Extreme mass-ratio gravitational-wave sources: Mass segregation and post
  binary tidal-disruption captures
  The gravitational-wave (GW) inspirals of stellar-mass compact objects onto a
supermassive black hole (MBH), 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 black-hole 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.
