Velocity bias in a Lambda cold dark matter model

We use a high-resolution N-body simulation to study the velocity bias of da rk matter halos, the difference in the velocity fields of dark matter and h alos, in a flat low-density cold dark matter (ACDM) model. The high force, 2 h(-1) kpc, and mass, 10(9) h(-1) M., resolution allows dark matter halos to survive in very dense environments of groups and clusters, making it pos sible to use halos as galaxy tracers. We find that the velocity bias, b(v,1 2), measured as a ratio of pairwise velocities of the halos to that of the dark matter, evolves with time and depends on scale. At high redshifts (z s imilar to 5), halos generally move faster than the dark matter on almost al l scales: b(v,12)(r) approximate to 1.2, r > 0.5 h(-1) Mpc. At later moment s, the bias decreases and gets below unity on scales less than r approximat e to 5 h(-1) Mpc: b(v,12)(r) approximate to (0.6-0.8) at z = 0. We find tha t the evolution of the pairwise velocity bias follows and probably is defin ed by the spatial antibias of the dark matter halos at small scales. The on e-point velocity bias, b(v), defined as the ratio of the rms velocities of halos and dark matter, provides a more direct measure of the difference in velocities, ;because it is less sensitive to the spatial bias. We analyze b (v) in clusters of galaxies and find that halos are "hotter" than the dark matter: b(v) = 1.2-1.3 for r = (0.2-0.8)r(vir), where r(vir) is the virial radius. At larger radii, b(v) decreases and approaches unity at r = (1-2)r( vir). We argue that dynamical friction may be responsible for this small po sitive velocity bias (b(v) > 1) found in the central parts of clusters. We do not find significant systematic difference in the velocity anisotropy of halos and the dark matter. The velocity anisotropy function, beta, of dark matter particles can be approximated as beta(x)= 0.15 + 2x/(x(2) + 4), whe re the distance x is measured in units of the virial radius.