Redshift distortions of galaxy correlation functions
Abstract
To examine how peculiar velocities can affect the 2, 3, and 4point correlation functions, we evaluate volumeaverage correlations for configurations that emphasize and minimize distortions for four different volumelimited samples from each of the CfA, SSRS, and IRAS redshift catalogs. We present the results as the correlation length r_{0} and power index gamma of the 2point correlation, barxi_{2} = (r_{0}/r)^{gamma),} and as the hierarchical amplitudes of the 3 and 4point functions, S_{3} = barxi_{3}/barxi_{2}^{2} and S_{4} = barxi/barxi)_{2}^{3}. We find a characteristic distortion for barxi_{2}: 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 Omega^{4/7}/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 barxi_{3} and barxi_{4} suffer similar redshift distortions, but in such a way that, within the accuracy of our analysis, the normalized amplitudes S_{3} and S_{4} are insensitive to this effect. The hierarchical amplitudes S_{3} and S_{4} are constant as a function of scale between 112 h^{1} Mpc and have similar values in all samples and catalogues, S_{3} approx. 2 and S_{4} approx. 6, despite the fact that barxi_{2}, barxi_{3}, and barxi_{4} differ from one sample to another by large factors. The agreement between the independent estimations of S_{3} and S_{4} 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.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 May 1993
 Bibcode:
 1993STIN...9412980F
 Keywords:

 Galactic Clusters;
 Galaxies;
 Red Shift;
 Universe;
 Infrared Astronomy Satellite;
 Luminosity;
 Mass Distribution;
 Astrophysics