Cluster versus POTENT Density and Velocity Fields: Cluster Biasing and Omega

The density and velocity fields as extracted from the Abell/ACO clusters are compared to the corresponding fields recovered by the POTENT method from the Mark III peculiar velocities of galaxies. In order to minimize non-linear effects and to deal with ill-sampled regions we smooth both fields using a Gaussian window with radii ranging between 12 − 20 hMpc. The density and velocity fields within 70hMpc exhibit similarities, qualitatively consistent with gravitational instability theory and a linear biasing relation between clusters and mass. The random and systematic errors are evaluated with the help of mock catalogs. Quantitative comparisons within a volume containing ∼ 12 independent samples yield βc ≡ Ω 0.6/bc = 0.22 ± 0.08, where bc is the cluster biasing parameter at 15 hMpc. If bc ∼ 4.5, as indicated by the cluster correlation function, our result is consistent with Ω ∼ 1.