The velocity shear tensor: tracer of halo alignment
  The alignment of DM halos and the surrounding large scale structure (LSS) is
examined in the context of the cosmic web. Halo spin, shape and the orbital
angular momentum of subhaloes is investigated relative to the LSS using the
eigenvectors of the velocity shear tensor evaluated on a grid with a scale of 1
Mpc/h, deep within the non-linear regime. Knots, filaments, sheets and voids
are associated with regions that are collapsing along 3, 2, 1 or 0 principal
directions simultaneously. Each halo is tagged with a web classification (i.e.
knot halo, filament halo, etc) according to the nature of the collapse at the
halo's position. The full distribution of shear eigenvalues is found to be
substantially different from that tagged to haloes, indicating that the
observed velocity shear is significantly biased. We find that larger mass
haloes live in regions where the shear is more isotropic, namely the expansion
or collapse is more spherical. A correlation is found between the halo's shape
and the eigenvectors of the shear tensor, with the longest (shortest) axis of
the halo's shape being aligned with the slowest (fastest) collapsing
eigenvector. This correlation is web independent, suggesting that the velocity
shear is a fundamental tracer of the halo alignment. A similar result is found
for the alignment of halo spin with the cosmic web. It has been shown that high
mass haloes exhibit a spin flip with respect to the LSS: we find the mass at
which this spin flip occurs is web dependent and not universal as suggested
previously. Although weaker than haloes, subhalo orbits too exhibit an
alignment with the LSS, providing a possible insight into the highly correlated
co-rotation of the Milky Way's satellite system. The present study suggests
that the velocity shear tensor constitutes the natural framework for studying
the directional properties of the non-linear LSS and of halos and galaxies.
