Monthly Notices of the Royal Astronomical Society, Volume 272, Issue 4, February 1995, Pages 869–877

Publication year: 1995

We derive the one-point probability density function (pdf) of the smoothed Abell-ACO cluster density field and we compare it with that of artificial cluster samples, generated as high peaks of a Gaussian field in such a way that they reproduce the low-order (two- and three-point) correlation functions and the observed cluster selection functions. We find that both real and simulated pdfs are well approximated by a log-normal distribution, even when the Gaussian smoothing radius is as large as 40 h−1h−1 Mpc. Furthermore, the low-order moments of the pdf are found to obey a relation γ≈1.8(±0.2)σ4γ≈1.8(±0.2)σ4, with γ being the skewness. Since clusters have not had enough time to depart significantly from their original birth-place positions, these results are consistent with the theory that clusters are high peaks of an underlying initial Gaussian density field.

A by-produce of our analysis is that when we re-scale the pdf cluster moments to those of the QDOT-*IRAS* galaxies, using linear biasing with *b*_{cI}∼4.5 and for the common smoothing radius of 20 h−1h−1 Mpc, we find them to be significantly smaller than those directly estimated from the QDOT data by Saunders et al.