Nonspinning Black-hole Binaries Research Articles

Impact of Higher Harmonics of Gravitational Radiation on the Population Inference of Binary Black Holes

Templates modeling just the dominant mode of gravitational radiation are generally sufficient for the unbiased parameter inference of near-equal-mass compact binary mergers. However, neglecting the subdominant modes can bias the inference if the binary is significantly asymmetric, very massive, or has misaligned spins. In this work, we explore if neglecting these subdominant modes in the parameter estimation of nonspinning binary black hole mergers can bias the inference of their population-level properties such as mass and merger redshift distributions. Assuming the design sensitivity of the advanced LIGO-Virgo detector network, we find that neglecting subdominant modes will not cause a significant bias in the population inference, although including them will provide more precise estimates. This is primarily because asymmetric binaries are expected to be rarer in our detected sample, due to their intrinsic rareness and the observational selection effects. The increased precision in the measurement of the maximum black hole mass can help in better constraining the upper mass gap in the mass spectrum.

Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter

We investigate the correction to the potential that gives rise to the bound orbits and radiation from non-spinning inspiralling binary black holes in a dark matter environment consisting of axion-like particles and dark photons using the techniques of Worldline Effective Field Theory. We compute the conservative dynamics up to 1PN order for gravitational, electromagnetic, and Proca fields and up to 2PN order for the scalar field. The effect of axion-electromagnetic coupling (gaγγ) arises to the conservative dynamics at 2.5PN order and the kinetic mixing constant (γ) at 1PN order. Furthermore, we calculate the radiation due to the various fields present in our theory. We find that the contribution of gaγγ to the gravitational radiation appears at N(7)LO and to the scalar radiation appears at N(5)LO. We also find that these radiative corrections due to the coupling gaγγ vanishes for any orbit confined to a plane because of the existence of a binormal like term in effective radiative action but give rise to non-zero contributions for any orbit that lies in three dimensions. Last but not the least, γ contributes to the gravitational radiation at N(2)LO and N(4)LO.

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.

Strong-field scattering of two black holes: Numerical relativity meets post-Minkowskian gravity

We compare numerical relativity (NR) data on the scattering of equal-mass, nonspinning binary black holes to various analytical predictions based on post-Minkowskian (PM) results. While the usual sequence of PM-expanded scattering angles shows a rather poor convergence towards NR data, we find that a reformulation of PM information in terms of effective-one-body radial potentials leads to remarkable agreement with NR data, especially when using the radiation-reacted 4PM information. Using Firsov's inversion formula we directly extract, for the first time, from NR simulations a (radiation-reacted) gravitational potential describing the scattering of equal-mass, nonspinning binary black holes. We urge the NR community to compute more sequences of scattering simulations, so as to extend this knowledge to a wider region of parameter space.

Eccentric binary black holes: Comparing numerical relativity and small mass-ratio perturbation theory

The modeling of unequal mass binary black hole systems is of high importance to detect and estimate parameters from these systems. Numerical relativity (NR) is well suited to study systems with comparable component masses, ${m}_{1}\ensuremath{\sim}{m}_{2}$, whereas small mass ratio (SMR) perturbation theory applies to binaries where $q={m}_{2}/{m}_{1}\ensuremath{\ll}1$. This work investigates the applicability for NR and SMR as a function of mass ratio for eccentric nonspinning binary black holes. We produce 52 NR simulations with mass ratios between $1:10$ and $1:1$ and initial eccentricities up to 0.8. From these we extract quantities like gravitational wave energy and angular momentum fluxes and periastron advance, and assess their accuracy. To facilitate comparison, we develop tools to map between NR and SMR inspiral evolutions of eccentric binary black holes. We derive post-Newtonian accurate relations between different definitions of eccentricity. Based on these analyses, we introduce a new definition of eccentricity based on the (2,2)-mode of the gravitational radiation, which reduces to the Newtonian definition of eccentricity in the Newtonian limit. From the comparison between NR simulations and SMR results, we quantify the unknown next-to-leading order SMR contributions to the gravitational energy and angular momentum fluxes, and periastron advance. We show that in the comparable mass regime these contributions are subdominant and higher order SMR contributions are negligible.

Surrogate model for gravitational wave signals from nonspinning, comparable-to large-mass-ratio black hole binaries built on black hole perturbation theory waveforms calibrated to numerical relativity

We present a reduced-order surrogate model of gravitational waveforms from non-spinning binary black hole systems with comparable to large mass-ratio configurations. This surrogate model, \texttt{BHPTNRSur1dq1e4}, is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) with mass ratios varying from 2.5 to 10,000. \texttt{BHPTNRSur1dq1e4} extends an earlier waveform model, \texttt{EMRISur1dq1e4}, by using an updated transition-to-plunge model, covering longer durations up to 30,500 $m_1$ (where $m_1$ is the mass of the primary black hole), includes several more spherical harmonic modes up to $\ell=10$, and calibrates subdominant modes to numerical relativity (NR) data. In the comparable mass-ratio regime, including mass ratios as low as $2.5$, the gravitational waveforms generated through ppBHPT agree surprisingly well with those from NR after this simple calibration step. We also compare our model to recent SXS and RIT NR simulations at mass ratios ranging from $15$ to $32$, and find the dominant quadrupolar modes agree to better than $\approx 10^{-3}$. We expect our model to be useful to study intermediate-mass-ratio binary systems in current and future gravitational-wave detectors.

Comparing second-order gravitational self-force, numerical relativity, and effective one body waveforms from inspiralling, quasicircular, and nonspinning black hole binaries

We present the first systematic comparison between gravitational waveforms emitted by inspiralling, quasi-circular and nonspinning black hole binaries computed with three different approaches: second-order gravitational self-force (2GSF) theory, as implemented in the 1PAT1 model; numerical relativity (NR), as implemented by the SXS collaboration; and the effective one body (EOB) formalism, as implemented in the TEOBResumS waveform model. To compare the models we use both a standard, time-domain waveform alignment and a gauge-invariant analysis based on the dimensionless function $Q_\omega(\omega)\equiv \omega^2/\dot{\omega}$, where $\omega$ is the gravitational wave frequency. We analyse the domain of validity of the 1PAT1 model, deriving error estimates and showing that the effects of the final transition to plunge, which the model neglects, extend over a significantly larger frequency interval than one might expect. Restricting to the inspiral regime, we find that, while for mass ratios $q = m_1/m_2\le 10$ TEOBResumS is largely indistinguishable from NR, 1PAT1 has a significant dephasing $\gtrsim 1$rad; conversely, for $q\gtrsim 100$, 1PAT1 is estimated to have phase errors $<0.1$rad on a large frequency interval, while TEOBResumS develops phase differences $\gtrsim1$rad with it. Most crucially, on that same large frequency interval we find good agreement between TEOBResumS and 1PAT1 in the intermediate regime $15\lesssim q\lesssim 64$, with $<0.5$rad dephasing between them. A simple modification to the TEOBResumS flux further improves this agreement for $q\gtrsim 30$, reducing the dephasing to $\approx0.27$rad even at $q=128$. Our results pave the way for the construction of GSF-informed EOB models for both intermediate and extreme mass ratio inspirals for the next generation of gravitational wave detectors.

Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasicircular and nonspinning black hole binaries. II. The large-mass-ratio case

We compare recently computed waveforms from second-order gravitational self-force (GSF) theory to those generated by a new, GSF-informed, effective one body (EOB) waveform model for (spin-aligned, eccentric) inspiralling black hole binaries with large mass ratios. We focus on quasi-circular, nonspinning, configurations and perform detailed GSF/EOB waveform phasing comparisons, either in the time domain or via the gauge-invariant dimensionless function $Q_\omega\equiv \omega^2/\dot{\omega}$, where $\omega$ is the gravitational wave frequency. The inclusion of high-PN test-mass terms within the EOB radiation reaction (notably, up to 22PN) is crucial to achieve an EOB/GSF phasing agreement below 1~rad up to the end of the inspiral for mass ratios up to 500. For larger mass ratios, up to $5\times 10^4$, the contribution of horizon absorption becomes more and more important and needs to be accurately modeled. Our results indicate that our GSF-informed EOB waveform model is a promising tool to describe waveforms generated by either intermediate or extreme mass ratio inspirals for future gravitational wave detectors

Electromagnetic Signatures from Supermassive Binary Black Holes Approaching Merger

Abstract We present fully relativistic predictions for the electromagnetic emission produced by accretion disks surrounding spinning and nonspinning supermassive binary black holes on the verge of merging. We use the code Bothros to post-process data from 3D general relativistic magnetohydrodynamic simulations via ray-tracing calculations. These simulations model the dynamics of a circumbinary disk and the mini-disks that form around two equal-mass black holes orbiting each other at an initial separation of 20 gravitational radii, and evolve the system for more than 10 orbits in the inspiral regime. We model the emission as the sum of thermal blackbody radiation emitted by an optically thick accretion disk and a power-law spectrum extending to hard X-rays emitted by a hot optically thin corona. We generate time-dependent spectra, images, and light curves at various frequencies to investigate intrinsic periodic signals in the emission, as well as the effects of the black hole spin. We find that prograde black hole spin makes mini-disks brighter since the smaller innermost stable circular orbit angular momentum demands more dissipation before matter plunges to the horizon. However, compared to mini-disks in larger separation binaries with spinning black holes, our mini-disks are less luminous: unlike those systems, their mass accretion rate is lower than in the circumbinary disk, and they radiate with lower efficiency because their inflow times are shorter. Compared to a single black hole system matched in mass and accretion rate, these binaries have spectra noticeably weaker and softer in the UV. Finally, we discuss the implications of our findings for the potential observability of these systems.

Training strategies for deep learning gravitational-wave searches

Compact binary systems emit gravitational radiation which is potentially detectable by current Earth bound detectors. Extracting these signals from the instruments' background noise is a complex problem and the computational cost of most current searches depends on the complexity of the source model. Deep learning may be capable of finding signals where current algorithms hit computational limits. Here we restrict our analysis to signals from non-spinning binary black holes and systematically test different strategies by which training data is presented to the networks. To assess the impact of the training strategies, we re-analyze the first published networks and directly compare them to an equivalent matched-filter search. We find that the deep learning algorithms can generalize low signal-to-noise ratio (SNR) signals to high SNR ones but not vice versa. As such, it is not beneficial to provide high SNR signals during training, and fastest convergence is achieved when low SNR samples are provided early on. During testing we found that the networks are sometimes unable to recover any signals when a false alarm probability $<10^{-3}$ is required. We resolve this restriction by applying a modification we call unbounded Softmax replacement (USR) after training. With this alteration we find that the machine learning search retains $\geq 91.5\%$ of the sensitivity of the matched-filter search down to a false-alarm rate of 1 per month.

From one to many: A deep learning coincident gravitational-wave search

Gravitational waves from the coalescence of compact-binary sources are now routinely observed by Earth bound detectors. The most sensitive search algorithms convolve many different pre-calculated gravitational waveforms with the detector data and look for coincident matches between different detectors. Machine learning is being explored as an alternative approach to building a search algorithm that has the prospect to reduce computational costs and target more complex signals. In this work we construct a two-detector search for gravitational waves from binary black hole mergers using neural networks trained on non-spinning binary black hole data from a single detector. The network is applied to the data from both observatories independently and we check for events coincident in time between the two. This enables the efficient analysis of large quantities of background data by time-shifting the independent detector data. We find that while for a single detector the network retains $91.5\%$ of the sensitivity matched filtering can achieve, this number drops to $83.9\%$ for two observatories. To enable the network to check for signal consistency in the detectors, we then construct a set of simple networks that operate directly on data from both detectors. We find that none of these simple two-detector networks are capable of improving the sensitivity over applying networks individually to the data from the detectors and searching for time coincidences.

Rapid identification of strongly lensed gravitational-wave events with machine learning

A small fraction of the gravitational-wave (GW) signals that will be detected by second and third generation detectors are expected to be strongly lensed by galaxies and clusters, producing multiple observable copies. While optimal Bayesian model selection methods are developed to identify lensed signals, processing tens of thousands (billions) of possible pairs of events detected with second (third) generation detectors is both computationally intensive and time consuming. To mitigate this problem, we propose to use machine learning to rapidly rule out a vast majority of candidate lensed pairs. As a proof of principle, we simulate non-spinning binary black hole events added to Gaussian noise, and train the machine on their time-frequency maps (Q-transforms) and localisation skymaps (using Bayestar), both of which can be generated in seconds. We show that the trained machine is able to accurately identify lensed pairs with efficiencies comparable to existing Bayesian methods.

Deep learning model on gravitational waveforms in merging and ringdown phases of binary black hole coalescences

The waveform templates of the matched filtering-based gravitational-wave search ought to cover wide range of parameters for the prosperous detection. Numerical relativity (NR) has been widely accepted as the most accurate method for modeling the waveforms. Still, it is well-known that NR typically requires a tremendous amount of computational costs. In this paper, we demonstrate a proof-of-concept of a novel deterministic deep learning (DL) architecture that can generate gravitational waveforms from the merger and ringdown phases of the non-spinning binary black hole coalescence. Our model takes ${\cal O}$(1) seconds for generating approximately $1500$ waveforms with a 99.9\% match on average to one of the state-of-the-art waveform approximants, the effective-one-body. We also perform matched filtering with the DL-waveforms and find that the waveforms can recover the event time of the injected gravitational-wave signals.

Gravitational waves from binary black hole mergers surrounded by scalar field clouds: Numerical simulations and observational implications

We show how gravitational-wave observations of binary black hole (BBH) mergers can constrain the physical characteristics of a scalar field cloud parameterized by mass $\tilde{\mu}$ and strength $\phi_0$ that may surround them. We numerically study the inspiraling equal-mass, non-spinning BBH systems dressed in such clouds, focusing especially on the gravitational-wave signals emitted by their merger-ringdown phase. These waveforms clearly reveal that larger values of $\tilde{\mu}$ or $\phi_0$ cause bigger changes in the amplitude and frequency of the scalar-field-BBH ringdown signals. We show that the numerical waveforms of scalar-field-BBHs can be modelled as chirping sine-Gaussians, with matches in excess of 95%. This observation enables one to employ computationally expensive Bayesian studies for estimating the parameters of such binaries. Using our chirping sine-Gaussian signal model we establish that observations of BBH mergers at a distance of 450 Mpc will allow to distinguish BBHs without any scalar field from those with a field strength $\phi_0 \gtrsim 5.5\times 10^{-3}$, at any fixed value of $\tilde \mu \in [0.3,0.8]$, with 90% confidence or better, in single detectors with Advanced LIGO/Virgo type sensitivities. This provides hope for the possibility of determining or constraining the mass of ultra-light bosons with gravitational-wave observations of BBH mergers.

Fusing numerical relativity and deep learning to detect higher-order multipole waveforms from eccentric binary black hole mergers

We determine the mass-ratio, eccentricity and binary inclination angles that maximize the contribution of the higher-order waveform multipoles $(\ell, \, |m|)= \{(2,\,2),\, (2,\,1),\, (3,\,3),\, (3,\,2), \, (3,\,1),\, (4,\,4),\, (4,\,3),\, (4,\,2),\,(4,\,1)\}$ for the gravitational wave detection of eccentric binary black hole mergers. We carry out this study using numerical relativity waveforms that describe non-spinning black hole binaries with mass-ratios $1\leq q \leq 10$, and orbital eccentricities as high as $e_0=0.18$ fifteen cycles before merger. For stellar-mass, asymmetric mass-ratio, binary black hole mergers, and assuming LIGO's Zero Detuned High Power configuration, we find that in regions of parameter space where black hole mergers modeled with $\ell=|m|=2$ waveforms have vanishing signal-to-noise ratios, the inclusion of $(\ell, \, |m|)$ modes enables the observation of these sources with signal-to-noise ratios that range between 30\% to 45\% the signal-to-noise ratio of optimally oriented binary black hole mergers modeled with $\ell=|m|=2$ numerical relativity waveforms. Having determined the parameter space where $(\ell, \, |m|)$ modes are important for gravitational wave detection, we construct waveform signals that describe these astrophysically motivate scenarios, and demonstrate that these topologically complex signals can be detected and characterized in real LIGO noise with deep learning algorithms.

Including mode mixing in a higher-multipole model for gravitational waveforms from nonspinning black-hole binaries

As gravitational-wave (GW) observations of binary black holes are becoming a precision tool for physics and astronomy, several subdominant effects in the GW signals need to be accurately modeled. Previous studies have shown that neglecting subdominant modes in the GW templates causes an unacceptable loss in detection efficiency and large systematic errors in the estimated parameters for binaries with large mass ratios. Our recent work [Mehta et al., Phys. Rev. D 96, 124010 (2017)] constructed a phenomenological gravitational waveform family for nonspinning black-hole binaries that includes subdominant spherical harmonic modes $(\ensuremath{\ell}=2,m=\ifmmode\pm\else\textpm\fi{}1)$, $(\ensuremath{\ell}=3,m=\ifmmode\pm\else\textpm\fi{}3)$, and $(\ensuremath{\ell}=4,m=\ifmmode\pm\else\textpm\fi{}4)$ in addition to the dominant quadrupole mode, $(\ensuremath{\ell}=2,m=\ifmmode\pm\else\textpm\fi{}2)$. In this article, we construct analytical models for the ($\ensuremath{\ell}=3,m=\ifmmode\pm\else\textpm\fi{}2$) and ($\ensuremath{\ell}=4,m=\ifmmode\pm\else\textpm\fi{}3$) modes and include them in the existing waveform family. Accurate modeling of these modes is complicated by the mixing of multiple spheroidal harmonic modes. We develop a method for accurately modeling the effect of mode mixing, thus producing an analytical waveform family that has faithfulness greater than 99.6%.

Black holes and binary mergers in scalar Gauss-Bonnet gravity: Scalar field dynamics

We study the nonlinear dynamics of black holes that carry scalar hair and binaries composed of such black holes. The scalar hair is due to a linear or exponential coupling between the scalar and the Gauss--Bonnet invariant. We work perturbatively in the coupling constant of that interaction but nonperturbatively in the fields. We first consider the dynamical formation of hair for isolated black holes of arbitrary spin and determine the final state. This also allows us to compute for the first time the scalar quasinormal modes of rotating black holes in the presence of this coupling. We then study the evolution of nonspinning black-hole binaries with various mass ratios and produce the first scalar waveform for a coalescence. An estimate of the energy loss in scalar radiation and the effect this has on orbital dynamics and the phase of the GWs (entering at quadratic order in the coupling) show that GW detections can set the most stringent constraint to date on theories that exhibit a coupling between a scalar field and the Gauss--Bonnet invariant.

Eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory

We present a prescription for computing gravitational waveforms for the inspiral, merger and ringdown of non-spinning eccentric binary black hole systems. The inspiral waveform is computed using the post-Newtonian expansion and the merger waveform is computed by interpolating a small number of quasi-circular NR waveforms. The use of circular merger waveforms is possible because eccentric binaries circularize in the last few cycles before the merger, which we demonstrate up to mass ratio $q = m_1/m_2 = 3$. The complete model is calibrated to 23 numerical relativity (NR) simulations starting ~20 cycles before the merger with eccentricities $e_\text{ref} \le 0.08$ and mass ratios $q \le 3$, where $e_\text{ref}$ is the eccentricity ~7 cycles before the merger. The NR waveforms are long enough that they start above 30 Hz (10 Hz) for BBH systems with total mass $M \ge 80 M_\odot$ ($230 M_\odot$). We find that, for the sensitivity of advanced LIGO at the time of its first observing run, the eccentric model has a faithfulness with NR of over 97% for systems with total mass $M \ge 85 M_\odot$ across the parameter space ($e_\text{ref} \le 0.08, q \le 3$). For systems with total mass $M \ge 70 M_\odot$, the faithfulness is over 97% for $e_\text{ref} \lesssim 0.05$ and $q \le 3$. The NR waveforms and the Mathematica code for the model are publicly available.

Orbit classification in an equal-mass non-spinning binary black hole pseudo-Newtonian system

The dynamics of a test particle in a non-spinning binary black hole system of equal masses is numerically investigated. The binary system is modeled in the context of the pseudo-Newtonian circular restricted three-body problem, such that the primaries are separated by a fixed distance and move in a circular orbit around each other. In particular, the Paczy\'{n}ski-Wiita potential is used for describing the gravitational field of the two non-Newtonian primaries. The orbital properties of the test particle are determined through the classification of the initial conditions of the orbits, using several values of the Jacobi constant, in the Hill's regions of possible motion. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) displaying close encounters. Using the smaller alignment index (SALI) chaos indicator, we further classify bounded orbits into regular, sticky or chaotic. To gain a complete view of the dynamics of the system, we define grids of initial conditions on different types of two-dimensional planes. The orbital structure of the configuration plane, along with the corresponding distributions of the escape and collision/close encounter times, allow us to observe the transition from the classical Newtonian to the pseudo-Newtonian regime. Our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant as well as with the Schwarzschild radius of the black holes.

Shadows of Bonnor black dihole by chaotic lensing

We have studied numerically the shadows of Bonnor black dihole through the technique of backward ray-tracing. The presence of magnetic dipole yields non-integrable photon motion, which affects sharply the shadow of the compact object. Our results show that there exists a critical value for the shadow. As the magnetic dipole parameter is less than the critical value, the shadow is a black disk, but as the magnetic dipole parameter is larger than the critical one, the shadow becomes a concave disk with eyebrows possessing a self-similar fractal structure. These behavior are very similar to those of the equal-mass and non-spinning Majumdar-Papapetrou binary black holes. However, we find that the two larger shadows and the smaller eyebrow-like shadows are joined together by the middle black zone for the Bonnor black dihole, which is different from that in the Majumdar-Papapetrou binary black holes spacetime where they are disconnected. With the increase of magnetic dipole parameter, the middle black zone connecting the main shadows and the eyebrow-like shadows becomes narrow. Our result show that the spacetime properties arising from the magnetic dipole yields the interesting patterns for the shadow casted by Bonnor black dihole.