Projection effects in cluster catalogues

We investigate the importance of projection effects in the identification of galaxy clusters in 2D galaxy maps and their effect on the estimation of cluster velocity dispersions. From large N-body simulations of a standard cold dark matter universe, we construct volume-limited galaxy catalogues that have similar low-order clustering properties to those of the observed galaxy distribution. We then select clusters using criteria tailored to match those employed in the construction of real cluster catalogues such as Abell’s. We find that our mock Abell cluster catalogues are heavily contaminated and incomplete. Over one third (34±6 per cent) of clusters of richness class R≥1 are miclassifications arising from the projection of one or more sub-clumps onto an intrinsically poor cluster. Conversely, 32±5 per cent of intrinsically rich clusters are missed altogether from the R≥1 catalogues, mostly because of statistical fluctuations in the background count. Selection by X-ray luminosity rather than optical richness reduces, but does not completely eliminate, these problems. Contamination by unvirialised sub-clumps near a cluster leads to an overestimation of the cluster velocity dispersion which can be very substantial even if the analysis is restricted only to galaxies close to the cluster centre. Thus, the distribution of cluster masses – often used to test cosmological models – is a highly unreliable statistic. The median value of the distribution, however, is considerably more robust because the main effect of contamination is to create an artificial tail of high velocity dispersion clusters. Improved estimates of the cluster velocity dispersion distribution require constructing new cluster catalogues in which clusters are defined according to the number of galaxies within a radius about three times smaller than the Abell radius.