THE SHAPES OF GALAXY CLUSTERS

We have reanalysed a data set of 99 low-redshift (z < 0.1) Abell clusters studied previously by Rhee, van Haarlem & Katgert, and determined their shapes. For this, three different measures are used: two of which were originally used by Rhee et al., and one of which was used by Plionis, Barrow & Frenk in their investigation of clusters in the Lick catalogue. We use Monte Carlo simulations of clusters to investigate the errors in the methods. For low ellipticity, all methods overestimate the cluster elongation, whereas the opposite is true for a highly flattened system. Also background galaxies and shot noise have a rather large influence on the measured quantities. The corrected distribution of cluster ellipticities shows a peak at epsilon similar to 0.4 and extends to epsilon similar to 0.8, consistent with results of some previous studies. However, the present study uses more than twice as many clusters as the earlier studies, and is self-consistent. That is, with the corrected distribution over projected cluster shapes we can reconstruct the observed distribution over projected cluster shapes and the observed relation between the number of galaxies in a cluster and its ellipticity. To achieve this, we have to assume that there is an anti-correlation between the true (projected) ellipticity of a cluster and its number of galaxies. It is not necessary to assume that the ellipticity of a cluster increases when one only includes the brighter galaxies (as suggested by Binney). Using a redshift-independent richness criterion of Vink & Katgert, it is shown that the richer clusters are intrinsically more nearly spherical than the poorer ones. Furthermore, the corrected distribution of cluster shapes is found to be more consistent with a population that consists of purely prolate clusters than with a purely oblate population. We compare the corrected true distribution of (projected) ellipticities with predictions from N-body simulations. For this, we use a catalogue of 75 N-body simulated clusters which assume a CDM spectrum with Omega = 1.0. The simulations include a recipe for galaxy formation and merging. The model clusters are expected to be a representative sample of all real clusters. They show a good resemblance with the data in both radial profile and number of galaxies. 'Observation' of these simulated clusters in exactly the same way as the real clusters produces an ellipticity distribution that extends to much higher epsilon and that has too few nearly spherical clusters. Preliminary results of simulations of the formation of clusters in an Omega = 0.2 universe suggest that, on average, clusters are more nearly spherical in this case, as is expected on theoretical grounds. This shows that the elongations of clusters can provide a useful constraint on the value of Omega.