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 total gravitational wave impulse is also evaluated. Typically for a non head-on collision the net momentum flux carried out by gravitational waves is nonzero for equal-mass colliding black holes. The distribution of $V_{k}$ as a function of the symmetric mass ratio $η$ is well fitted by a modified Fitchett $η$-scaling law, the additional parameter modifying the law being a measure of the nonzero gravitational wave momentum flux for equal-mass initial black holes. For an initial infalling velocity $v/c \simeq 0.462$ of the colliding black holes, and incidence angle of collision $ρ_0=21^{o}$, we obtain a maximum $V_{k} \sim 121 {\rm km/s}$ located at $η\simeq 0.226$. For initial equal-mass black holes ($η=0.25$) we obtain $V_{k} \sim 107 {\rm km/s}$. Based on the integrated Bondi-Sachs momentum conservation law we discuss a possible definition of the center-of-mass velocity of the binary merged system and show that -- in an appropriate inertial frame -- it approaches asymptotically the net kick velocity, which is the velocity of the remnant black hole in this inertial frame. For larger values of $v/c$ we obtain substantially larger values of the net kick velocity, e.g., for $v/c \simeq 0.604$ a maximum $V_{k} \sim 610 {\rm km/s}$ is obtained.
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…
Recent calculations of the recoil velocity in binary black hole mergers have found the kick velocity to be of the order of a few hundred km/s in the case of non-spinning binaries and about $500 $km/s in the case of spinning configurations, and have lead to predictions of a maximum kick of up to $1300 $km/s. We test these predictions and demonstrate that kick velocities of at least $2500 $km/s are possible for equal-mass binaries with anti-aligned spins in the orbital plane. Kicks of that magnitude are likely to have significant repercussions for models of black-hole formation, the population o…
Gravitational waves from the coalescence of binary black holes carry linear momentum, causing center of mass recoil. This ``radiation rocket'' has important implications for systems with escape speeds of order the recoil velocity. We describe new recoil calculations using high precision black hole perturbation theory to estimate the magnitude of the recoil for the slow ``inspiral'' coalescence phase; coupled with a cruder calculation for the final ``plunge'', we estimate the total recoil imparted to a merged black hole. We find that velocities of many tens to a few hundred km/sec can be achiev…
In vacuum, the gravitational recoil of the final black hole from the merger of two black holes depends exclusively on the mass ratio and spins of the coalescing black holes, and on the eccentricity of the binary. If matter is present, accretion by the merging black holes may modify significantly their masses and spins, altering both the dynamics of the binary and the gravitational recoil of the remnant black hole. This paper considers such scenario. We investigate the effects on the kick of the final black hole from immersing the binary in a scalar field cloud. We consider two types of configu…
When unequal-mass black holes merge, the final black hole receives a ``kick'' due to the asymmetric loss of linear momentum in the gravitational radiation emitted during the merger. The magnitude of this kick has important astrophysical consequences. Recent breakthroughs in numerical relativity allow us to perform the largest parameter study undertaken to date in numerical simulations of binary black hole inspirals. We study non-spinning black-hole binaries with mass ratios from $q=M_1/M_2=1$ to $q =0.25$ ($η= q/(1 + q)^2$ from 0.25 to 0.16). We accurately calculate the velocity of the kick to…
We examine the gravitational wave recoil waves and the associated net kick velocities in non-axisymmetric Robinson-Trautman spacetimes. We use characteristic initial data for the dynamics corresponding to non-head-on collisions of black holes. We make a parameter study of the kick distributions, corresponding to an extended range of the incidence angle $ρ_0$ in the initial data. For the range of $ρ_0$ examined ($3^{\circ} \leq ρ_0 \leq 110^{\circ}$) the kick distributions as a function of the symmetric mass parameter $η$ satisfy a law obtained from an empirical modification of the Fitchett law…
Gravitational waves from the coalescence of binary black holes carry away linear momentum, causing center of mass recoil. This "radiation rocket" effect has important implications for systems with escape speeds of order the recoil velocity. We revisit this problem using black hole perturbation theory, treating the binary as a test mass spiraling into a spinning hole. For extreme mass ratios (q = m1/m2 << 1) we compute the recoil for the slow inspiral epoch of binary coalescence very accurately; these results can be extrapolated to q ~ 0.4 with modest accuracy. Although the recoil from the fina…
A complete measurement of a black-hole recoil through higher-order gravitational-wave modes
Instituto Galego de Física de Altas Enerxías, Universidade de Santiago de Compostela（加利西亚高能物理研究所，圣地亚哥-德孔波斯特拉大学）；The Chinese University of Hong Kong（香港中文大学）；Indian Institute of Technology Bombay（印度理工学院孟买分校）；Pennsylvania State University（宾夕法尼亚州立大学）
Gravitational waves carry energy, angular momentum, and linear momentum. In generic binary black hole mergers, the loss of linear momentum imparts a recoil velocity, or a "kick", to the remnant black hole. We exploit recent advances in gravitational waveform and remnant black hole modeling to extract information about the kick from the gravitational wave signal. Kick measurements such as these are astrophysically valuable, enabling independent constraints on the rate of second-generation mergers. Further, we show that kicks must be factored into future ringdown tests of general relativity with…
Binary black holes emit gravitational radiation with net linear momentum leading to a retreat of the final remnant black hole that can reach up to $\sim5,000$ km/s. Full numerical relativity simulations are the only tool to accurately compute these recoils since they are largely produced when the black hole horizons are about to merge and they are strongly dependent on their spin orientations at that moment. We present eight new numerical simulations of BBH in the hangup-kick configuration family, leading to the maximum recoil. Black holes are equal mass and near maximally spinning ($|\vec{S}_…
Asymmetric binary systems radiate linear momentum through gravitational waves, leading to the recoil of the merger remnant. Black-hole kicks have attracted much attention because of their astrophysical implications. However, little information can be extracted from the observations made by LIGO and Virgo so far. In this work, we discuss how the gravitational recoil, an effect that is encoded in the gravitational signal, can be used to test the accuracy of waveform models. Gravitational-wave models of merging binary systems have become fundamental to detect potential signals and infer the param…
The radiation of linear momentum imparts a recoil (or "kick") to the center of mass of a merging black hole binary system. Recent numerical relativity calculations have shown that eccentricity can lead to an approximate 25% increase in recoil velocities for equal-mass, spinning binaries with spins lying in the orbital plane ("superkick" configurations) [U Sperhake et al. Phys. Rev. D 101 (2020) 024044 (arXiv:1910.01598)]. Here we investigate the impact of nonzero eccentricity on the kick magnitude and gravitational-wave emission of nonspinning, unequal-mass black hole binaries. We confirm that…
Gravitational waves emitted from a generic binary black-hole merger carry away linear momentum anisotropically, resulting in a gravitational recoil, or "kick", of the center of mass. For certain merger configurations the time evolution of the magnitude of the kick velocity has a local maximum followed by a sudden drop. Perturbative studies of this "antikick" in a limited range of black hole spins have found that the antikick decreases for retrograde orbits as a function of negative spin. We analyze this problem using a recently developed code to evolve gravitational perturbations from a point-…
We revisit the scenario of the gravitational radiation recoil acquired by the final remnant of a black-hole-binary merger by studying a set of configurations that have components of the spin both aligned with the orbital angular momentum and in the orbital plane. We perform a series of 42 new full numerical simulations for equal-mass and equal-spin-magnitude binaries. We extend previous recoil fitting formulas to include nonlinear terms in the spins and successfully include both the new and known results. The new predicted maximum velocity approaches 5000km/s for spins partially aligned with t…
The gravitational recoil or "kick" of a black hole formed from the merger of two orbiting black holes, and caused by the anisotropic emission of gravitational radiation, is an astrophysically important phenomenon. We combine (i) an earlier calculation, using post-Newtonian theory, of the kick velocity accumulated up to the merger of two non-spinning black holes, (ii) a "close-limit approximation" calculation of the radiation emitted during the ringdown phase, and based on a solution of the Regge-Wheeler and Zerilli equations using initial data accurate to second post-Newtonian order. We prove …
The final black hole left behind after a binary black hole merger can attain a recoil velocity, or a "kick", reaching values up to 5000 km/s. This phenomenon has important implications for gravitational wave astronomy, black hole formation scenarios, testing general relativity, and galaxy evolution. We consider the gravitational wave signal from the binary black hole merger GW200129_065458 (henceforth referred to as GW200129), which has been shown to exhibit strong evidence of orbital precession. Using numerical relativity surrogate models, we constrain the kick velocity of GW200129 to $v_f \s…
Several groups have recently computed the gravitational radiation recoil produced by the merger of two spinning black holes. The results suggest that spin can be the dominant contributor to the kick, with reported recoil speeds of hundreds to even thousands of kilometers per second. The parameter space of spin kicks is large, however, and it is ultimately desirable to have a simple formula that gives the approximate magnitude of the kick given a mass ratio, spin magnitudes, and spin orientations. As a step toward this goal, we perform a systematic study of the recoil speeds from mergers of bla…
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…
Recent numerical relativistic results demonstrate that the merger of comparable-mass spinning black holes has a maximum ``recoil kick'' of up to $\sim 4000 \kms$. However the scaling of these recoil velocities with mass ratio is poorly understood. We present new runs showing that the maximum possible kick perpendicular to the orbital plane does not scale as $\simη^2$ (where $η$ is the symmetric mass ratio), as previously proposed, but is more consistent with $\simη^3$, at least for systems with low orbital precession. We discuss the effect of this dependence on galactic ejection scenarios and …
Using the Multipolar post-Minskowskian formalism, we compute the linear momentum flux from black-hole binaries in circular orbits and having no spins. The total linear momentum flux contains various types of instantaneous (which are functions of the retarded time) and hereditary (which depends on the dynamics of the binary in the past) terms both of which are analytically computed. In addition to the inspiral contribution, we use a simple model of plunge to compute the kick or recoil accumulated during this phase.
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…
Binary black holes radiate linear momentum in gravitational waves as they merge. Recoils imparted to the black-hole remnant can reach thousands of km/s, thus ejecting black holes from their host galaxies. We exploit recent advances in gravitational waveform modeling to quickly and reliably extract recoils imparted to generic, precessing, black hole binaries. Our procedure uses a numerical-relativity surrogate model to obtain the gravitational waveform given a set of binary parameters, then from this waveform we directly integrate the gravitational-wave linear momentum flux. This entirely bypas…
We report the first results from evolutions of a generic black-hole binary, i.e. a binary containing unequal mass black holes with misaligned spins. Our configuration, which has a mass ratio of 2:1, consists of an initially non-spinning hole orbiting a larger, rapidly spinning hole (specific spin a/m = 0.885), with the spin direction oriented -45 degrees with respect to the orbital plane. We track the inspiral and merger for ~2 orbits and find that the remnant receives a substantial kick of 454 km/s, more than twice as large as the maximum kick from non-spinning binaries. The remnant spin dire…
The final evolution of a binary black-hole system gives rise to a recoil velocity if an asymmetry is present in the emitted gravitational radiation. Measurements of this effect for non-spinning binaries with unequal masses have pointed out that kick velocities $\sim~175$ km/s can be reached for a mass ratio $\simeq 0.36$. However, a larger recoil can be obtained for equal-mass binaries if the asymmetry is provided by the spins. Using two independent methods we show that the merger of such binaries yields velocities as large as $\sim 440$ km/s for black holes having unequal spins that are antia…
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 present results from an extensive study of 88 precessing, equal-mass black-hole binaries with large spins (83 with intrinsic spins of 0.8 and 5 with intrinsic spins of 0.9)and use these data to model new nonlinear contributions to the gravitational recoil imparted to the merged black hole. We find a new effect, the cross kick, that enhances the recoil for partially aligned binaries beyond the hangup kick effect. This has the consequence of increasing the probabilities of recoils larger than 2000 km/s by nearly a factor two, and, consequently, of black holes getting ejected from galaxies, as…
The inspiral and merger of binary black holes will likely involve black holes with both unequal masses and arbitrary spins. The gravitational radiation emitted by these binaries will carry angular as well as linear momentum. A net flux of emitted linear momentum implies that the black hole produced by the merger will experience a recoil or kick. Previous studies have focused on the recoil velocity from unequal mass, non-spinning binaries. We present results from simulations of equal mass but spinning black hole binaries and show how a significant gravitational recoil can also be obtained in th…
We present results from fully nonlinear simulations of unequal mass binary black holes plunging from close separations well inside the innermost stable circular orbit with mass ratios q = M_1/M_2 = {1,0.85,0.78,0.55,0.32}, or equivalently, with reduced mass parameters $η=M_1M_2/(M_1+M_2)^2 = {0.25, 0.248, 0.246, 0.229, 0.183}$. For each case, the initial binary orbital parameters are chosen from the Cook-Baumgarte equal-mass ISCO configuration. We show waveforms of the dominant l=2,3 modes and compute estimates of energy and angular momentum radiated. For the plunges from the close separations…
The inspiral and merger of a binary black hole system generally leads to an asymmetric distribution of emitted radiation, and hence a recoil of the remnant black hole directed opposite to the net linear momentum radiated. The recoil velocity is generally largest for comparable mass black holes and particular spin configurations, and approaches zero in the extreme mass ratio limit. It is generally believed that for extreme mass ratios eta<<1, the scaling of the recoil velocity is V {\propto} eta^2, where the proportionality coefficient depends on the spin of the larger hole and the geometry of …
Generic inspirals and mergers of binary black holes produce beamed emission of gravitational radiation that can lead to a gravitational recoil or kick of the final black hole. The kick velocity depends on the mass ratio and spins of the binary as well as on the dynamics of the binary configuration. Studies have focused so far on the most astrophysically relevant configuration of quasi-circular inspirals, for which kicks as large as 3,300 km/s have been found. We present the first study of gravitational recoil in hyperbolic encounters. Contrary to quasi-circular configurations, in which the bea…
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+ …
Supermassive black holes (SMBHs) may not always reside right at the centers of their host galaxies. This is a prediction of numerical relativity simulations, which imply that the newly formed single SMBH, after binary coalescence in a galaxy merger, can receive kick velocities up to several 1000 km/s due to anisotropic emission of gravitational waves. Long-lived oscillations of the SMBHs in galaxy cores, and in rare cases even SMBH ejections from their host galaxies, are the consequence. Observationally, accreting recoiling SMBHs would appear as quasars spatially and/or kinematically off-set f…
Coalescing binary black holes emit anisotropic gravitational radiation. This causes a net emission of linear momentum that produces a gradual acceleration of the source. As a result, the final remnant black hole acquires a characteristic velocity known as recoil velocity or gravitational kick. The symmetries of gravitational wave emission are reflected in the interactions of the gravitational wave modes emitted by the binary. In this work we make use of the rich information encoded in the higher-order modes of the gravitational wave emission to infer the component of the kick along the line-of…
We present a study of spinning black hole binaries focusing on the spin dynamics of the individual black holes as well as on the gravitational recoil acquired by the black hole produced by the merger. We consider two series of initial spin orientations away from the binary orbital plane. In one of the series, the spins are anti-aligned; for the second series, one of the spins points away from the binary along the line separating the black holes. We find a remarkable agreement between the spin dynamics predicted at 2nd post-Newtonian order and those from numerical relativity. For each configura…
The generation of a large recoil velocity from the inspiral and merger of binary black holes represents one of the most exciting results of numerical-relativity calculations. While many aspects of this process have been investigated and explained, the "antikick", namely the sudden deceleration after the merger, has not yet found a simple explanation. We show that the antikick can be understood in terms of the radiation from a deformed black hole where the anisotropic curvature distribution on the horizon correlates with the direction and intensity of the recoil. Our analysis is focussed on Rob…
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 calculate the linear momentum flux from merging black holes (BHs) with arbitrary masses and spin orientations, using the effective-one-body (EOB) model. This model includes an analytic description of the inspiral phase, a short merger, and a superposition of exponentially damped quasi-normal ringdown modes of a Kerr BH. By varying the matching point between inspiral and ringdown, we can estimate the systematic errors generated with this method. Within these confidence limits, we find close agreement with previously reported results from numerical relativity. Using a Monte Carlo implementati…
The merger process of a binary black hole system can have a strong impact on a circumbinary disk. In the present work we study the effect of both central mass reduction (due to the energy loss through gravitational waves) and a possible black hole recoil (due to asymmetric emission of gravitational radiation). For the mass reduction case and recoil directed along the disk's angular momentum, oscillations are induced in the disk which then modulate the internal energy and bremsstrahlung luminosities. On the other hand, when the recoil direction has a component orthogonal to the disk's angular m…
We present accurate fits for the remnant properties of generically precessing binary black holes, trained on large banks of numerical-relativity simulations. We use Gaussian process regression to interpolate the remnant mass, spin, and recoil velocity in the 7-dimensional parameter space of precessing black-hole binaries with mass ratios $q\leq2$, and spin magnitudes $χ_1,χ_2\leq0.8$. For precessing systems, our errors in estimating the remnant mass, spin magnitude, and kick magnitude are lower than those of existing fitting formulae by at least an order of magnitude (improvement is also repor…
Coalescing binary black holes experience an impulsive kick due to anisotropic emission of gravitational waves. We discuss the dynamical consequences of the recoil accompanying massive black hole mergers. Recoil velocities are sufficient to eject most coalescing black holes from dwarf galaxies and globular clusters, which may explain the apparent absence of massive black holes in these systems. Ejection from giant elliptical galaxies would be rare, but coalescing black holes are displaced from the center and fall back on a time scale of order the half-mass crossing time. Displacement of the bla…
We test the accuracy of our recently proposed empirical formula to model the recoil velocity imparted to the merger remnant of spinning, unequal-mass black-hole binaries. We study three families of black-hole binary configurations, all with mass ratio q=3/8 (to maximize the unequal-mass contribution to the kick) and spins aligned (or counter aligned) with the orbital angular momentum, two with spin configurations chosen to minimize the spin-induced tangential and radial accelerations of the trajectories respectively, and a third family where the trajectories are significantly altered by spin-o…
Recent numerical relativity simulations have shown that the final black hole produced in a binary merger can recoil with a velocity as large as 5,000 km/s. Because of enhanced gravitational-wave emission in the so-called "hang-up" configurations, this maximum recoil occurs when the black-hole spins are partially aligned with the orbital angular momentum. We revisit our previous statistical analysis of post-Newtonian evolutions of black-hole binaries in the light of these new findings. We demonstrate that despite these new configurations with enhanced recoil velocities, spin alignment during th…
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…
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 galaxy. 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 trajecto…
Generic black hole binaries radiate gravitational waves anisotropically, imparting a recoil, or kick, velocity to the merger remnant. If a component of the kick along the line of sight is present, gravitational waves emitted during the final orbits and merger will be gradually Doppler shifted as the kick builds up. We develop a simple prescription to capture this effect in existing waveform models, showing that future gravitational wave experiments will be able to perform direct measurements, not only of the black hole kick velocity, but also of its accumulation profile. In particular, the eLI…
Recent calculations of the recoil velocity in black-hole binary mergers have found kick velocities of $\approx2500 $km/s for equal-mass binaries with anti-aligned initial spins in the orbital plane. In general the dynamics of spinning black holes can be extremely complicated and are difficult to analyze and understand. In contrast, the ``superkick'' configuration is an example with a high degree of symmetry that also exhibits exciting physics. We exploit the simplicity of this ``test case'' to study more closely the role of spin in black-hole recoil and find that: the recoil is with good accur…
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…
The close-limit method has given approximations in excellent agreement with those of numerical relativity for collisions of equal mass black holes. We consider here colliding holes with unequal mass, for which numerical relativity results are not available. We try to ask two questions: (i) Can we get approximate answers to astrophysical questions (ideal mass ratio for energy production, maximum recoil velocity, etc.), and (ii) can we better understand the limitations of approximation methods. There is some success in answering the first type of question, but more with the second, especially in…
Recent developments in numerical relativity have made it possible to follow reliably the coalescence of two black holes from near the innermost stable circular orbit to final ringdown. This opens up a wide variety of exciting astrophysical applications of these simulations. Chief among these is the net kick received when two unequal mass or spinning black holes merge. The magnitude of this kick has bearing on the production and growth of supermassive black holes during the epoch of structure formation, and on the retention of black holes in stellar clusters. Here we report the first accurate n…
