Gravitational waves emitted during the inspiral, plunge and merger of a black hole binary carry linear momentum. This results in an astrophysically important recoil to the final merged black hole, a ``kick that can eject it from the nucleus of a gala
xy. In a previous paper we showed that the puzzling partial cancellation of an early kick by a late antikick, and the dependence of the cancellation on black hole spin, can be understood from the phenomenology of the linear momentum waveforms. Here we connect that phenomenology to its underlying cause, the spin-dependence of the inspiral trajectories. This insight suggests that the details of plunge can be understood more broadly with a focus on inspiral trajectories.
The coalescence of massive black holes is one of the primary sources of gravitational waves (GWs) for LISA. Measurements of the GWs can localize the source on the sky to an ellipse with a major axis of a few tens of arcminutes to a few degrees, depen
ding on source redshift, and a minor axis which is 2--4 times smaller. The distance (and thus an approximate redshift) can be determined to better than a per cent for the closest sources we consider, although weak lensing degrades this performance. It will be of great interest to search this three-dimensional `pixel for an electromagnetic counterpart to the GW event. The presence of a counterpart allows unique studies which combine electromagnetic and GW information, especially if the counterpart is found prior to final merger of the holes. To understand the feasibility of early counterpart detection, we calculate the evolution of the GW pixel with time. We find that the greatest improvement in pixel size occurs in the final day before merger, when spin precession effects are maximal. The source can be localized to within 10 square degrees as early as a month before merger at $z = 1$; for higher redshifts, this accuracy is only possible in the last few days.
During the inspiral and merger of black holes, the interaction of gravitational wave multipoles carries linear momentum away, thereby providing an astrophysically important recoil, or kick to the system and to the final black hole remnant. It has bee
n found that linear momentum during the last stage (quasinormal ringing) of the collapse tends to provide an antikick that in some cases cancels almost all the kick from the earlier (quasicircular inspiral) emission. We show here that this cancellation is not due to peculiarities of gravitational waves, black holes, or interacting multipoles, but simply to the fact that the rotating flux of momentum changes its intensity slowly. We show furthermore that an understanding of the systematics of the emission allows good estimates of the net kick for numerical simulations started at fairly late times, and is useful for understanding qualitatively what kinds of systems provide large and small net kicks.
We have performed a detailed analysis of orbital motion in the vicinity of a nearly extremal Kerr black hole. For very rapidly rotating black holes (spin a=J/M>0.9524M) we have found a class of very strong field eccentric orbits whose angular momentu
m L_z increases with the orbits inclination with respect to the equatorial plane, while keeping latus rectum and eccentricity fixed. This behavior is in contrast with Newtonian intuition, and is in fact opposite to the normal behavior of black hole orbits. Such behavior was noted previously for circular orbits; since it only applies to orbits very close to the black hole, they were named nearly horizon-skimming orbits. Our analysis generalizes this result, mapping out the full generic (inclined and eccentric) family of nearly horizon-skimming orbits. The earlier work on circular orbits reported that, under gravitational radiation emission, nearly horizon-skimming orbits tend to evolve to smaller orbit inclination, toward prograde equatorial configuration. Normal orbits, by contrast, always demonstrate slowly growing orbit inclination (orbits evolve toward the retrograde equatorial configuration). Using up-to-date Teukolsky-fluxes, we have concluded that the earlier result was incorrect: all circular orbits, including nearly horizon-skimming ones, exhibit growing orbit inclination. Using kludge fluxes based on a Post-Newtonian expansion corrected with fits to circular and to equatorial Teukolsky-fluxes, we argue that the inclination grows also for eccentric nearly horizon-skimming orbits. We also find that the inclination change is, in any case, very small. As such, we conclude that these orbits are not likely to have a clear and peculiar imprint on the gravitational waveforms expected to be measured by the space-based detector LISA.
