Cluster versus POTENT density and velocity fields: Cluster biasing and Ω

The density and velocity fields as extracted from the Abell/ACO clusters are compared with 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 and 20 h^-1 Mpc. The density and velocity fields within 70 h^-1 Mpc 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 catalogues. Quantitative comparisons within a volume containing ∼12 independent samples yield β_c = Ω^0.6/b_c = 0.22 ± 0.08, where b_c is the cluster biasing parameter at 15 h^-1 Mpc. If b_c ∼ 4.5, as indicated by the cluster correlation function, our result is consistent with Ω ∼ 1.