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The non-linear, scale-dependent bias in the mass distribution of galaxies andthe underlying dark matter is a key systematic affecting the extraction ofcosmological parameters from galaxy clustering. Using 95 million halos from theMillennium-XXL N-body simulation, we find that the mass bias is scaleindependent only for $k<0.1 h{\rm Mpc}^{-1}$ today ($z=0$) and for $k<0.2 h{\rmMpc}^{-1}$ at $z=0.7$. We test analytic halo bias models against our simulationmeasurements and find that the model of Tinker et al. 2005 is accurate tobetter then 5% at $z=0$. However, the simulation results are better fit by anellipsoidal collapse model at $z=0.7$. We highlight, for the first time,another potentially serious systematic due to a sampling bias in the halovelocity divergence power spectra which will affect the comparison betweenobservations and any redshift space distortion model which assumes dark mattervelocity statistics with no velocity bias. By measuring the velocity divergencepower spectra for different sized halo samples, we find that there is asignificant bias which increases with decreasing number density. This bias isapproximately 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 velocitydivergence auto power spectrum. Given the importance of redshift spacedistortions as a probe of dark energy and the on-going major effort to advancemodels for the clustering signal in redshift space, our results show thisvelocity bias introduces another systematic, alongside scale-dependent halomass bias, which cannot be neglected.

Velocity and mass bias in the distribution of dark matter halos