On the application of the spherical infall model to real (anisotropic and/or non-isolated) mass concentrations

Abstract

We have studied analytically the mean pull on shells of real (anisotropic and/or non-isolated) mass concentrations. Using a non-linear scheme, the radial component of the peculiar velocity is averaged over solid angle (V0) and mass-averaged (V*0) for several different generic configurations. Nine Local Supercluster(LS)-like objects and six Great Attractor(GA)-like structures enabled us to compare the corresponding true density parameters, Ω0, with the estimates for the standard spherical infall model Ωest (using V0) and Ω*est (via V*0). The results for LS-like superclusters are consistent with those derived for GA-like ones. If we focus our attention on the LS-like objects, the accuracy of Ω*est is very poor: absolute values of the relative errors greater than 20 per cent are common and they can reach a level of 50–70 per cent. Underestimates of the density parameter are related to superclusters that are spherical within the reference shell at 15 h−1 Mpc but have an exterior anisotropic tail. The remaining cases (with interior anisotropy and/or companions) lead to overestimates. A clear conclusion is that the spherical infall model is not a good approximation for estimating Ω0 by means of measurements, V*0, in the halo of an LS-like supercluster. In contrast, the accuracy of Ωest is relatively good, even in extreme situations with either a dominant companion or dipole anisotropy plus companion (all absolute values of the relative errors are less than 20 per cent). Therefore, the peculiar motions when averaged over 4π sr (V0) fit a spherical model relatively well. However, the link between our results and the well-known measurements in the Local Supercluster and the Great Attractor (at the corresponding Local Group radius) is not evident. At the end of the paper we present a discussion on the reliability of the standard view that density–velocity data in both structures suggest an open universe. It is remarked that the estimation of the true density enhancement in the Local Supercluster must be improved (by consideration of a full survey and true distances) before one decides on the value of Ω0.