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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 scatterings and gravitational wave emission, and calculate the EMRI formation rate, eccentricity distribution and EMRI-to-plunge ratio. Our model predicts: (I) A stronger segregation than previously estimated at the outskirts of the sphere of influence (at 0. 01 pc to 2 pc for a Milky-way like galaxy). (II) An increased EMRI-to-plunge ratio, favoring EMRIs at galaxies where stellar-mass black holes are scarce. (III) A detection of about 210³ resolvable EMRIs, with a signal-to-noise ratio above 20, along a 4 year LISA mission time. (IV) A confusion noise, induced by a cosmological population of unresolved EMRIs, reducing LISA sensitivity in the 1-10\ mHz frequency range by up to a factor of 3. 5, relative to the instrumental noise.
Rom et al. (Thu,) studied this question.