The Scaling Relations of Galaxy Clusters and Their Dark Matter Halos

Like early-type galaxies, nearby galaxy clusters also define fundamental plane, luminosity-radius, and luminosity-velocity dispersion relations, whose physical origins are still unclear. By means of high-resolution N-body simulations of massive dark matter halos in a ΛCDM (Λ cold dark matter) cosmology, we find that scaling relations similar to those observed for galaxy clusters are already defined by their dark matter hosts. The slopes, however, are not the same, and among the various possibilities in principle able to bring the simulated and the observed scaling relations into mutual agreement, we show that the preferred solution is a luminosity-dependent mass-to-light ratio (M/L ∝ L~0.3) that corresponds well to what is inferred observationally. We then show that at galactic scales there is a conflict between the cosmological predictions of structure formation, the observed trend of the mass-to-light ratio in elliptical galaxies, and the slope of their luminosity-velocity dispersion relation (which significantly differs from the analogous one followed by clusters). The conclusion is that the scaling laws of elliptical galaxies might be the combined result of the cosmological collapse of density fluctuations at the epoch when galactic scales became nonlinear plus important modifications afterward due to early-time dissipative merging. Finally, we briefly discuss the possible evolution of the cluster scaling relations with redshift.