A New Local Temperature Distribution Function for X-ray Clusters: Cosmological Applications

(abridged) We present a new determination of the local temperature function of X-ray clusters. We use a new sample comprising fifty clusters for which temperature information is now available, making it the largest complete sample of its kind. It is therefore expected to significantly improve the estimation of the temperature distribution function of moderately hot clusters. We find that the resulting temperature function is higher than previous estimations, but agrees well with the temperature distribution function inferred from the BCS and RASS luminosity function. We have used this sample to constrain the amplitude of the matter fluctuations on cluster's scale of $8\sqrt[3]{\Omega_0}^{-1}h^{-1}$Mpc, assuming a mass-temperature relation based on recent numerical simulations. We find $\sigma_8 = 0.6\pm 0.02$ for an $\Omega_0 = 1$ model. Our sample provides an ideal reference at $z \sim 0$ to use in the application of the cosmological test based on the evolution of X-ray cluster abundance (Oukbir & Blanchard 1992, 1997). Using Henry's sample, we find that the abundance of clusters at $z = 0.33$ is significantly smaller, by a factor larger than 2, which shows that the EMSS sample provides strong evidence for evolution of the cluster abundance. A likelihood analysis leads to a rather high value of the mean density parameter of the universe: $\Omega =0.92 \pm 0.22$ (open case) and $\Omega =0.86 \pm 0.25$ (flat case), which is consistent with a previous, independent estimation based on the full EMSS sample by Sadat et al.(1998). Some systematic uncertainties which could alter this result are briefly discussed.Comment: 31 pages, 12 figures, mathches the version published in Astronomy and Astrophysic

An Approximation to the Likelihood Function for Band-Power Estimates of CMB Anisotropies

Band-power estimates of cosmic microwave background fluctuations are now routinely used to place constraints on cosmological parameters. For this to be done in a rigorous fashion, the full likelihood function of band-power estimates must be employed. Even for Gaussian theories, this likelihood function is not itself Gaussian, for the simple reason that band-powers measure the {\em variance} of the random sky fluctuations. In the context of Gaussian sky fluctuations, we use an ideal situation to motivate a general form for the full likelihood function from a given experiment. This form contains only two free parameters, which can be determined if the 68% and 95% confidence intervals of the true likelihood function are known. The ansatz works remarkably well when compared to the complete likelihood function for a number of experiments. For application of this kind of approach, we suggest that in the future both 68% and 95% (and perhaps also the 99.7%) confidence intervals be given when reporting experimental results.Comment: Published versio