Structure, mass and distance of the Virgo cluster from a Tolman-Bondi model

We have applied a relativistic Tolman-Bondi model of the Virgo cluster to a sample of 183 galaxies with measured distances within a radius of 8 degree s from M 87. We find that the sample is significantly contaminated by backg round galaxies which lead to too large a cluster mean distance if not exclu ded. The Tolman-Bondi model predictions, together with the HI deficiency of spiral galaxies, allows one to identify these background galaxies. One suc h galaxy is clearly identified among the 6 calibrating galaxies with Cephei d distances. As the Tolman-Bondi model predicts the expected distance ratio to the Virgo distance, this galaxy can still be used to estimate the Virgo distance, and the average value over the 6 galaxies is 15.4 +/-0.5 Mpc. We ll-known background groups of galaxies are clearly recovered, together with filaments of galaxies which link these groups to the main cluster, and are falling into it. No foreground galaxy is clearly detected in our sample. A pplying the B-band Tully-Fisher method to a sample of 51 true members of th e Virgo cluster according to our classification gives a cluster distance of 18.0 +/-1.2 Mpc, larger than the mean Cepheid distance. Finally, the same model is used to estimate the Virgo cluster mass, which is M = 1.2 x 10(15) M-circle dot within 8 degrees from the cluster center (2.2 Mpc radius), an d amounts to 1.7 virial mass.