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

¹ Observatoire de Paris-Meudon DESPA, 92195 Meudon Cedex, France
² European Southern Observatory, Casilla 19001, Santiago 19, Chile
³ Departament d'Enginyeria Informàtica i Matemàtiques, Escola Tècnica Superior d'Enginyeria, Universitat Rovira i Virgili, Carretera de Salou, s/n; 43006 Tarragona, Spain e-mail: jsolanes@etse.urv.es
⁴ Departament d'Astronomia i Meteorologia, Facultat de Físiques, Universitat de Barcelona C/ Martí i Franqués 1, 08028 Barcelona, Spain e-mail: tsanchis@am.ub.es
⁵ Observatoire de Paris-Meudon DAEC, 92195 Meudon Cedex, France e-mail: Chantal.Balkowski@obspm.fr

Corresponding author: P. Fouqué, pfouque@eso.org

Received: 3 April 2001
Accepted: 31 May 2001

Abstract

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 degrees from M 87. We find that the sample is significantly contaminated by background galaxies which lead to too large a cluster mean distance if not excluded. The Tolman-Bondi model predictions, together with the HI deficiency of spiral galaxies, allows one to identify these background galaxies. One such galaxy is clearly identified among the 6 calibrating galaxies with Cepheid 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 Mpc. Well-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. Applying the B-band Tully-Fisher method to a sample of 51 true members of the Virgo cluster according to our classification gives a cluster distance of Mpc, larger than the mean Cepheid distance. Finally, the same model is used to estimate the Virgo cluster mass, which is within 8 degrees from the cluster center (2.2 Mpc radius), and amounts to 1.7 virial mass.