The Virgo Cluster Distance from 21 Centimeter Line Widths

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Abstract
The distance of the Virgo cluster is derived in the B band from the 21 cm line width-absolute magnitude relation. This relation is calibrated using 18 spirals with Cepheid distances, mainly from the Hubble Space Telescope. The calibration is applied to a complete sample of nonpeculiar spirals with i > 45° lying within the optical (n = 49) or X-ray (n = 35) contour of the cluster, resulting in a mean cluster distance of (m - M)0 = 31.58 ± 0.24 mag (external error), or 20.7 ± 2.4 Mpc. The mean distance of subcluster A is 0.46 ± 0.18 mag smaller than that of subcluster B, but the individual distances of the members of the two substructures show considerable overlap. Cluster spirals with 30° < i < 45° yield distances almost as good as those of more inclined galaxies. H I-truncated galaxies are overluminous by 0.8 mag at a given line width. The distance modulus is corrected by -0.07 mag for the fact that cluster members have lower H I surface fluxes and are redder in (B-I) at a given line width than the (field) calibrators. Different sources for the B magnitudes and line widths have little effect on the resulting distance. Different precepts for the internal absorption correction change the result by no more than ±0.17 mag. The individual distances of the cluster members do not show any dependence on recession velocity, inclination, Hubble type, or line width. The dependence on apparent magnitude reflects the considerable depth effect of the cluster. The adopted distance is in good agreement with independent distance determinations of the cluster. Combining the cluster distance with the corrected cluster velocity of 1142 ± 61 km s-1 gives H0 = 55 ± 7 km s-1 Mpc-1 (external error). If the Virgo cluster distance is inserted into the tight Hubble diagram of clusters out to 11,000 km s-1 using relative distances to the Virgo cluster, one obtains a global value of H0 = 57 ± 7 km s-1 Mpc-1.
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