Gaussian streaming with the truncated Zel’dovich approximation

We calculate the halo correlation function in redshift space using the Gaussian streaming model (GSM). To determine the scale-dependent functions entering the GSM, we use local Lagrangian bias together with convolution Lagrangian perturbation theory (CLPT), which constitutes an approximation to the Post-Zel'dovich approximation. On the basis of N-body simulations, we demonstrate that a smoothing of the initial conditions with the Lagrangian radius improves the Zel'dovich approximation and its ability to predict the displacement field of protohalos. Based on this observation, we implement a "truncated" CLPT by smoothing the initial power spectrum and investigate the dependence of the streaming model ingredients on the smoothing scale. We find that the real space correlation functions of halos and their mean pairwise velocity are optimized if the coarse graining scale is chosen to be 1 Mpc/h at z = 0, while the pairwise velocity dispersion is optimized if the smoothing scale is chosen to be the Lagrangian size of the halo. We compare theoretical results for the halo correlation function in redshift space to measurements within the Horizon run 2 N-body simulation halo catalog. We find that this simple two-filter smoothing procedure in the spirit of the truncated Zel'dovich approximation significantly improves the GSM + CLPT prediction of the redshift space halo correlation function over the whole mass range from large galaxy to galaxy cluster-sized halos. We expect that the necessity for two filter scales is an artifact of our local bias model, and that once a more physical bias model is implemented in CLPT, the only physically relevant smoothing scale will be related to the Lagrangian radius, in accord with our findings based on N-body simulations.