Formation Of Black Hole Binaries Research Articles

The Metallicity Dependence and Evolutionary Times of Merging Binary Black Holes: Combined Constraints from Individual Gravitational-wave Detections and the Stochastic Background

The advent of gravitational-wave astronomy is now allowing for the study of compact binary merger demographics throughout the Universe. This information can be leveraged as tools for understanding massive stars, their environments, and their evolution. One active question is the nature of compact binary formation: the environmental and chemical conditions required for black hole birth and the time delays experienced by binaries before they merge. Gravitational-wave events detected today, however, primarily occur at low or moderate redshifts due to current interferometer sensitivity, therefore limiting our ability to probe the high-redshift behavior of these quantities. In this work, we circumvent this limitation by using an additional source of information: observational limits on the gravitational-wave background from unresolved binaries in the distant Universe. Using current gravitational-wave data from the first three observing runs of LIGO–Virgo–KAGRA, we combine catalogs of directly detected binaries and limits on the stochastic background to constrain the time-delay distribution and metallicity dependence of binary black hole evolution. Looking to the future, we also explore how these constraints will be improved at the Advanced LIGO A+ sensitivity. We conclude that, although binary black hole formation cannot be strongly constrained with today’s data, the future detection (or a nondetection) of the gravitational-wave background with Advanced LIGO A+ will carry strong implications for the evolution of binary black holes.

Constraints on peculiar velocity distribution of binary black holes using gravitational waves with GWTC-3

Peculiar velocity encodes rich information about the formation, dynamics, evolution, and merging history of binary black holes. In this work, we employ a hierarchical Bayesian model to infer the peculiar velocity distribution of binary black holes. We use the data from GWTC-3 and assume a Maxwell-Boltzmann distribution for the peculiar velocities, but do not consider the dependence of peculiar velocity on the masses of black hole binaries. The constraint on the peculiar velocity distribution parameter, v 0, is weak and uninformative. However, the determination of peculiar velocity distribution can be significantly improved with next-generation ground-based gravitational wave detectors. For the Einstein Telescope, the relative uncertainty of v 0 will reduce to ∼ 10% using 103 golden binary black hole events. Our statistical approach thus provides a robust and prospective inference for determining the peculiar velocity distribution.

Space-based gravitational wave observatories will be able to use eccentricity to unveil stellar-mass binary black hole formation

Space-based gravitational wave observatories will be able to use eccentricity to unveil stellar-mass binary black hole formation

On the origin of outward migration of Population III stars

ABSTRACT Outward migration of massive binary stars or black holes in their circumbinary disc is often observed in simulations and it is key to the formation of wide black hole binaries. Using numerical simulations of Population III (Pop III) star formation, we study the angular momentum of Pop III binaries and the torques between stars and gas discs to understand the origin of outward migration and high ellipticity. The outward migration of protostars is produced by gravitational torques exerted on them by their circumstellar minidiscs. The minidiscs, on the other hand, migrate outward mainly by gaining angular momentum by accreting gas from the circumbinary disc. The angular momentum transfer is most efficient for rapidly accreting equal-mass binaries, and weaker when the secondary mass is small or the massive companion evaporates the gas disc via radiative feedback. We conclude that outward migration and the formation of wide equal-mass massive binaries is common in metal-free/metal-poor star formation, mainly driven by their large accretion rates. We expect that the lower gas temperature and accretion rates in metal-enriched circumstellar discs would lead more often to inward migration and closer binary separations. We also observe inward migration for smaller mass Pop III protostars/fragments, leading to the rapid merging of sink particles and likely the formation of close binary black holes that, however, reach separations below the resolution of our simulations. We discuss the implications that Pop III separations and ellipticity may have on the interpretation that gravitational wave signals from merging intermediate-mass black holes come from Pop III remnants.

Dynamical Friction Models for Black Hole Binary Formation in Active Galactic Nucleus Disks

Stellar-mass black holes (sBHs) embedded in gaseous disks of active galactic nuclei (AGN) can be important sources of detectable gravitational radiation for LIGO/Virgo when they form binaries and coalesce due to orbital decay. In this paper, we study the effect of dynamical friction (DF) on the formation of BH binaries in AGN disks using N-body simulations. We employ two simplified models of DF, with the force on the BH depending on Δ v , the velocity of the sBH relative to the background Keplerian gas. We integrate the motion of two sBHs initially on circular orbits around the central supermassive black hole (SMBH) and evaluate the probability of binary formation under various conditions. We find that both models of DF (with different dependence of the frictional coefficient on ∣Δ v ∣) can foster the formation of binaries when the effective friction timescale τ satisfies ΩK τ ≲ 20–30 (where ΩK is the Keplerian frequency around the SMBH): prograde binaries are formed when the DF is stronger (smaller τ), while retrograde binaries dominate when the DF is weaker (larger τ). We determine the distribution of both prograde and retrograde binaries as a function of initial orbital separation and the DF strength. Using our models of DF, we show that for a given sBH number density in the AGN disk, the formation rate of sBH binaries increases with decreasing τ and can reach a moderate value with a sufficiently strong DF.

Constraints on cosmologically coupled black holes from gravitational wave observations and minimal formation mass

ABSTRACT We test the possibility that the black holes (BHs) detected by LIGO-Virgo-KAGRA (LVK) may be cosmologically coupled and grow in mass proportionally to the cosmological scale factor to some power k, which may also act as the dark energy source if k ≈ 3. This approach was proposed as an extension of Kerr BHs embedded in cosmological backgrounds and possibly without singularities or horizons. In our analysis, we develop and apply two methods to test these cosmologically coupled BHs (CCBHs) either with or without connection to dark energy. We consider different scenarios for the time between the binary BH formation and its merger, and we find that the standard log-uniform distribution yields weaker constraints than the CCBH-corrected case. Assuming that the minimum mass of a BH with stellar progenitor is 2 M⊙, we estimate the probability that at least one BH among the observed ones had an initial mass below this threshold. We obtain these probabilities either directly from the observed data or by assuming the LVK power-law-plus-peak mass distribution. In the latter case, we find at 2σ level, that k < 2.1 for the standard log-uniform distribution, or k < 1.1 for the CCBH-corrected distribution. Slightly weaker bounds are obtained in the direct method. Considering the uncertainties on the nature of CCBHs, we also find that the required minimum CCBH mass value to eliminate the tensions for k = 3 should be lower than 0.5 M⊙ (again at 2σ). Finally, we show that future observations have the potential to decisively confirm these bounds.

Accelerated binary black holes in globular clusters: forecasts and detectability in the era of space-based gravitational-wave detectors

ABSTRACT The motion of the centre of mass of a coalescing binary black hole (BBH) in a gravitational potential, imprints a line-of-sight acceleration (LOSA) on to the emitted gravitational-wave (GW) signal. The acceleration could be sufficiently large in dense stellar environments, such as globular clusters (GCs), to be detectable with next-generation space-based detectors. In this work, we use outputs of the cluster monte carlo (cmc) simulations of dense star clusters to forecast the distribution of detectable LOSAs in DECIGO and LISA eras. We study the effect of cluster properties – metallicity, virial and galactocentric radii – on the distribution of detectable accelerations, account for cosmologically motivated distributions of cluster formation times, masses, and metallicities, and also incorporate the delay time between the formation of BBHs and their merger in our analysis. We find that larger metallicities provide a larger fraction of detectable accelerations by virtue of a greater abundance of relatively lighter BBHs, which allow a higher number of GW cycles in the detectable frequency band. Conversely, smaller metallicities result in fewer detections, most of which come from relatively more massive BBHs with fewer cycles but larger LOSAs. We similarly find correlations between the virial radii of the clusters and the fractions of detectable accelerations. Our work, therefore, provides an important science case for space-based GW detectors in the context of probing GC properties via the detection of LOSAs of merging BBHs.

Black hole binary mergers in dense star clusters: the importance of primordial binaries

Abstract Dense stellar clusters are expected to house the ideal conditions for binary black hole (BBH) formation, both through binary stellar evolution and through dynamical encounters. We use theoretical arguments as well as N-body simulations to make predictions for the evolution of BBHs formed through stellar evolution inside clusters from the cluster birth (which we term primordial binaries), and for the sub-population of merging BBHs. We identify three key populations: (i) BBHs that form in the cluster, and merge before experiencing any strong dynamical interaction; (ii) binaries that are ejected from the cluster after only one dynamical interaction; and, (iii) BBHs that experience more than one strong interaction inside the cluster. We find that population (i) and (ii) are the dominant source of all BBH mergers formed in clusters with escape velocity vesc ≤ 30 km s−1. At higher escape velocities, dynamics are predicted to play a major role both for the formation and subsequent evolution of BBHs. Finally, we argue that for sub-Solar metallicity clusters with vesc ≲ 100 km s−1, the dominant form of interaction experienced by primordial BBHs (BBHs formed from primordial binaries) within the cluster is with other BBHs. The complexity of these binary-binary interactions will complicate the future evolution of the BBH and influence the total number of mergers produced.

What’s in a binary black hole’s mass parameter?

ABSTRACT The black hole (BH) masses measured from gravitational wave observations appear to cluster around specific mass values. Consequently, the primary (and chirp) mass distribution of binary black holes (BBHs) inferred using these measurements shows four emerging peaks. These peaks are approximately located at a primary (chirp) mass value of 10 $\, \mathrm{M}_\odot$ (8$\, \mathrm{M}_\odot$), 20 $\, \mathrm{M}_\odot$ (14 $\, \mathrm{M}_\odot$), 35 $\, \mathrm{M}_\odot$ (28 $\, \mathrm{M}_\odot$), and 63 $\, \mathrm{M}_\odot$ (49 $\, \mathrm{M}_\odot$). Although the presence of the first and third peaks has been attributed to BBH formation in star clusters or due to the evolution of stellar binaries in isolation, the second peak has received relatively less attention because it lacks significance in the primary mass distribution. In this article, we report that confidence in the second peak depends on the mass parameter we choose to model the population on. Unlike primary mass, this peak is significant when modelled on the chirp mass. We discuss the disparity as a consequence of mass asymmetry in the observations that cluster at the second peak. Finally, we report this asymmetry as part of a potential trend in the mass ratio distribution manifested as a function of the chirp mass, but not as a function of primary mass, when we include the observation GW190814 in our modelling. The chirp mass is not a parameter of astrophysical relevance. Features present in the chirp mass, but not in the primary mass, are relatively difficult to explain and expected to garner significant interest.

Things That Might Go Bump in the Night: Assessing Structure in the Binary Black Hole Mass Spectrum

Several features in the mass spectrum of merging binary black holes (BBHs) have been identified using data from the Third Gravitational Wave Transient Catalog (GWTC-3). These features are of particular interest as they may encode the uncertain mechanism of BBH formation. We assess if the features are statistically significant or the result of Poisson noise due to the finite number of observed events. We simulate catalogs of BBHs whose underlying distribution does not have the features of interest, apply the analysis previously performed on GWTC-3, and determine how often such features are spuriously found. We find that one of the features found in GWTC-3, the peak at ∼35 M ☉, cannot be explained by Poisson noise alone: peaks as significant occur in 1.7% of catalogs generated from a featureless population. This peak is therefore likely to be of astrophysical origin. The data is suggestive of an additional significant peak at ∼10 M ☉, though the exact location of this feature is not resolvable with current observations. Additional structure beyond a power law, such as the purported dip at ∼14 M ☉, can be explained by Poisson noise. We also provide a publicly available package, GWMockCat, that creates simulated catalogs of BBH events with correlated measurement uncertainty and selection effects according to user-specified underlying distributions and detector sensitivities.

Light axion emission and the formation of merging binary black holes

Light axion emission and the formation of merging binary black holes

Black hole binary formation in AGN discs: from isolation to merger

ABSTRACT Motivated by the increasing number of detections of merging black holes by LIGO-VIRGO-KAGRA, black hole (BH) binary mergers in the discs of active galactic nuclei (AGNs) is investigated as a possible merger channel. In this pathway, BH encounters in the gas disc form mutually bound BH binary systems through interaction with the gas in the disc and subsequently inspiral through gravitational torques induced by the local gas. To determine the feasibility of this merger pathway, we present the first three-dimensional global hydrodynamic simulations of the formation and evolution of a stellar-mass BH binaries AGN discs with three different AGN disc masses and five different initial radial separations. These 15 simulations show binary capture of prograde and retrograde binaries can be successful in a range of disc densities including cases well below that of a standard radiatively efficient alpha disc, identifying that the majority of these captured binaries are then subsequently hardened by the surrounding gas. The eccentricity evolution depends strongly on the orbital rotation where prograde binaries are governed by gravitational torques form their circumbinary mini disc, with eccentricities being damped, while for retrograde binaries the eccentricities are excited to >∼ 0.9 by accretion torques. In two cases, retrograde binaries ultimately undergo a close periapsis passage which results in a merger via gravitational waves after only a few thousand binary orbits. Thus, the merger time-scale can be far shorter than the AGN disc lifetime. These simulations support an efficient AGN disc merger pathway for BHs.

Close encounters of black hole—star binaries with stellar-mass black holes

ABSTRACT Dynamical interactions involving binaries play a crucial role in the evolution of star clusters and galaxies. We continue our investigation of the hydrodynamics of three-body encounters, focusing on binary black hole (BBH) formation, stellar disruption, and electromagnetic (EM) emission in dynamical interactions between a BH-star binary and a stellar-mass BH, using the moving-mesh hydrodynamics code AREPO. This type of encounters can be divided into two classes depending on whether the final outcome includes BBHs. This outcome is primarily determined by which two objects meet at the first closest approach. BBHs are more likely to form when the star and the incoming BH encounter first with an impact parameter smaller than the binary’s semimajor axis. In this case, the star is frequently disrupted. On the other hand, when the two BHs encounter first, frequent consequences are an orbit perturbation of the original binary or a binary member exchange. For the parameters chosen in this study, BBH formation, accompanied by stellar disruption, happens in roughly one out of four encounters. The close correlation between BBH formation and stellar disruption has possible implications for EM counterparts at the binary’s merger. The BH that disrupts the star is promptly surrounded by an optically and geometrically thick disc with accretion rates exceeding the Eddington limit. If the debris disc cools fast enough to become long-lived, EM counterparts can be produced at the time of the BBH merger.

Inferring eccentricity evolution from observations of coalescing binary black holes

The origin and formation of stellar-mass binary black holes remains an open question that can be addressed by precise measurements of the binary and orbital parameters from their gravitational-wave signal. Such binaries are expected to circularize due to the emission of gravitational waves as they approach merger. However, depending on their formation channel, some binaries could have a non-negligible eccentricity when entering the frequency band of current gravitational-wave detectors. In order to measure eccentricity in an observed gravitational-wave signal, accurate waveform models that describe binaries in eccentric orbits are necessary. In this work we demonstrate the efficacy of the improved TEOBResumS waveform model for eccentric coalescing binaries with aligned spins. We first validate the model against mock signals of aligned-spin binary black hole mergers and quantify the impact of eccentricity on the estimation of other intrinsic binary parameters. We then perform a fully Bayesian reanalysis of GW150914 with the eccentric waveform model. We find (i) that the model is reliable for aligned-spin binary black holes and (ii) that GW150914 is consistent with a non-eccentric merger although we cannot rule out small values of initial eccentricity at a reference frequency of $20$ Hz. Finally, we present a systematic method to measure the eccentricity and its evolution directly from the gravitational-wave posterior samples. Such an estimator is useful when comparing results from different analyses as the definition of eccentricity may differ between models. Our scheme can be applied even in the case of small eccentricities and can be adopted straightforwardly in post-processing to allow for direct comparison between models.

Hydrodynamical Simulations of Black Hole Binary Formation in AGN Disks

We study close encounters between two single black holes (BHs) embedded in an AGN disk using a series of global 2D hydrodynamics simulations. We find that when the disk density is sufficiently high, bound BH binaries can be formed by the collision of their circum-single disks. Our analysis demonstrates that, after a BH pair passes the pericenter of their relative trajectory, post-collision gas drag may slow down the BHs, possibly forcing the two BHs to stay tightly bound. A binary formed by a close encounter can have a compact semimajor axis, large eccentricity, and retrograde orbital angular momentum. We provide a fitting formula that can accurately predict whether a close encounter can form a binary based on the gas mass and the incoming energy of the encounter. This fitting formula can be easily implemented in other long-term simulations that study the dynamical evolution of BHs in active galactic nucleus disks.

Isolated and dynamical black hole mergers withB-POP: the role of star formation and dynamics, star cluster evolution, natal kicks, mass and spins, and hierarchical mergers

ABSTRACTThe current interpretation of LIGO–Virgo–KAGRA data suggests that the primary mass function of merging binary black holes (BBHs) at redshift z ≲ 1 contains multiple structures, while spins are relatively low. Theoretical models of BBH formation in different environments can provide a key to interpreting the population of observed mergers, but they require the simultaneous treatment of stellar evolution and dynamics, galaxy evolution, and general relativity. We present B-POP, a population synthesis tool to model BBH mergers formed in the field or via dynamical interactions in young, globular, and nuclear clusters. Using B-POP, we explore how black hole (BH) formation channels, star cluster evolution, hierarchical mergers, and natal BH properties affect the population of BBH mergers. We find that the primary mass distribution of BBH mergers extends beyond $M_1 \simeq 200\, {}$ M⊙, and the effective spin parameter distribution hints at different natal spins for single and binary BHs. Observed BBHs can be interpreted as members of a mixed population comprised of $\sim 34{{\ \rm per\ cent}} \, {}(66{{\ \rm per\ cent}})$ isolated (dynamical) BBHs, with the latter likely dominating at redshift z > 1. Hierarchical mergers constitute the $4.6\!-\!7.9{{\ \rm per\ cent}}$ of all mergers in the reference model, dominating the primary mass distribution beyond $M_1 \gt 65\, {}$ M⊙. The inclusion of cluster mass-loss and expansion causes an abrupt decrease in the probability for mergers beyond the third generation to occur. Considering observational biases, we find that $2.7\!-\!7.5{{\ \rm per\ cent}}$ of mock mergers involve intermediate-mass black hole (IMBH) seeds formed via stellar collisions. Comparing this percentage to observed values will possibly help us to constrain IMBH formation mechanisms.

On the Jacobi capture origin of binaries with applications to the Earth-Moon system and black holes in galactic nuclei

ABSTRACT Close encounters between two bodies in a disc often result in a single orbital deflection. However, within their Jacobi volumes, where the gravitational forces between the two bodies and the central body become competitive, temporary captures with multiple close encounters become possible outcomes: a Jacobi capture. We perform three-body simulations in order to characterize the dynamics of Jacobi captures in the plane. We find that the phase space structure resembles a Cantor-like set with a fractal dimension of about 0.4. The lifetime distribution decreases exponentially, while the distribution of the closest separation follows a power law with index 0.5. In our first application, we consider the Jacobi capture of the Moon. We demonstrate that both tidal captures and giant impacts are possible outcomes. The impact speed is well approximated by a parabolic encounter, while the impact angles follow that of a uniform beam on a circular target. Jacobi captures at larger heliocentric distances are more likely to result in tidal captures. In our second application, we find that Jacobi captures with gravitational wave dissipation can result in the formation of binary black holes in galactic nuclei. The eccentricity distribution is approximately superthermal and includes both prograde and retrograde orientations. We conclude that dissipative Jacobi captures form an efficient channel for binary formation, which motivates further research into establishing the universality of Jacobi captures across multiple astrophysical scales.

Constraints on compact dark matter from lensing of gravitational waves for the third-generation gravitational wave detector

ABSTRACT Since the first gravitational wave (GW) event from binary black hole (BBH) was detected by LIGO-Virgo, GWs have become a useful probe on astrophysics and cosmology. If compact dark matter (DM) objects e.g. primordial black holes, contribute a significant fraction of DM at wide mass range, they will cause microlensing in the GW signals with long wavelengths that are distinct from the lensing effects of electromagnetic signals from astrophysical objects. In this paper, we apply the lensing effect of GW from BBH to derive constraints on the abundance of compact DM for the Cosmic Explorer, a third-generation ground-based GW detector. We first consider two channels of formation of BBH that contribute to low- and high-redshift GW sources, including the astrophysical origin BBH scenario, and the primordial origin BBH scenario. Secondly, comparing with the method of optical depth, we use the Bayesian analysis to derive constraints on the abundance of compact DM with different mass function of lens taken into consideration. For a null search with 1000 detected GW events of BBH, we find that the abundance of compact DM could be constrained to $\lesssim 0.1\,\mathrm{ per}\,\mathrm{ cent}$ in the mass range $\ge 500\, {\rm M}_{\odot }$ at 68 per cent confidence level. In addition, if a GW event lensed by a compact DM object with $M_{\rm l}\in [100\, {\rm M}_{\odot },300\, {\rm M}_{\odot }]$ is detected in 100 detected GW events of BBH, we can derive that the estimation of the abundance of compact DM is from $2.3$ to $25.2$ per cent in this mass range with the Bayesian analysis.

Toward a Precision Measurement of Binary Black Holes Formation Channels Using Gravitational Waves and Emission Lines

The formation of compact objects—neutron stars, black holes, and supermassive black holes—and their connection to the chemical composition of galaxies is one of the central questions in astrophysics. We propose a novel data-driven, multi-messenger technique to address this question by exploiting the inevitable correlation between gravitational waves and atomic/molecular emission-line signals. For a fiducial probability distribution function of time delays, this method can provide a measurement of the minimum delay time of 0.5 Gyr and a power-law index of κ = 1 with a standard deviation of 0.12 (and 0.45) and 0.06 (and 0.34), respectively, from five years of LIGO–Virgo–KAGRA observations in synergy with SPHEREx line intensity mapping (and DESI emission-line galaxies). Such measurements will provide data-driven, multi-messenger constraints on the delay time distribution which is currently not well known.

A Rosetta Stone for Eccentric Gravitational Waveform Models

Orbital eccentricity is a key signature of dynamical binary black hole formation. The gravitational waves from a coalescing binary contain information about its orbital eccentricity, which may be measured if the binary retains sufficient eccentricity near merger. Dedicated waveforms are required to measure eccentricity. Several models have been put forward, and show good agreement with numerical relativity at the level of a few percent or better. However, there are multiple ways to define eccentricity for inspiralling systems, and different models internally use different definitions of eccentricity, making it difficult to compare eccentricity measurements directly. In this work, we systematically compare two eccentric waveform models, SEOBNRE and TEOBResumS, by developing a framework to translate between different definitions of eccentricity. This mapping is constructed by minimizing the relative mismatch between the two models over eccentricity and reference frequency, before evolving the eccentricity of one model to the same reference frequency as the other model. We show that for a given value of eccentricity passed to SEOBNRE, one must input a 20%–50% smaller value of eccentricity to TEOBResumS in order to obtain a waveform with the same empirical eccentricity. We verify this mapping by repeating our analysis for eccentric numerical relativity simulations, demonstrating that TEOBResumS reports a correspondingly smaller value of eccentricity than SEOBNRE.