Bias Properties of Extragalactic Distance Indicators. II. Bias Corrections to Tully-Fisher Distances for Field Galaxies

Observational selection bias in samples of field galaxies used with the Tully-Fisher (TF) method of distance determination can be detected using the internal properties of the sample. The method is to divide the data into bins by line width and show that the apparent Hubble constant is multivalued for different line widths at given redshifts. The method is the same as used previously (Sandage 1988a, 1994) in samples composed of a fixed galaxy type by adding a fainter similar sample. If bias is present, the bias properties will disappear at a bright level but will reappear with the same properties at the corresponding fainter level. The procedure is generalized here to develop a method to determine statistically correct distances using the Tully-Fisher method. A triple-entry correction to ridge-line TF absolute magnitudes is derived that depends on (1) redshift, (2) the apparent magnitude limit of the flux-limited sample, and (3) the line width. The Hubble constant will incorrectly be derived to increase outward and will also have too high a mean value if the intrinsic dispersion of the TF relation is either not accounted for at every redshift and every line width, or is underestimated. The highest weight sample of field galaxies from the distance-limited 500 km s^-1^ catalog of Kraan-Korteweg & Tammann (1979) is used with the absolute calibration of the Tully-Fisher relation by Richter & Huchtmeier (1984) based on 64 galaxies in nearby groups, generally calibrated with Cepheids, to give a bias-free Hubble constant of H_0_ = 48 +/- 5 km s^-1^ Mpc^-1^. All other TF data for the biased samples of field galaxies discussed here show that the short distance scale with H_0_ ~ 85 is not supported by the present TF calibration using the adopted intrinsic dispersion of the TF relation. Unless the effects of observational bias in flux-limited samples are identified and corrected in each particular data sample, conclusions concerning both the Hubble constant and the existence of streaming motions about the cosmological expansion are suspect.