Towards an accurate model of the redshift-space clustering of haloes in the quasi-linear regime

Observations of redshift-space distortions in spectroscopic galaxy surveys offer an attractive method for measuring the build-up of cosmological structure, which depends both on the expansion rate of the Universe and on our theory of gravity. The statistical precision with which redshift-space distortions can now be measured demands better control of our theoretical systematic errors. While many recent studies focus on understanding dark matter clustering in redshift space, galaxies occupy special places in the universe: dark matter haloes. In our detailed study of halo clustering and velocity statistics in 67.5 h^-3 Gpc³ of N-body simulations, we uncover a complex dependence of redshift-space clustering on halo bias. We identify two distinct corrections which affect the halo redshift-space correlation function on quasi-linear scales (∼30-80 h^-1 Mpc): the non-linear mapping between real-space and redshift-space positions, and the non-linear suppression of power in the velocity divergence field. We model the first non-perturbatively using the scale-dependent Gaussian streaming model, which we show is accurate at the <0.5 (2) per cent level in transforming real-space clustering and velocity statistics into redshift space on scales s > 10 (s > 25) h^-1 Mpc for the monopole (quadrupole) halo correlation functions. The dominant correction to the Kaiser limit in this model scales like b³. We use standard perturbation theory to predict the real-space pairwise halo velocity statistics. Our fully analytic model is accurate at the 2 per cent level only on scales s > 40 h^-1 Mpc for the range of halo masses we studied (with b= 1.4-2.8). We find that recent models of halo redshift-space clustering that neglect the corrections from the bispectrum and higher order terms from the non-linear real-space to redshift-space mapping will not have the accuracy required for current and future observational analyses. Finally, we note that our simulation results confirm the essential but non-trivial assumption that on large scales, the bias inferred from the real-space clustering of haloes is the same as the one that determines their pairwise infall velocity amplitude at the per cent level.