Binary Black Hole Simulations Research Articles

Rapid likelihood free inference of compact binary coalescences using accelerated hardware

Abstract We report a gravitational-wave parameter estimation algorithm, AMPLFI, based on likelihood-free inference using normalizing flows. The focus of AMPLFI is to perform real-time parameter estimation for candidates detected by machine-learning based compact binary coalescence search, Aframe. We present details of our algorithm and optimizations done related to data-loading and pre-processing on accelerated hardware. We train our model using binary black-hole (BBH) simulations on real LIGO-Virgo detector noise. Our model has ∼6 million trainable parameters with training times ≦ 24 hours. Based on online deployment on a mock data stream of LIGO-Virgo data, Aframe+AMPLFI is able to pick up BBH candidates and infer parameters for real-time alerts from data acquisition with a net latency of ∼6 seconds.

Worldtube excision method for intermediate-mass-ratio inspirals: Self-consistent evolution in a scalar-charge model

This is a third installment in a program to develop a method for alleviating the scale disparity in binary black hole simulations with mass ratios in the intermediate astrophysical range, where simulation cost is prohibitive while purely perturbative methods may not be adequate. The method is based on excising a “worldtube” around the smaller object, much larger than the object itself, replacing it with an analytical model that approximates a tidally deformed black hole. Previously [N. A. Wittek , Worldtube excision method for intermediate-mass-ratio inspirals: Scalar-field model in 3+1 dimensions, ] we have tested the idea in a toy model of a scalar charge in a fixed circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field in 3+1 dimensions on the p platform. Here we take the significant further step of allowing the orbit to evolve radiatively, in a self-consistent manner, under the effect of back-reaction from the scalar field. We compute the inspiral orbit and the emitted scalar-field waveform, showing a good agreement with perturbative calculations in the adiabatic approximation. We also demonstrate how our simulations accurately resolve postadiabatic effects (for which we do not have perturbative results). In this work we focus on quasicircular inspirals. Our implementation is publicly accessible in the p numerical relativity code. Published by the American Physical Society 2024

Final parsec problem of black hole mergers and ultralight dark matter

When two galaxies merge, they often produce a supermassive black hole binary (SMBHB) at their center. Numerical simulations with stars and cold dark matter show that SMBHBs typically stall out at a distance of a few parsecs apart and take billions of years to coalesce. This is known as the final parsec problem. We suggest that ultralight dark matter (ULDM) halos around SMBHBs can generate dark matter waves due to dynamical friction. These waves can effectively carry away orbital energy from the black holes, rapidly driving them together. To test this hypothesis, we performed numerical simulations of black hole binaries inside ULDM halos. Due to gravitational cooling and quasi-normal modes, the loss-cone problem can be avoided. The decay time scale gives lower bounds on masses of the ULDM particles and SMBHBs comparable to observational data. Our results imply that ULDM waves can lead to the rapid orbital decay of black hole binaries.

Success of the small mass-ratio approximation during the final orbits of binary black hole simulations

Recent studies have shown the surprising effectiveness of the small mass-ratio approximation (SMR) in modeling the relativistic two-body problem even at comparable masses. Up to now this effectiveness has been demonstrated only during inspiral, before the binary transitions into plunge and merger. Here we examine the binding energy of nonspinning binary black hole simulations with mass ratios from $20\ensuremath{\mathbin:}1$ to equal mass. We show for the first time that the binaries undergo a transition to plunge as predicted by analytic theory, and estimate the size of the transition region, which is $\ensuremath{\sim}10$ gravitational wave cycles for equal mass binaries. By including transition, the SMR expansion of the binding energy is accurate until the last cycle of gravitational wave emission. This is true even for comparable mass binaries such as those observed by current gravitational wave detectors, where the transition often makes up much of the observed signal. Our work provides further evidence that the SMR approximation can be directly applied to current gravitational wave observations.

Massively parallel simulations of binary black holes with adaptive wavelet multiresolution

We present results from the new dendro-gr code. These include simulations of binary black hole mergers for mass ratios up to $q=16$. dendro-gr uses wavelet adaptive multiresolution to generate an unstructured grid adapted to the spacetime geometry together with an octree-based data structure. We demonstrate good scaling, improved convergence properties, and efficient use of computational resources. We validate the code with comparisons to lazev.

Eccentricity estimation from initial data for numerical relativity simulations

We describe and study an instantaneous definition of eccentricity to be applied at the initial moment of full numerical simulations of binary black holes. The method consists of evaluating the eccentricity at the moment of maximum separation of the binary. We estimate it using up to third post-Newtonian (3PN) order, and compare these results with those of evolving (conservative) 3PN equations of motion for a full orbit and compute the eccentricity $e_r$ from the radial turning points, finding excellent agreement. We next include terms with spins up to 3.5PN, and then compare this method with the corresponding estimates of the eccentricity $e_r^{NR}$ during full numerical evolutions of spinning binary black holes, characterized invariantly by a fractional factor $0\leq f\leq1$ of the initial tangential momenta. It is found that our initial instantaneous definition is a very useful tool to predict and characterize even highly eccentric full numerical simulations.

Redshift factor and the small mass-ratio limit in binary black hole simulations

We present a calculation of the Detweiler redshift factor in binary black hole simulations based on its relation to the surface gravity. The redshift factor has far-reaching applications in analytic approximations, gravitational self-force calculations, and conservative two-body dynamics. By specializing to nonspinning, quasicircular binaries with mass ratios ranging from ${m}_{A}/{m}_{B}=1$ to ${m}_{A}/{m}_{B}=9.5$ we are able to recover the leading small-mass-ratio (SMR) prediction with relative differences of order ${10}^{\ensuremath{-}5}$ from simulations alone. The next-to-leading order term that we extract agrees with the SMR prediction arising from self-force calculations, with differences of a few percent. These deviations from the first-order conservative prediction are consistent with nonadiabatic effects that can be accommodated in an SMR expansion. This fact is also supported by a comparison to the conservative post-Newtonian prediction of the redshifts. For the individual redshifts, a reexpansion in terms of the symmetric mass ratio $\ensuremath{\nu}$ does not improve the convergence of the series. However we find that when looking at the sum of the redshift factors of both back holes, ${z}_{A}+{z}_{B}$, which is symmetric under the exchange of the masses, a reexpansion in $\ensuremath{\nu}$ accelerates its convergence. Our work provides further evidence of the surprising effectiveness of SMR approximations in modeling even comparable mass binary black holes.

Fourth RIT binary black hole simulations catalog: Extension to eccentric orbits

This fourth release of the RIT public catalog of numerical relativity black-hole-binary waveforms consists of 1881 accurate simulations that include 446 precessing and 611 nonprecessing quasicircular/inspiraling binary systems with mass ratios $q={m}_{1}/{m}_{2}$ in the range $1/128\ensuremath{\le}q\ensuremath{\le}1$ and individual spins up to $s/{m}^{2}=0.95$; and 824 in eccentric orbits in the range $0<e\ensuremath{\le}1$. The catalog also provides initial parameters of the binary, trajectory information, peak radiation, and final remnant black hole properties. The waveforms are corrected for the center of mass drifting and are extrapolated to future null infinity. As an application of this waveform catalog we reanalyze all of the peak radiation and remnant properties to find new, simple, correlations among them, valid in the presence of eccentricity, for practical astrophysical usage.

Quasinormal modes of slowly-rotating black holes in dynamical Chern-Simons gravity

The detection of gravitational waves from compact binary mergers by the LIGO/Virgo Collaboration has, for the first time, allowed us to test relativistic gravity in its strong, dynamical, and nonlinear regime, thus opening a new arena to confront general relativity (and modifications thereof) against observations. We consider a theory which modifies general relativity by introducing a scalar field coupled to a parity-violating curvature term known as dynamical Chern-Simons gravity. In this theory, spinning black holes are different from their general relativistic counterparts and can thus serve as probes to this theory. We study linear gravito-scalar perturbations of black holes in dynamical Chern-Simons gravity at leading order in spin and (i) obtain the perturbed field equations describing the evolution of the perturbed gravitational and scalar fields, (ii) numerically solve these equations by direct integration to calculate the quasinormal mode frequencies for the dominant and higher multipoles and tabulate them, (iii) find strong evidence that these rotating black holes are linearly stable, and (iv) present general fitting functions for different multipoles for gravitational and scalar quasinormal mode frequencies in terms of spin and Chern-Simons coupling parameter. Our results can be used to validate the ringdown of small-spin remnants of numerical relativity simulations of black hole binaries in dynamical Chern-Simons gravity and pave the way towards future tests of this theory with gravitational wave ringdown observations.

Fast hyperbolic relaxation elliptic solver for numerical relativity: Conformally flat, binary puncture initial data

We introduce nrpyelliptic, an elliptic solver for numerical relativity (NR) built within the nrpy+ framework. As its first application, nrpyelliptic sets up conformally flat, binary black hole (BBH) puncture initial data (ID) on a single numerical domain, similar to the widely used twopunctures code. Unlike twopunctures, nrpyelliptic employs a hyperbolic relaxation scheme, whereby arbitrary elliptic partial differential equations (PDEs) are trivially transformed into a hyperbolic system of PDEs. As consumers of NR ID generally already possess expertise in solving hyperbolic PDEs, they will generally find nrpyelliptic easier to tweak and extend than other NR elliptic solvers. When evolved forward in (pseudo)time, the hyperbolic system exponentially reaches a steady state that solves the elliptic PDEs. Notably nrpyelliptic accelerates the relaxation waves, which makes it many orders of magnitude faster than the usual constant wave speed approach. While it is still $\ensuremath{\sim}12\mathrm{x}$ slower than twopunctures at setting up full-3D BBH ID, nrpyelliptic requires only $\ensuremath{\approx}0.3%$ of the runtime for a full BBH simulation in the einstein toolkit. Future work will focus on improving performance and generating other types of ID, such as binary neutron stars.

Final velocity and radiated energy in numerical simulations of binary black holes

The evolution of global binary black holes variables such as energy or linear momentum are mainly obtained by applying numerical methods near coalescence, post-Newtonian (PN) expansions, or a combination of both. In this paper, we use a fully relativistic formalism presented several years ago that only uses global variables defined at null infinity together with the gravitational radiation emitted by the source to obtain the time evolution of such variables for binary black holes (BBH) systems. For that, we use the Rochester catalog composed of 776 BBHs simulations. We compute the final velocity, radiated energy, and intrinsic angular momentum predicted by the dynamical equations in this formalism for nonspinning, aligned and antialigned spins, and several different precessing configurations. We compare obtained values with reported values in numerical simulations. As BBHs parameter space is still not completely covered by numerical simulations, we fit phenomenological formulas for practical applications to the radiated energy and final velocities obtained. Also, we compare the fits with reported values. In conclusion, we see that our formulae and correlations for the variables described in this work are consistent with those found in the general literature.

High-overtone fits to numerical relativity ringdowns: Beyond the dismissed n=8 special tone

In general relativity, the remnant object originating from an uncharged black hole merger is a Kerr black hole. The approach to this final state is reached through the emission of a late train of radiation known as the black hole ringdown. The ringdown morphology is described by a countably infinite set of damped sinusoids, whose complex frequencies are solely determined by the final black hole's mass and spin. Recent results advocate that ringdown waveforms from numerical relativity can be fully described from the peak of the strain onwards if quasi-normal mode models with $N_{max}=7$ overtones are used. In this work we extend this analysis to models with $N_{max}\geq 7$ up to $N_{max}=16$ overtones by exploring the parameter bias on the final mass and final spin obtained by fitting the nonprecessing binary black hole simulations from the SXS catalogue. To this aim, we have computed the spin weight $-2$ quasi-normal mode frequencies and angular separation constants for the special $(l=m=2, n=8,9)$ overtones for the Kerr spacetime. We find that a total of $N_{max}\sim 6$ overtones are on average sufficient to model the ringdown starting at the peak of the strain, although about $21\%$ of the cases studied require at least $N_{max}\sim 12$ overtones to reach a comparable accuracy on the final state parameters. Considering the waveforms from an earlier or later point in time, we find that a very similar maximum accuracy can be reached in each case, occurring at a different number of overtones $N_{max}$. We provide new error estimates for the SXS waveforms based on the extrapolation and the resolution uncertainties of the gravitational wave strain. Finally, we observe substantial instabilities on the values of the best-fit amplitudes of the tones beyond the fundamental mode and the first overtone, that, nevertheless, do not impact significantly the mass and spin estimates.

Efficient simulations of high-spin black holes with a new gauge

We present a new choice of initial data for binary black hole simulations that significantly improves the efficiency of high-spin simulations. We use spherical Kerr-Schild coordinates, where the horizon of a rotating black hole is spherical, for each black hole. The superposed spherical Kerr-Schild initial data reduce the runtime by a factor of 2 compared to standard superposed Kerr-Schild for an intermediate resolution spin-0.99 binary-black-hole simulation. We also explore the possibility of delaying the transition from the initial data gauge to the evolution gauge, which produces an additional speed-up of 1.3.

Numerical evolution of the center of mass and angular momentum for binary black holes

The asymptotic approach derived by Kozameh-Quiroga provides a modern framework to obtain the evolution of global variables of isolated sources of gravitational radiation. We test the Kozameh-Quiroga formalism evolving the equations of motion for the center of mass, the intrinsic angular momentum, and several other global variables, for black hole binary coalescence. First, we evolve the equations of motion using 777 simulations from the RIT catalog of numerical data of ${\ensuremath{\psi}}_{4}$ [J. Healy and C. O. Lousto, Third RIT binary black hole simulations catalog, Phys. Rev. D 102, 104018 (2020).]. We then analyze the trajectory of the center of mass and compute the final state of other physical variables after the coalescence has taken place. Finally, we show that the results obtained from our equations of motion are consistent with those in the Rochester metadata.

Extending superposed harmonic initial data to higher spin

Numerical simulations of binary black holes are accompanied by an initial spurious burst of gravitational radiation (called `junk radiation') caused by a failure of the initial data to describe a snapshot of an inspiral that started at an infinite time in the past. A previous study showed that the superposed harmonic (SH) initial data gives rise to significantly smaller junk radiation. However, it is difficult to construct SH initial data for black holes with dimensionless spin $\chi\gtrsim0.7$. We here provide a class of spatial coordinate transformations that extend SH to higher spin. The new spatial coordinate system, which we refer to as superposed modified harmonic (SMH), is characterized by a continuous parameter -- Kerr-Schild and harmonic spatial coordinates are only two special cases of this new gauge. We compare SMH with the superposed Kerr-Schild (SKS) initial data by evolving several binary black hole systems with $\chi=0.8$ and $0.9$. We find that the new initial data still leads to less junk radiation and only small changes of black hole parameters (e.g. mass and spin). We also find that the volume-weighted constraint violations for the new initial data converge with resolution during the junk stage $(t\lesssim700M)$, which means there are fewer high-frequency components in waveforms at outer regions.

Orbital Evolution of Binary Black Holes in Active Galactic Nucleus Disks: A Disk Channel for Binary Black Hole Mergers?

Abstract We perform a series of high-resolution 2D hydrodynamical simulations of equal-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) accretion disks to study whether these binaries can be driven to merger by the surrounding gas. We find that the gravitational softening adopted for the BBH has a profound impact on this result. When the softening is less than 10% of the binary separation, we show that, in agreement with recent simulations of isolated equal-mass binaries, prograde BBHs expand in time rather than contract. Eventually, however, the binary separation becomes large enough that the tidal force of the central AGN disrupts them. Only when the softening is relatively large do we find that prograde BBHs harden. We determine through detailed analysis of the binary torque, that this dichotomy is due to a loss of spiral structure in the circum-single disks orbiting each black hole when the softening is a significant fraction of the binary separation. Properly resolving these spirals—both with high resolution and small softening—results in a significant source of binary angular momentum. Only for retrograde BBHs do we find consistent hardening, regardless of softening, as these BBHs lack the important spiral structure in their circum-single disks. This suggests that the gas-driven inspiral of retrograde binaries can produce a population of compact BBHs in the gravitational-wave-emitting regime in AGN disks, which may contribute a large fraction to the observed BBH mergers.

Application of the third RIT binary black hole simulations catalog to parameter estimation of gravitational-wave signals from the LIGO-Virgo O1 and O2 observational runs

Using exclusively the 777 full numerical waveforms of the third binary black hole RIT catalog, we reanalyze the ten black hole merger signals reported in LIGO/Virgo's O1/O2 observation runs. We obtain binary parameters, extrinsic parameters, and the remnant properties of these gravitational waves events which are consistent with, but not identical to, previously presented results. We have also analyzed three additional events (GW170121, GW170304, GW170727) reported by Venumadhav, Zackay, Roulet, Dai, and Zaldarriaga [Phys. Rev. D 101, 083030 (2020)] and found closely matching parameters. We finally assess the accuracy of our waveforms with convergence studies applied to O1/O2 events and found them adequate for current estimation of parameters.

Third RIT binary black hole simulations catalog

The third release of the RIT public catalog of numerical relativity black-hole-binary waveforms \url{http://ccrg.rit.edu/~RITCatalog} consists of 777 accurate simulations that include 300 precessing and 477 nonprecessing binary systems with mass ratios $q=m_1/m_2$ in the range $1/15\leq q\leq1$ and individual spins up to $s/m^2=0.95$. The catalog also provides initial parameters of the binary, trajectory information, peak radiation, and final remnant black hole properties. The waveforms are corrected for the center of mass drifting and are extrapolated to future null infinity. We successfully test this correction comparing with simulations of low radition content initial data. As an initial application of this waveform catalog we reanalyze all the peak radiation and remnant properties to find new, simple, correlations among them for practical astrophysical usage.

Exploring the Small Mass Ratio Binary Black Hole Merger via Zeno's Dichotomy Approach.

We perform a sequence of binary black hole simulations with increasingly small mass ratios, reaching to a 128:1 binary that displays 13 orbits before merger. Based on a detailed convergence study of the q=m_{1}/m_{2}=1/15 nonspinning case, we apply additional mesh refinement levels around the smaller hole horizon [30] to reach successively the q=1/32, q=1/64, and q=1/128 cases. Roughly a linear computational resources scaling with 1/q is observed on eight-nodes simulations. We compute the remnant properties of the merger: final mass, spin, and recoil velocity, finding precise consistency between horizon and radiation measures. We also compute the gravitational waveforms: their peak frequency, amplitude, and luminosity. We compare those values with predictions of the corresponding phenomenological formulas, reproducing the particle limit within 2%, and we then use the new results to improve their fitting coefficients.

Inside the final black hole: puncture and trapped surface dynamics

A popular approach in numerical simulations of black hole binaries is to model black holes as punctures in the fabric of spacetime. The location and the properties of the black hole punctures are tracked with apparent horizons, namely outermost marginally outer trapped surfaces (MOTSs). As the holes approach each other, a common apparent horizon suddenly appears, engulfing the two black holes and signaling the merger. The evolution of common apparent horizons and their connection with gravitational wave emission have been studied in detail with the framework of dynamical horizons. We present a study of the dynamics of the MOTSs and their punctures in the interior of the final black hole. The study focuses on head-on mergers for various initial separations and mass ratios. We find that MOTSs intersect for most of the parameter space. We show that for those situations in which they do not, it is because of the singularity avoidance property of the moving puncture gauge condition used in the study. Although we are unable to carry out evolutions that last long enough to show the ultimate fate of the punctures, our results suggest that MOTSs always intersect and that at late times their overlap is only partial. As a consequence, the punctures inside the MOTSs, although close enough to each other to act effectively as a single puncture, do not merge.