Normalizing the Temperature Function of Clusters of Galaxies

We reexamine the constraints that can be robustly obtained from the observed temperature function of X-ray studies of cluster of galaxies. The cluster mass function has been thoroughly and analytically studied in simulations, but a direct simulation of the temperature function is presented here for the first time. Adaptive hydrodynamic simulations using the cosmological Moving Mesh Hydro code are used to calibrate the temperature function for different popular cosmologies. Applying the new normalizations to the present-day cluster abundances, we find σ₈=0.53±0.05Ω^−0.45₀ for a hyperbolic universe and σ₈ = 0.53±0.05Ω^−0.53₀ for a spatially flat universe with a cosmological constant. The simulations followed the gravitational shock heating of the gas and dark matter and used a crude model for energy injection by supernova heating. The error bars are dominated by uncertainties in the heating/cooling models. We present fitting formulae for the mass-temperature conversions and cluster abundances based on these simulations.