Recoil velocity at 2PN order for spinning black hole binaries
Etienne Racine, Alessandra Buonanno, Lawrence E. Kidder
备注：
28 pages (PRD format), 1 figure, reference added, version published in PRD, except that the PRD version contains a sign error: the sign of the RHS of Eqs.(4.26) and (4.27) is wrong; it has been corrected in this replacement
We compute the flux of linear momentum carried by gravitational waves emitted from spinning binary black holes at 2PN order for generic orbits. In particular we provide explicit expressions of three new types of terms, namely next-to-leading order spin-orbit terms at 1.5 PN order, spin-orbit tail terms at 2PN order, and spin-spin terms at 2PN order. Restricting ourselves to quasi-circular orbits, we integrate the linear momentum flux over time to obtain the recoil velocity as function of orbital frequency. We find that in the so-called superkick configuration the higher-order spin corrections can increase the recoil velocity up to about a factor 3 with respect to the leading-order PN prediction. Furthermore, we provide expressions valid for generic orbits, and accurate at 2PN order, for the energy and angular momentum carried by gravitational waves emitted from spinning binary black holes. Specializing to quasi-circular orbits we compute the spin-spin terms at 2PN order in the expression for the evolution of the orbital frequency and found agreement with Mikóczi, Vasúth and Gergely. We also verified that in the limit of extreme mass ratio our expressions for the energy and angular momentum fluxes match the ones of Tagoshi, Shibata, Tanaka and Sasaki obtained in the context of black hole perturbation theory.
We measure the gravitational recoil for unequal-mass-black- hole-binary mergers, with the larger BH having spin a/m^H=0.8, and the smaller BH non-spinning. We choose our configurations such that, initially, the spins lie on the orbital plane. The spin and orbital plane precess significantly, and we find that the out-of plane recoil (i.e. the recoil perpendicular to the orbital plane around merger) varies as η^2 / (1+q), in agreement with our previous prediction, based on the post-Newtonian scaling.
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…
Recently, we proposed an enhancement of the Regge-Wheeler-Zerilli formalism for first-order perturbations about a Schwarzschild background that includes first-order corrections due to the background black-hole spin. Using this formalism, we investigate gravitational wave recoil effects from a spinning black-hole binary system analytically. This allows us to better understand the origin of the large recoils observed in full numerical simulation of spinning black hole binaries.
In this comment, I argue that chaotic effects in binary black hole inspiral will not strongly impact the detection of gravitational waves from such systems.
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…
Binary systems of rapidly spinning compact objects, such as black holes or neutron stars, are prime targets for gravitational wave astronomers. The dynamics of these systems can be very complicated due to spin-orbit and spin-spin couplings. Contradictory results have been presented as to the nature of the dynamics. Here we confirm that the dynamics - as described by the second post-Newtonian approximation to general relativity - is chaotic, despite claims to the contrary. When dissipation due to higher order radiation reaction terms are included, the chaos is dampened. However, the inspiral-to…
We present the first fully-nonlinear numerical study of the dynamics of highly spinning black-hole binaries. We evolve binaries from quasicircular orbits (as inferred from Post-Newtonian theory), and find that the last stages of the orbital motion of black-hole binaries are profoundly affected by their individual spins. In order to cleanly display its effects, we consider two equal mass holes with individual spin parameters S/m^2=0.757, both aligned and anti-aligned with the orbital angular momentum (and compare with the spinless case), and with an initial orbital period of 125M. We find that …
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 evolve equal-mass, equal-spin black-hole binaries with specific spins of a/mH 0.925, the highest spins simulated thus far and nearly the largest possible for Bowen-York black holes, in a set of configurations with the spins counter-aligned and pointing in the orbital plane, which maximizes the recoil velocities of the merger remnant, as well as a configuration where the two spins point in the same direction as the orbital angular momentum, which maximizes the orbital hang-up effect and remnant spin. The coordinate radii of the individual apparent horizons in these cases are very small and t…
The loss of linear momentum by gravitational radiation and the resulting gravitational recoil of black-hole binary systems may play an important role in the growth of massive black holes in early galaxies. We calculate the gravitational recoil of non-spinning black-hole binaries at the second post-Newtonian order (2PN) beyond the dominant effect, obtaining, for the first time, the 1.5PN correction term due to tails of waves and the next 2PN term. We find that the maximum value of the net recoil experienced by the binary due to the inspiral phase up to the innermost stable circular orbit (ISCO)…
Spinning compact binaries are shown to be chaotic in the Post-Newtonian expansion of the two body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the evolution. As a result, the spinning pair will have unpredictable gravitational waveforms during coalescence. This poses a challenge to future gravity wave observatories which rely on a match between the data and a theoretical template.
Inspiral signals from binary compact objects (black holes and neutron stars) are primary targets of the ongoing searches by ground-based gravitational-wave interferometers (LIGO, Virgo, GEO-600 and TAMA-300). We present parameter-estimation simulations for inspirals of black-hole--neutron-star binaries using Markov-chain Monte-Carlo methods. For the first time, we have both estimated the parameters of a binary inspiral source with a spinning component and determined the accuracy of the parameter estimation, for simulated observations with ground-based gravitational-wave detectors. We demonstra…
Levin (gr-qc/9910040) has shown that spinning compact binaries can be chaotic at second post-Newtonian order. However, when higher order dissipational effects are included, the dynamics will no longer be chaotic, though the evolution may still be unpredictable in a practical sense. I discuss some of the additional work that needs to be done to decide how this unpredictability might affect gravitational wave detectors such as LIGO.
We derive a fully analytic Keplerian-type parametrization solution to conservative motion of spinning binary in ADM gauge. This solution is able to describe three dimensional motion of binaries of arbitrary eccentricity, mass ratio and initial configuration of spin angular momentum up to the leading order of post-Newtonian(PN) approximation and a linear order in spin. Based on our results waveforms can be quickly computed with high accuracy.
The rotation of the bodies and the eccentricity of the orbit have significant effects on the emitted gravitational radiation of binary systems. This work focuses on the evaluation of the gravitational wave polarization states for spinning compact binaries. We consider binaries on eccentric orbits and the spin-orbit interaction up to the 1.5 post-Newtonian order in a way which is independent of the parameterization of the orbit. The equations of motion for angular variables are included. The formal expressions of the polarization states are given with the inclusion of higher order corrections t…
In the context of black hole spin in X-ray binaries, we propose that certain type of quasi-period oscillations (QPOs) observed in the light curves of black hole binaries (BHBs) are produced by X-ray modulation at the precession frequency of accretion disks, due to relativistic dragging of inertial frames around spinning black holes. These QPOs tend to be relatively stable in their centroid frequencies. They have been observed in the frequency range of a few to a few hundred Hz for several black holes with dynamically determined masses. By comparing the computed disk precession frequency with t…
The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A canonical point transformation removes the leading order terms of the spin-orbit Hamiltonian which induce a wiggling precession of the orbital angular momentum around the conserved total angular momentum, a precession which disappears in the case of equal masses or one single spin. Action-angle variables are applied which make a canonical perturbation theor…
We present a prescription to compute the time-domain gravitational wave (GW) polarization states associated with spinning compact binaries inspiraling along quasi-circular orbits. We invoke the orbital angular momentum ${\bf L}$ rather than its Newtonian counterpart ${\bf L_{\rm N}}$ to describe the orbits and the two spin vectors are freely specified in the source frame associated with the initial direction of the total angular momentum. We discuss the various implications of our approach.
Compact binaries in hyperbolic orbits are plausible gravitational wave (GW) sources for the upcoming and planned GW observatories. We develop an efficient prescription to compute post-Newtonian (PN) accurate ready-to-use GW polarization states for spinning compact binaries, influenced by the dominant order spin-orbit interactions, in hyperbolic orbits. This is achieved by invoking the 1.5PN accurate quasi-Keplerian parameterization for the radial sector of the orbital dynamics. We probe the influences of spins and gravitational radiation reaction on $h_+$ and $h_{\times}$ during the hyperbolic…
We construct a closed-form, fully analytical 4-metric that approximately represents the spacetime evolution of non-precessing, spinning black hole binaries from infinite separations up to a few orbits prior to merger. We employ the technique of asymptotic matching to join a perturbed Kerr metric in the neighborhood of each spinning black hole to a near-zone, post-Newtonian metric farther out. The latter is already naturally matched to a far-zone, post-Minkowskian metric that accounts for full temporal retardation. The result is a 4-metric that is approximately valid everywhere in space and in …
We present a recently developed prescription to obtain ready-to-use gravitational wave (GW) polarization states for spinning compact binaries on hyperbolic orbits. We include leading order spin-orbit interactions, invoking 1.5PN-accurate quasi-Keplerian parametrization for the radial part of the orbital dynamics. We also include radiation reaction effects on $h_+$ and $h_{\times}$ during the interaction. In the GW signals from spinning binaries there is evidence of the memory effect in both polarizations, in contrast to the non-spinning case, where only the cross polarizations exhibits non-van…
A brief review is given of all the Hamiltonians and effective potentials calculated hitherto covering the post-Newtonian (pN) dynamics of a two body system. A method is presented to compare (conservative) reduced Hamiltonians with nonreduced potentials directly at least up to the next-to-leading-pN order.
We present the first analytical computation of the (conservative) gravitational self-force correction to the periastron advance around a spinning black hole. Our result is accurate to the second order in the rotational parameter and through the 9.5 post-Newtonian level. It has been obtained as the circular limit of the correction to the gyroscope precession invariant along slightly eccentric equatorial orbits in the Kerr spacetime. The latter result is also new and we anticipate here the first few terms only of the corresponding post-Newtonian expansion.
The leading-order spin-orbit coupling is included in a post-Newtonian Lagrangian formulation of spinning compact binaries, which consists of the Newtonian term, first post-Newtonian (1PN) and 2PN non-spin terms and 2PN spin-spin coupling. This makes a 3PN spin-spin coupling occur in the derived Hamiltonian. The spin-spin couplings are mainly responsible for chaos in the Hamiltonians. However, the 3PN spin-spin Hamiltonian is small and has different signs, compared with the 2PN spin-spin Hamiltonian equivalent to the 2PN spin-spin Lagrangian. As a result, the probability of the occurrence of ch…
A precessing source frame, constructed using the Newtonian orbital angular momentum ${\bf L_{\rm N}}$, can be invoked to model inspiral gravitational waves from generic spinning compact binaries. An attractive feature of such a precessing convention is its ability to remove all spin precession induced modulations from the orbital phase evolution. However, this convention usually employs a post-Newtonian (PN) accurate precessional equation, appropriate for the PN accurate orbital angular momentum ${\bf L}$, to evolve the ${\bf L_{\rm N}}$-based precessing source frame. This influenced us to dev…
Anisotropic emission of gravitational waves (GWs) from inspiralling compact binaries leads to the loss of linear momentum and hence gravitational recoil of the system. The loss rate of linear momentum in the far-zone of the source (a nonspinning binary system of black holes in quasicircular orbit) is investigated at the 2.5 post-Newtonian (PN) order and used to provide an analytical expression in harmonic coordinates for the 2.5PN accurate recoil velocity of the binary accumulated in the inspiral phase. We find that the recoil velocity at the end of the inspiral phase (i.e at the innermost sta…
It is customary to use a precessing convention, based on Newtonian orbital angular momentum ${\bf L}_{\rm N}$, to model inspiral gravitational waves from generic spinning compact binaries. A key feature of such a precessing convention is its ability to remove all spin precession induced modulations from the orbital phase evolution. However, this convention usually employs a post-Newtonian (PN) accurate precessional equation, appropriate for the PN accurate orbital angular momentum ${\bf L}$, to evolve the ${\bf L}_{\rm N}$-based precessing source frame. This motivated us to develop inspiral wa…
We investigate the non-adiabatic dynamics of spinning black hole binaries by using an analytical Hamiltonian completed with a radiation-reaction force, containing spin couplings, which matches the known rates of energy and angular momentum losses on quasi-circular orbits. We consider both a straightforward post-Newtonian-expanded Hamiltonian (including spin-dependent terms), and a version of the resummed post-Newtonian Hamiltonian defined by the Effective One-Body approach. We focus on the influence of spin terms onto the dynamics and waveforms. We evaluate the energy and angular momentum rele…
We derive Keplerian-type parametrization for the solution of post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The PN accurate dynamics that we consider consists of the third post-Newtonian accurate conservative orbital dynamics influenced by the leading order spin effects, namely the leading order spin-orbit interactions. The orbital elements of the representation are explicitly given in terms of the conserved orbital energy, angular momentum and a quantity that characterizes the leading order spin-orbit interactions in Arnowitt, Deser…
We calculate the evolution and gravitational-wave emission of a spinning compact object inspiraling into a substantially more massive (non-rotating) black hole. We extend our previous model for a non-spinning binary [Phys. Rev. D 93, 064024] to include the Mathisson-Papapetrou-Dixon spin-curvature force. For spin-aligned binaries we calculate the dephasing of the inspiral and associated waveforms relative to models that do not include spin-curvature effects. We find this dephasing can be either positive or negative depending on the initial separation of the binary. For binaries in which the sp…
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…
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…
We present an analytical waveform family describing gravitational waves (GWs) from the inspiral, merger and ringdown of non-spinning black-hole binaries including the effect of several non-quadrupole modes [($\ell = 2, m = \pm 1), (\ell = 3, m = \pm 3), (\ell = 4, m = \pm 4)$ apart from $(\ell = 2, m=\pm2)$]. We first construct spin-weighted spherical harmonics modes of hybrid waveforms by matching numerical-relativity simulations (with mass ratio $1-10$) describing the late inspiral, merger and ringdown of the binary with post-Newtonian/effective-one-body waveforms describing the early inspir…
The gravitational waveforms emitted during the adiabatic inspiral of precessing binaries with two spinning compact bodies of comparable masses, evaluated within the post-Newtonian approximation, can be reproduced rather accurately by the waveforms obtained by setting one of the two spins to zero, at least for the purpose of detection by ground-based gravitational-wave interferometers. Here we propose to use this quasi-physical family of single-spin templates to search for the signals emitted by double-spin precessing binaries, and we find that its signal-matching performance is satisfactory fo…
We consider different spin supplementary conditions (SSC) for a spinning compact binary with the leading-order spin-orbit (SO) interaction. The Lagrangian of the binary system can be constructed but it is acceleration-dependent in two cases of SSC. We rewrite the generalized Hamiltonian formalism proposed by Ostrogradsky and compute the conserved quantities and the dissipative part of relative motion during the gravitational radiation of each SSC. We give the orbital elements and observed quantities of the SO dynamics, for instance the energy and the orbital angular momentum losses and wavefor…
Building upon the Noether charge formalism of Iyer and Wald, we derive a variational formula for spacetimes admitting a Killing vector field, for a generic energy-momentum distribution with compact support. Applying this general result to the particular case of a binary system of spinning compact objects moving along an exactly circular orbit, modelled using the multipolar gravitational skeleton formalism, we derive a first law of compact binary mechanics at dipolar order. We prove the equivalence of this new result with the canonical Hamiltonian first law previously derived for binary systems…
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+ …
We propose a quasi-local formula for the linear momentum of black-hole horizons inspired by the formalism of quasi-local horizons. We test this formula using two complementary configurations: (i) by calculating the large orbital linear momentum of the two black holes in an unequal-mass, zero-spin, quasi-circular binary and (ii) by calculating the very small recoil momentum imparted to the remnant of the head-on collision of an equal-mass, anti-aligned-spin binary. We obtain results consistent with the horizon trajectory in the orbiting case, and consistent with the net radiated linear momentum…
We present a prescription to compute the time-domain gravitational wave (GW) polarization states associated with spinning compact binaries inspiraling along quasi-circular orbits. We invoke the orbital angular momentum $\vek L$ rather than its Newtonian counterpart $\vek L_{\rm N}$ to describe the binary orbits while the two spin vectors are freely specified in an inertial frame associated with the initial direction of the total angular momentum. We show that the use of $\vek L$ to describe the orbits leads to additional 1.5PN order amplitude contributions to the two GW polarization states com…
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…
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…
We present the gravitational-wave flux balance law in an extreme mass-ratio binary with a spinning secondary. This law relates the flux of energy (angular momentum) radiated to null infinity and through the event horizon to the local change in the secondary's orbital energy (angular momentum) for generic (non-resonant) bound orbits in Kerr spacetime. As an explicit example we compute these quantities for a spin-aligned body moving on a circular orbit around a Schwarzschild black hole. We perform this calculation both analytically, via a high-order post-Newtonian expansion, and numerically in t…
Gravitational waveforms from the inspiral and ring-down stages of the binary black hole coalescences can be modelled accurately by approximation/perturbation techniques in general relativity. Recent progress in numerical relativity has enabled us to model also the non-perturbative merger phase of the binary black-hole coalescence problem. This enables us to \emph{coherently} search for all three stages of the coalescence of non-spinning binary black holes using a single template bank. Taking our motivation from these results, we propose a family of template waveforms which can model the inspir…
The quest for gravitational waves from coalescing binaries is customarily performed by the LIGO-Virgo collaboration via matched filtering, which requires a detailed knowledge of the signal. Complete analytical coalescence waveforms are currently available only for the non-precessing binary systems. In this paper we introduce complete phenomenological waveforms for the dominant quadrupolar mode of generically spinning systems. These waveforms are constructed by bridging the gap between the analytically known inspiral phase, described by spin Taylor (T4) approximants in the restricted waveform a…
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…
We study the general relativistic periastron advance in spinning black hole binaries on quasi-circular orbits, with spins aligned or anti-aligned with the orbital angular momentum, using numerical-relativity simulations, the post-Newtonian approximation, and black hole perturbation theory. By imposing a symmetry by exchange of the bodies' labels, we devise an improved version of the perturbative result, and use it as the leading term of a new type of expansion in powers of the symmetric mass ratio. This allows us to measure, for the first time, the gravitational self-force effect on the perias…
This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or ini…
We compare results from numerical simulations of spinning binaries in the "orbital hangup" case, where the binary completes at least nine orbits before merger, with post-Newtonian results using the approximants TaylorT1, T4 and Et. We find that, over the ten cycles before the gravitational-wave frequency reaches $Mω= 0.1$, the accumulated phase disagreement between NR and 2.5PN results is less than three radians, and is less than 2.5 radians when using 3.5PN results. The amplitude disagreement between NR and restricted PN results increases with the black holes' spin, from about 6% in the equal…
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…
We demonstrate that numerical relativity codes based on the moving punctures formalism are capable of evolving nearly maximally spinning black hole binaries. We compare a new evolution of an equal-mass, aligned-spin binary with dimensionless spin chi=0.99 using puncture-based data with recent simulations of the SXS Collaboration. We find that the overlap of our new waveform with the published results of the SXS Collaboration is larger than 0.999. To generate our new waveform, we use the recently introduced HiSpID puncture data, the CCZ4 evolution system, and a modified lapse condition that hel…
We complete the computation of the gravitational waveform amplitude for non-spinning compact binaries to the third and a half post-Newtonian (PN) order in the quasi-circular case. This is done by performing a spin-weighted spherical harmonics decomposition of the amplitude. This computation is achieved using the post-Newtonian-Multipolar-post-Minkowskian formalism. The amplitude modes are written in a PN expanded way as well as a factorized form suitable for EOB template building. Combining this work with previous ones, we provide in the supplemental materials the expressions of the modes incl…
We present a new, tunable effective-one-body (EOB) model of the motion and radiation of coalescing black hole binaries with arbitrary mass ratio and aligned spins. The most novel feature of our formalism is the introduction, and systematic use, of the (gauge-invariant) concept of {\it centrifugal radius} $r_{c}$. In the spinning small mass-ratio limit, the main radial potential expressed in terms of $r_{c}$ differs very little (and only multiplicatively so) from the usual Schwarzschild potential $1-2M/r_{c}$. This motivates a new, multiplicative way of blending finite-mass-ratio deformations w…
Coalescing massive Black Hole binaries are the strongest and probably the most important gravitational wave sources in the LISA band. The spin and orbital precessions bring complexity in the waveform and make the likelihood surface richer in structure as compared to the non-spinning case. We introduce an extended multimodal genetic algorithm which utilizes the properties of the signal and the detector response function to analyze the data from the third round of mock LISA data challenge (MLDC 3.2). The performance of this method is comparable, if not better, to already existing algorithms. We …
Detection template families (DTFs) are built to capture the essential features of true gravitational waveforms using a small set of phenomenological waveform parameters. Buonanno, Chen, and Vallisneri [Phys. Rev. D 67, 104025 (2003)] proposed the ``BCV2'' DTF to perform computationally efficient searches for signals from precessing binaries of compact stellar objects. Here we test the signal-matching performance of the BCV2 DTF for asymmetric--mass-ratio binaries, and specifically for double--black-hole binaries with component masses (m1,m2): (6~12Msun, 1~3Msun), and for black-hole--neutron-st…
The leading order effect of the spin of a distant supermassive black hole (SMBH) on the orbit of compact binary revolving around it appears at the 1.5 post Newtonian (PN) expansion through coupling with the inner and outer orbital angular momenta, and makes an oscillating characteristic contribution to the secular evolution of the compact binary eccentricity over a long time scale compared to the Kozai-Lidov dynamics caused by a non-spinning SMBH.
The secular evolution of a spinning, massive binary system in eccentric orbit is analyzed, expanding and generalizing our previous treatments of the Lense-Thirring motion and the one-spin limit. The spin-orbit and spin-spin effects up to the 3/2 post-Newtonian order are considered, both in the equations of motion and in the radiative losses. The description of the orbit in terms of the true anomaly parametrization provides a simple averaging technique, based on the residue theorem, over eccentric orbits. The evolution equations of the angle variables characterizing the relative orientation of …
We propose a new way of analyzing, and analytically representing, the ringdown part of the gravitational wave signal emitted by coalescing black hole binaries.By contrast with the usual {\it linear} decomposition of the multipolar complex waveform $h(t)$ in a sum of quasi-normal modes, our procedure relies on a {\it multiplicative} decomposition of $h(t)$ as the product of the fundamental quasi-normal mode with a remaining time-dependent complex factor whose amplitude and phase are separately fitted. As an illustrative example, we apply our analysis and fitting procedure to the ringdown part o…
