Mixed dark matter in halos of clusters

We discuss the structure of clusters in a class of hat cosmological models with the fraction of mass Omega(CDM) similar or equal to 0.8 in cold dark matter, and the rest in hot dark matter in the form of massive neutrinos. These cold + hot dark matter (CHDM) models with one, two, or three massive neutrinos, with total mass similar or equal to 4.6 eV, are considered. Neutrinos of that mass range are too hot and cannot constitute the halos of galaxies and groups, but only of clusters of galaxies. The Limit on the density of neutrinos in the central parts of galaxy clusters is estimated from the phase-space density constraints. The ratio of the density of neutrinos to that of cold dark matter through the cluster is found analytically. It appears that the density of the neutrinos is suppressed within the Abell radius. However, neutrinos contribute similar to 20% of the mass density to the cluster halo. Our numerical simulations fairly match analytical results for the suppression factor. The simulations indicate that the cluster halo dark matter density profile has the power-law slope alpha similar or equal to 2.5, which is close to that in the model with the cosmological constant. We also found that in the CHDM models the velocity dispersion is almost constant across the cluster. This is quite different from the model with cosmological constant or from the open model where the velocity dispersion in the cluster outskirts declines. We discuss observational tests that can probe cold, neutrino, an baryonic components, unequally distributed in clusters: X-ray emission and weak gravitational lensing. Combing the spherically symmetric fit to the CHDM mass density profile found here with the X-ray surface brightness of the cluster A2256 and a simple model of the hydrostatic equilibrium of the hot gas, we derive the theoretical temperature distribution in the cluster. This distribution disagrees with the observational data near the cluster center. It also disagrees with the velocity dispersion of the cold particles in a numerical simulation to the extent that the dispersion corresponds to the gas temperature. We also find that the problem of high baryonic fraction in clusters is not resolved in the CHDM models.