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 $Mge 10^{14},h^{-1},M_{odot}$ 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.