ar X iv : a st ro - p h / 99 04 07 4 v 1 6 A pr 1 99 9 Measuring Ω with galaxy streaming velocities

The mean pairwise velocity of galaxies, v12 has traditionally been estimated from the redshift space galaxy correlation function. This method is notorious for being highly sensitive to the assumed model of the pairwise velocity dispersion. Here we propose an alternative method to estimate v12 directly from peculiar velocity samples, which contain redshift-independent distances as well as galaxy redshifts. This method can provide an estimate of Ω 0.6 σ8 2 for a range of σ8 where Ω is the cosmological density parameter, while σ8 is the standard normalization for the power spectrum of density fluctuations. We demonstrate how to measure this quantity from realistic catalogues and identify the main sources of bias and errors 1 A model of v 12 (r) In this presentation we report on the the possibility of using the " mean tendency of well-separated galaxies to approach each other " 10 to measure the cosmological density parameter, Ω. The statistic we consider 4 is the mean relative pairwise velocity of galaxies, v 12. It was introduced in the context of the BBGKY theory 2 , describing the dynamical evolution of a collection of particles interacting through gravity. In this discrete picture, v 12 is defined as the mean value of the peculiar velocity difference of a particle pair at separation r. In the fluid limit, its analogue is the pair-density weighted relative velocity 5,7 , v 12 (r) = v 1 − v 2 ρ = (v 1 − v 2)(1 + δ 1)(1 + δ 2) 1 + ξ(r) , (1) where v A and δ A = ρ A /ρ − 1 are the peculiar velocity and fractional density contrast of matter at a point r A , r = | r 1 − r 2 |, and ξ(r) = δ 1 δ 2 is the two-point correlation function. The pair-weighted average, · · · ρ , differs from simple spatial averaging, · · ·, by the weighting factor ρ 1 ρ 2 ρ 1 ρ 2 −1 , proportional to the number-density of particle pairs. In a recent letter 8 , one of us has shown 1