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 \bvs\ 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 a different factor, \bvp, 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 $\phi=-GM/(r+a)$ potential a $\bvs=0.9$ tracer indicates a virial mass about a factor of 5 low. The likely value of \bvs\ is estimated and the simple equilibrium model is tested for applicability using a $10^6$ particle simulation of the formation of a single cluster from cosmological initial conditions. From this simulation, the value of \bvs\ is estimated as $0.8\pm0.1$. The pairwise velocity dispersion bias, \bvp, which is equal to \bvs\ augmented with any anti-bias of galaxies against high velocity dispersion clusters. The value of \bvp\ is estimated to be 15\% less than \bvs, consequently $\bvp=0.6^{+0.2}_{-0.1}$. Comparison of cluster mass and luminosity profiles at large radii is a test for the existence of single particle velocity bias. [compressed postscript file cluster.ps.Z via anonymous ftp from orca.astro.washington.edu in ~ftp/pub/hpcc, or carlberg@astro.washington.edu]