Probing Formation Channels of Extreme Mass-Ratio Inspirals (2509.00469v1)

Abstract: The population study of stellar-mass black hole (sBH) binaries with ground-based gravitational wave detection has achieved tremendous success in recent years. Future observation of extreme mass-ratio inspirals will similarly require proper population analysis that identify the formation channels, measuring the branch ratio(s) and characterizing major properties within each major channel. In this work, we propose that the measurement of eccentricity, inclination, and component mass provides critical information to distinguish different formation channels and probe detailed formation mechanisms. Focusing on the dry and wet extreme mass-ratio inspirals, we establish the theoretical expectation of these observables in each formation channel. We also discuss how their distributions can be used to probe lifetime and turbulence level of active galactic nuclei disks, accretion patterns of supermassive black holes and population properties of sBHs within nuclear star clusters.