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

Yu. Kulinich, B. Novosyadlyj

Published 2003-02-18, updated 2003-03-04Version 2

We have analyzed the dependences of the threshold value of amplitude of linear density fluctuation collapsed at the current epoch, $\delta_c$, and its overdensity after virialization, $\Delta_c$, on matter density content, 3D curvature parameter and cosmological constant. Though the range for the threshold values of perturbation amplitude is quite narrow - $1.55\le \delta_c\le 1.75$ in the region of parameters $-0.4\le\Omega_k\le0.4$, $0\le\Omega_{\Lambda}\le 1$, $0.1\le\Omega_m\le 1$, the difference in the concentrations of rich clusters of galaxies (calculated within the Press-Schechter formalism framework) with real and with canonical values of $\delta_c$ reaches, and for some models exceeds, 30%. The range of changes for the overdensity after virialization, $\Delta_c$, is considerably wider for the same region of parameters: $60\le\Delta_c\le180$. 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 $\Delta_c=178$. Also we have found analytical approximations of the dependences $\delta_c(\Omega_m,\Omega_{\Lambda})$ and $\Delta_c(\Omega_m,\Omega_{\Lambda})$ with their accuracies for above mentioned region of parameters being no worse than 0.2% and 1.7% respectively.