Bias Properties of Extragalactic Distance Indicators. III. Analysis of Tully-Fisher Distances for the Mathewson-Ford-Buchhorn Sample of 1355 Galaxies

The observational selection bias properties of the large Mathewson- Ford-Buchhorn (MFB) sample of galaxies are demonstrated by showing that the apparent Hubble constant incorrectly increases outward when determined using Tully-Fisher (TF) photometric distances that are uncorrected for bias. It is further shown that the value of H_0_ so determined is also multivalued at a given redshift when it is calculated by the TF method using galaxies with different line widths. The method of removing this unphysical contradiction is developed following the model of the bias set out in Paper II. The model developed further here shows that the appropriate TF magnitude of a galaxy that is drawn from a flux- limited catalog not only is a function of line width but, even in the most idealistic cases, requires a triple-entry correction depending on line width, apparent magnitude, and catalog limit. Using the distance-limited subset of the data, it is shown that the mean intrinsic dispersion of a bias-free TF relation is high. The dispersion depends on line width, decreasing from σ(M) = 0.7 mag for galaxies with rotational velocities less than 100 km s^-1^ to σ(M) = 0.4 mag for galaxies with rotational velocities greater than 250 km s^-1^. These dispersions are so large that the random errors of the bias-free TF distances are too gross to detect any peculiar motions of individual galaxies, but taken together the data show again the offset of 500 km s^- 1^ found both by Dressler & Faber and by MFB for galaxies in the direction of the putative Great Attractor but described now in a different way. The maximum amplitude of the bulk streaming motion at the Local Group is ~500 km s^-1^, but the perturbation dies out, approaching the Machian frame defined by the CMB at a distance of ~80 Mpc (v ~ 4000 km s^-1^). This decay to zero perturbation at v ~ 4000 km s^-1^ argues against existing models with a single attractor at ~4500 km s^-1^ (the Great Attractor model) pulling the local region. Rather, the cause of the perturbation appears to be the well-known clumpy mass distribution within 4000 km s^-1^ in the busy directions of Hydra, Centaurus, Antlia, and Dorado, as postulated earlier (Tammann & Sandage 1985).