The velocity shear tensor: tracer of halo alignment

The alignment of dark matter (DM) haloes 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 are investigated relative to the LSS using the eigenvectors of the velocity shear tensor evaluated on a grid with a scale of 1 Mpc h^-1, 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 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 shape and the eigenvectors of the shear tensor, with the longest (shortest) axis of the halo 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 that 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 corotation 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 those of haloes and galaxies.