Observability of gravitational waves excited by binary stars orbiting around a supermassive black hole by space-based gravitational wave observatory

Abstract We produce the gravitational waveforms for the extreme mass ratio inspiral systems (EMRIs) of binary stars moving around central supermassive black hole (SBH), or called B-EMRIs. We calculate the external orbits of the binary stars via the commonly used Hamilton–Jacobi (HJ) approach, and calculate the internal orbits of the binary stars via Lagrangican approach. To improve accuracy we adopt the quadrupole-octupole expression of gravitational wave (GW) and study the contribution of radiation reaction. Compared to the waveforms of EMRIs, there are higher frequency oscillations superposed on the waveforms of B-EMRIs. We perform frequency spectrum analysis of the GW waveforms, and find that higher frequency signals give their prominency in the waveforms of B-EMRIs. To obtain high precise result for future observation of GWs from space-based detector, we take into account gravito-electromagnetic (GEM) force, and compare the waveforms of B-EMRIs with GEM effects against those of B-EMRIs without GEM effects and against those of EMRIs. The result of mismatch shows that the waveforms of B-EMRIs are credibly distinguishable by the space-based GW detectors when GEM force is considered.