Abstract The disks of Active Galactic Nuclei (AGNs) provide a natural environment where stellar mass-black holes (BHs) can dynamically pair, undergo repeated interactions, and eventually merge. It is commonly assumed that gas accretion will both efficiently spin-up disk-embedded black holes and align the orbits of embedded binaries with the disk plane, leading to mergers with preferentially positive effective spin parameters (χeff). Such predictions have motivated the use of χeff as a diagnostic for identifying candidate AGN-embedded mergers in the LIGO-Virgo-KAGRA gravitational wave catalog. In this work, we perform post-Newtonian N-body simulations of nearly planar binary-single encounters and apply an empirically motivated gas-driven alignment prescription to characterize the expected χeff −eccentricity correlations of AGN-embedded mergers. By comparing the alignment and gravitational wave inspiral timescales, we identify the regions of parameter space, across both disk location and binary properties, where full disk-spin-orbit alignment is effective and where it is not. We find that quasi-circular binaries typically align by the time they merge, supporting the standard picture of spin-orbit aligned orientations. By contrast, eccentric binaries (with in-band eccentricity e10Hz ≳ 0.1) typically inspiral too quickly for gas torques to act, preserving the post-encounter spin–orbit misalignments and yielding more isotropic χeff distributions when disk densities and torque efficiencies are modest. This interplay naturally establishes a correlation between binary eccentricity and χeff in AGN disks, highlighting a new key observable of the AGN channel and a potential explanation for massive events such as GW190521 and GW231123.
Fabj et al. (Tue,) studied this question.