Virial Scaling of Massive Dark Matter Halos: Why Clusters Prefer a High Normalization Cosmology

We present a precise estimate of the bulk virial scaling relation of halos formed via hierarchical clustering in an ensemble of simulated cold dark matter cosmologies. The result is insensitive to cosmological parameters; the presence of a trace, dissipationless gas component; and numerical resolution down to a limit of ~1000 particles. The dark matter velocity dispersion scales with total mass as log [σ DM ( M,z )] = = log(1082.9 ± 4.0 km s −1 ) + (0.3361 ± 0.0026)log[ h ( z ) M 200 /10 15 M ☉ ], with h ( z ) being the dimensionless Hubble parameter. At fixed mass, the velocity dispersion likelihood is nearly lognormal, with scatter σ ln σ = 0.0426 ± 0.015, except for a tail with higher dispersions containing 10% of the population that are merger transients. We combine this relation with the halo mass function in ΛCDM models and show that a low normalization condition, S 8 = σ 8 (Ω m /0.3) 0.35 = 0.69, favored by recent WMAP and SDSS analysis requires that galaxy and gas-specific energies in rich clusters be 50% larger than that of the underlying dark matter. Such large energetic biases are in conflict with the current generation of direct simulations of cluster formation. A higher normalization, S 8 = 0.80, alleviates this tension and implies that the hot gas fraction within r 500 is , a value consistent with recent Sunyaev-Zel'dovich observations.