The multi-stream flows and the dynamics of the cosmic web

A new numerical technique to identify the cosmic web is proposed. It is based on locating multi-stream flows, i.e. the places where the velocity field is multi-valued. The method is local in Eulerian space, simple and computationally efficient. This technique uses the velocities of particles and thus takes into account the dynamical information. This is in contrast with the majority of standard methods that use the coordinates of particles only. Two quantities are computed in every mesh cell: the mean and variance of the velocity field. Ideally in the cells where the velocity is single-valued the variance must be equal to zero exactly, therefore the cells with non-zero variance are identified as multi-stream flows. The technique has been tested in the Zel'dovich approximation and in the N-body simulation of the ACDM model. The effect of numerical noise is discussed. The web identified by the new method has been compared with the web identified by the standard technique using only the particle coordinates. The comparison has shown overall similarity of two webs as expected, however they by no means are identical. For example, the isocontours of the corresponding, fields have significantly different shapes and sonic density peaks of similar heights exhibit significant differences in the velocity variance and vice versa. This suggests that the density and velocity variance have a significant degree of independence. The shape of the two-dimensional pdf of density and velocity variance confirms this proposition. Thus, we conclude that the dynamical information probed by this technique introduces an additional dimension into analysis of the web.