The Ellipticity and Orientation of Clusters of Galaxies in N-Body Experiments

In this study we use simulations of 128³ particles to study the ellipticity and orientation of clusters of galaxies in N-body simulations in a controlled way based on nearly 3000 clusters. We use power-law initial spectra [P(k) ∝ kⁿ, n = +1, 0, -1, -2] and density parameters (Ω₀ = 0.2-1.0). Unlike most theoretical studies we mimic observational studies by removing all particles that lie at distances greater than 2 h^-1 Mpc from the cluster center of mass.

We computed the axial ratio and the principal axes using the inertia tensor of each cluster. The mean ellipticity of clusters increases strongly with increasing n. We also find that clusters tend to become more spherical at smaller radii.

We compared the orientation of a cluster to the orientation of neighboring clusters as a function of distance (correlation). In addition, we considered whether a cluster's major axis tends to lie along the line connecting it to a neighboring cluster, as a function of distance (alignment). Both alignments and correlations were computed in three dimensions and in projection to mimic observational surveys. Our results show that alignments exist for all spectra at small separations (D < 15 h^-1 Mpc) but drop off at larger distances in an n-dependent way. Therefore, the most useful study for observers is the variation of alignment with distance. Correlations exist, but at a weaker level.

We found that differences in Ω had no measurable effect on mean ellipticity and a weak effect on cluster alignments and correlations. Biasing was able to totally hide the effect of greater nonlinearity. Therefore, we suggest that any effort to probe Ω in this manner be abandoned unless it can be unambiguously proven to exist on smaller scales. However, there are systematic effects due to the primordial spectral index, n. Our results suggest that cluster ellipticity and the scale dependence of cluster alignments probe the primordial power spectrum independently of the parameters of the background cosmology. Future work should concentrate on these parameters.