Multipole Analysis of Kicks in Collision of Binary Black Holes
Sarah H. Miller, R. A. Matzner
备注：
14 pages, 2 figures. Version 2: Title refined, slight wording and typo changes, new reference. Version 3: Version in press at General relativity and Gravitation
Thorne and Kidder give expressions which allow for analytical estimates of the "kick", it i.e. the recoil, produced from asymmetrical gravitational radiation during the interaction of black holes, or in fact any gravitating compact bodies. (The Thorne-Kidder formula uses momentum flux calculations based on the linearized General Relativity of gravitational radiation.) We specifically treat kicks arising in the binary interaction of equal mass black holes, when at least one of the black holes has significant spin, a. Such configurations can produce very large kicks in computational simulations. We consider both fly-by and quasicircular orbits. For fly-by orbits we find substantial kicks from those Thorne-Kidder terms which are linear in a. For the quasi-circular case, we consider in addition the nonlinear contribution (O(a^2)) to the kicks, and provide a dynamical explanation for such terms. However, in the cases of maximal kick velocities, the dependence on spin is largely linear (reproduced in numerical results).
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 been 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, b…
Recoil ``kicks'' induced by gravitational radiation are expected in the inspiral and merger of black holes. Recently the numerical relativity community has begun to measure the significant kicks found when both unequal masses and spins are considered. Because understanding the cause and magnitude of each component of this kick may be complicated in inspiral simulations, we consider these effects in the context of a simple test problem. We study recoils from collisions of binaries with initially head-on trajectories, starting with the simplest case of equal masses with no spin and then adding s…
We examine numerically the process of gravitational wave recoil in the merger of two black holes in non head-on collision, in the realm of Robinson-Trautman spacetimes. Characteristic initial data for the system are constructed, and the evolution covers the post-merger phase up to the final configuration of the remnant black hole. The net momentum flux carried out by gravitational waves and the associated impulses are evaluated. Our analysis is based on the Bondi-Sachs conservation laws for the energy momentum of the system. The net kick velocity $V_{k}$ imparted to the merged system by the to…
We consider binary systems of coalescing, nonspinning, black holes of masses $m_{1}$ and $m_{2}$ and show that the gravitational recoil velocity for any mass ratio can be obtained accurately by extrapolating the waveform of the test-mass limit case. The waveform obtained in the limit $m_1/m_2\ll 1$ via a perturbative approach is extrapolated in $ν= m_{1} m_{2}/(m_{1}+m_{2})^{2} $ multipole by multipole using the corresponding, analytically known, leading-in-$ν$ behavior. The final kick velocity computed from this $ν$-flexed waveform is written as $v(ν)/c = 0.04457 ν^2\sqrt{1-4ν}\,(1-2.07106ν+ …
Using the gravitational potential and source multipole moments bilinear in the spins, first computed to next-to-leading order (NLO) in the post-Newtonian (PN) expansion within the effective field theory (EFT) framework, we complete here the derivation of the dynamical invariants and flux-balance equations, including energy and angular momentum. We use these results to calculate spin-spin effects in the orbital frequency and accumulated phase to NLO for circular orbits. We also derive the linear momentum and center-of-mass fluxes and associated kick-velocity, to the highest relevant PN order. W…
We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole (BH) coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including l=4 are sufficient to accurately reproduce the final recoil velocity (within ~2%) and that only a few dominant modes contribute significantly to it (within ~5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and …
We examine numerically the gravitational wave recoil in non-axisymmetric Robinson-Trautman spacetimes. We construct characteristic initial data for the Robinson-Trautman dynamics which are interpreted as corresponding to the early post-merger state of two boosted colliding black holes with a common apparent horizon. Our analysis is based on the Bondi-Sachs energy-momentum conservation laws which regulate the radiative transfer processes involved in the emission of gravitational waves. We evaluate the Bondi-Sachs momentum flux carried out by gravitational waves and the associated net kick veloc…
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Numerical calculations of merging black hole binaries indicate that asymmetric emission of gravitational radiation can kick the merged black hole at up to thousands of km/s, and a number of systems have been observed recently whose properties are consistent with an active galactic nucleus containing a supermassive black hole moving with substantial velocity with respect to its broader accretion disk. We study here the effect of an impulsive kick delivered to a black hole on the dynamical evolution of its accretion disk using a smoothed particle hydrodynamics code, focusing attention on the rol…
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We present the first numerical simulations of an initially non-spinning black-hole binary with mass ratio as large as 10:1 in full general relativity. The binary completes approximately 3 orbits prior to merger and radiates about 0.415% of the total energy and 12.48% of the initial angular momentum in the form of gravitational waves. The single black hole resulting from the merger acquires a kick of about 66.7 km/s relative to the original center of mass frame. The resulting gravitational waveforms are used to validate existing formulas for the recoil, final spin and radiated energy over a wid…
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Scalar fields pervade theoretical physics and are a fundamental ingredient to solve the dark matter problem, to realize the Peccei-Quinn mechanism in QCD or the string-axiverse scenario. They are also a useful proxy for more complex matter interactions, such as accretion disks or matter in extreme conditions. Here, we study the collision between scalar "clouds" and rotating black holes. For the first time we are able to compare analytic estimates and strong field, nonlinear numerical calculations for this problem. As the black hole pierces through the cloud it accretes according to the Bondi-H…
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Supermassive black hole binaries (BHBs) produced in galaxy mergers recoil at the time of their coalescence due to the emission of gravitational waves (GWs). We simulate the response of a thin, 2D disk of collisionless particles, initially on circular orbits around a 10^6 M_sun BHB, to kicks that are either parallel or perpendicular to the initial orbital plane. Typical kick velocities (v_k) can exceed the sound speed in a circumbinary gas disk. While the inner disk is strongly bound to the recoiling binary, the outer disk is only weakly bound or unbound. This leads to differential motions in t…
We study ultrarelativistic encounters of two spinning, equal-mass black holes through simulations in full numerical relativity. Two initial data sequences are studied in detail: one that leads to scattering and one that leads to a grazing collision and merger. In all cases, the initial black hole spins lie in the orbital plane, a configuration that leads to the so-called "superkicks". In astrophysical, quasicircular inspirals, such kicks can be as large as ~3,000 km/s; here, we find configurations that exceed ~15,000 km/s. We find that the maximum recoil is to a good approximation proportional…
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Saha Institute of Nuclear Physics（萨哈核物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institute)（马克斯·普朗克引力物理学研究所（阿尔伯特·爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；Niels Bohr International Academy, Niels Bohr Institute（尼尔斯·玻尔国际学院，尼尔斯·玻尔研究所）；Institute for Mathematics, Astrophysics and Particle Physics, Radboud University（拉德堡德大学数学、天体物理与粒子物理研究所）
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