A Multidimensional Dependence of the Substructure Evolution on the Tidal
  Coherence
  We numerically explore how the subhalo mass-loss evolution is affected by the
tidal coherences measured along different eigenvector directions. The mean
virial-to-accretion mass ratios of the subhalos are used to quantify the
severity of their mass-loss evolutions within the hosts, and the tidal
coherence is expressed as an array of three numbers each of which quantifies
the alignment between the tidal fields smoothed on the scales of $2$ and
$30\,h^{-1}$Mpc in each direction of three principal axes. Using a Rockstar
halo catalog retrieved from a N-body simulation, we investigate if and how the
mass-loss evolutions of the subhalos hosted by distinct halos at fixed mass
scale of [$1$-$3$]$10^{14}\,h^{-1}\,M_{\odot}$ are correlated with three
components of the tidal coherence. The tides coherent along different
eigenvector directions are found to have different effects on the subhalo
mass-loss evolution, which cannot be ascribed to the differences in the
densities and ellipticities of the local environments. It is shown that the
substructures surrounded by the tides highly coherent along the first
eigenvector direction and highly {\it incoherent} along the third eigenvector
direction experience the least severe mass-loss evolution, while the tides
highly {\it incoherent} only along the first eigenvector direction is
responsible for the most severe mass-loss evolution of the subhalos. Explaining
that the coherent tides have an obstructing effect on the satellite infalls
onto their hosts and that the strength of the obstruction effect depends on
which directions the tides are coherent or {\it incoherent} along, we suggest
that the multidimensional dependence of the substructure evolution on the tidal
coherence should be deeply related to the complex nature of the large-scale
assembly bias.
