Normalizing the Temperature Function of Clusters of Galaxies

We re-examine the constraints which can be robustly obtained from theobserved temperature function of X-ray cluster of galaxies. The cluster massfunction has been thoroughly studied in simulations and analytically, but adirect simulation of the temperature function is presented here for the firsttime. Adaptive hydrodynamic simulations using the cosmological Moving MeshHydro code of Pen (1997a) are used to calibrate the temperature function fordifferent popular cosmologies. Applying the new normalizations to thepresent-day cluster abundances, we find $\sigma_8=0.53\pm 0.05\Omega_0^{-0.45}$ for a hyperbolic universe, and $\sigma_8=0.53\pm 0.05\Omega_0^{-0.53}$ for a spatially flat universe with a cosmological constant.The simulations followed the gravitational shock heating of the gas and darkmatter, and used a crude model for potential energy injection by supernovaheating. The error bars are dominated by uncertainties in the heating/coolingmodels. We present fitting formulae for the mass-temperature conversions andcluster abundances based on these simulations.Comment: 20 pages incl 5 figures, final version for ApJ, corrected open universe \gamma relation, results unchange