Evolution of the cluster mass function: Gpc³ dark matter simulations

High-resolution N-body simulations of four popular cold dark matter cosmologies (LCDM, OCDM, QCDM, and tilted SCDM), each containing ∼ 10⁵ clusters of galaxies of mass M_1.5 > 5 × 10¹³ h^-1 M _⊙ in a Gpc³ volume, are used to determine the evolution of the cluster mass function from z = 3 to 0. The large volume and high resolution of these simulations allow an accurate measure of the evolution of cosmologically important (but rare) massive clusters at high redshift. The simulated mass function is presented for cluster masses within several radii typically used observationally (R = 0.5, 1.0, and 1.5 h^-1 Mpc, both comoving and physical) in order to enable direct comparison with current and future observations. The simulated evolution is compared with current observations of massive clusters at redshifts 0.3 ≲ z ≲ 0.8. The Ω_m = 1 tilted SCDM model, which exhibits very rapid evolution of the cluster abundance, produces too few clusters at z ≳ 0.3 and no massive clusters at z ≳ 0.5, in stark contradiction to observations. The Ω_m = 0.3 models - LCDM, OCDM, and QCDM - all exhibit considerably weaker evolution and are consistent with current data. Among these low-density models, OCDM evolves the least. These trends are enhanced at high redshift and can be used to discriminate between flat and open low-density models. The simulated mass functions are compared with the Press-Schechter approximation. Standard Press-Schechter predicts too many low-mass clusters at z = 0, and too few clusters at higher redshift. We modify the approximation by a simple parameterization of the density contrast threshold for collapse, which has a redshift dependence. This modified Press-Schechter approximation provides a good fit to the simulated mass functions.