Ω and biasing from optical galaxies versus POTENT mass

The mass density field in the local universe, recovered by the POTENT method from peculiar velocities of ∼ 3000 galaxies, is compared with the density field of optically selected galaxies. Both density fields are smoothed with a Gaussian filter of radius 12h⁻¹ Mpc. Under the assumptions of gravitational instability and a linear biasing parameter b_o between optical galaxies and mass, we obtain $$\beta_\text O\equiv\Omega^{0.6}/b_\text O=0.74\pm0.13$$. This result is obtained from a regression of POTENT mass density on optical density after correcting the mass density field for systematic biases in the velocity data and POTENT method. The error quoted is just the 1σ formal error estimated from the observed scatter in the density-density scatterplot; it does not include the uncertainty due to cosmic scatter in the mean density or in the biasing relation. We do not attempt a formal analysis of the goodness of fit, but the scatter about the fit is consistent with our estimates of the uncertainties.