Dark energy in the environments of the Local Group, the M 81 group, and the CenA group: the normalized Hubble diagram

Context. Type Ia supernova observations on scales of thousands of Mpc show that the global expansion of the universe is accelerated by antigravity produced by the enigmatic dark energy contributing 3/4 of the total energy of the universe. Aims. Does antigravity act on small scales as well as large? As a continuation of our efforts to answer this crucial question we combine high accuracy observations of the galaxy flows around the Local Group and the nearby M 81 and CenA groups to observe the effect of the dark energy density on local scales of a few Mpc. Methods. We use an analytical model to describe non-uniform static space-time regions around galaxy groups. In this context it is useful to present the Hubble flow in a normalized Hubble diagram $V/H_{\rm v} R_{\rm v}$ vs. $r/R_{\rm v}$, where the vacuum Hubble constant Hv depends only on the cosmological vacuum density and the zero-gravity distance Rv depends on the vacuum density and on the mass of the galaxy group. We have prepared the normalized Hubble diagrams for the LG, M 81 and CenA group environments for different values of the assumed vacuum energy density, using a total of about 150 galaxies, for almost all of which the distances have been measured by the HST. Results. The normalized Hubble diagram, where we identify dynamically different regions, is in agreement with the standard vacuum density $(\Omega_{\rm v} = 0.77~h_{\rm 70}^{-2})$, the out-flow of galaxies clearly being controlled by the minimum energy condition imposed by the central mass plus the vacuum density. A high vacuum density $1.6~h_{\rm 70}^{-2}$ violates the minimum energy limit, while a low density $0.1~h_{\rm 70}^{-2}$ leaves the start of the Hubble flow around 1-2 Mpc with the slope close to the global value obscure. We also consider the subtle relation of the zero-gravity radius Rv to the zero-velocity distance R0 appearing in the usual retarded expansion around a mass M: in a vacuum-dominated flat universe R0 ≈ 0.76 Rv. Conclusions. The normalized Hubble diagram appears to be a good way to present and analyze physically different regions around mass clumps embedded in cosmological vacuum. The most natural interpretation of the diagram is that the local density of the dark energy is approximately equal to the density known from studies on global scales