THE EXTRAGALACTIC DISTANCE SCALE .2. THE UNBIASED DISTANCE TO THE VIRGO CLUSTER FROM THE B-BAND TULLY-FISHER RELATION

The behavior of the B-band Tully-Fisher relation with respect to the observational biases and parameters uncertainties is studied from an almost complete sample of spiral galaxies belonging to the Virgo Cluster. The strong influence of the limiting apparent magnitude when using the direct Tully-Fisher relation (all the errors on magnitude) is confirmed. The inverse regression (all the errors on line width) leads to a similar bias if the sample is limited in line width; moreover, the slope of this inverse regression strongly depends on the errors on the magnitudes, which prevents applying the same universal relation to different data samples. Both regressions applied to the complete Virgo sample give a distance modulus of 31.4 ± 0.2. The error includes all known sources of errors (accidental and systematic). The corresponding Hubble constant is H0 = 68 ± 8 km s-1 Mpc-1, assuming a cosmological velocity of the cluster V = 1300 ± 100 km s-1. The Virgo S and S′ clouds are shown to lie at significantly different distances. The difference with the higher distance modulus recently obtained by Kraan-Korteweg, Cameron, and Tammann, μ = 31.60, comes only from different distances adopted for the calibrators, and not from different systems of corrections to the observables. The use of only three calibrators, with good distance determinations but corrected parameters still subject to small variations, is responsible of the lower distance modulus found by Pierce and Tully, μ = 30.96. Such accidental errors are reduced by the use of the largest number of available calibrators, even with distances not so well determined.