Eccentric Black Hole Mergers in Active Galactic Nuclei
  The astrophysical origin of gravitational wave (GW) transients is a timely
open question in the wake of discoveries by LIGO/Virgo. In active galactic
nuclei (AGNs), binaries form and evolve efficiently by interaction with a dense
population of stars and the gaseous AGN disk. Previous studies have shown that
stellar-mass black hole (BH) mergers in such environments can explain the
merger rate and the number of suspected hierarchical mergers observed by
LIGO/Virgo. The binary eccentricity distribution can provide further
information to distinguish between astrophysical models. Here we derive the
eccentricity distribution of BH mergers in AGN disks. We find that eccentricity
is mainly due to binary-single (BS) interactions, which lead to most BH mergers
in AGN disks having a significant eccentricity at $0.01\,\mathrm{Hz}$,
detectable by LISA. If BS interactions occur in isotropic-3D directions, then
$8$--$30\%$ of the mergers in AGN disks will have eccentricities at
$10\,\mathrm{Hz}$ above $e_{10\,\rm Hz}\gtrsim 0.03$, detectable by
LIGO/Virgo/KAGRA, while $5$--$17\%$ of mergers have $e_{10\,\rm Hz}\geq 0.3$.
On the other hand, if BS interactions are confined to the AGN-disk plane due to
torques from the disk, with 1-20 intermediate binary states during each
interaction, or if BHs can migrate to $\lesssim10^{-3}\,\mathrm{pc}$ from the
central supermassive black hole, then $10$--$70\%$ of the mergers will be
highly eccentric ($e_{10\,\rm Hz} \geq 0.3$), consistent with the possible high
eccentricity in GW190521.
