Peculiar velocity effect on galaxy correlation functions in nonlinear clustering regime

We studied the distortion of the apparent distribution of galaxies in redshift space contaminated by the peculiar velocity effect. Specifically we obtained the expressions for N-point correlation functions in redshift space with given functional form for velocity distribution f (v) and evaluated two- and three-point correlation functions quantitatively. The effect of velocity correlations is also discussed. When the two-point correlation function in real space has a power-law form, ξ^ (r) ^ (r) is proportional to r^-γ^, the redshift-space counterpart on small scales also has a power-law form but with an increased power-law index: ξ^ (s) ^ (S) is proportional to s¹-γ^. When the three-point correlation function has the hierarchical form and the two-point correlation function has the power-law form in real space, the hierarchical form of the three-point correlation function is almost preserved in redshift space. The above analytic results are compared with the direct analysis based on fit-body simulation data for -cold dark matter models. Implications on the hierarchical clustering ansatz are discussed in detail.