The behaviour of shape and velocity anisotropy in dark matter haloes
  Dark matter haloes from cosmological N-body simulations typically have
triaxial shapes and anisotropic velocity distributions. Recently it has been
shown that the velocity anisotropy, beta, of cosmological haloes and major
merger remnants depends on direction in such a way that beta is largest along
the major axis and smallest along the minor axis. In this work we use a wide
range of non-cosmological N-body simulations to examine halo shapes and
direction-dependence of velocity anisotropy profiles. For each of our simulated
haloes we define 48 cones pointing in different directions, and from the
particles inside each cone we compute velocity anisotropy profiles. We find
that elongated haloes can have very distinct velocity anisotropies. We group
the behaviour of haloes into three different categories, that range from
spherically symmetric profiles to a much more complex behaviour, where
significant differences are found for beta along the major and minor axes. We
encourage future studies of velocity anisotropies in haloes from cosmological
simulations to calculate beta-profiles in cones, since it reveals information,
which is hidden from a spherically averaged profile. Finally, we show that
spherically averaged profiles often obey a linear relation between beta and the
logarithmic density slope in the inner parts of haloes, but this relation is
not necessarily obeyed, when properties are calculated in cones.
