On the Clustering of Rich Clusters of Galaxies
T. Kiang · Monthly Notices of the Royal Astronomical Society · 1967
The methods developed by Neyman & Scott (1953), Neyman, Scott & Shane (1954) and Scott, Shane & Swanson (1954) are adapted to the problem of clustering of the rich clusters of galaxies found by Abell (1958). From an analysis on the index of clumpiness, parameters in the model of uniform clusters are found to be: size σ = 24 Mpc, average membership ν1 = 4; a high degree of interlocking is implied. Random realizations of the model are effected to produce synthetic surface distributions, which are then compared with the observed surface distribution. The variations with separation k of the quasi-correlations Q ( k ; z ) for two cell-sizes z are found to be little different from each other in the synthetic distributions, whilst they are very different in the observed distribution–thus echoing a previous result by Neyman, Scott & Shane (1956) with regard to the (first-order) clustering of galaxies. The indications are that galaxies are clustered on all scales, that there are no preferred size of clusters, and that the clusters have little physical individuality. It is pointed out that this picture of indefinite clustering may fit in with McCrea's (1964) idea of continual creation.