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

We consider a situation where the density and peculiar velocities in real s pace are linear. and we calculate xi (s), the two-point correlation functio n in redshift space, incorporating all nonlinear effects which arise as a c onsequence of the map from real to redshift space. Our result is non-pertur bative and it includes the effects of possible multi-streaming in redshift space. We find that the deviations from the predictions of the linear redsh ift distortion analysis increase for the higher spherical harmonics of xi ( s). While the deviations are insignificant for the monopole eo, the hexadec apole xi (4) exhibits large deviations from the linear predictions. For a C OBE 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 possibilit y of removing the degeneracy that exists between these two parameters in th e linear analysis of redshift surveys which yields only beta = f(Omega)/b. We also show that the commonly used phenomenological model. where the non-l inear redshift two-point correlation function is calculated by convolving t he linear redshift correlation function with an isotropic pair velocity dis tribution function, is a limiting case of our result.