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 $12-20\text{hmpc}$. The density and velocity fields within $70\text{hmpc}$ 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 $\sim \text{\hspace{0.17em}⁣}12$ independent samples yield $\text{betac}\equiv {\mathrm{\Omega }}^{0.6}\mathrm{/}{b}_c=0.22\pm 0.08$, where $b_c$ is the cluster biasing parameter at $15\text{hmpc}$. If $b_c\sim 4.5$, as indicated by the cluster correlation function, our result is consistent with $\mathrm{\Omega }\sim 1$.