THE OMEGA-DEPENDENCE OF PECULIAR VELOCIEITES INDUCED BY SPHERICAL DENSITY PERTURBATIONS

The velocity of a shell surrounding a spherical density perturbation with average fractional overdensity DELTA-rho/rho in an otherwise Friedmann universe is expanded in powers of DELTA-rho/rho. Taking nu to be the velocity of an unperturbed shell of the same radius, the fractional velocity change of the perturbed shell is given by (graphics) where OMEGA is the usual cosmological density parameter, and where the expansion is exact to first order in OMEGA - 1. Commonly used expansions approximate the OMEGA dependence of the leading term as OMEGA-0.6.