A dynamical classification of the cosmic web

In this paper, we propose a new dynamical classification of the cosmic web. Each point in space is classified in one of four possible web types: voids, sheets, filaments and knots. The classification is based on the evaluation of the deformation tensor (i.e. the Hessian of the gravitational potential) on a grid. The classification is based on counting the number of eigenvalues above a certain threshold, lambda(th), at each grid point, where the case of zero, one, two or three such eigenvalues corresponds to void, sheet, filament or a knot grid point. The collection of neighbouring grid points, friends of friends, of the same web type constitutes voids, sheets, filaments and knots as extended web objects. A simple dynamical consideration of the emergence of the web suggests that the threshold should not be null, as in previous implementations of the algorithm. A detailed dynamical analysis would have found different threshold values for the collapse of sheets, filaments and knots. Short of such an analysis a phenomenological approach has been opted for, looking for a single threshold to be determined by analysing numerical simulations. Our cosmic web classification has been applied and tested against a suite of large (dark matter only) cosmological N-body simulations. In particular, the dependence of the volume and mass filling fractions on lambda(th) and on the resolution has been calculated for the four web types. We also study the percolation properties of voids and filaments. Our main findings are as follows. (i) Already at lambda(th) = 0.1 the resulting web classification reproduces the visual impression of the cosmic web. (ii) Between 0.2 less than or similar to lambda(th) less than or similar to 0.4, a system of percolated voids coexists with a net of interconnected filaments. This suggests a reasonable choice for lambda(th) as the parameter that defines the cosmic web. (iii) The dynamical nature of the suggested classification provides a robust framework for incorporating environmental information into galaxy formation models, and in particular to semi-analytical models.