REDSHIFT DISTORTIONS OF GALAXY CORRELATION-FUNCTIONS

To examine how peculiar velocities can affect the two-, three-, and four-point redshift correlation functions, we evaluate volume-average correlations for configurations that emphasize and minimize redshift 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 gamma of the two-point correlations, xiBAR0 = (r0/r)gamma, and as the hierarchical amplitudes of the three- and four-point functions, S3 = xiBAR3/xiBAR2(2) and S4 = xiBAR4/xiBAR2(3). We find a characteristic distortion for xiBAR2; the slope gamma 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 (up to 12 Mpc), the extra power in the redshift distribution is compatible with OMEGA4/7/b almost-equal-to 1. We estimate OMEGA4/7/b to be 0.53 +/- 0.15, 1.10 +/- 0.16, and 0.84 +/- 0.45 for the CfA, SSRS, and IRAS catalogs. Higher order correlations xiBAR3 and xiBAR4 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 and 12 Mpc and have similar values in all samples and catalogs, S3 almost-equal-to 2 and S4 almost-equal-to 6, despite the fact that xiBAR2, xiBAR3, and xiBAR4 differ from one sample to another by large factors (up to a factor of 4 in xiBAR2, 8 for xiBAR3, and 12 for xiBAR4). 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.