The Distance to the Virgo Cluster from a Recalibrated Tully-Fisher Relation Based on HST Cepheids and a Demonstrated Teerikorpi Cluster Incompleteness Bias

Abstract

The importance of the distance of the Virgo cluster in the ongoing debate on the value of the Hubble constant is reviewed. A new calibration of the Tully-Fisher 21-cm line width-absolute magnitude relation is made using Cepheid distances to 25 galaxies determined in various HST programs and reduced with the new Cepheid P-L relations that vary from galaxy-to galaxy. The calibration is applied to a complete sample of Virgo cluster spirals for the purpose of demonstrating the Teerikorpi cluster incompleteness bias. A diagnostic test is shown that should be useful in identifying the presence of bias in incompletely sampled data for distant clusters. The bias-free TF distance modulus for the Virgo cluster is m - M = 31.67 (D = 21.6 Mpc). A systematic correction of 0.07 mag is made because the cluster members are redder in B I on average than the calibrators at a given line width, giving a final adopted modulus for the Virgo cluster core of 31.60 + 0.09. If we assign a generous range of systematic error of ~ 0.3 mag, the distance D = 20.9 Mpc (m - M = 31.60) has a range from 24.0 Mpc to 18.2 Mpc (m - M between 31.9 and 31.3), and a Hubble constant of Ho = 56 between the limits of 49 and 65 when used with a cosmic expansion velocity of 1175 km s-1 determined by the method of distance ratios of remote clusters to Virgo. This range overlaps our preferred value of Ho = 62 from the HST Cepheid calibration of type Ia supernovae recently determined. The TF modulus of Virgo determined here cannot be reconciled with the recent high value of Ho = 72 from Freedman et al.