  A new multi-dimensional Hierarchical Structure Finder (HSF) to study the
phase-space structure of dark matter in N-body cosmological simulations is
presented. The algorithm depends mainly on two parameters, which control the
level of connectivity of the detected structures and their significance
compared to Poisson noise. By working in 6D phase-space, where contrasts are
much more pronounced than in 3D position space, our HSF algorithm is capable of
detecting subhaloes including their tidal tails, and can recognise other
phase-space structures such as pure streams and candidate caustics. If an
additional unbinding criterion is added, the algorithm can be used as a
self-consistent halo and subhalo finder. As a test, we apply it to a large halo
of the Millennium Simulation, where 19 % of the halo mass are found to belong
to bound substructures, which is more than what is detected with conventional
3D substructure finders, and an additional 23-36 % of the total mass belongs to
unbound HSF structures. The distribution of identified phase-space density
peaks is clearly bimodal: high peaks are dominated by the bound structures and
low peaks belong mostly to tidal streams. In order to better understand what
HSF provides, we examine the time evolution of structures, based on the merger
tree history. Bound structures typically make only up to 6 orbits inside the
main halo. Still, HSF can identify at the present time at least 80 % of the
original content of structures with a redshift of infall as high as z <= 0.3,
which illustrates the significant power of this tool to perform dynamical
analyses in phase-space.
