SAMPLING FUNCTIONS FOR MEASURING THE COSMIC MASS DENSITY

A method is proposed for analyzing the anisotropy of the two-point correlation function in velocity space with axisymmetric sampling functions as filters of the cosmic density field. The ratio of variances in density samples taken with these functions at different orientations relative to an observer's line of sight depends only on the velocity factor f(OMEGA) in the linear theory of gravitational clustering. Therefore, this ratio can provide an estimate of the cosmic mass density from redshift surveys. The method is applied to simulated density fields in velocity space to assess its feasibility; the best results are achieved with sampling functions of characteristic sizes around 1600 km s-1. A similar, preliminary analysis of real redshift data from the Giovanelli and Haynes survey of the Pisces-Perseus region, acquired at the Arecibo Observatory, yields values of OMEGA almost-equal-to 0.6.