REDSHIFT DISTORTIONS OF GALAXY CORRELATION-FUNCTIONS

To examine how peculiar velocities can affect the two-, three-, and fo ur-point redshift correlation functions, we evaluate volume-average co rrelations for configurations that emphasize and minimize redshift dis tortions for four different volume-limited samples from each of the Cf A, SSRS, and IRAS redshift catalogs. We present the results as the cor relation length r0 and power index gamma of the two-point correlations , xiBAR0 = (r0/r)gamma, and as the hierarchical amplitudes of the thre e- and four-point functions, S3 = xiBAR3/xiBAR2(2) and S4 = xiBAR4/xiB AR2(3). We find a characteristic distortion for xiBAR2; the slope gamm a is flatter and the correlation length is larger in redshift space th an 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. Highe r order correlations xiBAR3 and xiBAR4 suffer similar redshift distort ions but in such a way that, within the accuracy of our analysis, the normalized amplitudes S3 and S4 are insensitive to this effect. The hi erarchical amplitudes S3 and S4 are constant as a function of scale be tween 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 xiBA R4). 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, luminosit ies, and locations between samples.