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 similar to 1000 particles. The dark matter velocity dispersion scales with total mass as log sigma(DM)(M, z) = log(1082.9 +/- 4.0 km s(-1)) + (0.3361 +/- 0.0026) log [h(z)M-200/10(15) M-circle dot], with h(z) being the dimensionless Hubble parameter. At fixed mass, the velocity dispersion likelihood is nearly lognormal, with scatter sigma (ln) (sigma) = 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 Lambda CDM 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.