双星系统中大质量比致密天体质量四极矩对轨道频率的影响分析

极端质量比旋进系统是空间引力波探测器最重要的波源之一。对引力波的探测需要高精度波形模版。当前主流的极端质量比旋进系统引力波计算模型中,人们一般将小质量天体当作试验粒子进行计算,而忽略了其结构及自身引力对背景引力场的影响。利用Mathisson-Papapetrou-Dixon方程研究延展体在弯曲时空中的运动,以及小天体自旋和质量多极矩对引力波信号识别产生的影响。结果表明,质量比在10?6-10?4范围的旋进系统,其自旋达到很大时,自旋对延展体的轨道运动有不可忽略的影响;在质量比10?4-10?2区间内,需要考虑中心黑洞潮汐作用导致的白矮星形变;在质量比大于10?4,且白矮星自旋很大时,其自旋产生的形变会对小天体轨道运动产生不可忽略的影响。大质量黑洞潮汐作用导致的恒星级黑洞或中子星产生的形变可以忽略,中子星和黑洞的自旋会对轨道运动产生不可忽略的影响,而自旋产生的四极矩对轨道运动不产生影响。

Analysis of the Influence of the Mass Quadrupole Moment of Compact Objects on the Orbital Frequency in the Mass-to-mass Ratio Binary System

The extreme mass ratio inspiral system is one of the most important wave sources for space gravitational wave detectors.In gravitational wave detection,a high precision gravity waveform template is required.Many gravitational wave calculation models use test particles as small-mass objects at present,while ignoring the influence of objects structure and its own gravity on the background gravitational field in extreme mass ratio inspiral for gravitational wave detectors.We investigate the motion of the extended body in curved spacetime using the Mathisson-Papapetrou-Dixon equation,and the effects of stellar mass object spin and mass multipole moment on gravitational wave signal recognition.The results show that there is a non-negligible influence on the orbital motion of the extended body when the spin reaches a large value in the range of 10?6～10?4.At a mass ratio range of about 10?4～10?2,the influences of deformation induced by tidal of the center massive black holes on the white dwarfs needs to be considered.At a mass ratio range of about 10?4 or more,when the physical spin reaches a large value,the induced-spin quadrupole moment of the white dwarfs will have an effect on the orbital motion of the objects.The influence of tidle effect which induced by the massive black holes on the mass deformation of a black holes or a neutron stars is negligible.Neutron stars and black hole spins have a non-negligible effect on orbital motion,but the quadrupole moment induced by spin of the neutron stars or black holes does not affect the orbital motion.