# Probing Formation Channels of Extreme Mass-Ratio Inspirals

## TL;DR

This paper explores how measuring eccentricity, inclination, and mass in extreme mass-ratio inspirals can reveal their formation channels and underlying astrophysical environments, aiding future gravitational wave observations.

## Contribution

It establishes theoretical expectations for observable properties in different formation channels of extreme mass-ratio inspirals and discusses their use in probing astrophysical environments.

## Key findings

- Distinct distributions of observables can differentiate formation channels.
- Eccentricity and inclination measurements inform about galactic nucleus environments.
- Component mass data helps characterize black hole populations.

## 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.