The 3-D Distribution of Abell Clusters

Extract

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(Δz|θ,D₁,D₂), is a fair sample of the true distribution. Then by normalising to the “correct” angular correlation function, we obtain the joint distribution f(Δz,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⁻¹Mpc)^−1.8, just slightly smaller than the result of Bahcall & Soneira, but here ξ(r) ≈ 0 for r ≥ 50⁻¹Mpc.