Redshift-space bias and β from the halo model

We analyse scale dependence of redshift-space bias b and β  ≡ 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 <0.1  h  Mpc⁻¹ . On intermediate scales the virial motions of galaxies cause a suppression of the power spectrum relative to the linear one and the suppression differs from the same effect in dark matter. This can potentially mimic the effect of massive neutrinos, and the degeneracy can only be broken if the power spectrum is measured for k ≪0.1  h  Mpc⁻¹ . Different methods to determine β converge for k <0.1  h  Mpc⁻¹ , but give drastically different results on smaller scales, which explains some of the trends observed in the real data. We also assess 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 >0.1  h  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.