A complete galaxy redshift sample - I. The peculiar velocities between galaxy pairs and the mean mass density of the Universe

We have measured redshifts for a new sample of 320 galaxies complete to $$J\approx17$$. The two-point correlation function has been estimated using both redshift and positional information. This has been used to estimate the mean-square relative peculiar velocities $$\langle W^2\rangle$$ for galaxy pairs with projected separations in the range 0 ≲ σ ≲ 4 h⁻¹ Mpc (h is Hubble's constant in units of 100 km s⁻¹ Mpc⁻¹). We find line-of-sight velocity differences of $ $\langle W^2\rangle^{1/2}$$ = 250 ± 50 km s⁻¹ independent of projected separation. The two-point correlation function is well approximated by the power-law model $$\xi(r)=(r_0/r)^{1.8}$$ with r₀ = (4.1 ± 0.3) h⁻¹ Mpc. In addition, we estimate the amplitude of the three-point correlation function. We find Q = 0.60 ± 0.06, where Q is the ratio of the three-point correlation function to the square of the two-point function. These results are used in the cosmic virial theorem to obtain an estimate of the contribution to the mean density from material that is clustered like galaxies. The result is Ω = 0.14 × 2^±1. In order for our results to be compatible with a high density Universe (Ω = 1), most of the dark material must be in a component that is much less strongly clustered than galaxies on scales of 4 h⁻¹ Mpc or less.