Constrained simulations of the local universe: I. Mass and motion in the Local Volume

It has been recently claimed that there is no correlation between the distribution of galaxies and their peculiar velocities within the Local Volume (LV), namely a sphere of R = 7hMpc around the Local Group (LG). It has been then stated that this implies that either locally dark matter is not distributed in the same way as luminous matter, or peculiar velocities are not due to fluctuations in mass. To test that statement a set of constrained N-body cosmological simulations, designed to reproduce the main observed large scale structure, have been analyzed. The simulations were performed within the flat-Λ, open and flat matter only CDM cosmogonies. Two unconstrained simulations of the flat-Λ and open CDM models were performed for comparison. LG-like objects have been selected so as to mimic the real LG environment. The local gravitational field due to all halos found within each LV is compared with the exact gravitational field induced by all matter in the simulation. We conclude that there is no correlation between the exact and the local gravitational field obtained by pairwise newtonian forces between halos. Moreover, the local gravitational field is uncorrelated with the peculiar velocities of halos. The exact gravitational field has a linear correlation with peculiar velocities but the proportionality constant relating the velocity with gravitational field falls below the prediction of the linear theory. Upon considering all matter inside the LVs, the exact and local gravitational accelerations show a much better correlation, but with a considerable scatter independent on the cosmological models. The main conclusion is that the lack of correlation between the local gravitation and the peculiar velocity fields around LG-like objects is naturally expected in the CDM cosmologies.