Non-linear redshift distortions: the two-point correlation function

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 nonlinear 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 eo, the hexadecapole xi (4) exhibits large deviations from the linear predictions. For a COBE normalized Gamma = 0.25, h = 0.5 cold dark matter (CDM) power spectrum, our results for xi (4) deviate from the linear predictions by a factor of two on the scale of similar to 10 h(-1) Mpc. The deviations from the linear predictions depend separately on f(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 = f(Omega)/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.