Spinning Black Hole Binaries Research Articles

Self-consistent effective-one-body theory for spinning binaries based on post-Minkowskian approximation

This paper extends the research on the self-consistent effective-one-body theory of a real spinless two-body system based on the post-Minkowskian approximation (Science China, 65, 100411, (2022)) to the case of a binary system for the spinning black holes. An effective rotating metric and an improved Hamiltonian for the spinning black hole binaries were constructed. The decoupled equation for the null tetrad component of the gravitational perturbed Weyl tensor $\psi^B_{4}$ in the effective rotating spacetime is found with the help of the gauge transform characteristics of the Weyl tensors. The decoupled equation is then separated between radial and angular variables in the slowly rotating background spacetime, and a formal solution of $\psi^B_{4}$ is obtained. On this basis, the formal expressions of the radiation reaction force and the waveform for the ``plus'' and ``cross'' modes of the gravitational wave are presented. These results, obtained in the same effective spacetime, constitute a self-consistent effective-one-body theory for the spinning black hole binaries based on the post-Minkowskian approximation.

Minidisc influence on flow variability in accreting spinning black hole binaries: simulations in full general relativity

ABSTRACT We perform magnetohydrodynamic simulations of accreting, equal-mass binary black holes in full general relativity focusing on the effect of spin and minidiscs on the accretion rate and Poynting luminosity variability. We report on the structure of the minidiscs and periodicities in the mass of the minidiscs, mass accretion rates, and Poynting luminosity. The accretion rate exhibits a quasi-periodic behaviour related to the orbital frequency of the binary in all systems that we study, but the amplitude of this modulation is dependent on the existence of persistent minidiscs. In particular, systems that are found to produce persistent minidiscs have a much weaker modulation of the mass accretion rate, indicating that minidiscs can increase the inflow time of matter on to the black holes, and dampen out the quasi-periodic behaviour. This finding has potential consequences for binaries at greater separations where minidiscs can be much larger and may dampen out the periodicities significantly.

Minidisk Accretion onto Spinning Black Hole Binaries: Quasi-periodicities and Outflows

Abstract We perform a full 3D general relativistic magnetohydrodynamical (GRMHD) simulation of an equal-mass, spinning, binary black hole approaching merger, surrounded by a circumbinary disk and with a minidisk around each black hole. For this purpose, we evolve the ideal GRMHD equations on top of an approximated spacetime for the binary that is valid in every position of space, including the black hole horizons, during the inspiral regime. We use relaxed initial data for the circumbinary disk from a previous long-term simulation, where the accretion is dominated by a m = 1 overdensity called the lump. We compare our new spinning simulation with a previous non-spinning run, studying how spin influences the minidisk properties. We analyze the accretion from the inner edge of the lump to the black hole, focusing on the angular momentum budget of the fluid around the minidisks. We find that minidisks in the spinning case have more mass over a cycle than the non-spinning case. However, in both cases we find that most of the mass received by the black holes is delivered by the direct plunging of material from the lump. We also analyze the morphology and variability of the electromagnetic fluxes, and we find they share the same periodicities of the accretion rate. In the spinning case, we find that the outflows are stronger than the non-spinning case. Our results will be useful to understand and produce realistic synthetic light curves and spectra, which can be used in future observations.

Initial data and eccentricity reduction toolkit for binary black hole numerical relativity waveforms

The production of numerical relativity waveforms that describe quasi-circular binary black hole mergers requires high-quality initial data, and an algorithm to iteratively reduce residual eccentricity. To date, these tools remain closed source, or in commercial software that prevents their use in high performance computing platforms. To address these limitations, and to ensure that the broader numerical relativity community has access to these tools, herein we provide all the required elements to produce high-quality numerical relativity simulations in supercomputer platforms, namely: open source parameter files to numerically simulate spinning black hole binaries with asymmetric mass-ratios; open source Python tools to produce high-quality initial data for numerical relativity simulations of spinning black hole binaries on quasi-circular orbits; and open source Python tools for eccentricity reduction, both as stand-alone software and also deployed in the Einstein Toolkit’s software infrastructure. This open source toolkit fills in a void in the literature at a time when numerical relativity has an ever increasing role in the study and interpretation of gravitational wave sources. As part of our community building efforts, and to streamline and accelerate the use of these resources, we provide tutorials that describe, step by step, how to obtain and use these open source numerical relativity tools.

Circumbinary Disk Accretion into Spinning Black Hole Binaries

Abstract Supermassive black hole binaries are likely to accrete interstellar gas through a circumbinary disk. Shortly before merger, the inner portions of this circumbinary disk are subject to general relativistic effects. To study this regime, we approximate the spacetime metric of close orbiting black holes by superimposing two boosted Kerr–Schild terms. After demonstrating the quality of this approximation, we carry out very long-term general relativistic magnetohydrodynamic simulations of the circumbinary disk. We consider black holes with spin dimensionless parameters of magnitude 0.9, in one simulation parallel to the orbital angular momentum of the binary, but in another anti-parallel. These are contrasted with spinless simulations. We find that, for a fixed surface mass density in the inner circumbinary disk, aligned spins of this magnitude approximately reduce the mass accretion rate by 14% and counter-aligned spins increase it by 45%, leaving many other disk properties unchanged.

Minidisk Dynamics in Accreting, Spinning Black Hole Binaries: Simulations in Full General Relativity

Abstract We perform magnetohydrodynamic simulations of accreting, equal-mass binary black holes in full general relativity focusing on the impact of black hole spin on the dynamical formation and evolution of minidisks. We find that during the late inspiral the sizes of minidisks are primarily determined by the interplay between the tidal field and the effective innermost stable orbit around each black hole. Our calculations support that a minidisk forms when the Hill sphere around each black hole is significantly larger than the black hole’s effective innermost stable orbit. As the binary inspirals, the radius of the Hill sphere decreases, and minidisks consequently shrink in size. As a result, electromagnetic signatures associated with minidisks may be expected to gradually disappear prior to merger when there are no more stable orbits within the Hill sphere. In particular, a gradual disappearance of a hard electromagnetic component in the spectrum of such systems could provide a characteristic signature of merging black hole binaries. For a binary of given total mass, the timescale to minidisk “evaporation” should therefore depend on the black hole spins and the mass ratio. We also demonstrate that accreting binary black holes with spin have a higher efficiency for converting accretion power to jet luminosity. These results could provide new ways to estimate black hole spins in the future.

Evolutions of unequal mass, highly spinning black hole binaries

We evolve a binary black hole system bearing a mass ratio of $q=m_1/m_2=2/3$ and individual spins of $S^z_1/m_1^2=0.95$ and $S^z_2/m_2^2=-0.95$ in a configuration where the large black hole has its spin antialigned with the orbital angular momentum, $L^z$, and the small black hole has its spin aligned with $L^z$. This configuration was chosen to measure the maximum recoil of the remnant black hole for nonprecessing binaries. We find that the remnant black hole recoils at 500km/s, the largest recorded value from numerical simulations for aligned spin configurations. The remnant mass, spin, and gravitational waveform peak luminosity and frequency also provide a valuable point in parameter space for source modeling.

Hangup effect in unequal mass binary black hole mergers and further studies of their gravitational radiation and remnant properties

We present the results of 74 new simulations of nonprecessing spinning black hole binaries with mass ratios $q=m_1/m_2$ in the range $1/7\leq q\leq1$ and individual spins covering the parameter space $-0.95\leq\alpha_{1,2}\leq0.95$ with one runs with spins of $\pm0.95$. We supplement those runs with 107 previous simulations to study the hangup effect in black hole mergers, i.e. the delay or prompt merger of spinning holes with respect to non spinning binaries. We perform the numerical evolution for typically the last ten orbits before the merger and down to the formation of the final remnant black hole. This allows us to study the hangup effect for unequal mass binaries leading us to identify the spin variable that controls the number of orbits before merger as $\vec{S}_{hu}\cdot{\hat{L}},$ where $\vec{S}_{hu}=(1+\frac12\frac{m_2}{m_1})\vec{S}_1+(1+\frac12\frac{m_1}{m_2})\vec{S}_2$. We also combine the total results of those 181 simulations to obtain improved fitting formulae for the remnant final black hole mass, spin and recoil velocity as well as for the peak luminosity and peak frequency of the gravitational strain, and find new correlations among them. This accurate new set of simulations enhances the number of available numerical relativity waveforms available for parameter estimation of gravitational wave observations.

Evolutions of nearly maximally spinning black hole binaries using the moving puncture approach

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 helps keep the horizon radii reasonably large.

Remnant of binary black-hole mergers: New simulations and peak luminosity studies

We present the results of 61 new simulations of nonprecessing spinning black hole binaries with mass ratios $q={m}_{1}/{m}_{2}$ in the range $1/3\ensuremath{\le}q\ensuremath{\le}1$ and individual spins covering the parameter space $\ensuremath{-}0.85\ensuremath{\le}{\ensuremath{\alpha}}_{1,2}\ensuremath{\le}0.85$. We additionally perform ten new simulations of nonspinning black hole binaries with mass ratios covering the range $1/6\ensuremath{\le}q<1$. We follow the evolution for typically the last ten orbits before merger down to the formation of the final remnant black hole. This allows for assessment of the accuracy of our previous empirical formulas for relating the binary parameters to the remnant final black hole mass, spin and recoil. We use the new simulation to improve the fit to the above remnant formulas and add a formula for the peak luminosity of gravitational waves, produced around the merger of the two horizons into one. We find excellent agreement (typical errors $\ensuremath{\sim}0.1%--0.2%$) for the mass and spin, and within $\ensuremath{\sim}5%$ for the recoil and peak luminosity. These formulas have direct application to parameter estimation techniques applied to LIGO observations of gravitational waves from binary black hole mergers.

Energetics and phasing of nonprecessing spinning coalescing black hole binaries

We present an improved numerical relativity (NR) calibration of the new effective-one-body (EOB) model for coalescing non precessing spinning black hole binaries recently introduced by Damour and Nagar [Physical Review D 90, 044018 (2014)]. We do so by comparing the EOB predictions to both the phasing and the energetics provided by two independent sets of NR data covering mass ratios $1\leq q \leq 9.989$ and dimensionless spin range $-0.95\leq \chi\leq +0.994$. One set of data is a subset of the Simulating eXtreme Spacetimes (SXS) catalog of public waveforms; the other set consists of new simulations obtained with the Llama code plus Cauchy Characteristic Evolution. We present the first systematic computation of the gauge-invariant relation between the binding energy and the total angular momentum, $E_{b}(j)$, for a large sample of, spin-aligned, SXS and Llama data. The dynamics of the EOB model presented here involves only two free functional parameters, one ($a_6^c(\nu)$) entering the non spinning sector, as a 5PN effective correction to the interaction potential, and one ($c_3(\tilde{a}_1,\tilde{a}_2,\nu))$ in the spinning sector, as an effective next-to-next-to-next-to-leading order correction to the spin-orbit coupling. These parameters are determined (together with a third functional parameter $\Delta t_{\rm NQC}(\chi)$ entering the waveform) by comparing the EOB phasing with the SXS phasing, the consistency of the energetics being checked afterwards. The quality of the analytical model for gravitational wave data analysis purposes is assessed by computing the EOB/NR faithfulness. Over the NR data sample and when varying the total mass between 20 and 200~$M_\odot$ the EOB/NR unfaithfulness (integrated over the NR frequency range) is found to vary between $99.493\%$ and $99.984\%$ with a median value of $99.944\%$.

New analytic representation of the ringdown waveform of coalescing spinning black hole binaries

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 of a sample of sixteen $\ell=m=2$ equal-mass, spinning, nonprecessing, numerical waveforms computed with the SP$_{\rm E}$C code,now publicly available in the SXS catalogue. Our approach yields an efficient and accurate way to represent the ringdown waveform, thereby offering a new way to complete the analytical effective-one-body inspiral-plus-plunge waveform.

Erratum: Computing waveforms for spinning compact binaries in quasi-eccentric orbits [Phys. Rev. D82, 044028 (2010)

Several scenarios have been proposed in which the orbits of binary black holes enter the band of a gravitational wave detector with significant eccentricity. To avoid missing these signals or biasing parameter estimation it is important that we consider waveform models that account for eccentricity. The ingredients needed to compute post-Newtonian (PN) waveforms produced by spinning black holes inspiralling on quasi-eccentric orbits have been available for almost two decades at 2 PN order, and this work has recently been extended to 2.5 PN order. However, the computational cost of directly implementing these waveforms is high, requiring many steps per orbit to evolve the system of coupled differential equations. Here we employ the standard techniques of a separation of timescales and a generalized Keplerian parameterization of the orbits to produce efficient waveforms describing spinning black hole binaries with arbitrary masses and spins on quasi-eccentric orbits to 1.5 PN order. We separate the fast orbital timescale from the slow spin-orbit precession timescale by solving for the orbital motion in a non-interial frame of reference that follows the orbital precession. We outline a scheme for extending our approach to higher post-Newtonian order.

Characterizing spinning black hole binaries in eccentric orbits with LISA

The Laser Interferometer Space Antenna (LISA) is designed to detect gravitational wave signals from astrophysical sources, including those from coalescing binary systems of compact objects such as black holes. Colliding galaxies have central black holes that sink to the center of the merged galaxy and begin to orbit one another and emit gravitational waves. Some galaxy evolution models predict that the binary black hole system will enter the LISA band with significant orbital eccentricity, while other models suggest that the orbits will already have circularized. Using a full 17 parameter waveform model that includes the effects of orbital eccentricity, spin precession, and higher harmonics, we investigate how well the source parameters can be inferred from simulated LISA data. Defining the reference eccentricity as the value one year before merger, we find that for typical LISA sources, it will be possible to measure the eccentricity to an accuracy of parts in a thousand. The accuracy with which the eccentricity can be measured depends only very weakly on the eccentricity, making it possible to distinguish circular orbits from those with very small eccentricities. LISA measurements of the orbital eccentricity can help constraints theories of galaxy mergers in the early universe. Failing to account for the eccentricity in the waveform modeling can lead to a loss of signal power and bias the estimation of parameters such as the black hole masses and spins.

Matching post-Newtonian and numerical relativity waveforms: Systematic errors and a new phenomenological model for nonprecessing black hole binaries

We present a new phenomenological gravitational waveform model for the inspiral and coalescence of nonprecessing spinning black hole binaries. Our approach is based on a frequency-domain matching of post-Newtonian inspiral waveforms with numerical relativity based binary black hole coalescence waveforms. We quantify the various possible sources of systematic errors that arise in matching post-Newtonian and numerical relativity waveforms, and we use a matching criteria based on minimizing these errors; we find that the dominant source of errors are those in the post-Newtonian waveforms near the merger. An analytical formula for the dominant mode of the gravitational radiation of nonprecessing black hole binaries is presented that captures the phenomenology of the hybrid waveforms. Its implementation in the current searches for gravitational waves should allow cross-checks of other inspiral-merger-ringdown waveform families and improve the reach of gravitational-wave searches.

Computing waveforms for spinning compact binaries in quasi-eccentric orbits

Several scenarios have been proposed in which the orbits of binary black holes enter the band of a gravitational wave detector with significant eccentricity. To avoid missing these signals or biasing parameter estimation it is important that we consider waveform models that account for eccentricity. The ingredients needed to compute post-Newtonian (PN) waveforms produced by spinning black holes inspiralling on quasi-eccentric orbits have been available for almost two decades at 2 PN order, and this work has recently been extended to 2.5 PN order. However, the computational cost of directly implementing these waveforms is high, requiring many steps per orbit to evolve the system of coupled differential equations. Here we employ the standard techniques of a separation of time scales and a generalized Keplerian parameterization of the orbits to produce efficient waveforms describing spinning black hole binaries with arbitrary masses and spins on quasi-eccentric orbits to 1.5 PN order. We separate the fast orbital time scale from the slow spin-orbit precession time scale by solving for the orbital motion in a noninterial frame of reference that follows the orbital precession. We outline a scheme for extending our approach to higher post-Newtonian order.

Transformation of the multipolar components of gravitational radiation under rotations and boosts

We study the transformation of multipolar decompositions of gravitational radiation under rotations and boosts. Rotations to the remnant black hole's frame simplify the waveforms from the merger of generic spinning black hole binaries. Boosts may be important to get an accurate gravitational-wave phasing, especially for configurations leading to large recoil velocities of the remnant. As a test of the formalism we revisit the classic problem of point particles falling into a Schwarzschild black hole. Then we highlight by specific examples the importance of choosing the right frame in numerical simulations of unequal mass, spinning binary black-hole mergers.