Velocity and mass bias in the distribution of dark matter haloes

The non-linear, scale-dependent bias in the mass distribution of galaxies and the underlying dark matter is a key systematic affecting the extraction of cosmological parameters from galaxy clustering. Using 95 million haloes from the Millennium-XXL N-body simulation, we find that the mass bias is scale independent only for k < 0.1 h Mpc(-1) today (z = 0) and for k < 0.2 h Mpc(-1) at z = 0.7. We test analytic halo bias models against our simulation measurements and find that the model of Tinker et al. is accurate to better than 5 per cent at z = 0. However, the simulation results are better fitted by an ellipsoidal collapse model at z = 0.7. We highlight, for the first time, another potentially serious systematic due to a sampling bias in the halo velocity divergence power spectra which will affect the comparison between observations and any redshift-space distortion model which assumes dark matter velocity statistics with no velocity bias. By measuring the velocity divergence power spectra for different sized halo samples, we find that there is a significant bias which increases with decreasing number density. This bias is approximately 20 per cent at k = 0.1 h Mpc(-1) for a halo sample of number density (n) over bar = 10(-3)(h/Mpc)(3) at both z = 0 and 0.7 for the velocity divergence auto power spectrum. Given the importance of redshift-space distortions as a probe of dark energy and the major ongoing effort to advance models for the clustering signal in redshift space, our results show that this velocity bias introduces another systematic, alongside scale-dependent halo mass bias, which cannot be neglected.