The shapes of galaxy clusters

Abstract

We have reanalyzed a data set of 99 low redshift (z < 0:1) Abell clusters studied previously by Rhee, van Haarlem & Katgert (1989), and determined their shapes. For this, three di erent measures are used: two of which were originally used by Rhee et al., and one of which was used by Plionis, Barrow & Frenk (1991) 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 attened system. Also background galaxies and shot noise have a rather large in uence on the measured quantities. The corrected distribution of cluster ellipticities shows a peak at 0:4 and extends to 0:8, consistent with results of some previous studies. However, the present study uses more than twice the number of 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 1977). Using a redshift-independent richness criterion of Vink & Katgert (1994), 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 pre-2 P.A.M. de Theije, P. Katgert & E. van Kampen dictions from N-body simulations. For this, we use a catalogue of 75 N-body simulated clusters (van Kampen 1994) which assume a CDM spectrum with = 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 both in radial pro le and number of galaxies. 'Observing' these simulated clusters in exactly the same way as the real clusters produces an ellipticity distribution that extends to much higher and that has too few nearly spherical clusters. Preliminary results of simulations of the formation of clusters in an = 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 .

RASS-SDSS galaxy cluster survey

“…Adami et al (1998b) have shown that enforcing circularity could create a central artificial cusp in the number density profile of the stacked cluster. However, lower mass clusters are more elongated than higher mass clusters (see Fasano et al 1993;de Theije et al 1995;Plionis et al 2004), so the effect of assuming circularity should lead to more cuspy density profiles for lower mass clusters, which is opposite to what we find. Indeed, the effect reported by Adami et al does not seem to be strong enough to account for the differences seen in the density profiles of the stacked clusters of different masses (compare Fig.…”

Phase-space shapes of clusters and rich groups of galaxies

“…the selection clusters or member galaxies. Neglecting all these differences, we find that most measurements of the shapes inferred from galaxy positions in clusters and massive groups point to a mean axial ratio of ∼(0.5−0.6) and an intrinsic scatter of ∼0.15 (Binggeli 1982;Plionis et al 1991;de Theije et al 1995;Basilakos et al 2000). Our results are fully compatible with these findings, although slightly larger mean and smaller scatter is preferred.…”

The ESO Nearby Abell Cluster Survey. XII. The Mass and Mass‐to‐Light Ratio Profiles of Rich Clusters

“…An analysis of cluster ellipticities is beyond the scope of this paper, but we expect them not to be very large for the following reasons. First, our clusters are rich, and de Theije, Katgert, & van Kampen (1995) showed ellipticity to decrease significantly with increasing richness, reaching a value of $0.2 for Abell richness k80. Second, our clusters are nearby, and both Melott et al (2001) and Plionis (2002) showed cluster ellipticity to decrease with decreasing redshift, reaching $0.3 at z $ 0:05.…”