Gravitational radiation from a spinning compact object around a supermassive Kerr black hole in circular orbit

The gravitational waves and energy radiation from a spinning compact object with stellar mass in a circular orbit in the equatorial plane of a supermassive Kerr black hole are investigated in this paper. The effect of how the spin acts on energy and angular moment fluxes is discussed in detail. The calculation results indicate that the spin of a small body should be considered in waveform-template production for the upcoming gravitational wave detections. It is clear that when the direction of spin axes is the same as the orbitally angular momentum (“positive” spin), spin can decrease the energy fluxes which radiate to infinity. For antidirection spin (“negative”), the energy fluxes to infinity can be enlarged. And the relations between fluxes (both infinity and horizon) and spin look like quadratic functions. From frequency shift due to spin, we estimate the wave-phase accumulation during the inspiraling process of the particle. We find that the time of particle inspiral into the black hole is longer for positive spin and shorter for negative compared with the nonspinning particle. Especially, for extreme spin value, the energy radiation near the horizon of the extreme Kerr black hole is much more than that for the nonspinning one. And consequently, the maximum binging energy of the extreme spinning particle is much larger than that of the nonspinning particle.

Figure 1

Comparison of the energy flux at infinity for orbit at $r=25M$ as a function of Kerr parameter $a$ for $l=3$, $m=1$. Agreement between the numerical and post-Newtonian fluxes is good.

Figure 2

The shift of the orbital frequencies between spin and nonspinning particles as a function of radius $r$ while $a=0$. From the top down, the spin magnitude $S$ is $-{10}^{-2}$, $-{10}^{-3}$, ${10}^{-3}$, ${10}^{-2}$, respectively.

Figure 3

The shift of the orbital frequencies between spin and nonspinning particles as a function of radius $r$ while $a=0.996$. From the top down, the spin magnitude $S$ is $-{10}^{-2}$, $-{10}^{-3}$, ${10}^{-3}$, ${10}^{-2}$, respectively.

Figure 4

The energy fluxes of $l=2$ modes at infinity and the horizon as a function of the spin magnitude $S$. Where the Kerr parameter $a=0$ and the orbital radius $r=10M$.

Figure 5

The energy fluxes of $l=2$ modes at infinity and the horizon as a function of the spin magnitude $S$. Where the Kerr parameter $a=0.996$ and the orbital radius $r=10M$.

Figure 6

The energy fluxes of $l=2$ modes at infinity and the horizon as a function of the spin magnitude $S$. Where the Kerr parameter $a=-0.996$ and the orbital radius $r=10M$.

Figure 7

The gravitational wave luminosity at infinity and the horizon (up through $l=8$ to produce the accuracy) as a function of the spin magnitude $S$. Where the Kerr parameter $a=0.996$ and the orbital radius $r=10M$.