Velocity bias in clusters

Hierarchical gravitational clustering creates galaxies that usually do not fully share the dynamical history of an average particle in the mass field. In particular, galaxy tracers identified in numerical simulations can have individual velocity dispersions in virialized regions a factor bᵥ_ (1) lower than the dark matter. The field average of the pairwise velocity dispersion depends on the statistical weighting of collapsed regions, so that the tracer pairwise dispersion is at different factor, bᵥ_ (2), times the density field value. A model of a cool equilibrium tracer population demonstrates that mass-to-light segregation is very sensitive to single particle velocity bias. For the φ~ = - GM/ (r + a) potential a bᵥ_ (1) = 0. 9 tracer indicates a virial mass about a factor of 5 low. The likely value of bᵥ_ (1) is estimated and the simple equilibrium model is tested for applicability using a 10⁶^ particle simulation of the formation of a single cluster from cosmological initial conditions. A striking outcome is that the dense central cores of infalling galaxy scale dark matter halos survive infall and virialization within the cluster. These dense cores do not have the dissipationless infall of the bulk of mass, but during their first cluster crossing lose energy to the cluster background to become systematically more bound, thereafter orbiting freely as coherent, self-gravitating units. From this simulation, the value of bᵥ_ (1) is estimated as 0. 8+/-0. 1. The pairwise velocity dispersion bias, bᵥ_ (2), which is equal to bᵥ_ (1) augmented with any anti-bias of galaxies against high-velocity dispersion clusters. The value of bᵥ_ (2) is estimated to be 15% less than bᵥ_ (1) on the basis of a biasing model where the M/L ratio rises a factor of 10 from binaries to clusters, consequently bᵥ_ (2) = 0. 6_-0. 1_^+0. 2^. The Cosmic Virial Theorem measures the combination bᵥ_²^ (2) OMEGA/b (where b is the clustering bias) to be in the range 0. 20-0. 36, which at bᵥ_ (2) = 0. 6 is compatible with OMEGA = 1 for clustering bias b ~ 1 (IRAS galaxies) to b ~ 1. 8 (optical galaxies) but is incompatible with the full COBE normalized CDM spectrum. Comparison of cluster mass and luminosity profiles at large radii is a test for the existence of single particle velocity bias.