting observational consequence of the simulations is that the linear regression of the galaxy formation density field on the galaxy density field, b∗gr∗g = 〈δ∗δg〉/〈δ 2 g〉, evolves from about 0.9 at z = 1 to 0.35 at z = 0. Measuring this evolution, which should be possible using the Sloan Digital Sky Survey, would place constraints on models for galaxy formation. In addition, we evaluate the effects of the evolution of galaxy formation on estimates of Ω from cluster mass-to-light ratios, finding that while Ω(z) increases with z, the estimated Ωest(z) actually decreases. This effect is due to the combination of galaxy bias and the relative fading of cluster galaxies with respect to field galaxies. Finally, these effects provide a possible explanation for the Butcher-Oemler effect, the excess of blue galaxies in clusters at redshift z ∼ 0.5.