Constructing effective one-body dynamics with numerical energy flux for intermediate-mass-ratio inspirals

A new scheme for computing dynamical evolutions and gravitational radiations for intermediate-mass-ratio inspirals (IMRIs) based on an effective one-body (EOB) dynamics plus Teukolsky perturbation theory is built in this paper. In the EOB framework, the dynamic essentially affects the resulted gravitational waveform for a binary compact star system. This dynamic includes two parts. One is the conservative part, which comes from effective one-body reduction. The other part is the gravitational backreaction, which contributes to the shrinking process of the inspiral of a binary compact star system. Previous works used an analytical waveform to construct this backreaction term. Since the analytical form is based on post-Newtonian expansion, the consistency of this term is always checked by numerical energy flux. Here, we directly use numerical energy flux by solving the Teukolsky equation via the frequency-domain method to construct this backreaction term. The conservative correction to the leading order terms in mass-ratio is included in the deformed-Kerr metric and the EOB Hamiltonian. We try to use this method to simulate not only quasicircular adiabatic inspiral, but also the nonadiabatic plunge phase. For several different spinning black holes, we demonstrate and compare the resulted dynamical evolutions and gravitational waveforms.

Figure 1

Comparison of our method (solid line) with EOB (dashed line, the data are calculated by Dr. Bernuzzi). Left panel: Transition from quasicircular inspiral orbit to plunge from $r_0=7M$ and $\nu =0.01$. The dashed-dotted line circle is the ISCO at $r_{\mathrm{ISCO}}=6M$ and the dotted circle the horizon of black hole; Right panel: Orbital frequency ${\Omega }_{\varphi }$ versus coordinate time.

Figure 2

Convergence of the waveform when $\nu \to 0$ for $a=0$. The values of $\nu$ are 0.01, 0.001, 0.0001. $t=0$ is time for the maximum of the waveform modulus and spatial position is the light ring at $r=3M$ for each value of $\nu$.

Figure 3

Inspiralling and plunge of a small body into a Kerr black hole with mass ratio 0.01. The dashed line represents ISCO and dotted line the light ring. Left panel: retrograde orbit $a=-0.9$ beginning at $r=10M$; right panel: retrograde orbit $a=0.7$ beginning at $r=3.5M$.

Figure 4

GW signal shown through the $l=m=2\mathrm{\text{mode of}}+\mathrm{\text{polarization}}$ corresponding to the dynamics depicted in Fig. 3. The left panel is the retrograde orbit $a=-0.9$ and the right one is the retrograde orbit $a=0.7$.