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.
