1999ApJ...527..479S

Relative, reduced to absolute, magnitude distributions are obtained for Sb, Sbc, and Sc galaxies in the flux-limited Revised Shapley-Ames Catalog (RSA2) for each van den Bergh luminosity class (L), within each Hubble type (T). The method to isolate bias-free subsets of the total sample is via Spaenhauer diagrams, as in previous papers of this series. The distance-limited type and class-specific luminosity functions are normalized to numbers of galaxies per unit volume (10⁵ Mpc³), rather than being left as relative functions, as in Paper V. The functions are calculated using kinematic absolute magnitudes, based on an arbitrary trial value of H₀=50. Gaussian fits to the individual normalized functions are listed for each T and L subclass. As in Paper V, the data can be freed from the T and L dependencies by applying a correction of 0.23T+0.5L to the individual absolute magnitudes. Here, T=3 for Sb, 4 for Sbc, and 5 for Sc galaxies, and the L values range from 1 to 6 as the luminosity class changes from I to III-IV. The total luminosity function, obtained by combining the volume-normalized Sb, Sbc, and Sc individual luminosity functions, each corrected for the T and L dependencies, has an rms dispersion of 0.67 mag, similar to much of the Tully-Fisher parameter space.

Absolute calibration of the trial kinematic absolute magnitudes is made using 27 galaxies with known T and L that also have Cepheid distances. This permits the systematic correction to the H₀=50 kinematic absolute magnitudes of 0.22±0.12 mag, giving

H₀=55±3(internal) km.s^–1.Mpc^–1.

The Cepheid distances are based on the Madore/Freedman Cepheid period-luminosity (PL) zero point that requires (m-M)₀=18.50 for the LMC. Using the modern LMC modulus of (m-M)₀=18.58 requires a 4% decrease in H₀, giving a final value of H₀=53±7 (external) by this method. These values of H₀, based here on the method of luminosity functions, are in good agreement with (1) H₀=55±5 by Theureau and coworkers from their bias-corrected Tully-Fisher method of ``normalized distances'' for field galaxies; (2) H<sub>0</sub>=56±4 from the method through the Virgo Cluster, as corrected to the global kinematic frame (Tammann and coworkers); and (3) H<sub>0</sub>=58±5 from Cepheid-calibrated Type Ia supernovae (Saha and coworkers). Our value here also disagrees with the final value from the NASA ``Key Project'' group value of H₀=70±7.

Analysis of the total flux-limited sample of Sb, Sbc, and Sc galaxies in the RSA2 by the present method, but uncorrected for selection bias, would give an incorrect value of H₀=71 using the same Cepheid calibration. The effect of the bias is pernicious at the 30% level; either it must be corrected by the methods in the papers of this series, or the data must be restricted to the distance-limited subset of any sample, as is done here.