Dynamics Around Supermassive Black Holes: Extreme-mass-ratio Inspirals as Gravitational-wave Sources

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 ∼0.01-2 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 × 10³ resolvable EMRIs, with a signal-to-noise ratio above 20, along a 4 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 mHz frequency range by up to a factor of ≈2, relative to the instrumental noise.