An Eulerian Perturbation Approach to Large Scale Structures: Extending the Adhesion Approximation

Abstract

A description of the dynamics of a collisionless, self-gravitating fluid is developed and applied to follow the development of Large Scale Structures in the Universe. Such description takes on one of the assumptions of the Adhesion Approximation (AA) model, i.e., the introduction of an artificial viscosity $ν$ in the Euler equation, but extends it to deeper non-linear stages, where the extrapolation of the linear relation $ψ=-ϕ$ between the velocity and the gravitational potentials -- at the basis of both the Zel'dovich and the Adhesion models -- is no longer valid. This is achieved by expanding the relation bewteen the gravitational potential $ϕ$ and the velocity potential $ψ$, in powers of the small viscosity $ν$. When the results are compared to the outcomes of an N-body simulation, the proposed extension of the Adhesion approach provides a better description of small-scale, deeply non-linear regions, as it is quantitatively shown by the computation of some statistical indicators. At larger scales, the satisfactory description of the large scale texture and of the voids given by the canonical Adhesion Approximation is preserved in the extended model.