THE SHAPES OF GALAXY CLUSTERS

We have reanalysed a data set of 99 low-redshift (z < 0.1) Abell clust ers studied previously by Rhee, van Haarlem & Katgert, and determined their shapes. For this, three different measures are used: two of whic h were originally used by Rhee et al., and one of which was used by Pl ionis, Barrow & Frenk in their investigation of clusters in the Lick c atalogue. We use Monte Carlo simulations of clusters to investigate th e errors in the methods. For low ellipticity, all methods overestimate the cluster elongation, whereas the opposite is true for a highly fla ttened system. Also background galaxies and shot noise have a rather l arge influence on the measured quantities. The corrected distribution of cluster ellipticities shows a peak at epsilon similar to 0.4 and ex tends to epsilon similar to 0.8, consistent with results of some previ ous studies. However, the present study uses more than twice as many c lusters as the earlier studies, and is self-consistent. That is, with the corrected distribution over projected cluster shapes we can recons truct 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 ellipti city of a cluster increases when one only includes the brighter galaxi es (as suggested by Binney). Using a redshift-independent richness cri terion of Vink & Katgert, it is shown that the richer clusters are int rinsically more nearly spherical than the poorer ones. Furthermore, th e corrected distribution of cluster shapes is found to be more consist ent with a population that consists of purely prolate clusters than wi th a purely oblate population. We compare the corrected true distribut ion of (projected) ellipticities with predictions from N-body simulati ons. For this, we use a catalogue of 75 N-body simulated clusters whic h assume a CDM spectrum with Omega = 1.0. The simulations include a re cipe 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 galaxie s. 'Observation' of these simulated clusters in exactly the same way a s 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 near ly spherical in this case, as is expected on theoretical grounds. This shows that the elongations of clusters can provide a useful constrain t on the value of Omega.