The 3-D distribution of Abell clusters

Abstract

The spatial distribution of the Struble & Rood catalogue of all measured Abell cluster redshifts is analysed, with correction for the redshift incompleteness in the D=5 and 6 subsamples. The D≼4, R≽0 subsample has nearly complete redshift data; thus the agreement between results for D≼4 and D≽5 supports the fairness of the weighting procedure. Clear evidence for projection effects in the Abell catalogue is found (i.e. part of the observed angular correlation is not due to genuine clustering in redshift space); this accounts for the elongation of ξcc in the line-of-sight direction seen by Bahcall, Soneira & Burgett. Thus the large peculiar velocities ∼2000 km s−1, which they inferred are not necessary to explain the elongation of ξcc. Finally, the projection effects are compensated for, and a much reduced correlation amplitude is derived, with |$\xi_\text {cc}\approx(\frac {r}{14h^{-1}\text{Mpc}})^{-1.8}$|⁠, and an upper limit ∼800 km s−1 is placed on cluster peculiar velocities. The data are consistent with |$\xi_\text {cc}(r)=0$| for r≽50 h−1 Mpc; thus the standard cold dark matter model should not be excluded.