  Based on the Millennium Simulation we examine assembly bias for the halo
properties: shape, triaxiality, concentration, spin, shape of the velocity
ellipsoid and velocity anisotropy. For consistency we determine all these
properties using the same set of particles, namely all gravitationally
self-bound particles belonging to the most massive sub-structure of a given
friends-of-friends halo. We confirm that near-spherical and high-spin halos
show enhanced clustering. The opposite is true for strongly aspherical and
low-spin halos. Further, below the typical collapse mass, M*, more concentrated
halos show stronger clustering whereas less concentrated halos are less
clustered which is reversed for masses above M*. Going beyond earlier work we
show that: (1) oblate halos are more strongly clustered than prolate ones; (2)
the dependence of clustering on the shape of the velocity ellipsoid coincides
with that of the real-space shape, although the signal is stronger; (3) halos
with weak velocity anisotropy are more clustered, whereas radially anisotropic
halos are more weakly clustered; (4) for all highly clustered subsets we find
systematically less radially biased velocity anisotropy profiles. These
findings indicate that the velocity structure of halos is tightly correlated
with environment.

Cosmology and Nongalactic Astrophysics