Effects of Distance Uncertainties on Determinations of the Galaxy Peculiar Velocity Field

Galaxy distance indicators are subject to different uncertainties and biases, which may be reflected in the peculiar velocity field. In this work, we present different statistical analysis applied to the peculiar velocities of samples of galaxies and mock catalogs taken from numerical simulations considering these observational effects. Our statistical studies comprise the mean relative velocity and velocity correlation for pairs of galaxies as a function of separation, and a bulk flow analysis of spheres of 10 h-1 Mpc radius. In order to test the statistical analysis, we use COBE-normalized cold dark matter (CDM) numerical simulations with different density parameters and cosmological constant, and take into account the Tully-Fisher (TF) scatter and a possible TF zero-point offset, as well as variations in the results of the simulations arising from different observer positions. We compare the results of the mock catalogs with samples of spiral galaxies taken from the Mark III catalog. The results of our analysis indicate the importance of errors in deriving the density parameter Ω from statistics applied to the observational data, and it is found that large values of Ω ≥ 0.8 may be derived from the analysis if errors are not taken into account. However, the observed value of the TF scatter (≃0.35 mag) produce CDM models with Ω > 0.6, inconsistent with the statistical tests involving relative velocities. A suitable agreement is found for models with Ω ≤ 0.6, although this requires a TF zero-point offset on the order of a tenth of a magnitude to provide consistency with the observed flow coherence.