Analytic model for the bispectrum of galaxies in redshift space

Abstract

We develop an analytic theory for the redshift space bispectrum of dark matter, haloes, and galaxies. This is done within the context of the halo model of structure formation, as this allows for the self-consistent inclusion of linear and nonlinear redshift-space distortions and also for the nonlinearity of the halo bias. The model is applicable over a wide range of scales: on the largest scales the predictions reduce to those of the standard perturbation theory (PT); on smaller scales they are determined primarily by the nonlinear virial velocities of galaxies within haloes, and this gives rise to the $U$-shaped anisotropy in the reduced bispectrum---a finger print of the Finger-Of-God distortions. We then confront the predictions with measurements of the redshift-space bispectrum of dark matter from an ensemble of numerical simulations. On very large scales, $k=0.05h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, we find reasonably good agreement between our halo model, PT and the data, to within the errors. On smaller scales, $k=0.1h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, the measured bispectra differ from the PT at the level of $\ensuremath{\sim}10%--20%$, especially for colinear triangle configurations. The halo model predictions improve over PT, but are accurate to no better than 10%. On smaller scales $k=0.5--1.0h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, our model provides a significant improvement over PT, which breaks down. This implies that studies which use the lowest order PT to extract galaxy bias information are not robust on scales $k\ensuremath{\gtrsim}0.1h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$. The analytic and simulation results also indicate that there is no observable scale for which the configuration dependence of the reduced bispectrum is constant---hierarchical models for the higher-order correlation functions in redshift space are unlikely to be useful. It is hoped that our model will facilitate extraction of information from large-scale structure surveys of the Universe, because different galaxy populations are naturally included into our description.