In the grip of the disk: dragging the companion through an AGN

Active galactic nuclei (AGN) have been proposed as environments that can facilitate the capture of extreme-mass-ratio binaries and accelerate their inspiral beyond the rate expected from gravitational wave emission alone. In this work, we explore binaries shortly after capture, focusing on the evolution of the binary parameters when the system is still far from merger. We find that repeated interactions with the AGN disk typically reduce both the inclination and semi-major axis of the orbit. The evolution of the eccentricity is more intricate, exhibiting phases of growth and decay. Nevertheless, as the binary gradually aligns with the disk plane, the system tends to circularize. Interestingly, we also identify scenarios where initially highly eccentric, nearly counter-rotating orbits can undergo a rapid transition to co-rotation while maintaining a constant eccentricity. These dynamical effects could have significant implications for the modeling and interpretation of LISA sources.