The Spatial Correlation Function of Galaxy Clusters: Optical to X-Ray

Abstract

Correlation studies of galaxy clusters using the Abell catalogue have been unable to provide firm constraints on theoretical models of galaxy formation. This reflects both the subjective nature of the Abell catalogue and the discovery of strong redshift-space anisotropies in the clustering pattern. Digitised galaxy surveys, such as the Edinburgh/Durham Cluster Catalogue (EDCC), have established a more accurate estimate of the amplitude of the two-point cluster correlation function and strongly suggest that the anisotropies seen in the Abell catalogue are spurious. Selecting clusters by virtue of their X-ray emission has significant advantages over optical catalogues for this kind of study. We report on the correlation function of 128 X-ray emitting clusters selected from the all-sky survey carried out by the ROSAT X-ray satellite. The correlation function for the sample can be approximated by ξ cc(r) = (r / r o)-1.9±0.4 , where r 0 = 13.7 ± 2.3 over the range 3... 85 h -1Mpc (h ≡ H 0 / 100kms-1 Mpc-1). The amplitude of the correlation function is consistent with a recent determination using the EDCC. The line-of-sight elongations in the cluster pair distribution, seen in the ξ cc of the Abell catalogue, are not reproduced in our sample. This demonstrates that the features are not due to real clustering or large cluster peculiar velocities. We are able to rule out cluster peculiar velocities as large as 1000 kms-1 at the 3σ level. This provides convincing evidence that the Abell catalogue is seriously affected by projection effects. In terms of models for the formation of structure, these results are not inconsistent with standard Cold Dark Matter (CDM), although detailed modelling of a flux limited X-ray selected sample is required before a definitive test can be made.