THE X-RAY CLUSTER NORMALIZATION OF THE MATTER POWER SPECTRUM

The number density of galaxy clusters provides tight statistical constraints on the matter fluctuation power spectrum normalization, traditionally phrased in terms of sigma(8), the root-mean-square mass fluctuation in spheres with radius 8 h(-1) Mpc. We present constraints on sigma(8) and the total matter density Omega(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 sigma(8)(Omega(m0)/0.32)(alpha) = 0.86 +/- 0.04 with alpha = 0.30 and 0.41 for Omega(m0) <= 0.32 and Omega(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 Omega(m0) = 0.30(-0.02)(+0.03) and sigma(8) = 0.85(-0.02)(+0.04) (68% confidence for two parameters).