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 gamma of the 2-point correlation, bar-xi2 = (r0/r)gamma), and as the hierarchical amplitudes of the 3- and 4-point functions, S3 = bar-xi3/bar-xi22 and S4 = bar-xi/bar-xi)23. We find a characteristic distortion for bar-xi2: 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, extra power in the redshift distribution is compatible with Omega4/7/b approx. 1; we find 0.53 plus/minus 0.15, 1.10 plus/minus 0.16 and 0.84 plus/minus 0.45 for the CfA, SSRS and IRAS catalogs. Higher order correlations bar-xi3 and bar-xi4 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 approx. 2 and S4 approx. 6, despite the fact that bar-xi2, bar-xi3, and bar-xi4 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.
NASA STI/Recon Technical Report N
- Pub Date:
- May 1993
- Galactic Clusters;
- Red Shift;
- Infrared Astronomy Satellite;
- Mass Distribution;