The Scaling Relations of Galaxy Clusters and Their Dark Matter Halos

Like early-type galaxies, also nearby galaxy clusters define a FundamentalPlane, a luminosity-radius, and a luminosity-velocity dispersion relations,whose physical origin is still unclear. By means of high resolution N--bodysimulations of massive dark matter halos in a Lambda-CDM cosmology, we findthat scaling relations similar to those observed for galaxy clusters arealready defined by their dark matter hosts. The slopes however are not thesame, and among the various possibilities in principle able to bring thesimulated and the observed scaling relations in mutual agreement, we show thatthe preferred solution is a luminosity dependent mass-to-light ratio (M/L ~L^0.3), that well corresponds to what inferred observationally. We then showthat at galactic scales there is a conflict between the cosmologicalpredictions of structure formation, the observed trend of the mass-to-lightratio in ellipticals, and the slope of their luminosity-velocity dispersionrelation (that significantly differs from the analogous one followed byclusters). The conclusion is that the scaling laws of elliptical galaxies mightbe the combined result of the cosmological collapse of density fluctuations atthe epoch when galactic scales became non-linear, plus important modificationsafterward due to early-time dissipative merging. Finally, we briefly discussthe possible evolution of the cluster scaling relations with redshift.Comment: 18 pages, 3 figures, ApJ, accepted version. A new Table added, some extended discussion, conclusions unchange