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The distances to spiral galaxies of the Virgo cluster are estimated using the B-band Tully-Fisher (TF) relation, and the three-dimensional structure of the cluster is studied. The analysis is made for a complete spiral sample taken from the Virgo Cluster catalog of Binggeli, Sandage, & Tammann. The sample contains virtually all spiral galaxies down to MBT=-15 mag at 40 Mpc. A careful examination is made of the selection effect and errors of the data. We estimate distance to 181 galaxies, among which distances to 89 galaxies are reasonably accurate. We compare these distances to those obtained by other authors on a galaxy-by-galaxy basis. We find reasonable consistency of the Tully-Fisher distance among various authors. In particular, it is found that the discrepancy in the distance among the different analyses with different data is about 15%, when good H I and photometric data are available. We clarify that the different results on the Virgo distance among authors arise from the choice of the sample and interpretation of the data. We confirm that the Tully-Fisher relation for the Virgo cluster shows an unusually large scatter σ = 0.67 mag, compared to that for other clusters. We conclude that this scatter is not due to the intrinsic dispersion of the Tully-Fisher relation, but due to a large depth effect of the Virgo cluster, which we estimate to be extended from 12 Mpc to 30 Mpc. The distribution of H I-deficient galaxies is concentrated at around 14-20 Mpc, indicating the presence of a core at this distance, and this agrees with the distance estimated for M87 and other elliptical galaxies with other methods. We show also that the spatial number density of spiral galaxies takes a peak at this distance, while a simple average of all spiral galaxy distances gives 20 Mpc. The fact that the velocity dispersion of galaxies takes a maximum at 14-18 Mpc lends an additional support for the distance to the core. These features cannot be understood if the large scatter of the TF relation is merely due to the intrinsic dispersion. The structure of the Virgo Cluster we infer from the Tully-Fisher analysis looks like a filament which is familiar to us in a late phase of structure formation in the pancake collapse in hierarchical clustering simulations. This Virgo filament lies almost along the line of sight, and this is the origin that has led a number of authors to much confusion in the Virgo distance determinations. We show that the M87 subcluster is located around 15-18 Mpc, and it consists mainly of early-type type spiral galaxies in addition to elliptical and S0 galaxies. There are very few late-type spiral galaxies in this subcluster. The spiral rich M49 subcluster consists of a mixture of all types of spiral galaxies and is located at about 22 Mpc. The two other known clouds, W and M, are located at about 30-40 Mpc and undergo infall toward the core. The M cloud contains few early type spirals. We cannot discriminate, however, whether these subclusters or clouds are isolated aggregates or merely parts of filamentary structure. Finally, we infer the Hubble constant to be 82 ± 10 km s-1 Mpc-1.
Yasuda et al. (Sat,) studied this question.