Dark matter haloes: a multistream view

Mysterious dark matter constitutes about 85% of all mass in the Universe. Clustering of dark matter plays the dominant role in the formation of all observed structures on scales from a fraction to a few hundreds of Mega-parsecs. Galaxies play a role of lights illuminating these structures so they can be observed. The observations in the last several decades have unveiled opulent geometry of these structures currently known as the cosmic web. Haloes are the highest concentrations of dark matter and host luminous galaxies. Currently the most accurate modeling of dark matter haloes is achieved in cosmological N-body simulations. Identifying the haloes from the distribution of particles in N-body simulations is one of the problems attracting both considerable interest and efforts. We propose a novel framework for detecting potential dark matter haloes using the field unique for dark matter -- multistream field. The multistream field emerges at the nonlinear stage of the growth of perturbations because the dark matter is collisionless. Counting the number of velocity streams in gravitational collapses supplements our knowledge of spatial clustering. We assume that the virialized haloes have convex boundaries. Closed and convex regions of the multistream field are hence isolated by imposing a positivity condition on all three eigenvalues of the Hessian estimated on the smoothed multistream field. In a single-scale analysis of high multistream field resolution and low softening length, the halo substructures with local multistream maxima are isolated as individual halo sites.