The Most Massive Distant Clusters: Determining Omega and sigma_8

TL;DR

This study uses the most massive distant galaxy clusters to break the degeneracy between the cosmological density parameter $\Omega$ and the amplitude of mass fluctuations $\sigma_8$ by analyzing their abundance evolution with redshift. Using robust, multi-method mass measurements (weak lensing, X-ray temperature, and velocity dispersion) within a $1.5\ h^{-1}$ Mpc radius and a $M_{1.5\text{-}com}$ threshold, the authors compare observed counts to Press–Schechter predictions. The resulting constraints favor a low-$\Omega$, high-$\sigma_8$ universe ($\Omega\approx0.2$, $\sigma_8\approx1.2$), effectively ruling out $\Omega=1$ Gaussian models with high confidence. The conclusions are stable against changes in the power spectrum, $H_0$, and modest mass-threshold uncertainties, reinforcing a nearly unbiased large-scale matter distribution.

Abstract

The existence of the three most massive clusters of galaxies observed so far at z>0.5 is used to constrain the mass density parameter of the universe, Omega, and the amplitude of mass fluctuations, sigma_8. We find Omega=0.2 (+0.3,-0.1), and sigma_8=1.2 (+0.5,-0.4) (95 %). We show that the existence of even the single most distant cluster at z=0.83, MS1054-03, with its large gravitational lensing mass, high temperature, and large velocity dispersion, is sufficient to establish powerful constraints. High-density, Omega=1 (sigma_8 ~ 0.5-0.6) Gaussian models are ruled out by these data (< 10^{-6} probability); the Omega=1 models predict only ~10^{-5} massive clusters at z > 0.65 (~10^{-3} at z > 0.5) instead of the 1 (3) clusters observed.

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