Galaxies and Clusters of Galaxies in Observations and Numerical Models

An analysis of the properties of 1157 galaxies, groups and clusters of galaxies confirms the dependence of the virial velocity on the halo mass v(vir) = v(m)(M-vir/10(12)M(circle dot))(1/3) with a single exponent and different values of v(m) similar or equal to 400 vm km/s for galaxies with M-vir <= 10(12) M-circle dot and V-m similar or equal to 160 km/s for galaxy clusters with M-vir >= 10(12) M-circle dot. A single exponent confirms the high degree of universality of the dark matter halo formation processes, and the difference in values of v(m) corresponds to the well-known difference in the average densities of galaxies and galaxy clusters and introduces a new scale M similar or equal to 10(12) M-circle dot into the perturbation power spectrum. Modern numerical models using the power spectrum obtained from the WMAP and Planck observations reproduce well the observed properties of galaxy clusters, but cannot reproduce the observed parameters of galaxies. It is also shown that the cusp in the dark matter density profile leads to a finite density of gas and stars at the center of the halos (Burkert profile).