Evolution 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.

Impact of gas hardening on the population properties of hierarchical black hole mergers in active galactic nucleus disks

Hierarchical black hole (BH) mergers in active galactic nuclei (AGNs) are unique among formation channels of binary black holes (BBHs) because they are likely associated with electromagnetic counterparts and can efficiently lead to the mass growth of BHs. Here, we explore the impact of gas accretion and migration traps on the evolution of BBHs in AGNs. We have developed a new fast semi-analytic model, that allows us to explore the parameter space while capturing the main physical processes involved. We find that an effective exchange of energy and angular momentum between the BBH and the surrounding gas (i.e., gas hardening) during inspiral greatly enhances the efficiency of hierarchical mergers, leading to the formation of intermediate-mass BHs (up to 104 M⊙) and triggering spin alignment. Moreover, our models with efficient gas hardening show both an anticorrelation between the BBH mass ratio and the effective spin and a correlation between the primary BH mass and the effective spin. In contrast, if gas hardening is inefficient, the hierarchical merger chain is already truncated after the first two or three generations. We compare the BBH population in AGNs with other dynamical channels as well as isolated binary evolution.

Hydrodynamical evolution of black hole binaries embedded in AGN discs: II. dependence on equation of state, binary mass, and separation scales

ABSTRACT Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) discs offer a promising dynamical channel to produce black hole mergers that are detectable by LIGO/Virgo. Modelling the interactions between the disc gas and the embedded BBHs is crucial to understand their orbital evolution. Using a suite of 2D high-resolution simulations of prograde equal-mass circular binaries in local disc models, we systematically study how their hydrodynamical evolution depends on the equation of state (EOS; including the γ-law and isothermal EOS) and on the binary mass and separation scales (relative to the supermassive black hole mass and the Hill radius, respectively). We find that binaries accrete slower and contract in orbit if the EOS is far from isothermal such that the surrounding gas is diffuse, hot, and turbulent. The typical orbital decay rate is of the order of a few times the mass doubling rate. For a fixed EOS, the accretion flows are denser, hotter, and more turbulent around more massive or tighter binaries. The torque associated with accretion is often comparable to the gravitational torque, so both torques are essential in determining the long-term binary orbital evolution. We carry out additional simulations with non-accreting binaries and find that their orbital evolution can be stochastic and is sensitive to the gravitational softening length, and the secular orbital evolution can be very different from those of accreting binaries. Our results indicate that stellar-mass BBHs may be hardened efficiently under ideal conditions, namely less massive and wider binaries embedded in discs with a non-isothermal EOS.

The Hydrodynamic Evolution of Binary Black Holes Embedded within the Vertically Stratified Disks of Active Galactic Nuclei

Stellar-mass black holes can become embedded within the disks of active galactic nuclei (AGNs). Afterwards, their interactions are mediated by their gaseous surroundings. Here, we study the evolution of stellar-mass binary black holes (BBHs) embedded within AGN disks using three-dimensional hydrodynamic simulations and analytic methods, focusing on environments where the AGN disk scale height H is ≳ the BBH sphere of influence. We model the local surroundings of the embedded BBHs using a wind tunnel formalism and characterize different accretion regimes based on the local properties of the disk. We develop prescriptions for accretion and drag for embedded BBHs. Using these prescriptions with AGN disk models that can represent the Toomre-unstable outer regions of AGN disks, we study the long-term evolution of BBHs as they migrate through the disk. We find that BBHs typically merge within ≲1–30 Myr, increasing their mass significantly in the process, allowing BBHs to enter (or cross) the pair-instability supernova mass gap. The BBH accretion rate often exceeds the Eddington limit, sometimes by several orders of magnitude. Many embedded BBHs will merge before migrating significantly in the disk. We also discuss possible electromagnetic signatures during and following the inspiral, finding that it is generally unlikely for the bolometric luminosity of the BBH to exceed the AGN luminosity.

Binary orbital evolution driven by a circumbinary disc

The question whether the interaction of a circumbinary disc with the central binary system leads to a shrinking or to an expansion of the binary orbit has attracted considerable interest as it impacts the evolution of binary black holes and stellar binary stars in their formation phase. We performed two-dimensional hydrodynamical simulations of circumbinary discs for a large parameter set of disc viscosities and thicknesses and for two different binary mass ratios for binaries on circular orbits. We measured the net angular momentum and mass transfer between disc and binary system, and evaluated the normalised specific angular momentum accretion, js. This was compared to the theoretical, critical specific angular momentum change js,crit that separates contracting from expanding cases, which depends on the binary mass ratio and on the relative accretion onto the two stars. Using finite and infinite disc models, we show that the inferred binary evolution is very similar for both setups, and we confirm that js can be measured accurately with cylindrical simulations that do not include the central binary. However, to obtain the relative accretion onto the stars for non-equal mass binaries, simulations that cover the whole domain including the binary are required. We find that for thick discs with aspect ratio h = 0.1, the binaries expand for all viscosities, while discs with h = 0.05 lead to an expansion only for higher viscosities with α exceeding ∼0.005. Overall, the regime of binary expansion extends to a much wider parameter space than previously anticipated, but for thin, low-viscosity discs, the orbits shrink.

Resolving Massive Black Hole Binary Evolution via Adaptive Particle Splitting

Abstract The study of the interaction of a massive black hole binary with its gaseous environment is crucial in order to be able to predict merger rates and possible electromagnetic counterparts of gravitational-wave signals. The evolution of the binary semimajor axis resulting from this interaction has been recently debated, and a clear consensus is still missing because of several numerical limitations, i.e., fixed orbit binaries or lack of resolution inside the cavity carved by the binary in its circumbinary disk. Using on-the-fly particle splitting in the 3D meshless code gizmo, we achieve hyper-Lagrangian resolution, which allows us to properly resolve the dynamics inside the cavity—in particular, for the first time, the disks that form around the two components of a live binary surrounded by a locally isothermal gaseous circumbinary disk. We show that the binary orbit decays with time for very cold and very warm disks and that the result of the interaction in the intermediate regime is strongly influenced by the disk viscosity, as this essentially regulates the fraction of mass contained in the disks around the binary components, as well as the fraction that is accreted by the binary. We find the balance between these two quantities to determine whether the binary semimajor axis decreases with time.

Model systematics in time domain tests of binary black hole evolution

We perform several consistency tests between different phases of binary black hole dynamics; the inspiral, the merger, and the ringdown on the gravitational wave events GW150914 and GW170814. These tests are performed explicitly in the time domain, without any spectral leakage between the different phases. We compute posterior distributions on the mass and spin of the initial black holes and the final black hole. We also compute the initial areas of the two individual black holes and the final area from the parameters describing the remnant black hole. This facilitates a test of Hawking's black hole area theorem. We use different waveform models to quantify systematic waveform uncertainties for the area increase law with the two events. We find that these errors may lead to overstating the confidence with which the area theorem is confirmed. For example, we find $>99\%$ agreement with the area theorem for GW150914 if a damped sinusoid consisting of a single-mode is used at merger to estimate the final area. This is because this model overestimates the final mass. Including an overtone of the dominant mode decreases the confidence to $\sim94\%$; using a full merger-ringdown model further decreases the confidence to $\sim 85-90\%$. We find that comparing the measured change in the area to the expected change in area yields a more robust test, as it also captures over estimates in the change of area. We find good agreement with GR when applying this test to GW150914 and GW170814.

The cosmic evolution of binary black holes in young, globular, and nuclear star clusters: rates, masses, spins, and mixing fractions

ABSTRACT The growing population of binary black holes (BBHs) observed by gravitational wave (GW) detectors is a potential Rosetta stone for understanding their formation channels. Here, we use an upgraded version of our semi-analytical codes fastcluster and cosmo$\mathcal {R}$ate to investigate the cosmic evolution of four different BBH populations: isolated BBHs and dynamically formed BBHs in nuclear star clusters (NSCs), globular clusters (GCs), and young star clusters (YSCs). With our approach, we can study different channels assuming the same stellar and binary input physics. We find that the merger rate density of BBHs in GCs and NSCs is barely affected by stellar metallicity (Z), while the rate of isolated BBHs changes wildly with Z. BBHs in YSCs behave in an intermediate way between isolated and GC/NSC BBHs. The local merger rate density of Nth-generation black holes (BHs), obtained by summing up hierarchical mergers in GCs, NSCs, and YSCs, ranges from ∼1 to ∼4 Gpc−3 yr−1 and is mostly sensitive to the spin parameter. We find that the mass function of primary BHs evolves with redshift in GCs and NSCs, becoming more top-heavy at higher z. In contrast, the primary BH mass function almost does not change with redshift in YSCs and in the field. This signature of the BH mass function has relevant implications for Einstein Telescope and Cosmic Explorer. Finally, our analysis suggests that multiple channels contribute to the BBH population of the second GW transient catalogue.

Adapted gauge to small mass ratio binary black hole evolutions

We explore the benefits of adapted gauges to small mass ratio binary black hole evolutions in the moving puncture formulation. We find expressions that approximate the late time behavior of the lapse and shift, $({\ensuremath{\alpha}}_{0},{\ensuremath{\beta}}_{0})$, and use them as initial values for their evolutions. We also use a position and black hole mass dependent damping term, $\ensuremath{\eta}[{\stackrel{\ensuremath{\rightarrow}}{x}}_{1}(t),{\stackrel{\ensuremath{\rightarrow}}{x}}_{2}(t),{m}_{1},{m}_{2}]$, in the shift evolution, rather than a constant or conformal-factor dependent choice. We have found that this substantially reduces noise generation at the start of the numerical integration and keeps the numerical grid stable around both black holes, allowing for more accuracy with lower resolutions. We test our choices for this gauge in detail in a case study of a binary with a $7\ensuremath{\mathbin:}1$ mass ratio, and then use $15\ensuremath{\mathbin:}1$ and $32\ensuremath{\mathbin:}1$ binaries for a convergence study. Finally, we apply our new gauge to a $64\ensuremath{\mathbin:}1$ binary and a $128\ensuremath{\mathbin:}1$ binary to well cover the comparable and small mass ratio regimes.

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.

On the orbital evolution of binaries with circumbinary discs

Circumbinary discs are generally thought to take up angular momentum and energy from the binary orbit over time through gravitational torques that are mediated by orbital resonances. This process leads to the shrinkage of the binary orbit over time, and it is important in a variety of astrophysical contexts including the orbital evolution of stellar binaries, the migration of planets in protoplanetary discs, and the evolution of black hole binaries (stellar and supermassive). The merger of compact object binaries provides a source of gravitational waves in the Universe. Recently, several groups have reported numerical simulations of circumbinary discs that yield the opposite result, finding that the binary expands with time. Here we argue that this result is primarily due to the choice of simulation parameters, made for numerical reasons, which differ from realistic disc parameters in many cases. We provide physical arguments, and then demonstrate with 3D hydrodynamical simulations, that thick (high pressure, high viscosity) discs drive sufficient accretion of high angular momentum material to force binary expansion, while in the more realistic case of thin (low pressure, low viscosity) discs there is less accretion and the binary shrinks. In the latter case, tides, which generally transfer angular momentum and energy from the more rapidly rotating object (the binary) to the less rapidly rotating object (the disc), are the dominant driver of disc-binary evolution. This causes the binary to shrink. We therefore conclude that for common circumbinary disc parameters, binaries with non-extreme mass ratios are expected to shrink over time. Expansion of the binary can occur if the disc viscosity is unusually high, which may occur in the very thick discs encountered in, for example, circumplanetary discs, super-Eddington AGN, or the outer regions of passive protostellar discs that are heated by the central protostar. We also provide discussion of the impact that some simplifications to the problem, that are prevalent in the literature and usually made for numerical convenience, have on the disc-binary evolution.

Supermassive binary black hole evolution can be traced by a small SKA pulsar timing array

Supermassive black holes are commonly found in the center of galaxies and evolve with their hosts. The supermassive binary black holes (SMBBH) are thus expected to exist in close galaxy pairs, however, none has been unequivocally detected. The square kilometre array (SKA) is a multi-purpose radio telescope with a collecting area approaching 1 million square metres, with great potential for detecting nanohertz gravitational waves (GWs). In this paper, we quantify the GW detectability by SKA for a realistic SMBBH population using pulsar timing array (PTA) technique and quantify its impact on revealing SMBBH evolution with redshift for the first time. With only $\sim20$ pulsars, much smaller a requirement than in previous work, the SKA PTA is expected to obtain detection within about 5 years of operation and to achieve a detection rate of more than 100 SMBBHs/yr after about 10 years. Although beyond the scope of this paper, we must acknowledge that the presence of persistent red noise will reduce the number of expected detections here. It is thus imperative to understand and mitigate red noise in the PTA data. The GW signatures from a few well-known SMBBH candidates, such as OJ 287, 3C 66B, NGC 5548 and Ark 120, will be detected given the currently best-known parameters of each system. Within 30 years of operation, about 60 individual SMBBHs detection with $z<0.05$ and more than $10^4$ with $z<1$ are expected. The detection rate drops precipitately beyond $z=1$. The substantial number of expected detections and their discernible evolution with redshift by SKA PTA will make SKA a significant tool for studying SMBBHs.

Evolution of binary black holes in AGN accretion discs: Disc-binary interaction and gravitational wave emission

Binary black hole (BBH) mergers are the primary sources of gravitational wave (GW) events detected by LIGO/Virgo. Binary black holes embedded in the accretion discs of active galactic nuclei (AGN) are possible candidates for such GW events. We have developed an idealised analytic model for the orbital evolution of BBHs in AGN accretion discs by combining the evolution equations of disc-binary interaction and GW inspiral. We investigated the coupled “disc+GW”-driven evolution of BBHs transitioning from the disc-driven regime at large orbital separations into the GW-driven regime at small separations. In this evolution channel, BBH mergers are accelerated by a combination of orbital decay and orbital eccentricity growth in the disc-dominated regime. We provide a quantification of the resulting merger timescale τmerger, and analyse its dependence on both the accretion disc and binary orbital parameters. By computing the evolution of the orbital eccentricity as a function of the GW frequency, we predict that most binaries in AGN discs should have significant residual eccentricities (e ∼ 0.01 − 0.1), potentially detectable by LISA. We further discuss the potentials and caveats of this particular BBH-in-AGN channel in the framework of binary evolutionary paths.

What GW170729's Exceptional Mass and Spin Tells Us about Its Family Tree

Gravitational-wave observations give a unique insight into the formation and evolution of binary black holes. We use gravitational-wave measurements to address the question of whether GW170729's source, which is (probably) the most massive binary and the system with the highest effective inspiral spin, could contain a black hole which is a previous merger remnant. Using the inferred mass and spin of the system, and the empirically determined population of binary black holes, we compute the evidence for the binary being second-generation compared with first-generation. We find moderate evidence (a Bayes factor of ~6-7) that the mass and spin better match a second-generation merger, but folding in the expectation that only a small fraction of mergers are second-generation, we conclude that there is no strong evidence that GW170729 was the result of a second-generation merger. The results are sensitive to the assumed mass distribution, and future detections will provide more robust reconstructions of the binary black hole population.

The Star Clusters That Make Black Hole Binaries across Cosmic Time

Abstract We explore the properties of dense star clusters that are likely to be nurseries of stellar black holes pairing in close binaries. We combine a cosmological model of globular cluster formation with analytic prescriptions for the dynamical assembly and evolution of black hole binaries (BHBs) to constrain which types of clusters are most likely to form binaries tight enough to coalesce within a Hubble time. We find that BHBs that are ejected and later merge ex situ form in clusters of a characteristic mass , whereas binaries that merge in situ form in more massive clusters, . The clusters that dominate the production of BHBs are similar in age and metallicity to the entire population. Finally, we estimate an approximate cosmic black hole merger rate of dynamically assembled binaries using the mean black hole mass for each cluster, given its metallicity. We find an intrinsic rate of at z = 0, a weakly increasing merger rate out to z = 1.5, and then a decrease out to z = 4. Our results can be used to provide a cosmological context and choose initial conditions in numerical studies of BHBs assembled in star clusters.

Merging black hole binaries with the SEVN code

Studying the formation and evolution of black hole binaries (BHBs) is essential for the interpretation of current and forthcoming gravitational wave (GW) detections. We investigate the statistics of BHBs that form from isolated binaries, by means of a new version of the SEVN population-synthesis code. SEVN integrates stellar evolution by interpolation over a grid of stellar evolution tracks. We upgraded SEVN to include binary stellar evolution processes and we used it to evolve a sample of $1.5\times{}10^8$ binary systems, with metallicity in the range $\left[10^{-4};4\times 10^{-2}\right]$. From our simulations, we find that the mass distribution of black holes (BHs) in double compact-object binaries is remarkably similar to the one obtained considering only single stellar evolution. The maximum BH mass we obtain is $\sim 30$, $45$ and $55\, \mathrm{M}_\odot$ at metallicity $Z=2\times 10^{-2}$, $6\times 10^{-3}$, and $10^{-4}$, respectively. A few massive single BHs may also form ($\lesssim 0.1\%$ of the total number of BHs), with mass up to $\sim 65$, $90$ and $145\, \mathrm{M}_\odot$ at $Z=2\times 10^{-2}$, $6\times 10^{-3}$, and $10^{-4}$, respectively. These BHs fall in the mass gap predicted from pair-instability supernovae. We also show that the most massive BHBs are unlikely to merge within a Hubble time. In our simulations, merging BHs like GW151226 and GW170608, form at all metallicities, the high-mass systems (like GW150914, GW170814 and GW170104) originate from metal poor ($Z\lesssim{}6\times 10^{-3}$) progenitors, whereas GW170729-like systems are hard to form, even at $Z = 10^{-4}$. The BHB merger rate in the local Universe obtained from our simulations is $\sim 90 \mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$, consistent with the rate inferred from LIGO-Virgo data.

A flat-spectrum candidate for a track-type high-energy neutrino emission event, the case of blazar PKS 0723−008

Abstract By cross-correlating both the Parkes Catalogue and the Second Planck Catalogue of Compact Sources with the arrival direction of the track-type neutrinos detected by the IceCube Neutrino Observatory, we find the flat-spectrum blazar PKS 0723−008 as a good candidate for the high-energy neutrino event 5 (ID5). Apart from its coordinates matching those of ID5, PKS 0723−008 exhibits further interesting radio properties. Its spectrum is flat up to high Planck frequencies, and it produced a fivefold-increased radio flux density through the last decade. Based upon these radio properties we propose a scenario of binary black hole evolution leading to the observed high-energy neutrino emission. The main contributing events are the spin-flip of the dominant black hole, the formation of a new jet with significant particle acceleration and interaction with the surrounding material, with the corresponding increased radio flux. Doppler boosting from the underlying jet pointing to the Earth makes it possible to identify the origin of the neutrinos, so the merger itself is the form of an extended flat-spectrum radio emission, a key selection criterion to find traces of this complex process.

Improvements to the construction of binary black hole initial data

Construction of binary black hole initial data is a prerequisite for numerical evolutions of binary black holes. This paper reports improvements to the binary black hole initial data solver in the spectral Einstein code, to allow robust construction of initial data for mass-ratio above 10:1, and for dimensionless black hole spins above 0.9, while improving efficiency for lower mass-ratios and spins. We implement a more flexible domain decomposition, adaptive mesh refinement and an updated method for choosing free parameters. We also introduce a new method to control and eliminate residual linear momentum in initial data for precessing systems, and demonstrate that it eliminates gravitational mode mixing during the evolution. Finally, the new code is applied to construct initial data for hyperbolic scattering and for binaries with very small separation.

Astrophysical constraints on massive black hole binary evolution from pulsar timing arrays

Abstract We consider the information that can be derived about massive black hole binary (MBHB) populations and their formation history solely from current and possible future pulsar timing array (PTA) results. We use models of the stochastic gravitational-wave background from circular MBHBs with chirp mass in the range 106–1011 M⊙ evolving solely due to radiation reaction. Our parametrized models for the black hole merger history make only weak assumptions about the properties of the black holes merging over cosmic time. We show that current PTA results place an upper limit on the black hole merger density which does not depend on the choice of a particular merger history model; however, they provide no information about the redshift or mass distribution. We show that even in the case of a detection resulting from a factor of 10 increase in amplitude sensitivity, PTAs will only put weak constraints on the source merger density as a function of mass, and will not provide any additional information on the redshift distribution. Without additional assumptions or information from other observations, a detection cannot meaningfully bound the massive black hole merger rate above zero for any particular mass.

Solving the Hamiltonian constraint for1+logtrumpets

The puncture method specifies black hole data on a hypersurface with the aid of a conformal rescaling of the metric that exhibits a coordinate singularity at the puncture point. When constructing puncture initial data by solving the Hamiltonian constraint for the conformal factor, the coordinate singularity requires special attention. The standard way to treat the pole singularity occurring in wormhole puncture data is not generally applicable to trumpet puncture data. We investigate a new approach based on inverse powers of the conformal factor and present numerical examples for single punctures of the wormhole and 1+log-trumpet type. Additionally, we describe a method to solve the Hamiltonian constraint for two 1+log trumpets for a given extrinsic curvature with non-vanishing trace. We investigate properties of this constructed initial data during binary black hole evolutions and find that the initial gauge dynamics is reduced.