Frequency distributions of cos θ, where θ is the positional alignment angle between the spin vector and the line defined by the position of the CH and its NN1. Only close halo pairs (i.e., CHs separated from their NN1 by 1 < R_isol/r_vir < 4) in two different in environments are considered for this figure: CHs separated from their NN2 by 1 < R_isol2/r_vir < 4 (red) and 20 < R_isol2/r_vir < 63 (blue).