Correlation Function of Galaxy Groups

We use the Updated Zwicky Catalog of galaxies to generate a catalog of groups by means of a friends-of-friends algorithm. The groups identified have four or more members and a surrounding density contrast δρ/ρ = 80. They cover the region -4° < δ < 90°, |b| > 20° spanning the radial velocity range of 2000 < cz < 15,000 km s-1. The total sample (hereafter GUZC) comprises 517 groups. The correlation length of the total sample is well fitted with a power law ξ(r) = (r/r0)γ, with parameters r0 = 9.0 ± 0.4 h-1 Mpc and γ = -1.67 ± 0.09 for values of r < 70 h-1 Mpc, declining to homogeneity at larger scales. Three subsamples defined by the range of group virial masses M were used to examine their clustering properties throughout the autocorrelation function. We find an increase of the amplitude of the correlation function according to the group masses, which extends the results of the r0-dc relation for galaxy systems at small dc. We obtain r0 = 9.5 ± 0.5 h-1 Mpc (γ = -1.81 ± 0.12), r0 = 10.8 ± 0.7 h-1 Mpc (γ = -1.77 ± 0.17), and r0 = 14.1 ± 1.2 h-1 Mpc (γ = -1.65 ± 0.22) for mass ranges 5 × 1012 < M < 4 × 1014 M☉ , 2 × 1013 < M < 4 × 1014 M☉, and 5 × 1013 < M < 4 × 1014 M☉, respectively. For completeness, we have also analyzed a sample of groups obtained from the Southern Sky Redshift Survey in the range of virial masses 5 × 1012 < M < 4 × 1014 M☉ to compare the results with those obtained from GUZC. The correlation function of this sample can be fitted with a power law with parameters r0 = 8.4 ± 1.8 h-1 Mpc and γ = -2.0 ± 0.7.