Formation Of Compact 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.

Compact Binary Formation in Open Star Clusters II: Difficulty of Gaia NS formation in low-mass star clusters

Gaia mission offers opportunities to search for compact binaries not involved in binary interactions (hereafter inert compact binaries), and results in the discoveries of binaries containing one black hole (BH) or one neutron star (NS), called “Gaia BHs’’ and”Gaia NSs’’, respectively. We have assessed if Gaia BHs and NSs can be formed in open clusters through dynamical interactions. In order to obtain a large number of inert compact binaries similar to Gaia BHs and NSs, we have performed gravitational N-body simulations for a large number of open clusters whose total mass is 1.2×108M⊙. These clusters have various masses, metallicities, densities, and binary fractions. We have found that open clusters form Gaia BHs ( 10−6- 10−5M⊙−1) much more efficiently than Gaia NSs ( ≲10−7M⊙−1) for any cluster parameters. This is quite inconsistent with observational results, because the reported numbers of Gaia BHs and NSs are 3 and 21, respectively. Additionally, we have switched off NS natal kicks for 104 open clusters each weighing 103M⊙ in order to retain a large number of NSs in open clusters. Then, open clusters form inert NS binaries originating from primordial binaries rather than formed through dynamical interactions. This means that Gaia NSs are formed dominantly on isolated fields, not in open clusters, if there is no NS natal kick. We have concluded that Gaia BHs can be dominantly formed in open clusters, however Gaia NSs cannot.

Expansion of Accreting Main-sequence Stars during Rapid Mass Transfer

Accreting main-sequence stars expand significantly when the mass accretion timescale is much shorter than their thermal timescales. This occurs during mass transfer from an evolved giant star onto a main-sequence companion in a binary system and is an important phase in the formation of compact binaries including X-ray binaries, cataclysmic variables, and gravitational-wave sources. In this study, we compute 1D stellar models of main-sequence accretors with different initial masses and accretion rates. The calculations are used to derive semianalytical approximations to the maximum expansion radius. We assume that mass transfer remains fully conservative as long as the inflated accretor fits within its Roche lobe, leading stars to behave like hamsters, stuffing excess material behind their expanding cheeks. We suggest a physically motivated prescription for the mass growth of such “hamstars,” which can be used to determine mass-transfer efficiency in rapid binary population synthesis models. With this prescription, we estimate that progenitors of high-mass X-ray binaries and gravitational-wave sources may have experienced highly nonconservative mass transfer. In contrast, for low-mass accretors, the accretion timescale can exceed the thermal timescale by a larger factor without causing significant radial expansion.

Compact binary formation in open star clusters – I. High formation efficiency of Gaia BHs and their multiplicities

ABSTRACT Gaia BHs, black hole (BH) binaries discovered from data base of an astrometric telescope Gaia, pose a question to the standard binary evolution model. We have assessed whether Gaia BHs can be formed through dynamical capture in open clusters rather than through isolated binary evolution. We have performed gravitational N-body simulations of 100 open clusters with $10^5 \, \mathrm{M}_\odot$ in total for each metallicity Z = 0.02, 0.01, and 0.005. We have discovered one Gaia BH-like binary escaping from an open cluster, and found that the formation efficiency of Gaia BHs in open clusters ($\sim 10^{-5} \, \mathrm{M}_\odot ^{-1}$) is larger than in isolated binaries ($\sim 10^{-8} \, \mathrm{M}_\odot ^{-1}$) by 3 orders of magnitude. The Gaia BH-like binary is the inner binary of a triple star system. Gaia BHs can have tertiary stars frequently, if they are formed in open clusters. Combining additional N-body simulations with 8000 open clusters with $8 \times 10^6 \, \mathrm{M}_\odot$, we have estimated the number of Gaia BHs in the Milky Way disc to 104–105 (depending on the definitions of Gaia BHs), large enough for the number of Gaia BHs discovered so far. Our results indicate that the discoveries of Gaia BHs do not request the reconstruction of the standard binary evolution model, and that Gaia BHs are a probe for the dynamics of open clusters already evaporated.

Born to Be Wide: The Distribution of Wide Binaries in the Field and Soft Binaries in Clusters

Most stars, binaries, and higher-multiplicity systems are thought to form in stellar clusters and associations that later dissociate. Very wide binaries can be easily disrupted in clusters due to dynamical evaporation (soft binaries) and/or tidal disruption by the gravitational potential of the cluster. Nevertheless, wide binaries are quite frequent in the field, where they can sometimes play a key role in the formation of compact binaries and serve as tools to study key physical processes. Here we use analytic tools to study the dynamical formation of soft binaries in clusters and their survival as field binaries following cluster dispersion. We derive the expected properties of very wide binaries both in clusters and in the field. We analytically derive their detailed distributions, including the wide binary fraction as a function of mass in different cluster environments, binary mass functions and mass ratios, and the distribution of their orbital properties. We show that our calculations agree well in most aspects with the results of N-body simulations but show some different binary fraction dependence on the cluster mass. We find that the overall fraction of wide binaries scales as , where N ⋆ is the size of the cluster, even for non-equal-mass stars. More massive stars are more likely to capture wide companions, with most stars above 5 M ⊙ likely to capture at least one stellar companion, and formation of triples is found to be frequent.

One to many: comparing single gravitational-wave events to astrophysical populations

ABSTRACT Gravitational-wave observations have revealed sources whose unusual properties challenge our understanding of compact-binary formation. Inferring the formation processes that are best able to reproduce such events may therefore yield key astrophysical insights. A common approach is to count the fraction of synthetic events from a simulated population that are consistent with some real event. Though appealing owing to its simplicity, this approach is flawed because it neglects the full posterior information, depends on an ad hoc region that defines consistency, and fails for high signal-to-noise detections. We point out that a statistically consistent solution is to compute the posterior odds between two simulated populations, which crucially is a relative measure, and show how to include the effect of observational biases by conditioning on source detectability. Applying the approach to several gravitational-wave events and simulated populations, we assess the degree to which we can conclude model preference not just between distinct formation pathways but also between subpopulations within a given pathway.

An interconnect-free micro-electromechanical 7-bit arithmetic device for multi-operand programmable computing

Computational power density and interconnection between transistors have grown to be the dominant challenges for the continued scaling of complementary metal–oxide–semiconductor (CMOS) technology due to limited integration density and computing power. Herein, we designed a novel, hardware-efficient, interconnect-free microelectromechanical 7:3 compressor using three microbeam resonators. Each resonator is configured with seven equal-weighted inputs and multiple driven frequencies, thus defining the transformation rules for transmitting resonance frequency to binary outputs, performing summation operations, and displaying outputs in compact binary format. The device achieves low power consumption and excellent switching reliability even after 3 × 103 repeated cycles. These performance improvements, including enhanced computational power capacity and hardware efficiency, are paramount for moderately downscaling devices. Finally, our proposed paradigm shift for circuit design provides an attractive alternative to traditional electronic digital computing and paves the way for multioperand programmable computing based on electromechanical systems.

Eccentricity or spin precession? Distinguishing subdominant effects in gravitational-wave data

ABSTRACT Eccentricity and spin precession are key observables in gravitational-wave astronomy, encoding precious information about the astrophysical formation of compact binaries together with fine details of the relativistic two-body problem. However, the two effects can mimic each other in the emitted signals, raising issues around their distinguishability. Since inferring the existence of both eccentricity and spin precession simultaneously is – at present – not possible, current state-of-the-art analyses assume that either one of the effects may be present in the data. In such a setup, what are the conditions required for a confident identification of either effect? We present simulated parameter inference studies in realistic LIGO/Virgo noise, studying events consistent with either spin precessing or eccentric binary black hole coalescences and recovering under the assumption that either of the two effects may be at play. We quantify how the distinguishability of eccentricity and spin precession increases with the number of visible orbital cycles, confirming that the signal must be sufficiently long for the two effects to be separable. The threshold depends on the injected source, with inclination, eccentricity, and effective spin playing crucial roles. In particular, for injections similar to GW190521, we find that it is impossible to confidently distinguish eccentricity from spin precession.

Rejuvenated Accretors Have Less Bound Envelopes: Impact of Roche Lobe Overflow on Subsequent Common Envelope Events

Common envelope (CE) evolution is an outstanding open problem in stellar evolution, critical to the formation of compact binaries including gravitational-wave sources. In the “classical” isolated binary evolution scenario for double compact objects, the CE is usually the second mass transfer phase. Thus, the donor star of the CE is the product of a previous binary interaction, often stable Roche lobe overflow (RLOF). Because of the accretion of mass during the first RLOF, the main-sequence core of the accretor star grows and is “rejuvenated.” This modifies the core-envelope boundary region and decreases significantly the envelope binding energy for the remaining evolution. Comparing accretor stars from self-consistent binary models to stars evolved as single, we demonstrate that the rejuvenation can lower the energy required to eject a CE by ∼42%–96% for both black hole and neutron star progenitors, depending on the evolutionary stage and final orbital separation. Therefore, binaries experiencing first stable mass transfer may more easily survive subsequent CE events and result in possibly wider final separations compared to current predictions. Despite their high mass, our accretors also experience extended “blue loops,” which may have observational consequences for low-metallicity stellar populations and asteroseismology.

Which black hole formed first? Mass-ratio reversal in massive binary stars from gravitational-wave data

ABSTRACT Population inference of gravitational-wave catalogues is a useful tool to translate observations of black hole mergers into constraints on compact-binary formation. Different formation channels predict identifiable signatures in the astrophysical distributions of source parameters, such as masses and spins. One example within the scenario of isolated binary evolution is mass-ratio reversal: even assuming efficient core–envelope coupling in massive stars and tidal spin-up of the stellar companion by the first-born black hole, a compact binary with a lighter, non-spinning first-born black hole and a heavier, spinning second-born black hole can still form through mass transfer from the initially more to less massive progenitor. Using current LIGO/Virgo observations, we measure the fraction of sources in the underlying population with this mass–spin combination and interpret it as a constraint on the occurrence of mass-ratio reversal in massive binary stars. We modify commonly used population models by including negligible-spin subpopulations and, most crucially, non-identical component spin distributions. We do not find evidence for subpopulations of black holes with negligible spins and measure the fraction of massive binary stars undergoing mass-ratio reversal to be consistent with zero and $\lt 32{{\ \rm per\ cent}}$ ($99{{\ \rm per\ cent}}$ confidence). The dimensionless spin peaks around 0.2–0.3 appear robust, however, and are yet to be explained by progenitor formation scenarios.

Joint constraints on the field-cluster mixing fraction, common envelope efficiency, and globular cluster radii from a population of binary hole mergers via deep learning

The recent release of the second Gravitational-Wave Transient Catalog (GWTC-2) has increased significantly the number of known GW events, enabling unprecedented constraints on formation models of compact binaries. One pressing question is to understand the fraction of binaries originating from different formation channels, such as isolated field formation versus dynamical formation in dense stellar clusters. In this paper, we combine the $\texttt{COSMIC}$ binary population synthesis suite and the $\texttt{CMC}$ code for globular cluster evolution to create a mixture model for black hole binary formation under both formation scenarios. For the first time, these code bodies are combined self-consistently, with $\texttt{CMC}$ itself employing $\texttt{COSMIC}$ to track stellar evolution. We then use a deep-learning enhanced hierarchical Bayesian analysis to constrain the mixture fraction $f$ between formation models, while simultaneously constraining the common envelope efficiency $\alpha$ assumed in $\texttt{COSMIC}$ and the initial cluster virial radius $r_v$ assumed in $\texttt{CMC}$. Under specific assumptions about other uncertain aspects of isolated binary and globular cluster evolution, we report the median and $90\%$ confidence interval of three physical parameters $(f,\alpha,r_v)=(0.20^{+0.32}_{-0.18},2.26^{+2.65}_{-1.84},2.71^{+0.83}_{-1.17})$. This simultaneous constraint agrees with observed properties of globular clusters in the Milky Way and is an important first step in the pathway toward learning astrophysics of compact binary formation from GW observations.

Simulations of common envelope evolution in triple systems: circumstellar case

ABSTRACT The dynamical evolution of triple stellar systems could induce the formation of compact binaries and binary mergers. Common envelope (CE) evolution, which plays a major role in the evolution of compact binary systems, can similarly play a key role in the evolution of triples. Here, we use hydrodynamical simulations coupled with few-body dynamics to provide the first detailed models of the triple common envelope (TCE) evolution. We focus on the circumstellar case, where the envelope of an evolved giant engulfs a compact binary orbiting the giant, which then in-spirals into the core of the evolved star. Through our exploratory modelling, we find several possible outcomes of such TCE: the merger of the binary inside the third star’s envelope; the disruption of the in-spiralling binary following its plunge, leading to a chaotic triple dynamics of the stellar core and the two components of the former disrupted binary. The chaotic evolution typically leads to the in-spiral and merger of at least one of the former binary components with the core, and sometimes to the ejection of the second, or alternatively its further now-binary CE evolution. The in-spiral in TCE leads to overall slower in-spiral, larger mass ejection, and the production of more aspherical remnant, compared with a corresponding binary case of similar masses, due to the energy/momentum extraction from the inner-binary. We expect TCE to play a key role in producing various types of stellar-mergers and unique compact binary systems, and potentially induce transient electromagnetic and gravitational wave sources.

Dynamics of black hole–neutron star binaries in young star clusters

ABSTRACT Young star clusters are likely the most common birthplace of massive stars across cosmic time and influence the formation of compact binaries in several ways. Here, we simulate the formation of black hole–neutron star binaries (BHNSs) in young star clusters, by means of the binary population synthesis code MOBSE interfaced with the N-body code NBODY6++GPU. BHNSs formed in young star clusters (dynamical BHNSs) are significantly more massive than BHNSs formed from isolated binaries (isolated BHNSs): ∼40 per cent of the dynamical BHNS mergers have a total mass of >15 M⊙, while only ∼0.01 per cent of the isolated BHNS mergers have mass in excess of this value. Hence, our models strongly support a dynamical formation scenario for GW190814, given its total mass of ∼26 M⊙, if this event is a BHNS merger. All our dynamical BHNSs are ejected from their parent star cluster before they reach coalescence. Thus, a significant fraction of BHNS mergers occurring in the field might have originated in a young star cluster. The mass spectrum of BHNS mergers from gravitational-wave detections will provide a clue to differentiate between dynamical and isolated formation of BHNSs.

Dynamically formed black hole binaries: In-cluster versus ejected mergers

AbstractThe growing number of black hole binary (BHB) mergers detected by the Laser Interferometer Gravitational-Wave Observatory have the potential to enable an unprecedented characterisation of the physical processes and astrophysical conditions that govern the formation of compact binaries. In this paper, we focus on investigating the dynamical formation of BHBs in dense star clusters through a state-of-the-art set of 58 direct N-body simulations with N$\leqslant200\,000$particles which include stellar evolution, gravitational braking, orbital decay through gravitational radiation, and galactic tidal interactions. The simulations encompass a range of initial conditions representing typical young globular clusters, including the presence of primordial binaries. The systems are simulated for$\sim 12$Gyr. The dataset yields 117 BHB gravitational wave (GW) events, with 97 binaries merging within their host cluster and 20 merging after having been ejected. Only 8% of all ejected BHBs merge within the age of the Universe. Systems in this merging subset tend to have smaller separations and larger eccentricities, as this combination of parameters results in greater emission of gravitational radiation. We confirm known trends from Monte Carlo simulations, such as the anti-correlation between the mass of the binary and age of the cluster. In addition, we highlight for the first time a difference at low values of the mass ratio distribution between in-cluster and ejected mergers. However, the results depend on assumptions on the strength of GW recoils, thus in-cluster mergers cannot be ruled out at a significant level of confidence. A more substantial catalogue of BHB mergers and a more extensive library of N-body simulations are needed to constrain the origin of the observed events.

Properties of the post-inspiral common envelope ejecta – I. Dynamical and thermal evolution

ABSTRACT We investigate the common envelope binary interaction, that leads to the formation of compact binaries, such as the progenitors of Type Ia supernovae or of mergers that emit detectable gravitational waves. In this work, we diverge from the classic numerical approach that models the dynamic inspiral. We focus instead on the asymptotic behaviour of the common envelope expansion after the dynamic inspiral terminates. We use the SPH code phantom to simulate one of the set-ups from Passy et al., with a 0.88 M⊙, 83 R⊙ RGB primary and a 0.6 M⊙ companion, then we follow the ejecta expansion for 50 yr. Additionally, we utilize a tabulated equation of state including the envelope recombination energy in the simulation (Reichardt et al.), achieving a full unbinding. We show that, as time passes, the envelope’s radial velocities dominate over the tangential ones, hence allowing us to apply an homologous expansion kinematic model to the ejecta. The external layers of the envelope become homologous as soon as they are ejected, but it takes 5000 d (14 yr) for the bulk of the unbound gas to achieve the homologously expanding regime. We observe that the complex distribution generated by the dynamic inspiral evolves into a more ordered, shell-like shaped one in the asymptotic regime. We show that the thermodynamics of the expanding envelope are in very good agreement with those expected for an adiabatically expanding sphere under the homologous condition and give a prediction for the location and temperature of the photosphere assuming dust to be the main source of opacity. This technique ploughs the way to determining the long-term light behaviour of common envelope transients.

Gravitational-wave astrophysics with effective-spin measurements: Asymmetries and selection biases

Gravitational waves emitted by coalescing compact objects carry information about the spin of the individual bodies. However, with present detectors only the mass-weighted combination of the components of the spin along the orbital angular momentum can be measured accurately. This quantity, the effective spin ${\ensuremath{\chi}}_{\mathrm{eff}}$, is conserved up to at least the second post-Newtonian order. The measured distribution of ${\ensuremath{\chi}}_{\mathrm{eff}}$ values from a population of detected binaries, and in particular whether this distribution is symmetric about zero, encodes valuable information about the underlying compact-binary formation channels. In this paper we focus on two important complications of using the effective spin to study astrophysical population properties: (i) an astrophysical distribution for ${\ensuremath{\chi}}_{\mathrm{eff}}$ values which is symmetric does not necessarily lead to a symmetric distribution for the detected effective spin values, leading to a selection bias; and (ii) the posterior distribution of ${\ensuremath{\chi}}_{\mathrm{eff}}$ for individual events is asymmetric and it cannot usually be treated as a Gaussian. We find that the posterior distributions for ${\ensuremath{\chi}}_{\mathrm{eff}}$ systematically show fatter tails toward larger positive values, unless the total mass is large or the mass ratio ${m}_{2}/{m}_{1}$ is smaller than $\ensuremath{\sim}1/2$. Finally we show that uncertainties in the measurement of ${\ensuremath{\chi}}_{\mathrm{eff}}$ are systematically larger when the true value is negative than when it is positive. All these factors can bias astrophysical inference about the population when we have more than $\ensuremath{\sim}100$ events and should be taken into account when using gravitational-wave measurements to characterize astrophysical populations.

Dissipative Evolution of Unequal-mass Binary–single Interactions and Its Relevance to Gravitational-wave Detections

Abstract We present a study of binary–single interactions with energy-loss terms such as tidal dissipation and gravitational-wave (GW) emission added to the equation of motion. The inclusion of such terms leads to the formation of compact binaries that form during the three-body interaction through two-body captures. These binaries predominantly merge relatively promptly at high eccentricity, with several observable and dynamical consequences to follow. Despite their possibility for being observed in both present and upcoming transient surveys, their outcomes are not firmly constrained. In this paper, we present an analytical framework that allows to estimate the cross section of such two-body captures, which permits us to study how the corresponding rates depend on the initial orbital parameters, the mass hierarchy, the type of interacting object, and the energy dissipation mechanism. This formalism is applied here to study the formation of two-body GW captures, for which we estimate absolute and relative rates relevant to Advanced LIGO detections. It is shown that two-body GW captures should have compelling observational implications if a sizable fraction of detected compact binaries are formed via dynamical interactions.

Hierarchical analysis of gravitational-wave measurements of binary black hole spin–orbit misalignments

Binary black holes may form both through isolated binary evolution and through dynamical interactions in dense stellar environments. The formation channel leaves an imprint on the alignment between the black hole spins and the orbital angular momentum. Gravitational waves from these systems directly encode information about the spin--orbit misalignment angles, allowing them to be (weakly) constrained. Identifying sub-populations of spinning binary black holes will inform us about compact binary formation and evolution. We simulate a mixed population of binary black holes with spin--orbit misalignments modelled under a range of assumptions. We then develop a hierarchical analysis and apply it to mock gravitational-wave observations of these populations. Assuming a population with dimensionless spin magnitudes of $\chi = 0.7$, we show that tens of observations will make it possible to distinguish the presence of subpopulations of coalescing binary black holes based on their spin orientations. With $100$ observations it will be possible to infer the relative fraction of coalescing binary black holes with isotropic spin directions (corresponding to dynamical formation in our models) with a fractional uncertainty of $\sim 40\%$. Meanwhile, only $\sim 5$ observations are sufficient to distinguish between extreme models---all binary black holes either having exactly aligned spins or isotropic spin directions.

Web based visualization of large climate data sets

We have implemented the USGS National Climate Change Viewer (NCCV), which is an easy-to-use web application that displays future projections from global climate models over the United States at the state, county and watershed scales. We incorporate the NASA NEX-DCP30 statistically downscaled temperature and precipitation for 30 global climate models being used in the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC), and hydrologic variables we simulated using a simple water-balance model. Our application summarizes very large, complex data sets at scales relevant to resource managers and citizens and makes climate-change projection information accessible to users of varying skill levels. Tens of terabytes of high-resolution climate and water-balance data are distilled to compact binary format summary files that are used in the application. To alleviate slow response times under high loads, we developed a map caching technique that reduces the time it takes to generate maps by several orders of magnitude. The reduced access time scales to >500 concurrent users. We provide code examples that demonstrate key aspects of data processing, data exporting/importing and the caching technique used in the NCCV.

Black hole remnant of black hole-neutron star coalescing binaries with arbitrary black hole spin

A model for determining the dimensionless spin parameter and mass of the black hole remnant of black hole-neutron star mergers with arbitrary initial black hole spin angular momentum, binary mass ratio, and neutron star mass and cold equation of state is formulated. Tests against numerical-relativity results are carried out, showing that both the dimensionless spin parameter and the final mass are accurately reproduced. For the first time, the behaviour of both quantities and of the l = 2, m = 2, n = 0 quasinormal mode frequency is inspected throughout the parameter space. Predictions of this frequency may be exploited to guide gravitational wave modelling and detection efforts, and to extract physical information from detected gravitational wave signals that would help us break degeneracies between binary black hole and black hole-neutron star systems, improve our understanding of compact binary formation, and constrain the neutron star equation of state.