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The number density of galaxy clusters provides tight statistical constraints on the matter fluctuation power spectrum normalization, traditionally phrased in terms of sigma₈, the root mean square mass fluctuation in spheres with radius 8 h^-1 Mpc. We present constraints on sigma₈ and the total matter density Omegaₘ0 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 sigma₈ (Omegaₘ0/0. 32) ᵃlpha = 0. 86+/-0. 04 with alpha = 0. 30 (0. 41) for Omegaₘ0 0. 32) (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: Omegaₘ0 = 0. 30+0. 03/-0. 02 and sigma₈ = 0. 85+0. 04/-0. 02 (68% confidence for two parameters).
Henry et al. (Sun,) studied this question.