Evolution of the Cluster Mass Function: Gpc3Dark Matter Simulations

High-resolution N-body simulations of four popular Cold Dark Mattercosmologies (LCDM, OCDM, QCDM, and tilted SCDM), each containing 10^5 clustersof galaxies in a cubic gigaparsec volume, are used to determine the evolutionof the cluster mass function from z=3 to z=0. The large volume and highresolution of these simulations allow an accurate measure of the evolution ofcosmologically important (but rare) massive clusters at high redshift. Thesimulated mass function is presented for cluster masses within several radiitypically used observationally (R=0.5, 1.0, and 1.5 Mpc/h, both comoving andphysical) in order to enable direct comparison with current and futureobservations. The simulated evolution is compared with current observations ofmassive clusters at redshifts 0.30.3 and no massive clusters at z>0.5, in stark contradiction withobservations. The Omega_m=0.3 models- LCDM, OCDM, and QCDM- all exhibitconsiderably weaker evolution and are consistent with current data. Among theselow density models, OCDM evolves the least. These trends are enhanced at highredshift and can be used to discriminate between flat and open low densitymodels. The simulated mass functions are compared with the Press-Schechterapproximation. Standard Press-Schechter predicts too many low mass clusters atz=0, and too few clusters at higher redshift. We modify the approximation by asimple parameterization of the density contrast threshold for collapse, whichhas a redshift dependence. This modified Press-Schechter approximation providesa good fit to the simulated mass functions.Comment: 12 pages including 10 figures; matches published versio