Bias properties of extragalactic distance indicators. 1: The Hubble constant does not increase outward

Observational selection bias in flux-limited catalogs of field galaxies can be detected using a diagram in which the calculated intrinsic luminosity of each galaxy is plotted against its redshift. Apparent correlations of absolute magnitude with redshift that are not real, but rather are caused by selection effects can be identified by adding a fainter sample. If an apparent correlation is due to bias, it will disappear at the original flux level but will reappear with the same properties near the limit of the fainter catalog. The method is illustrated using S0 + Sa galaxies from two catalogs with different apparent magnitude limits. The demonstration is the same as that made earlier using Sc I galaxies (Sandage 1988a). To avoid photometric distance determinations that are systematically incorrect as a function of redshift, it is necessary to use mean absolute magnitudes, M(m, v_i_), that are functions of the apparent magnitude limit of the catalog, m, and of the observed individual redshifts, v_i_. This double-entry M_0_ - M(m, v_i_) correction to the proper volume- limited absolute magnitude M_0_ is calculated and is listed in a table. Failure to apply this bias correction at every redshift will give an incorrect Hubble constant that apparently increases outward. The clue that bias corrections are needed is that the apparent Hubble constant calculated using uncorrected data from two catalogs with different flux limits will be double-valued at a given redshift, one value for each catalog, which is a clear contradiction.