The Cluster Distribution as a Test for Dark Matter Models. II: The Dipole Structure

We study the dipole for a redshift sample of Abell/ACO clusters. To elucidate the constraints it places on dark matter models, we use numerical simulations based on the Zel'dovich approximation. We run 20 realizations of each of six different dark matter models: four of these have a density parameter $\Omega_0=1$, while the other two have $\Omega_0=0.2$, one with and one without a cosmological constant term. For the Abell/ACO sample, we evaluate the parameter $\beta=\Omega_0^{0.6}/b_{ cl}$, which reaches its asymptotic value at $R=160 Mpc/h$. We find $\beta=0.15\pm 0.04$ and $0.25\pm 0.06$ in LG and CMB frames respectively. After identifying in the simulations LG-like observers, we construct mock cluster samples. We find that an alignment between the cluster dipole and observer velocity, such as that observed (about 20 degrees) should not be expected necessarily in the simulations. This, together with the large observer-to-observer variance estimates of $\beta$, makes it difficult to place any firm constraints on cosmological models. Our results demonstrate that the large amplitude and convergence depth of the cluster dipole cannot be taken as strong evidence either for or against a low--density Universe.