Living with Neighbors. III. Scrutinizing the Spin$-$Orbit Alignment of Interacting Dark Matter Halo Pairs

We present that the spin$-$orbit alignment (SOA; i.e., the angular alignment between the spin vector of a halo and the orbital angular momentum vector of its neighbor) provides an important clue to how galactic angular momenta develop. In particular, we identify virial-radius-wise contact halo pairs with mass ratios from 1/3 to 3 in a set of cosmological $N$-body simulations, and divide them into merger and flyby subsamples according to their total (kinetic+potential) energy. In the spin$-$orbit angle distribution, we find a significant SOA in that $75.0\pm0.6$ % of merging neighbors and $58.7\pm0.6$ % of flybying neighbors are on the prograde orbit. The overall SOA of our sample is mainly driven by fast-rotating halos, corroborating that a well-aligned interaction spins a halo faster. More interestingly, we find for the first time a strong number excess of nearly perpendicular but still prograde interactions ($\sim75^{\circ}$) in the spin$-$orbit angle distribution for both the merger and flyby cases. Such prograde-polar interactions predominate for slow-rotating halos, testifying that misaligned interactions reduce the halos' spin. The frequency of the prograde-polar interactions correlates with the halo mass, yet anticorrelates with the large-scale density. This instantly invokes the spin-flip phenomenon that is conditional on the mass and environment. The prograde-polar interaction will soon flip the spin of a slow-rotator to align with its neighbor's orbital angular momentum. Finally, we propose a scenario that connects the SOA to the ambient large-scale structure based on the spin-flip argument.