The intrinsic alignment of dark halo substructures

We investigate the intrinsic alignments of dark halo substructures with their host halo major-axis orientations both analytically and numerically. Analytically, we derive the probability density distribution of the angles between the minor axes of the substructures and the major axes of their host halos from the physical principles, under the assumption that the substructure alignment on galaxy scales is a consequence of the tidal fields of the host halo gravitational potential. Numerically, we use a sample of four cluster-scale halos and their galaxy-scale substructures from recent high-resolution N-body simulations to measure the probability density distribution. We compare the numerical distribution with the analytic prediction, and find that the two results agree with each other very well. We conclude that our analytic model provides a quantitative physical explanation for the intrinsic alignment of dark halo substructures. We also discuss the possibility of differentiating our model from the anisotropic infall scenario by testing it against very large N-body simulations in the future.