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 $\sim0.01-2\rm pc$ 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.