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Journal of Physical Studies 7(2), 234–246 (2003)
DOI: https://doi.org/10.30970/jps.07.234 SPHERICAL COLLAPSE AND MASS FUNCTION OF RICH CLUSTERS IN MODELS WITH CURVATURE AND COSMOLOGICAL CONSTANTYu. Kulinich, B. Novosyadlyj
Astronomical Observatory of Ivan Franko National University of Lviv |
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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. It was shown that in models with negative or zero curvature ($k\le0$) and positive cosmological constant ($Λ>0$) despite smaller rate of perturbation growth, $δ_c$ appears to be smaller than its canonical value 1.686 ($k=Λ=0$) due to the longer duration of amplitude increase. However, in models with positive 3D curvature, $δ_c$ can be larger when the matter density parameter is small. In this case critical amplitude $δ_c$ approaches infinity when $Ω_m$ converges to its small critical value. 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 (as calculated within the Press-Schechter formalism framework) with real and 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 in the difference of up to $\sim40$\0etween 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 the above-mentioned region of parameters being no worse than 0.2\% and 1.7\%, respectively.
PACS number(s): 98.80.Ft, 98.80.Es, 98.65.Dx.