The most massive distant clusters: Determining Ω and σ₈

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, Ω, and the amplitude of mass fluctuations, σ₈. We find Ω = 0.2_-0.1^+0.3 and σ₈ = 1.2_-0.4^+0.5 (95%). We show that the existence of even the single most distant cluster at z = 0.83, MS 1054-03, with its large gravitational lensing mass, high temperature, and large velocity dispersion, is sufficient to establish powerful constraints. High-density, Ω = 1 (σ₈ ≃ 0.5-0.6) Gaussian models are ruled out by these data (10^-6 probability); the Ω = 1 models predict only 10^-5 massive clusters at z > 0.65 (∼10^-3 at z > 0.5) instead of the one (three) clusters observed.