6 Conclusion

The main conclusions are the following:

• We give the equations for drawing the Spaenhauer diagram. This allows us to determine unbiased distances for galaxies that are similar (sosie) to some galaxies, calibrated in distance with two independent Cepheid samples. From these unbiased distances we obtained simultaneously the Hubble constant in different regions and the infall velocity of the Local Group onto Virgo. The values of $\log H$ spread from 1.83 to 1.81 with an internal error of 0.01 or less. From Table 1, we can see that the mean uncertainty on the calibrator distance modulus is 0.19, i.e., 0.038 on $\log H$. Thus, from a quadratic summation, the total uncertainty on $\log H$ is 0.04. We will adopt:
  
  $$\log H = 1.82 \pm 0.04 \ \ \ (H \approx 66 \pm 6~ \rm km~s^{-1}~Mpc^{-1})$$
  
  
  and for the Local Group infall velocity:
  
  $$V_{\rm LG-infall} = 208 \pm 9~\rm km~s^{-1}.$$
  
  

• The front side and backside infalls are seen around Virgo and Fornax. Peebles's model is tested in a direct manner and we obtained:
  
  $$v_{\rm infall} = \frac{C}{r^{0.9 \pm 0.2}}$$
  
  
  with C=2800 for Virgo and C=1350 for Fornax using the classical units (km s^-1 and Mpc). There is no reason to expect an integer for $\gamma$. We will thus adopt the value we have found, although it does not differ significantly from an integer. We obtained the mean distance moduli:
  
  $$\mu _{\rm Virgo}=31.3 \pm 0.2$$
  
  
  
  
  $$\mu _{\rm Fornax}=31.7 \pm 0.3.$$
  
  

The next step will be an application of this model to nearby clusters. The purpose is to test quantitatively the amplitude of the distortion on the apparent galaxy distribution induced by infalls.

Acknowledgements

We thank the anonymous referee and P. Fouqué for their remarks. T.E. acknowledges the support by the Academy of Finland (the projects "Galaxy Streams and Structures in the nearby Universe'' and "Cosmology in the local to the deep galaxy universe'').