Redshift space bias and beta from the halo model

Abstract

We analyze scale dependence of redshift space bias $b$ and $β\equiv Ω_m^{0.6}/b$ in the context of the halo model. We show that linear bias is a good approximation only on large scales, for $k<0.1h$Mpc$^{-1}$. On intermediate scales the virial motions of the galaxies cause a suppression of the power spectrum relative to the linear one, which differs from the same effect in dark matter. This suppression can potentially mimic the effect of massive neutrinos and the degeneracy can only be broken if the power spectrum is measured for $k \ll 0.1h$Mpc$^{-1}$. Different methods to determine $β$ converge for $k<0.1h$Mpc$^{-1}$, but give drastically different results on smaller scales, which explains some of the trends observed in the real data. We also asses the level of stochasticity by calculating the cross-correlation coefficient between the reconstructed velocity field divergence and the galaxies and show that the two fields decorrelate for $k>0.1h$Mpc$^{-1}$. Most problematic are galaxies predominantly found in groups and clusters, such as bright, red or elliptical galaxies, where we find poor convergence to a constant bias or $β$ even on large scales.