The Combined Effects of Two-body Relaxation Processes and the Eccentric Kozai–Lidov Mechanism on the Extreme-mass-ratio Inspirals Rate

Gravitational wave (GW) emissions from extreme-mass-ratio inspirals (EMRIs) are promising sources for low-frequency GW detectors. They result from a compact object, such as a stellar-mass black hole (BH), captured by a supermassive BH (SMBH). Several physical processes have been proposed to form EMRIs. In particular, weak two-body interactions over a long timescale (i.e., relaxation processes) have been proposed as a likely mechanism to drive the BH orbit to high eccentricity. Consequently, it is captured by the SMBH and becomes an EMRI. Here we demonstrate that EMRIs are naturally formed in SMBH binaries. Gravitational perturbations from an SMBH companion, known as the eccentric Kozai–Lidov (EKL) mechanism, combined with relaxation processes, yield a significantly more enhanced rate than any of these processes operating alone. Because EKL is sensitive to the orbital configuration, two-body relaxation can alter the orbital parameters, rendering the system in a more EKL-favorable regime. As SMBH binaries are expected to be prevalent in the universe, this process predicts a substantially high EMRI rate.