The 3-D Distribution of Abell Clusters

Abstract

The Struble & Rood catalogue ( Ap. J. Supp , 63 , 543) of all measured Abell cluster redshifts is analysed, with corrections for the selection biases. This contains 533 redshifts with |b| ≥ 30°, z ≤ 0.3 compared with 104 in the sample of Bahcall & Soneira ( Ap. J. 270 , 20). Although the catalogue contains biases in angular position (redshifts are preferentially measured in apparent “supercluster” regions) the information on redshift clustering is effectively unbiased since one cannot tell a priori whether pairs of clusters close on the sky are really associated in redshift. Thus the distribution of redshift differences for pairs of given angle & distance classes, f (Δ z |θ, D 1 , D 2 ), is a fair sample of the true distribution. Then by normalising to the “correct” angular correlation function, we obtain the joint distribution f (Δ z ,θ) and hence ξ( r ). In practice, in the estimation of ξ we assign each pair a weight a where where w A is the correlation or cross correlation for the appropriate subset of the whole Abell catalogue. This gives ξ( r ) ≈ ( r /20 h −1 Mpc ) −1.8 , just slightly smaller than the result of Bahcall & Soneira, but here ξ( r ) ≈ 0 for r ≥ 50 −1 Mpc .