Peculiar Velocities and the Mean Density Parameter

We study the peculiar velocity field inferred from the Mark III spirals using a new method of analysis. We estimate optimal values of Tully-Fisher scatter and zero-point offset, and we derive the 3-dimensional rms peculiar velocity ($\sigma_v$) of the galaxies in the samples analysed. We check our statistical analysis using mock catalogs derived from numerical simulations of CDM models considering measurement uncertainties and sampling variations. Our best determination for the observations is $\sigma_v= (660\pm50) km/s$. We use the linear theory relation between $\sigma_v$, the density parameter $\Omega$, and the galaxy correlation function $\xi(r)$ to infer the quantity $\beta =\Omega^{0.6}/b = 0.60^{+0.13}_{-0.11}$ where $b$ is the linear bias parameter of optical galaxies and the uncertainties correspond to bootstrap resampling and an estimated cosmic variance added in quadrature. Our findings are consistent with the results of cluster abundances and redshift space distortion of the two-point correlation function. These statistical measurements suggest a low value of the density parameter $\Omega \sim 0.4$ if optical galaxies are not strongly biased tracers of mass.