Gravitational radiation from plunging orbits: Perturbative study

Numerical relativity has recently yielded a plethora of results about kicks from spinning mergers which has, in turn, vastly increased our knowledge about the spin interactions of black hole systems. In this work we use black hole perturbation theory to calculate accurately the gravitational waves emanating from the end of the plunging stage of an extreme mass ratio merger in order to further understand this phenomenon. This study focuses primarily on spin induced effects with emphasis on the maximally spinning limit and the identification of possible causes of generic behavior. We find that gravitational waves emitted during the plunging phase exhibit damped oscillatory behavior, corresponding to a coherent excitation of quasinormal modes by the test particle. This feature is universal in the sense that the frequencies and damping time do not depend on the orbital parameters of the plunging particle. Furthermore, the observed frequencies are distinct from those associated with the usual free quasinormal ringing. Our calculation suggests that a maximum in radiated energy and momentum occurs at spin parameters equal to $a/M=0.86$ and $a/M=0.81$, respectively, for the plunge stage of a polar orbit. The dependence of linear momentum emission on the angle at which a polar orbit impacts the horizon is quantified. One of the advantages of the perturbation approach adopted here is that insight into the actual mechanism of radiation emission and its relationship to black hole ringing is obtained by carefully identifying the dominant terms in the expansions used.

Figure 1

ISCO radius, orbital energy ($E$), and azimuthal angular momentum ($L_z$) as a function of the spin coefficient $q=a/M$.

Figure 2

Total energy radiated during the plunging phase of orbit from ISCO as a function of spin parameter. Plot (a) displays the energy radiated when plunging from an equatorial ISCO ($C=0$) in the co-rotating and counter-rotating cases. Plot (b) shows the radiated energy if the particle originates from a polar orbit for various horizon impact angles, $\theta =\frac{\pi }{6}$, $\frac{\pi }{3}$, $\frac{\pi }{2}$.

Figure 3

Total energy radiated during the plunging phase of a particle originating on a polar ISCO as a function of impact angle with the horizon. Radiation for background Kerr black holes with spin parameter $(a/M)=0.8$, 0.9, 0.99 are plotted.

Figure 4

Total momentum radiated during the final plunging phase of orbit at ISCO as a function of spin parameter. Plot (a) displays the momentum radiated when plunging from an equatorial ISCO ($C=0$) in the co-rotating and counter-rotating cases. Plot (b) shows the radiated momentum if the particle originates from a polar orbit ($L_z=0$) for various horizon impact angles, $\theta =\frac{\pi }{6}$, $\frac{\pi }{3}$, $\frac{\pi }{2}$.

Figure 5

Total momentum radiated during the plunging phase of a particle originating on a polar ISCO as a function of impact angle with the horizon. Radiation for background Kerr black holes with spin parameter $(a/M)=0.8$, 0.9, 0.99 are plotted.