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(sigma_{DM}(M,z)) = log(1082.9 +- 4.0 \kms) + (0.3361 +- 0.0026) log(h(z)M_{200}/10^{15} Msun), with h(z) the dimensionless Hubble parameter. At fixed mass, the velocity dispersion likelihood is nearly log-normal, with scatter sigma_{ln sigma} = 0.0426 +- 0.015, except for a tail to higher dispersions containing 10% of the population that are merger transients. We combine this relation with the halo mass function in LCDM models, and show that a low normalization condition, S_8 = sigma_8(Omega_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 (0.71 +- 0.09) h_{70}^{-3/2} Omega_b/\Omega_m, a value consistent with recent Sunyaev-Zel'dovich observations.