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.