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

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

7. Summary and conclusions

In this third paper of our series we have extended the discussion of Ekholm et al. (1999a; Paper II) to the background of Virgo cluster by selecting galaxies with as good distances as possible from the direct B-band magnitude Tully-Fisher (TF) relation. In the following list we summarize our main results:

Although having a rather large scatter the TF-galaxies reveal the expected Tolman-Bondi (TB) pattern well. We compared our data with TB-solutions for different distances to the Virgo cluster. It turned out that when the background galaxies fell clearly below the predicted curves. Hence the data does not support such distance scale (cf. Figs. 1 and 2).
When we examined the Hubble diagram for galaxies outside the Virgo cone (Fig. 5) we noticed that is a clear upper limit for these galaxies. Together with our preferred cosmological velocity of Virgo () we concluded that is a lower limit.
In both cases any residual Malmquist bias would move the sample galaxies further away and thus make the short distances even less believable.
We compared our sample galaxies with with the Table 3 of Federspiel et al. (1998) and found 33 galaxies in common. We established a plausible case for corresponding to (cf. Fig. 6). The difference between and is - in terms of the distance moduli - only , which is within the scatter of the TF-relation. Due to this scatter it is not possible to resolve the distance to Virgo with higher accuracy. Hence we claim that - .
Some of the kinematical features identified in Paper I were revealed also here, in particular the concentration of galaxies in front with very low velocities (interpreted as an expanding component; region B in Paper I) and the tight background concentration (region D in Paper I). The symmetric counterpart of region B (region C1) may actually be part of the primary TB-pattern.
The need for a better distance indicator (e.g. the I-band TF-relation) is imminent. As seen e.g. from Fig. 9, the scatter in the B-band TF-relation is disturbingly large. It is also necessary to re-examine the calibration of the TF-relation with the new, and better, PL-distances. It seems that the PL-distances and the TF-distances from Theureau et al. (1997) are not completely consistent. The former tend to be somewhat smaller. This is also seen from Figs. 6 and 8. TF-distances support and PL-distances . It is, however, worth reminding that our dynamical conclusions are insensitive to the actual distance scale.
When we examined the Hubble diagram as it would be seen from the origin of the TB-metric, galaxies with distances from the extragalactic PL-relation fitted best to a solution with in concordance with Paper II and with Federspiel et al. (1998). We are, however, not yet confident enough to assign any error bars to this value.
For the region D follows well the TB-pattern (cf. Fig. 3) lending some additional credence to this distance. We quite clearly identified this background feature as the subgroup "B" of Federspiel et al. (1998).
These high quality galaxies also clearly follow the expected velocity-distance behaviour in the virgocentric frame with much smaller scatter than for galaxies in Paper I or for the TF-galaxies used in this paper. The zero-velocity surface was detected at .
As in Teerikorpi et al. (1992; Paper I), the amplitude of the TB-pattern requires that the Virgo cluster mass must be at least its standard virial mass (Tully & Shaya 1984) or more. Our best estimate is - , where for .
Our results indicate that the density distribution of luminous matter is shallower than that of the total gravitating matter. The preferred exponent in the density power law, , agrees with the theoretical work on the universal density profile of dark matter clustering (Tittley & Couchman 1999) in the Einstein-deSitter universe.

Online publication: March 21, 2000
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