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<SUB>DM</SUB>(M,z)=log(1082.9+/-4.0 km s<SUP>-1</SUP>)+(0.3361+/-0.0026)log[h(z)M<SUB>200</SUB>/10<SUP>15</SUP> M<SUB>solar</SUB>, with h(z) being the dimensionless Hubble parameter. At fixed mass, the velocity dispersion likelihood is nearly lognormal, with scatter σ<SUB>lnσ</SUB>=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<SUB>8</SUB>=σ<SUB>8</SUB>(Ω<SUB>m</SUB>/0.3)<SUP>0.35</SUP>=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<SUB>8</SUB>=0.80, alleviates this tension and implies that the hot gas fraction within r<SUB>500</SUB> is (0.71+/-0.09) h<SUP>-3/2</SUP><SUB>70</SUB> Ω<SUB>b</SUB>/Ω<SUB>m</SUB>, a value consistent with recent Sunyaev-Zel'dovich observations.