Astron. Astrophys. 355, 835-847 (2000)

1. Introduction

Study of the local extragalactic velocity field has a considerable history. Rubin (1988) pinpoints the beginning of the studies concerning deviations from the Hubble law to a paper of Gamow (1946) where Gamow asked if galaxies partake of a large-scale systematic rotation in addition to the Hubble expansion. The pioneer works by Rubin (1951) and Ogorodnikov (1952) gave evidence that the local extragalactic velocity field is neither linear nor isotropic. De Vaucouleurs (1953) then interpreted the distribution of bright galaxies and proposed rotation in terms of a flattened local supergalaxy. This short but remarkable paper did not yet refer to differential expansion, introduced by de Vaucouleurs (1958) as an explanation of the "north-south anisotropy" which he stated was first pointed out by Sandage (Humason et al. 1956). Differential expansion was a milder form of Hubble's "the law of redshifts does not operate within the Local Group" and de Vaucouleurs pondered that "in condensed regions of space, such as groups or clusters, the expansion rate is greatly reduced...". Though there was a period of debate on the importance of the kinematic effects claimed by de Vaucouleurs and even on the reality of the local supergalaxy (presently termed as the Local Supercluster, LSC), already for two decades the reality of the differential peculiar velocity field around the Virgo cluster has been generally accepted. However, its amplitude and such details as the deviation from spherical symmetry and possible rotational component, are still under discussion.

A theoretical line of research related to de Vaucouleurs' differential expansion, has been motivated by the work on density perturbations in Friedmann cosmological models, resulting in infall models of matter (Silk 1974) which predict a connection between the infall peculiar velocity at the position of the Local Group towards the Virgo cluster and the density parameter of the Friedmann universe. Later on, Olson & Silk (1979) further developed the formalism in a way which was found useful in Teerikorpi et al. (1992; hereafter Paper I). The linearized approximation of Peebles (1976) has been often used for describing the velocity field and for making routine corrections for systemic velocities.

Using Tolman-Bondi model (Tolman 1934, Bondi 1947) Hoffman et al. (1980) calculated the expected velocity dispersions along line-of-sight as a function of angular distance from a supercluster and applied the results to Virgo. They derived a gravitating mass of about inside the cone of . The Tolman-Bondi (TB) model is the simplest inhomogeneous solution to the Einstein's field equations. It describes the time evolution of a spherically symmetric pressure-free dust universe in terms of comoving coordinates. For details of the TB-model cf. Ekholm et al. (1999a; hereafter Paper II).

Then, following the course of Hoffman et al. (1980), Tully & Shaya (1984) calculated the expected run of radial velocity vs. distance at different angular distances from Virgo and for different (point) mass-age models. Comparison of such envelope curves with available galaxy data agreed with the point mass having roughly the value of Virgo's virial mass () for reasonable Friedmann universe ages.

The Hubble diagram of Tully & Shaya contained a small number of galaxies and did not very well show the expected behaviour. With a larger sample of Tully-Fisher measured galaxies and attempting to take into account the Malmquist bias, Teerikorpi et al. (1992) were able to put in evidence the expected features: an initial steeply rising tight velocity-distance relation, the local maximum in front of Virgo and the final ascending part of the relation, expected to approach asymptotically the undisturbed Hubble law. Looking from the Virgo centre the zero-velocity surface was clearly seen around . Using either a continuous mass model or a two-component model, the conclusions of Tully & Shaya (1984) were generally confirmed and it was stated that "Various density distributions, constrained by the mass inside the Local Group distance (required to produce ), agree with the observations, but only if the mass within the Virgo region is close to or larger than the standard Virgo virial mass values. This is so independently of the value of , of the slope of the density distribution outside of Virgo, and of the values adopted for Virgo distance and velocity".

It is the aim of the present paper to use the available sample of galaxies with more accurate distances from Cepheids and Tully-Fisher relation to study the virgocentric velocity field. In Paper II galaxies with Cepheid-distances were used to map the velocity field in front of Virgo, here we add galaxies with good Tully-Fisher distances in order to see both the frontside and backside behaviour and investigate how conclusions of Paper I should be modified in the light of new data. It should be emphasized that also our Tully-Fisher distances are now better, after a programme to study the slope and the Hubble type dependence of the zero-point (see Theureau et al. 1997).

This paper is structured as follows. In Sect. 2 we shortly review the basics of the use of the direct Tully-Fisher relation, give the relation to be used and describe our sample and the restrictions put upon it. In Sect. 3 we examine our sample in terms of systemic velocity vs. distance diagrams and see which distance to Virgo will bring about best agreement between the TB-predictions and the observations. In Sect. 4 we try to answer the question whether we have actually found the Virgo cluster at the centre of the TB-metric. In Sect. 5 we re-examine our sample from a virgocentric viewpoint and compare our results from the TF-distances with the sample of galaxies with distances from the extragalactic Cepheid PL-relation. In Sect. 6 we shortly discuss the mass estimate and our density profile and, finally, in Sect. 7 we summarize our results with some conclusive remarks.

© European Southern Observatory (ESO) 2000

Online publication: March 21, 2000
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