Formation Rate of Extreme Mass Ratio Inspirals in Active Galactic Nuclei

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.