Nonlinear redshift distortions: The two-point correlation function

Abstract

We consider a situation where the density and peculiar velocities in real space are linear, and we calculate \xi_s the two-point correlation function in redshift space, incorporating all non-linear effects which arise as a consequence of the map from real to redshift space. Our result is non-perturbative and it includes the effects of possible multi-streaming in redshift space. We find that the deviations from the predictions of the linear redshift distortion analysis increase for the higher spherical harmonics of \xi_s. While the deviations are insignificant for the monopole \xi_0, the hexadecapole \xi_4 exhibits large deviations from the linear predictions. For a COBE normalised \Gamma=0.25, h=0.5 CDM power spectrum our results for \xi_4 deviate from the linear predictions by a factor of two at the scales ~10 h^{-1} Mpc. The deviations from the linear predictions depend separately on \Omega and b. This holds the possibility of removing the degeneracy that exists between these two parameters in the linear analysis of redshift surveys which yields only \beta=\Omega^0.6/b. We also show that the commonly used phenomenological model where the non-linear redshift two-point correlation function is calculated by convolving the linear redshift correlation function with an isotropic pair velocity distribution function is a limiting case of our result.