Spherical collapse and mass function of rich clusters in models with curvature and cosmological constant

Abstract

We have analyzed the dependences of the threshold value of amplitude of linear density fluctuation collapsed at the current epoch, $δ_c$, and its overdensity after virialization, $Δ_c$, on matter density content, 3D curvature parameter and cosmological constant. Though the range for the threshold values of perturbation amplitude is quite narrow - $1.55\le δ_c\le 1.75$ in the region of parameters $-0.4\leΩ_k\le0.4$, $0\leΩ_Λ\le 1$, $0.1\leΩ_m\le 1$, the difference in the concentrations of rich clusters of galaxies (calculated within the Press-Schechter formalism framework) with real and with canonical values of $δ_c$ reaches, and for some models exceeds, 30%. The range of changes for the overdensity after virialization, $Δ_c$, is considerably wider for the same region of parameters: $60\leΔ_c\le180$. It results into difference up to $\sim40$% between the X-ray temperatures of gas, as calculated for these values and for the canonical value of $Δ_c=178$. Also we have found analytical approximations of the dependences $δ_c(Ω_m,Ω_Λ)$ and $Δ_c(Ω_m,Ω_Λ)$ with their accuracies for above mentioned region of parameters being no worse than 0.2% and 1.7% respectively.