The impact of mass segregation and star-formation on the rates of
  gravitational-wave sources from extreme mass ratio inspirals
  Compact stellar objects inspiralling into massive black holes (MBHs) in
galactic nuclei are some of the most promising gravitational wave (GWs) sources
for next generation GW-detectors. The rates of such extreme mass ratio
inspirals (EMRIs) depend on the dynamics and distribution of compact objects
around the MBH. Here we study the impact of mass-segregation processes on EMRI
rates. In particular, we provide the expected mass function of EMRIs, given an
initial mass function of stellar BHs (SBHs), and relate it to the
mass-dependent detection rate of EMRIs. We then consider the role of star
formation on the distribution of compact objects and its implication on EMRI
rates. We find that the existence of a wide spectrum of SBH masses lead to the
overall increase of EMRI rates, and to high rates of the EMRIs from the
most-massive SBHs. However, it also leads to a relative quenching of EMRI rates
from lower-mass SBHs, and together produces a steep dependence of the EMRI mass
function on the highest-mass SBHs. Star-formation history plays a relatively
small role in determining the EMRI rates of SBHs, since most of them migrate
close to the MBH through mass-segregation rather than forming in-situ. However,
the EMRI rate of neutron stars can be significantly increased when they form
in-situ close to the MBH, as they can inspiral before relaxation processes
significantly segregates them outwards. A reverse but weaker effect of
decreasing the EMRI rates from neutron stars and white dwarfs occurs when
star-formation proceeds far from the MBH.
