Velocity and mass bias in the distribution of dark matter halos

TL;DR

This paper investigates scale-dependent biases in dark matter halo distributions and velocities, revealing significant systematic effects that impact cosmological parameter estimation from galaxy clustering and redshift space distortions.

Contribution

It provides the first detailed analysis of velocity divergence bias in halos, highlighting its significance for cosmological measurements.

Findings

Mass bias is scale independent only at large scales ($k<0.1 h/{ m Mpc}$) at $z=0$ and $k<0.2 h/{ m Mpc}$ at $z=0.7.

The Tinker et al. 2005 model accurately predicts halo bias to within 5% at $z=0$.

Velocity divergence bias increases with decreasing halo number density, reaching about 20% at $k=0.1h/{ m Mpc}$ for typical halo samples.

Abstract

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.