Cluster-supercluster alignments

We study correlations in spatial orientation between galaxy clusters and their host superclusters using a Hubble volume N-body realization of a concordance cosmology and an analytic model for tidally induced alignments. We derive an analytic form for the distributions of alignment angle as functions of halo mass (M), ellipticity (epsilon), distance (r), and velocity (v) and show that the model, after tuning of three parameters, provides a good fit to the numerical results. The parameters indicate a high degree of alignment along anisotropic, collapsed filaments. The degree of alignment increases with M and epsilon, while it decreases with r and is independent of v. We note the possibility of using the cluster-supercluster alignment effect as a cosmological probe to constrain the slope of the initial power spectrum.