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.
Modeling Extreme Mass Ratio Inspirals within the Effective-One-Body Approach
我们提出了第一个模型的极端质量比的有效单体（EOB）的形式主义，专注于非旋转黑洞的准圆形轨道内的吸气。我们发现，经过2年的演化，解析EOB和基于Teukolsky的数值重力波形之间的相位差和（牛顿归一化）振幅差可以分别减小到小于10^（-1）rad和小于2 x 10^（-3）。在EOB方法中包含后牛顿自作用力项导致经过2年的演化后相位不一致约为6-27 rad。这样的包含物还可以允许来自中间质量比、准圆形吸气的波形的EOB建模。
Relativistic Corrections to the Formation Rate of Extreme Mass-Ratio Inspirals
University of Chinese Academy of Sciences (UCAS)（中国科学院大学）；Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院，中国科学院大学）；International Center for Theoretical Physics Asia-Pacific（亚太理论物理国际中心）
