Dependence of the Substructure Abundance on the Orientation Coherence of
  the Halo Tidal Field
  A numerical evidence for the dependence of the substructure abundance of
cluster halos on the orientation coherence of the surrounding tidal fields is
presented. Applying the adapted minimal spanning tree (MST) algorithm to the
cluster halos with $M\ge 10^{14}\,h^{-1}\,M_{\odot}$ from the Big
MultiDark-Planck Simulations, we identify primary MST stems composed of
multiple nodes as the filaments and measure their specific sizes (spatial
extents per node), which quantify the orientation coherence of the tidal field
on the cluster scales. Classifying the cluster halos into five samples by the
specific sizes of their host filaments and tallying the mass distributions of
the five samples, we investigate if and how the substructure abundance of the
cluster halos differs among the five samples. It is found that the cluster
halos embedded in the filaments with larger specific sizes tend to possess less
substructures. This anti-correlation is also shown robust against narrowing
down the formation epochs of the cluster halos as well as against fixing the
node number of the filaments. Given that the filaments with larger specific
sizes form at the regions where the surrounding tidal fields are coherent over
large scales in the orientations of their principal axes, we suggest that in
the filaments with larger specific sizes the satellite infall and matter
accretion onto the cluster halos should be obstructed due to the development of
the tangential velocities in the plane perpendicular to the elongated axes of
the filaments.
