Spin-orbit misalignments of eccentric black hole mergers in AGN discs

ABSTRACT The discs of Active Galactic Nuclei (AGNs) provide a natural environment where stellar mass-black holes can dynamically pair, undergo repeated interactions, and eventually merge. It is commonly assumed that gas accretion will both efficiently spin-up disc-embedded black holes and align the orbits of embedded binaries with the disc plane, leading to mergers with preferentially positive effective spin parameters ($\chi _{\rm eff}$). Such predictions have motivated the use of $\chi _{\rm eff}$ as a diagnostic for identifying candidate AGN-embedded mergers in the LIGO-Virgo-KAGRA gravitational wave catalogue. 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 $\chi _{\rm eff}-$eccentricity correlations of AGN-embedded mergers. By comparing the alignment and gravitational wave inspiral time-scales, we identify the regions of parameter space, across both disc location and binary properties, where full disc-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 $e_{\rm 10Hz}\gtrsim 0.1$) typically inspiral too quickly for gas torques to act, preserving the post-encounter spin-orbit misalignments and yielding more isotropic $\chi _{\rm eff}$ distributions when disc densities and torque efficiencies are modest. This interplay naturally establishes a correlation between binary eccentricity and $\chi _{\rm eff}$ in AGN discs, highlighting a new key observable of the AGN channel and a potential explanation for massive events such as GW190521 and GW231123.