A mean density and a correlation function of rich clusters: theory and observations

In this paper we investigate a large-scale distribution of rich clusters of galaxies within the framework of the adiabatic theory of galaxy formation. It is shown that a mean density of ‘pancakes’ is close to the density of Abell's clusters. Angular correlation functions calculated for spatial correlation functions under different assumptions about the spectrum of initial perturbations are compared with Hauser & Peebles points derived from Abell's catalogue. It was assumed that the initial spectrum of perturbation was $$b^2_n(\kappa)\propto \kappa^{n-2}\enspace \text {exp}(-\kappa R_\text c)$$. The best values of the spectrum indices are found to be n = 2.1, 1.6, 1.3 and 0.7 for Ω = 0.1, 0.2, 0.3 and 1 respectively. The value of the amplitude of initial perturbations obtained from these arguments is close to the value based on other assumptions.