Galaxy clustering and the origin of large-scale flows
R. Juszkiewicz, A. Yahil · The Astrophysical Journal · 1989
Peebles's "cosmic virial theorem" is extended from its original range of validity at small separations, where hydrostatic equilibrium holds, to large separations, in which linear gravitational instability theory applies. The rms pairwise velocity difference at separation r, C(v_1_ - v_2_)^2^>, is shown to depend on the spatial galaxy correlation function ξ(x) only for x < r. Gravitational instability theory can therefore be tested by comparing the two up to the maximum separation for which both can reliably be determined, and there is no dependence on the poorly known large-scale density and velocity fields. The extant data show a significant systematic difference between the velocity data for elliptical and spiral galaxies, probably due to insufficient depth and sky coverage. At this stage, it is therefore only possible to restrict the cosmological density parameter to the range 0.1 <~ {OMEGA} <~ 1. With the expected improvement in the data over the next few years, however, our method should yield a reliable determination of {OMEGA}.