Measuring gravitational waves from binary black hole coalescences. I. Signal to noise for inspiral, merger, and ringdown

In the past few years, the detection of gravitational waves from compact binary coalescences with the Advanced LIGO and Advanced Virgo detectors has become routine. Future observatories will detect even larger numbers of gravitational-wave signals, which will also spend a longer time in the detectors' sensitive band. This will eventually lead to overlapping signals, especially in the case of Einstein Telescope (ET) and Cosmic Explorer (CE). Using realistic distributions for the merger rate as a function of redshift as well as for component masses in binary neutron star and binary black hole coalescences, we map out how often signal overlaps of various types will occur in an ET-CE network over the course of a year. We find that a binary neutron star signal will typically have tens of overlapping binary black hole and binary neutron star signals. Moreover, it will happen up to tens of thousands of times per year that two signals will have their end times within seconds of each other. In order to understand to what extent this would lead to measurement biases with current parameter estimation methodology, we perform injection studies with overlapping signals from binary black hole and/or binary neutron star coalescences. Varying the signal-to-noise ratios, the durations of overlap, and the kinds of overlapping signals, we find that in most scenarios the intrinsic parameters can be recovered with negligible bias. However, we find large offsets for a short binary black hole or a quieter binary neutron star signal overlapping with a long and louder binary neutron star event when the merger times are sufficiently close. Although based on a limited number of simulations, our studies may be an indicator of where improvements are required to ensure reliable estimation of source parameters for all detected compact binary signals as we go from second-generation to third-generation detectors.

We discuss the extraction of information from detected binary black hole (BBH) coalescence gravitational waves by the ground-based interferometers LIGO and VIRGO, and by the space-based interferometer LISA. We focus on the merger phase that occurs after the gradual inspiral and before the ringdown. Our results are (i) if numerical relativity simulations have not produced template merger waveforms before BBH events are detected, one can study the merger waves using simple band-pass filters. For BBHs smaller than about ${40M}_{\ensuremath{\bigodot}}$ detected via their inspiral waves, the band-pass filtering signal-to-noise ratio indicates that the merger waves should typically be just barely visible in the noise for initial and advanced LIGO interferometers. (ii) We derive an optimized maximum-likelihood method for extracting a best-fit merger waveform from the noisy detector output; one ``perpendicularly projects'' this output onto a function space (specified using wavelets) that incorporates our (possibly sketchy) prior knowledge of the waveforms. An extension of the method allows one to extract the BBH's two independent waveforms from outputs of several interferometers. (iii) We propose a computational strategy for numerical relativists to pursue, if they successfully produce computer codes for generating merger waveforms, but if running the codes is too expensive to permit an extensive survey of the merger parameter space. In this case, for LIGO-VIRGO data analysis purposes, it would be advantageous to do a coarse survey of the parameter space aimed at exploring several qualitative issues and at determining the ranges of the several key parameters which we describe. (iv) A complete set of templates could be used to test the nonlinear dynamics of general relativity and to measure some of the binary's parameters via matched filtering. We estimate the number of bits of information obtainable from the merger waves (about 10--60 for LIGO-VIRGO, up to 200 for LISA), estimate the information loss due to template numerical errors or sparseness in the template grid, and infer approximate requirements on template accuracy and spacing.

Waveform models are important to gravitational wave data analysis. People recently pay much attention to the waveform model construction for eccentric binary black hole (BBH) coalescence. Several effective-one-body (EOB) Numerical-Relativity waveform models of eccentric BBH coalescence have been constructed. But none of them can treat orbit eccentricity and spin-precessing simultaneously. The current paper focuses on this problem. The authors previously have constructed waveform model for spin-aligned eccentric BBH coalescence SEOBNRE. Here we extend such waveform model to describe eccentric spin-precessing BBH coalescence. We calculate the 2PN orbital radiation-reaction forces and the instantaneous part of the decomposed waveform for a general spinning precessing BBH system in EOB coordinates. We implement these results based on our previous SEOBNRE waveform model. We have also compared our model waveforms to both SXS and RIT numerical relativity waveforms. We find good consistency between our model and numerical relativity. Based on our new waveform model, we analyze the impact of the non-perpendicular spin contributions on waveform accuracy. We find that the non-perpendicular spin contributions primarily affect the phase of the gravitational waveforms. For the current gravitational wave detectors, this contribution is not significant. The future detectors may be affected by such non-perpendicular spin contributions. More importantly our SEOBNRE waveform model, as the first theoretical waveform model to describe eccentric spin-precessing BBH coalescence, can help people to analyze orbit eccentricity and spin precession simultaneously for gravitational wave detection data.

Massive black hole binaries (BHBs) are expected to form as the result of galaxy mergers; they shrink via dynamical friction and stellar scatterings, until gravitational waves (GWs) bring them to the final coalescence. It has been argued that BHBs may stall at a parsec scale and never enter the GW stage if stars are not continuously supplied to the BHB loss cone. Here we perform several N-body experiments to study the effect of an 80,000 solar masses stellar cluster (SC) infalling on a parsec-scale BHB. We explore different orbital elements for the SC and we perform runs both with and without accounting for the influence of a rigid stellar cusp (modelled as a rigid Dehnen potential). We find that the semi-major axis of the BHB shrinks by more than 10 per cent if the SC is on a nearly radial orbit; the shrinking is more efficient when a Dehnen potential is included and the orbital plane of the SC coincides with that of the BHB. In contrast, if the SC orbit has non-zero angular momentum, only a few stars enter the BHB loss cone and the resulting BHB shrinking is negligible. Our results indicate that SC disruption might significantly contribute to the shrinking of a parsec-scale BHB only if the SC approaches the BHB on a nearly radial orbit.

The coalescence of massive black hole (BH) binaries due to galaxy mergers provides a primary source of low-frequency gravitational radiation detectable by pulsar timing measurements and by the proposed the Laser Interferometry Space Antenna (LISA) observatory. We compute the expected gravitational radiation signal from sources at all redshifts by combining the predicted merger rate of galactic halos with recent measurements of the relation between BH mass, MBH, and the velocity dispersion of its host galaxy, ?. Our main findings are as follows: (1) the nHz frequency background is dominated by BH binaries at redshifts z 2, and existing limits from pulsar timing data place tight constraints on the allowed normalization and power-law slope of the MBH-? relation or on the fraction of BH binaries that proceed to coalescence; (2) more than half of all discrete mHz massive BH sources detectable by LISA are likely to originate at redshifts z 7; (3) the number of LISA sources per unit redshift per year should drop substantially after reionization as long as BH formation is triggered by gas cooling in galaxies. Studies of the highest redshift sources among the few hundred detectable events per year will provide unique information about the physics and history of black hole growth in galaxies.

Numerical relativity is an essential tool in studying the coalescence of binary black holes (BBHs). It is still computationally prohibitive to cover the BBH parameter space exhaustively, making phenomenological fitting formulas for BBH waveforms and final-state properties important for practical applications. We describe a general hierarchical bottom-up fitting methodology to design and calibrate fits to numerical relativity simulations for the three-dimensional parameter space of quasicircular nonprecessing merging BBHs, spanned by mass ratio and by the individual spin components orthogonal to the orbital plane. Particular attention is paid to incorporating the extreme-mass-ratio limit and to the subdominant unequal-spin effects. As an illustration of the method, we provide two applications, to the final spin and final mass (or equivalently: radiated energy) of the remnant black hole. Fitting to 427 numerical relativity simulations, we obtain results broadly consistent with previously published fits, but improving in overall accuracy and particularly in the approach to extremal limits and for unequal-spin configurations. We also discuss the importance of data quality studies when combining simulations from diverse sources, how detailed error budgets will be necessary for further improvements of these already highly accurate fits, and how this first detailed study of unequal-spin effects helps in choosing the most informative parameters for future numerical relativity runs.

Numerical relativity is central to the investigation of astrophysical sources in the dynamical and strong-field gravity regime, such as binary black hole and neutron star coalescences. Current challenges set by gravitational-wave and multimessenger astronomy call for highly performant and scalable codes on modern massively parallel architectures. We present GR-Athena++, a general-relativistic, high-order, vertex-centered solver that extends the oct-tree, adaptive mesh refinement capabilities of the astrophysical (radiation) magnetohydrodynamics code Athena++. To simulate dynamical spacetimes, GR-Athena++ uses the Z4c evolution scheme of numerical relativity coupled to the moving puncture gauge. We demonstrate stable and accurate binary black hole merger evolutions via extensive convergence testing, cross-code validation, and verification against state-of-the-art effective-one-body waveforms. GR-Athena++ leverages the task-based parallelism paradigm of Athena++ to achieve excellent scalability. We measure strong-scaling efficiencies above 95% for up to ∼1.2 × 104 CPUs and excellent weak scaling is shown up to ∼105 CPUs in a production binary black hole setup with adaptive mesh refinement. GR-Athena++ thus allows for the robust simulation of compact binary coalescences and offers a viable path toward numerical relativity at exascale.

Spectacular breakthroughs in numerical relativity now make it possible to compute spacetime dynamics in almost complete generality, allowing us to model the coalescence and merger of binary black holes with essentially no approximations. The primary limitation of these calculations is now computational. In particular, it is difficult to model systems with large mass ratio and large spins, since one must accurately resolve the multiple length scales that play a role in such systems. Perturbation theory can play an important role in extending the reach of computational modeling for binary systems. In this paper, we present first results of a code that allows us to model the gravitational waves generated by the inspiral, merger, and ringdown of a binary system in which one member of the binary is much more massive than the other. This allows us to accurately calibrate binary dynamics in the large mass ratio regime. We focus in this analysis on the recoil imparted to the merged remnant by these waves. We closely examine the ``antikick,'' an antiphase cancellation of the recoil arising from the plunge and ringdown waves, described in detail by Schnittman et al. We find that, for orbits aligned with the black hole spin, the antikick grows as a function of spin. The total recoil is smallest for prograde coalescence into a rapidly rotating black hole, and largest for retrograde coalescence. Amusingly, this completely reverses the predicted trend for kick versus spin from analyses that only include inspiral information.

If the activity of active galactic nuclei (AGNs) is predominantly induced by major galaxy mergers, then a significant fraction of AGNs should harbor binary massive black holes in their centers. We have studied the mass function of binary massive black holes in nearby AGNs based on the observed AGN black-hole mass function and the theory of evolution of binary massive black holes interacting with a massive circumbinary disk within the framework of the coevolution of massive black holes and their host galaxies. The circumbinary disk is assumed to be steady, axisymmetric, geometrically thin, self-regulated, self-gravitating but nonfragmenting with a fixed fraction of the Eddington accretion rate, which is typically one tenth of the Eddington value. The timescale of orbital decay is then estimated to be $\sim\ $10$^{8}\ $yr for equal mass black holes, being independent of the black-hole mass, semimajor axis, and viscosity parameter, but dependent on the black-hole mass ratio, Eddington ratio, and mass-to-energy conversion efficiency. This makes it possible for any binary massive black holes to merge within the Hubble time under the binary–disk interaction. We find that (1.5%$\ \pm\ $0.6%) of the total number of nearby AGNs for the equal-mass ratio and (1.3%$\ \pm\ $0.5%) for the one-to-ten mass ratio have close binary massive black holes with an orbital period of less than 10 yr in their centers, detectable with ongoing highly sensitive X-ray monitors, such as Monitor of All-sky X-ray Image and/or Swift/Burst Alert Telescope. Assuming that all binary massive black holes have the equal-mass ratio, about 10% of AGNs with black-hole masses of 10$^{6.5-7}\ M_{\odot}$ have close binaries, and thus provide the best chance to detect them.

We revisit the phases of the pairing and sinking of black holes (BHs) in galaxy mergers and circumnuclear discs in light of the results of recent simulations with massive BHs embedded in predominantly gaseous backgrounds. After a general overview we highlight for the first time the existence of a clear transition, for unequal mass BHs, between the regime in which the orbital decay is dominated by the conventional dynamical friction wake and one in which global disc torques associated with density waves launched by the secondary BH as well as co-orbital torques arising from gas gravitationally captured by the BH dominate and lead to faster decay. The new regime intervenes at BH binary separations of a few tens of parsecs and below, following a phase of orbital circularization driven dynamical friction. It bears some resemblance with planet migration in protoplanetary discs. While the orbital timescale is reasonably matched by the migration rate for the Type-I regime, the dominant negative torque arises near the co-rotation resonance, which is qualitatively similar to what is found in the so-called Type-III migration, the fastest migration regime identified so far for planets. This fast decay rate brings the BHs to separations of order 10−1 pc, the resolution limit of our simulations, in less than ∼107 yr in a smooth disc, while the decay timescale can increase to >108 yr in clumpy discs due to gravitational scattering with molecular clouds. Eventual gap opening at sub-pc scale separations will slow down the orbital decay subsequently. How fast the binary BH can reach the separation at which gravitational waves take over will be determined by the nature of the interaction with the circumbinary disc and the complex torques exerted the gas flowing through the edge of such disc, the subject of many recent studies. We also present a new intriguing connection between the conditions required for rapid orbital decay of massive BH binaries and those required for prominent gas inflows in gas-rich galaxies undergoing major mergers. We derive a condition for the maximum inflow rate that a circumnuclear disc can host while still maintaining a sufficiently high gas density at large radii to sustain the decay of a BH binary. We find that gas inflows rates exceeding 10 M⊙ yr−1, postulated to form massive BH seeds in some direct collapse models, would stifle the sinking of massive BH binaries in gas-dominated galactic nuclei. Vice-versa, lower inflow rates, below a solar mass per year, as required to feed typical active galactic nuclei (AGNs), are compatible with a fast orbital decay of BH binaries across a wide range of masses.

The Laser Interferometer Space Antenna (LISA) will be launched in the mid-2030s. It promises to observe the coalescence of massive black-hole (BH) binaries with signal-to-noise ratios (SNRs) reaching thousands. Crucially, it will detect some of these binaries with high SNR in both the inspiral and the merger-ringdown stages. Such signals are ideal for tests of general relativity (GR) using information from the whole waveform. Here, we consider astrophysically motivated binary systems at the high-mass end of the population observable by LISA and simulate their signals using the newly developed multipolar effective-one-body model: pSEOBNRv5HM. The merger-ringdown signal in this model depends on the binary properties (masses and spins) and also on parameters that describe fractional deviations from the GR quasinormal mode (complex) frequencies of the remnant BH. Performing full Bayesian analyses, we assess to which accuracy LISA will be able to constrain deviations from GR in the ringdown signal when using information from the whole signal. We find that these deviations can typically be constrained to within 10% and in the best cases to within 1%. We also show that with this model we can measure the binary masses and spins with great accuracy even for very massive BH systems with low SNR in the inspiral. In particular, individual source-frame masses can typically be constrained to within 10% and as precisely as 1%, and individual spins can typically be constrained to within 0.1 and, in the best cases, to within 0.001. We also probe the accuracy of the SEOBNRv5HM waveform family by performing synthetic injections of GR numerical-relativity waveforms. Using a novel method that we develop here to quantify the impact of systematic errors, we show that, already for sources with SNR O(100), we would measure erroneous deviations from GR due to waveform model inaccuracies. One of the main sources of error is the mismodeling of the relative alignment between harmonics. These results confirm the need for improving waveform models to perform tests of GR with binary BHs observed at high SNR by LISA. Published by the American Physical Society 2024

Gravitational wave (GW) detections of binary black hole (BH) mergers have begun to sample the cosmic BH mass distribution. The evolution of single stellar cores predicts a gap in the BH mass distribution due to pair-instability supernova (PISN). Determining the upper and lower edges of the BH mass gap can be useful for interpreting GW detections from merging BHs. We use \MESA\ to evolve single, non-rotating, massive helium cores with a metallicity of $Z = 10^{-5}$ until they either collapse to form a BH or explode as a PISN without leaving a compact remnant. We calculate the boundaries of the lower BH mass gap for S-factors in the range S(300 keV) = (77,203) keV b, corresponding to the $\pm 3\sigma$ uncertainty in our high resolution tabulated $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction rate probability distribution function. We extensively test the temporal and mass resolution to resolve the theoretical peak of the BH mass spectrum across the BH mass gap. We explore the convergence with respect to convective mixing and nuclear burning, finding that significant time resolution is needed to achieve convergence. We also test adopting a minimum diffusion coefficient to help lower resolution models reach convergence. We establish a new lower edge of the upper mass gap as M\textsubscript{lower} $\simeq$\,60$^{+32}_{-14}$\,\Msun\ from the $\pm 3\sigma$ uncertainty in the $^{12}\text{C}(\alpha, \gamma) ^{16}\text{O}$ rate. We explore the effect of a larger 3-$\alpha$ rate on the lower edge of the upper mass gap, finding M\textsubscript{lower} $\simeq$\,69$^{+34}_{-18}$\,\Msun. We compare our results with BHs reported in the Gravitational-Wave Transient Catalog.

Gravitational-wave (GW) detections of binary black hole (BH) mergers have begun to sample the cosmic BH mass distribution. The evolution of single stellar cores predicts a gap in the BH mass distribution due to pair-instability supernovae (PISNe). Determining the upper and lower edges of the BH mass gap can be useful for interpreting GW detections of merging BHs. We use MESA to evolve single, nonrotating, massive helium cores with a metallicity of Z = 10−5, until they either collapse to form a BH or explode as a PISN, without leaving a compact remnant. We calculate the boundaries of the lower BH mass gap for S-factors in the range S(300 keV) = (77,203) keV b, corresponding to the ±3σ uncertainty in our high-resolution tabulated 12C(α,γ)16O reaction rate probability distribution function. We extensively test temporal and spatial resolutions for resolving the theoretical peak of the BH mass spectrum across the BH mass gap. We explore the convergence with respect to convective mixing and nuclear burning, finding that significant time resolution is needed to achieve convergence. We also test adopting a minimum diffusion coefficient to help lower-resolution models reach convergence. We establish a new lower edge of the upper mass gap as M lower ≃ M ⊙ from the ±3σ uncertainty in the 12C(α, γ)16O rate. We explore the effect of a larger 3α rate on the lower edge of the upper mass gap, finding M lower ≃ M ⊙. We compare our results with BHs reported in the Gravitational-Wave Transient Catalog.

GW231123, the most massive binary black hole (BH) merger observed to date, involves component BHs with masses inside the pair-instability mass gap and unusually high spins. This challenges standard formation channels such as classical stellar evolution and hierarchical mergers. However, stellar rotation and magnetic fields, which have not been systematically incorporated in prior models, can strongly influence the BH properties. We present the first self-consistent simulations tracking a massive, low-metallicity helium star from helium core burning through collapse, BH formation, and post-BH formation accretion using 3D general-relativistic magnetohydrodynamic simulations. Starting from a 250 M ⊙ helium core, we show that collapse above the pair-instability mass gap, aided by rotation and magnetic fields, drives mass loss through disk winds and jet launching. This enables the formation of highly spinning BHs within the mass gap and reveals a BH spin–mass correlation. Strong magnetic fields extract angular momentum from the BH through magnetically driven outflows, which in turn suppress accretion, resulting in slowly spinning BHs within the mass gap. In contrast, stars with weak fields permit nearly complete collapse and spin-up of the BH to a ≈ 1. We show that massive low-metallicity stars with moderate magnetic fields naturally produce BHs whose masses and spins match those inferred for GW231123, and are also consistent with those of GW190521. The outflows launched during collapse may impart a BH kick, which can induce spin–orbit misalignment and widen the postcollapse orbit, delaying the merger. These outflows could further drive short-lived, high-luminosity jets comparable to the most energetic γ -ray bursts, offering a potential observational signature of such events in the early Universe.

ABSTRA C T Since many or most galaxies have central massive black holes (BHs), mergers of galaxies can form massive binary black holes (BBHs). In this paper we study the evolution of massive BBHs in realistic galaxy models, using a generalization of techniques used to study tidal disruption rates around massive BHs. The evolution of BBHs depends on BH mass ratio and host galaxy type. BBHs with very low mass ratios (say, &0.001) are hardly ever formed by mergers of galaxies, because the dynamical friction time-scale is too long for the smaller BH to sink into the galactic centre within a Hubble time. BBHs with moderate mass ratios are most likely to form and survive in spherical or nearly spherical galaxies and in highluminosity or high-dispersion galaxies; they are most likely to have merged in low-dispersion galaxies (line-of-sight velocity dispersion &90 km s 21 ) or in highly flattened or triaxial galaxies. The semimajor axes and orbital periods of surviving BBHs are generally in the range 10 23 ‐ 10 pc and 10 ‐ 10 5 yr; they are also larger in high-dispersion galaxies than in lowdispersion galaxies, larger in nearly spherical galaxies than in highly flattened or triaxial galaxies, and larger for BBHs with equal masses than for BBHs with unequal masses. The orbital velocities of surviving BBHs are generally in the range 10 2 ‐1 0 4 km s 21 . The methods of detecting surviving BBHs are also discussed. If no evidence of BBHs is found in AGNs, this may be either because gas plays a major role in BBH orbital decay or because nuclear activity switches on soon after a galaxy merger, and ends before the smaller BH has had time to spiral to the centre of the galaxy.