Symmetry Breaking in Dynamical Encounters in the Disks of Active Galactic Nuclei

Active galactic nucleus (AGN) disks may be important sites of binary black hole (BBH) mergers. Here we show via numerical experiments with the high-accuracy, high precision code {\tt SpaceHub} that broken symmetry in dynamical encounters in AGN disks can lead to an asymmetry between prograde and retrograde BBH mergers. The direction of the hardening asymmetry depends on the initial binary semi-major axis. An asymmetric distribution of mass-weighted projected spin $\chi_{\rm eff}$ should therefore be expected in LIGO-Virgo detections of BBH mergers from AGN disks. This channel further predicts that negative $\chi_{\rm eff}$ BBH mergers are most likely for massive binaries.