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, ${\delta }_c$, 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 $-0.4\le {\Omega }_k\le 0.4$, $0\le {\Omega }_{\Lambda }\le 1$, $0.1\le {\Omega }_m\le 1$, 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: $60\le {\Delta }_c\le 180$. It results into difference up to $\sim 40$% 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.

17 pages, 8 figures, LaTeX (Accepted for publication by Journal of Physical Studies, 2003, No1)