Dynamics around supermassive black holes: Extreme mass-ratio inspirals as gravitational-wave sources

TL;DR

This paper models the distribution and formation of extreme-mass-ratio inspirals (EMRIs) around supermassive black holes, predicting their rates, properties, and impact on gravitational-wave detection by LISA.

Contribution

It provides a steady-state distribution model for stellar-mass black holes near supermassive black holes, including EMRI formation rates and their influence on LISA's sensitivity.

Findings

Predicted about 2000 resolvable EMRIs for LISA.

Found stronger stellar black hole segregation than previous estimates.

Identified a significant confusion noise reducing LISA sensitivity.

Abstract

Supermassive black holes and their surrounding dense stellar environments nourish a variety of astrophysical phenomena. We focus on the distribution of stellar-mass black holes around the supermassive black hole and the consequent formation of extreme-mass-ratio inspirals (EMRIs). We derive a steady-state distribution, considering the effects of two-body scattering and gravitational-wave emission, and calculate the EMRI formation rate, eccentricity distribution, and EMRI-to-plunge ratio. Our model predicts: (a) a stronger segregation than previously estimated at the outskirts of the sphere of influence (at $\sim0.01-2\rm pc$ for a Milky Way-like galaxy); (b) an increased EMRI-to-plunge ratio, favoring EMRIs at galaxies where stellar-mass black holes are scarce; (c) a detection of about $2\times10^3$ resolvable EMRIs, with a signal-to-noise ratio above $20$, along a $4\ \rm yr$ LISA mission time; and (d) a confusion noise, induced by a cosmological population of unresolved EMRIs, reducing the LISA sensitivity in the $1-5\ \rm mHz$ frequency range by up to a factor of $\approx2$, relative to the instrumental noise.