Velocity and spatial biases in cold dark matter subhalo distributions

We present a statistical study of substructure within a sample of Lambda cold dark matter (LambdaCDM) clusters and galaxies simulated with up to 25 x 10(6) particles. With thousands of subhaloes per object we can accurately measure their spatial clustering and velocity distribution functions and compare these with observational data. The substructure properties of galactic haloes closely resemble those of galaxy clusters with a small scatter in the mass and circular velocity functions. The velocity distribution function is non-Maxwellian and flat topped with a negative kurtosis of approximately -0.7. Within the virial radius the velocity bias b = sigma(sub)/sigma(DM) similar to 1.12 +/- 0.04, increasing to b > 1.3 within the halo centres. Slow subhaloes are much less common, due to physical disruption by gravitational tides early in the merging history. This leads to a spatially antibiased subhalo distribution that is well fitted by a cored isothermal. Observations of cluster galaxies do not show such biases, which we interpret as a limitation of pure dark matter simulations - we estimate that we are missing half of the halo population, which has been destroyed by physical overmerging. High-resolution hydrodynamical simulations are required to study these issues further. If CDM is correct then the cluster galaxies must survive the tidal field, perhaps due to baryonic inflow during elliptical galaxy formation. Spirals can never exist near the cluster centres and the elliptical galaxies there will have little remaining dark matter. This implies that the morphology-density relation is set before the cluster forms, rather than a subsequent transformation of discs to S0s by virtue of the cluster environment.