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 Lagrangian 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.

Figures (15)

• Figure 1: A sketch of binary stars orbiting around the central SBH, in which the internal orbit is exaggerated to clearly show the positional relation
• Figure 2: The first panel displays the orbit of compact object in EMRIs, the second to fourth panels display the orbits of one of the compact objects in B-EMRIs. The lower four panels display the details of the corresponding orbits in the upper four panels in the x-y plane. For the first panel, the mass of the single compact object is set to be $m=18M_{\odot}$, the initial external orbit parameters are set to be $p(0)=10M, e(0)=0.3, \iota(0)=7\pi/9$. For the second to fourth panels, the masses of the compact objects are set to be $m_1=2M_{\odot}, m_2=3M_{\odot}$; $m_1=8M_{\odot}, m_2=10M_{\odot}$ and $m_1=20M_{\odot}, m_2=30M_{\odot}$ respectively. The initial external orbit parameters are set to be $p(0)=10M, e(0)=0.3$ as well, the internal orbit parameters are set to be $\tilde{p}=0.005M, \tilde{e}=0.2$. The rotation parameter of the SBH is set to be $a=0.9M$.
• Figure 3: $h_{+}$ waveforms of EMRIs and B-EMRIs with different masses. The parameters follow that given in Fig.\ref{['orbit']}, panel by panel.
• Figure 4: Comparisons between the $h_{+}$ waveforms of EMRIs and B-EMRIs with distinct semi-latus rectum $\tilde{p}$. The binary masses are fixed to be $m_1=8M_{\odot}$ and $m_2=10 M_{\odot}$, and mass of central SBH is $10^6M_{\odot}$. The external orbit parameters are set to be $p(0)=10M, e(0)=0.3, \iota(0)=7\pi/9, a=0.9M$, the internal orbit parameters of the binary stars are set to be $\tilde{e}=0.2, \theta_0=\frac{\pi}{3}$ and $\tilde{p}=0.003M, 0.004M, 0.005M, 0.006M, 0.007M$ respectively.
• Figure 5: Comparisons of $h_{+}$ waveforms of EMRIs and B-EMRIs by adjusting $\theta_0$. The external orbit parameters are set to be $p(0)=10M, e(0)=0.3, \iota(0)=7\pi/9, a=0.9M$, the internal orbit parameters are set to be $\tilde{p}=0.005M, \tilde{e}=0.2$, and $\theta_0=0, \frac{\pi}{6}, \frac{\pi}{3}, \frac{\pi}{2}, \frac{3\pi}{4}, \pi$ respectivly.