THE ELLIPTICITY AND ORIENTATION OF CLUSTERS OF GALAXIES IN N-BODY EXPERIMENTS

In this study we use simulations of 128(3) particles to study the elli pticity and orientation of clusters of galaxies in N-body simulations in a controlled way based on nearly 3000 clusters. We use power-law in itial spectra [P(k) proportional to k(n), n = +1, 0, -1, -2] and densi ty parameters (Omega(0) = 0.2-1.0). Unlike most theoretical studies we mimic observational studies by removing all particles that lie at dis tances greater than 2 h(-1) Mpc from the cluster center of mass. We co mputed 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 sphe rical at smaller radii. We compared the orientation of a cluster to th e orientation of neighboring clusters as a function of distance (corre lation). In addition, we considered whether a cluster's major axis ten ds to lie along the line connecting it to a neighboring cluster, as a function of distance (alignment). Both alignments and correlations wer e computed in three dimensions and in projection to mimic observationa l surveys. Our results show that alignments exist for all spectra at s mall separations (D < 15 h(-1) Mpc) but drop off at larger distances i n an n-dependent way. Therefore, the most useful study for observers i s the variation of alignment with distance. Correlations exist, but at a weaker level. We found that differences in n had no measurable effe ct on mean ellipticity and a weak effect on cluster alignments and cor relations. Biasing was able to totally hide the effect of greater nonl inearity. Therefore, we suggest that any effort to probe Omega in this manner be abandoned unless it can be unambiguously proven to exist on smaller scales. However, there are systematic effects due to the prim ordial spectral index, n. Our results suggest that cluster ellipticity and the scale dependence of cluster alignments probe the primordial p ower spectrum independently of the parameters of the background cosmol ogy. Future work should concentrate on these parameters.