Research Note

The Hubble diagram for a system within dark energy: the location of the zero-gravity radius and the global Hubble rate

¹ Tuorla Observatory, Department of Physics and Astronomy, University of Turku, 21500 Piikkiö, Finland e-mail: pekkatee@utu.fi
² Sternberg Astronomical Institute, Moscow University, Moscow 119899, Russia

Received: 3 March 2010
Accepted: 18 April 2010

Abstract

Aims. Here we continue to discuss the principle of the local measurement of dark energy using the normalized Hubble diagram describing the environment of a system of galaxies.

Methods. We calculate the present locus of test particles injected a fixed time ago (~the age of the universe), in the standard Λ cosmology and for different values of the system parameters (the model includes a central point mass M and a local dark energy density ρ_loc) and discuss the position of the zero-gravity distance R_v in the Hubble diagram.

Results. Our main conclusion are: 1) when the local DE density ρ_loc is equal to the global DE density ρ_v, the outflow reaches the global Hubble rate at the distance R₂ = (1+z_v)R_v, where z_v is the global zero-acceleration redshift (≈0.7 for the standard model). This is also the radius of the ideal Einstein-Straus vacuole, 2) for a wide range of the local-to-global dark energy ratio ρ_loc/ρ_v, the local flow reaches the known global rate (the Hubble constant) at a distance R₂ 1.5 × R_v. Hence, R_v will be between R₂/2 and R₂, giving upper and lower limits to ρ_loc/M. For the Local Group, this supports the view that the local density is near the global one.