Peculiar velocities and the mean density parameter

We study the peculiar velocity field inferred from the Mark III spirals usi ng a new method of analysis. We estimate optimal values of Tully-Fisher sca tter and zero-point offset, and we derive the three-dimensional rms peculia r velocity (sigma(upsilon)) of the galaxies in the samples analysed. We che ck our statistical analysis using mock catalogues derived from numerical si mulations of cold dark matter (CDM) models considering measurement uncertai nties and sampling variations. Our best determination for the observations is sigma(upsilon) = (660 +/- 50) km s(-1). We use the linear theory relatio n between sigma(upsilon), the density parameter Omega, and the galaxy corre lation function xi(r) to infer the quantity beta = Omega(0.6)/b = 0.60(-0.1 1)(+0.13), where b is the linear bias parameter of optical galaxies and the uncertainties correspond to bootstrap resampling and an estimated cosmic v ariance added in quadrature. Our findings are consistent with the results o f cluster abundances and redshift-space distortion of the two-point correla tion function. These statistical measurements suggest a low value of the de nsity parameter Omega similar to 0.4 if optical galaxies are not strongly b iased tracers of mass.