Bias Properties of Extragalactic Distance Indicators. VIII. H0 from Distance-limited Luminosity Class and Morphological Type-Specific Luminosity Functions for Sb, Sbc, and Sc Galaxies Calibrated Using Cepheids

Open Access
Publisher Website
Google Scholar
Abstract
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 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) H0 = 56 ± 4 from the method through the Virgo Cluster, as corrected to the global kinematic frame (Tammann and coworkers); and (3) H0 = 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.