Formation Rate of Extreme Mass Ratio Inspirals in Active Galactic Nuclei

TL;DR

This paper investigates an alternative formation channel for EMRIs involving accretion disks around active galactic nuclei, finding that this process significantly enhances EMRI rates and produces distinct orbital characteristics, impacting future gravitational wave observations.

Contribution

It introduces and quantifies a new EMRI formation mechanism via accretion disk interactions, showing it can dominate over traditional loss cone scenarios in active galactic nuclei.

Findings

Accretion disks boost EMRI formation rates by 10 to 1000 times.

Active galactic nuclei contribute significantly to the overall EMRI population.

Distinct eccentricity and inclination distributions can be used to differentiate formation channels.

Abstract

Extreme Mass Ratio Inspirals (EMRIs) are important sources for space-borne gravitational wave detectors, such as LISA (Laser Interferometer Space Antenna) and TianQin. Previous EMRI rate studies have focused on the "loss cone" scenario, where stellar-mass black holes (sBHs) are scattered into highly eccentric orbits near the central massive black hole (MBH) via multi-body interaction. In this work, we calculate the rate of EMRIs of an alternative formation channel: EMRI formation assisted by the accretion flow around accreting massive black holes. In this scenario, sBHs and stars on inclined orbits are captured by the accretion disk, and then subsequently migrate towards the MBH, under the influence of density wave generation and head wind. By solving the Fokker-Planck equation incorporating both sBH-sBH/sBH-star scatterings and sBH/star-disk interactions, we find that an accretion disk usually boosts the EMRI formation rate per individual MBH by $\mathcal O(10^1-10^3)$ compared with the canonical "loss cone" formation channel. Taking into account that the fraction of active galactic nucleus (AGNs) is $\sim \mathcal O(10^{-2}-10^{-1})$, where the MBHs are expected to be rapidly accreting, we expect EMRI formation assisted by AGN disks to be an important channel for all EMRIs observed by space-borne gravitational wave detectors. These two channels also predict distinct distributions of EMRI eccentricities and orbit inclinations with respect to the MBH spin equatorial plan, which can be tested by future gravitational wave observations.