Redshift distortions of galaxy correlation functions

To examine how peculiar velocities can affect the 2-, 3-, and 4-point correlation functions, we evaluate volume-average correlations for configurations that emphasize and minimize distortions for four different volume-limited samples from each of the CfA, SSRS, and IRAS redshift catalogs. We present the results as the correlation length r0 and power index γ of the 2-point correlation, anti Ξ2 = (r0/r)γ, and as the hierarchical amplitudes of the 3- and 4-point functions, S3 = anti Ξ3/anti Ξ22 and S4 = anti Ξ/anti Ξ23. We find a characteristic distortion for anti Ξ2: The slope γ is flatter and the correlation length is larger in redshift space than in real space; that is, redshift distortions ''move'' correlations from small to large scales. At the largest scales, extra power in the redshift distribution is compatible with Ω4/7/b ∼ 1; we find 0.53 ± 0.15, 1.10 ± 0.16 and 0.84 ± 0.45 for the CfA, SSRS and IRAS catalogs. Higher order correlations anti Ξ3 and anti Ξ4 suffer similar redshift distortions, but in such a way that, within the accuracy of our analysis, the normalized amplitudes S3 and S4 are insensitive to this effect. The hierarchical amplitudes S3 and S4 are constant as a function of scale between 1-12 h-1 Mpc and have similar values in all samples and catalogues, S3 ∼ 2 and S4 ∼ 6, despite the fact that anti Ξ2, anti Ξ3, and anti Ξ4 differ from one sample to another by large factors. The agreement between the independent estimations of S3 and S4 is remarkable given the different criteria in the selection of galaxies and also the difference in the resulting range of densities, luminosities and locations between samples