Extreme mass-ratio gravitational-wave sources: Mass segregation and post binary tidal-disruption captures

The gravitational-wave (GW) inspirals of stellar-mass compact objects on to a supermassive black hole (SMBH), are some of the most promising GW sources detectable by next-generation space-born GW-detectors. The rates and characteristics of such extreme mass ratio inspirals (EMRIs) sources are highly uncertain. They are determined by the dynamics of stars near MBHs and the rate at which compacts objects are driven to the close proximity of the MBH. Here, we consider weakly and strongly mass-segregated nuclear clusters and the evolution of stars captured into highly eccentric orbits following binary disruptions by the MBH. We make use of a Monte Carlo approach to model the diffusion of both captured objects and compact-objects brought through two-body relaxation processes. We calculate the rates of GW-inspirals resulting from relaxation-driven objects and characterize EMRIs properties. We correct previous studies and show that relaxation-driven sources produce GW-sources with lower-eccentricity than previously found and provide the detailed EMRI eccentricity distribution in the weak and strong mass-segregation regimes. We also show that binary-disruption captured-stars could introduce low-eccentricity GW-sources of stellar BH EMRIs in mass-segregated clusters. The eccentricities of the GW-sources from the capture channel, however, are strongly affected by relaxation processes and are significantly higher than previously suggested. We find that both the rate and eccentricity distribution of EMRIs could probe the dynamics near MBHs, and the contribution of captured stars, characterize the mass-function of stellar compact objects, and verify whether weak or strong mass-segregation processes take place near MBHs.