Dark energy and key physical parameters of clusters of galaxies

We study physics of clusters of galaxies embedded in the cosmic dark energy background. The equilibrium and stability of polytropic spheres with equation of state of the matter P = K rho^gamma, gamma = 1 + 1/n, in presence of a non-zero cosmological constant Lambda is investigated. The equilibrium state exists only for central densities rho_0 larger than the critical value rho_c and there are no static solutions at rho_0 < rho_c. At this density the radius of the configuration is equal to the zero-gravity radius, at which the dark matter gravity is balanced by the dark energy antigravity. It is shown, that dark energy reduces the dynamic stability of the configuration. We show that the dynamical effects of dark energy are strong in clusters like the Virgo cluster, which halo radius is close to the zero-gravity radius. It is shown, that the empirical data on clusters like the Virgo cluster or the Coma cluster, are consistent with the assumption that the local density of dark energy on the scale of clusters of galaxies is the same as on the global cosmological scales.