Cluster alignments and ellipticities in ACDM cosmology

The ellipticities and alignments of clusters of galaxies and their evolution with redshift are examined in the context of a Λ-dominated cold dark matter cosmology. We use a large-scale, high-resolution N-body simulation to model the matter distribution in a light cone containing ∼10⁶ clusters of mass M > 2 × 10¹³ h^-1 M _⊙ out to redshifts of z = 3. The best-fit three-dimensional ellipsoid of the mass distribution is determined for each cluster, and the results are used to analyze cluster ellipticities as a function of mass, radius, and redshift. A similar analysis is done in two dimensions in order to allow direct comparisons with future observations. Cluster ellipticities are determined within different radii, including 0.5, 1.0, and 1.5 h^-1 comoving Mpc. We find strong cluster ellipticities: 〈 1 - a ₂/a₁〉 ∼ 0.3-0.5. The mean ellipticity increases with redshift from 〈ε〉 ∼ 0.3 at z = 0 to 〈ε〉 ∼ 0.5 at z = 3 for both three-dimensional and two-dimensional ellipticities; the evolution is well fitted by 〈ε〉 = 0.33 + 0.05z. The ellipticities increase with cluster mass and with cluster radius; the main cluster body is more elliptical than the cluster cores, but the increase of ellipticities with redshift is preserved. Using the fitted cluster ellipsoids, we determine the alignment of clusters as a function of their separation. We find strong alignment of clusters for separations ≲100 h^-1 Mpc; the alignment increases with decreasing separation and with increasing redshift. The evolution of clusters from highly aligned and elongated systems at early times to lower alignment and elongation at present reflects the hierarchical and filamentary nature of structure formation. These measures of cluster ellipticity and alignment will provide a new test of the current cosmological model when compared with upcoming cluster surveys.