Redshift-Space Distortions of Group and Galaxy Correlations in the Updated Zwicky Catalog

The two-point correlation function is computed for galaxies and groups of galaxies selected using three-dimensional information from the Updated Zwicky Galaxy Catalog (UZC). The redshift-space distortion of the correlation function ξ(σ,π) in the directions parallel and perpendicular to the line of sight, induced by pairwise group peculiar velocities, is evaluated. Two methods are used to characterize the pairwise velocity field of groups and galaxies. The first method consists of fitting the observed ξ(σ,π) with a distorted model of an exponential one-dimensional pairwise velocity distribution, in fixed σ bins. The second method compares the contours of the constant predicted correlation function of this model with the data. The results are consistent with a one-dimensional pairwise rms velocity dispersion of groups 1/2 = 250 ± 110 km s-1. We find that UZC galaxy one-dimensional pairwise rms velocity dispersion is 1/2 = 460 ± 35 km s-1. Such findings point toward a smoothly varying peculiar velocity field from galaxies to systems of galaxies, as expected in a hierarchical scenario of structure formation. We find that the real-space correlation functions of galaxies and groups in UZC can be well approximated by power laws of the form ξ(r) = (r/r0)γ. The values of γ for each case are derived from the correlation function in projected separations ω(σ). Using these estimates, we obtain r0 from the projected correlation functions. The best-fitting parameters are γ = -1.89 ± 0.17 and r0 = 9.7 ± 4.5 h-1 Mpc for groups and γ = -2.00 ± 0.03 and r0 = 5.29 ± 0.21 h-1 Mpc for galaxies. The β-parameter (β = Ω0.6/b) is estimated for groups and galaxies using the linear approximation regime relating real- and redshift-space correlation functions. We find βgx = 0.51 ± 0.15 for galaxies, in agreement with previous works, while for groups we obtain a noisy estimate β < 1.5. Both methods used to characterize the pairwise velocity field are also tested on mock catalogs taken from numerical simulations. The results show that the conclusions derived from the application of both methods to the observations are reliable. We also find that the second method, developed in this paper, provides more stable and precise results.