Velocity and mass bias in the distribution of dark matter halos
  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 halos from the
Millennium-XXL N-body simulation, we find that the mass bias is scale
independent only for $k<0.1 h{\rm Mpc}^{-1}$ today ($z=0$) and for $k<0.2 h{\rm
Mpc}^{-1}$ at $z=0.7$. We test analytic halo bias models against our simulation
measurements and find that the model of Tinker et al. 2005 is accurate to
better then 5% at $z=0$. However, the simulation results are better fit 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% at $k=0.1h$Mpc$^{-1}$ for a halo sample of number density
$\bar{n} = 10^{-3} (h/$Mpc$)^3$ at both $z=0$ and $z=0.7$ for the velocity
divergence auto power spectrum. Given the importance of redshift space
distortions as a probe of dark energy and the on-going major effort to advance
models for the clustering signal in redshift space, our results show this
velocity bias introduces another systematic, alongside scale-dependent halo
mass bias, which cannot be neglected.
