Alignments of dark matter halos with large-scale tidal fields: mass and
  redshift dependence
  Large scale tidal field estimated directly from the distribution of dark
matter halos is used to investigate how halo shapes and spin vectors are
aligned with the cosmic web. The major, intermediate and minor axes of halos
are aligned with the corresponding tidal axes, and halo spin axes tend to be
parallel with the intermediate axes and perpendicular to the major axes of
tidal field. The strengths of these alignments generally increase with halo
mass and redshift, but the dependencies are only through the peak height,
{\nu}. The scaling relations of the alignment strengths with the value of {\nu}
indicate that the alignment strengths remain roughly constant when the
structures within which the halos reside are still in quasi-linear regime, but
decreases as nonlinear evolution becomes more important. We also calculate the
alignments in projection so that our results can be compared directly with
observations. Finally, we investigate the alignments of tidal tensors on large
scales, and use the results to understand alignments of halo pairs separated at
various distances. Our results suggest coherent structure of the tidal field is
the underlying reason for the alignments of halos and galaxies seen in
numerical simulations and in observations.
