2009ApJ...691.1307H

The number density of galaxy clusters provides tight statistical constraints on the matter fluctuation power spectrum normalization, traditionally phrased in terms of σ₈, the root-mean-square mass fluctuation in spheres with radius 8 h.^–1 Mpc. We present constraints on σ₈ and the total matter density Ω_m0 from local cluster counts as a function of X-ray temperature, taking care to incorporate and minimize systematic errors that plagued previous work with this method. In particular, we present new determinations of the cluster luminosity-temperature and mass-temperature relations, including their intrinsic scatter, and a determination of the Jenkins mass function parameters for the same mass definition as the mass-temperature calibration. Marginalizing over the 12 uninteresting parameters associated with this method, we find that the local cluster temperature function implies σ₈(Ω_m0/0.32)^α = 0.86±0.04 with α = 0.30 and 0.41 for Ω_m0≤ 0.32 and Ω_m0≥ 0.32, respectively (68% confidence for two parameters). This result agrees with a wide range of recent independent determinations, and we find no evidence of any additional sources of systematic error for the X-ray cluster temperature function determination of the matter power spectrum normalization. The joint WMAP5 + cluster constraints are Ω_m0 = 0.30^+0.03_–0.02 and σ₈= 0.85^+0.04_–0.02(68% confidence for two parameters).