Topology, Geometry and Morphology of the Dark Matter Web

Abstract

Spatial distribution of dark matter displays a variety of intricate three dimensional structures on the largest scales in the Universe, notably the massive haloes, long tubular filaments, flattened walls and the vast under-dense voids. Galaxies embedded in the dark matter structures have illuminated the rich geometry of these structures currently known as the cosmic web. Cosmological N-body simulations are indispensable tools for understanding the evolution of the dark matter web. Recent developments in the numerical analysis of these simulations have hinted towards incorporating the dynamical information of gravitational clustering of collisionless dark matter. This is inferred from a six-dimensional Lagrangian sub-manifold -- comprising of initial and final coordinates of the dark matter particles. Velocity multistream field derived from this sub-manifold sheds new light on the nature of gravitational collapse. Geometrical, topological, morphological and heuristic diagnostic tools used in this novel parameter space reveal features of the dark matter distribution. For instance, a single void structure not only percolates the multistream field in all the directions, but also occupies over 99 per cent of all the single-streaming regions. On the other hand, connected filaments display a rapid topological transition to isolated islands at high multistream values. Hessian analysis delineates structures with different shapes: tubular, sheet-like, or globular -- enabling detection of the dark matter haloes without ad hoc parameters related to matter density or distance field.