5 Discussion and conclusions

We may conclude that all the properties of the local Hubble flow, mentioned by Sandage, become even more remarkable when more accurate distances are used. Sandage (1986) noted that the derived velocity dispersion around the local Hubble law has progressively decreased together with increasing accuracy in distances, from Hubble's 200 kms^-1 to his 60 kms^-1. Our results confirm that this trend continues, and $\sigma_{\rm v} \leq 40$ kms^-1.

The velocity-distance diagrams (Figs. 2 and 3) show that the local Hubble constant is much the same as the more global value derived from the Tully-Fisher indicator from the KLUN sample (Theureau et al. 1997; Ekholm et al. 1999b). This also confirms Sandage's (1999) recent estimate that the very local Hubble constant is the same as the global H₀within 10 percent.

The third important feature is the small distance where the Hubble law emerges. The new data show that the linear Hubble law extends down to at least 1.5 Mpc. Hence, within the standard Friedman model (including the cosmological constant $\Lambda$; see Fig. 3), one gets an upper limit for the mass of the Local Group ($\approx$ $2~10^{12}~M_{\odot}$).

The quiet Hubble flow within the very clumpy local galaxy universe has always been a real riddle (Sandage et al. 1972; Sandage 1999). The problem of the local quiet Hubble flow was studied by Governato et al. (1997) using high-resolution CDM N-body simulations. They constructed a large sample of "Local Groups" and calculated the velocity dispersions in $5{\rm\ Mpc}$ volumes around the LG candidates. They found for $\Omega=1$ CDM model that the velocity dispersion is $300-700{\rm\ km\,s^{-1}}$ and for $\Omega=0.3$ CDM model $150-300{\rm\ km\,s^{-1}}$. They state that these simulations were unable to produce a single LG having a velocity dispersion as low as observed.

The very local Hubble diagram offers several important applications for cosmology when the number of accurate Cepheid distances to local galaxies is increased. The mass of the Local Group and the position of its barycenter may be determined more precisely. And recently it has been suggested (Chernin et al. 2000) that the quietness of the local Hubble flow is a signature of the cosmological vacuum (Einstein's $\Lambda$-constant corresponding to energy density $\rho_{\Lambda} = {\rm const.}$) dominated universe where the velocity perturbations are adiabatically decreasing. For solution of both problems - the small velocity dispersion and the Hubble law starting immediately at 1.5 Mpc with the global H₀ - Baryshev et al. (2000) proposed that there is a cosmological, homogeneous dark energy (quintessence) component with time-variable energy density $\rho_{\rm Q}(t)$ and equation of state $p_{\rm Q} = w~\rho_{\rm Q} c^2$ with $w \in [-1,0]$. These discussions show that the very local volume is extremely important for the study of global properties of the universe.

Acknowledgements

This work was partly supported by the Academy of Finland (project 45087: "Galaxy Streams and Structures in the nearby Universe" and project "Cosmology in the Local Galaxy Universe"). We have made use of the Lyon-Meudon Extragalactic Database LEDA and the Lyon Extragalactic Cepheid Database. We are grateful for the referee, M. Capaccioli, for his comments.