Cosmological Smoothed Particle Hydrodynamic Simulations with Four Million Particles: Statistical Properties of X-Ray Clusters in a Low-Density Universe

We present results from a series of cosmological smoothed particle hydrodynamics (SPH) simulations coupled with the particle-particle-particle-mesh solver for the gravitational force. The simulations are designed to predict the statistical properties of X-ray clusters of galaxies as well as to study the formation of galaxies. We have seven simulation runs with different assumptions about the thermal state of the intracluster gas. Following the recent work by Pearce and coworkers, we modify our SPH algorithm so as to phenomenologically incorporate galaxy formation by decoupling the cooled gas particles from the hot gas particles. All the simulations employ 128³ particles both for dark matter and for gas components and thus constitute the largest systematic catalogs of clusters simulated in the SPH method performed so far. These enable us to compare the analytical predictions about statistical properties of X-ray clusters against our direct simulation results in an unbiased manner. We find that the luminosities of the simulated clusters are quite sensitive to the thermal history and also to the numerical resolution of the simulations and thus are not reliable. On the other hand, the mass-temperature relation for the simulated clusters is fairly insensitive to the assumptions of the thermal state of the intracluster gas, is robust against the numerical resolution, and in fact agrees well with the analytic prediction. Therefore, prediction of the X-ray temperature functions of clusters on the basis of the Press-Schechter mass function and the virial equilibrium is fairly reliable.