Population Of Binary Black Holes Research Articles

Constraining the number of spacetime dimensions from GWTC-3 binary black hole mergers

In modified gravity models that allow for additional noncompact spacetime dimensions, energy from gravitational waves can leak into these extra spacetime dimensions, leading to a reduction in the amplitude of the observed gravitational waves, and thus are a source of potential systematics in the inferred luminosity distances to gravitational wave sources. Since binary black hole (BBH) mergers are standard sirens, we use the pair-instability supernova mass gap and its predicted features to determine a mass scale in order to break the mass-redshift degeneracy and thus infer the redshift of the source. We simultaneously fit the BBH population and the extra spacetime dimensions parameters from gravitational leakage models using BBH observations from the recently released GWTC-3 catalog. We set constraints on the number of spacetime dimensions and find that $D=3.9{3}_{\ensuremath{-}0.05}^{+0.08}$ at 68% C.L. for models that are independent of a screening scale, finding that the GWTC-3 constraint is as competitive as that set from GW170817 and its electromagnetic counterpart. For models where gravity leaks below a certain screening scale ${R}_{c}$, we find $D=4.4{9}_{\ensuremath{-}0.87}^{+1.63}$ and ${\mathrm{log}}_{10}\text{ }{R}_{c}/\mathrm{Mpc}=4.7{5}_{\ensuremath{-}0.99}^{+0.86}$ with a transition steepness ${\mathrm{log}}_{10}\text{ }n=0.8{5}_{\ensuremath{-}0.86}^{+0.76}$ for the leakage, which for the first time are constrained jointly with the BBH population at cosmological distances. These constraints are consistent with General Relativity (GR), where gravitational waves propagate in $D=3+1$ spacetime dimensions. Using the BBH population to probe modifications to standard cosmological models provides an independent test of GR that does not rely on any electromagnetic information but purely on gravitational wave observations.

Model exploration in gravitational-wave astronomy with the maximum population likelihood

Hierarchical Bayesian inference is an essential tool for studying the population properties of compact binaries with gravitational waves. The basic premise is to infer the unknown prior distribution of binary black hole and/or neutron star parameters such component masses, spin vectors, and redshift. These distributions shed light on the fate of massive stars, how and where binaries are assembled, and the evolution of the Universe over cosmic time. Hierarchical analyses model the binary black hole population using a prior distribution conditioned on hyperparameters, which are inferred from the data. However, a misspecified model can lead to faulty astrophysical inferences. In this paper we answer the question: given some data, which prior distribution---from the set of all possible prior distributions---produces the largest possible population likelihood? This distribution (which is not a true prior) is $\overline{)\ensuremath{\pi}}$ (pronounced ``pi stroke''), and the associated maximum population likelihood is $\overline{)\mathcal{L}}$ (pronounced ``L stroke''). The structure of $\overline{)\ensuremath{\pi}}$ is a linear superposition of delta functions, a result which follows from Carath\'eodory's theorem. We show how $\overline{)\ensuremath{\pi}}$ and $\overline{)\mathcal{L}}$ can be used for model exploration/criticism. We apply this $\overline{)\mathcal{L}}$ formalism to study the population of binary black hole mergers observed in the LIGO-Virgo-KAGRA Collaboration's third gravitational-wave transient catalog. Based on our results, we discuss possible improvements for gravitational-wave population models.

Cover Your Basis: Comprehensive Data-driven Characterization of the Binary Black Hole Population

We introduce the first complete nonparametric model for the astrophysical distribution of the binary black hole (BBH) population. Constructed from basis splines, we use these models to conduct the most comprehensive data-driven investigation of the BBH population to date, simultaneously fitting nonparametric models for the BBH mass ratio, spin magnitude and misalignment, and redshift distributions. With GWTC-3, we report the same features previously recovered with similarly flexible models of the mass distribution, most notably the peaks in merger rates at primary masses of ∼10M ⊙ and ∼35M ⊙. Our model reports a suppressed merger rate at low primary masses and a mass-ratio distribution consistent with a power law. We infer a distribution for primary spin misalignments that peaks away from alignment, supporting conclusions of recent work. We find broad agreement with the previous inferences of the spin magnitude distribution: the majority of BBH spins are small (a < 0.5), the distribution peaks at a ∼ 0.2, and there is mild support for a nonspinning subpopulation, which may be resolved with larger catalogs. With a modulated power law describing the BBH merger rate’s evolution in redshift, we see hints of the rate evolution either flattening or decreasing at z ∼ 0.2–0.5, but the full distribution remains entirely consistent with a monotonically increasing power law. We conclude with a discussion of the astrophysical context of our new findings and how nonparametric methods in gravitational-wave population inference are uniquely poised to complement to the parametric approach as we enter the data-rich era of gravitational-wave astronomy.

Impact of LIGO-Virgo black hole binaries on gravitational wave background searches

We study the impact of the black hole binary population currently probed by LIGO-Virgo on future searches for the primordial gravitational wave background. We estimate the foreground generated by the binaries using the observed event rate and a simple modeling of the black hole population. We subtract individually resolvable binaries from the foreground and utilize Fisher analysis to derive sensitivity curves for power-law signals including these astrophysical foregrounds. Even with optimistic assumptions, we find that the reach of future experiments will be severely reduced.

Understanding the high-mass binary black hole population from stable mass transfer and super-Eddington accretion in bpass

ABSTRACT With the remarkable success of the Ligo-Virgo-Kagra consortium in detecting binary black hole mergers, it has become possible to use the population properties to constrain our understanding of the progenitor stars’ evolution. The most striking features of the observed primary black hole mass distributions are the extended tail up to 100 M⊙ and an excess of masses at 35 M⊙. Currently, isolated binary population synthesis have difficulty explaining these features. Using the well-tested bpass detailed stellar binary evolution models to determine mass transfer stability, accretion rates, and remnant masses, we postulate that stable mass transfer with super-Eddington accretion is responsible for the extended tail. These systems are able to merge within the Hubble time due to more stable mass transfer at higher donor masses with higher mass ratios and spin-orbit coupling, allowing the orbits to shrink sufficiently. Furthermore, we find that in bpass the 35 M⊙ excess is not due to pulsational pair-instability, as previously thought, but a feature caused by stable mass transfer, whose regime is limited by the mass transfer stability, quasi-homogeneous evolution, and stellar winds. These findings are at odds with those from other population synthesis codes but in agreement with other recent studies using detailed binary evolution models.

Towards a reliable reconstruction of the power spectrum of primordial curvature perturbation on small scales from GWTC-3

Primordial black holes (PBHs) can be both candidates of dark matter and progenitors of binary black holes (BBHs) detected by the LIGO-Virgo-KAGRA collaboration. Since PBHs could form in the very early Universe through the gravitational collapse of primordial density perturbations, the population of BBHs detected by gravitational waves encodes much information on primordial curvature perturbation. In this work, we take a reliable and systematic approach to reconstruct the power spectrum of the primordial curvature perturbation from GWTC-3, under the hierarchical Bayesian inference framework, by accounting for the measurement uncertainties and selection effects. In addition to just considering the single PBH population model, we also report the results considering the multi-population model, i.e., the mixed PBH and astrophysical black hole binaries model. We find that the maximum amplitude of the reconstructed power spectrum of primordial curvature perturbation can be ∼2.5×10−2 at O(105)Mpc−1 scales, which is consistent with the PBH formation scenario from inflation at small scales.

Potential Subpopulations and Assembling Tendency of the Merging Black Holes

The origins of coalescing binary black holes (BBHs) detected by the advanced LIGO/Virgo are still under debate, and clues may be present in the joint mass-spin distribution of these merger events. Here we construct phenomenological models containing two subpopulations to investigate the BBH population detected in gravitational-wave observations. We find that our models can explain the GWTC-3 data rather well, and several constraints to our model are required by the data: first, the maximum mass for the component with a stellar-origin, , is at 90% credibility; second, about 15% of the mergers happen in dynamical environments, in which 7%–16% of events are hierarchical mergers, and these BHs have an average spin magnitude significantly larger than the first-generation mergers, with d μ a > 0.4 at 99% credibility; third, the dynamical component BHs tend to pair with each other with larger total mass and higher mass ratio. An independent analysis focusing on spins is also carried out, and we find that the spin amplitude of component BHs can be divided into two groups according to a division mass . These constraints can be naturally explained by current formation channels, and our results suggest that some of the observed events were likely from active galactic nucleus disks.

Constraints on the contributions to the observed binary black hole population from individual evolutionary pathways in isolated binary evolution

ABSTRACT Gravitational waves from merging binary black holes can be used to shed light on poorly understood aspects of massive binary stellar evolution, such as the evolution of massive stars (including their mass-loss rates), the common envelope phase, and the rate at which massive stars form throughout the cosmic history of the Universe. In this paper, we explore the correlated impact of these phases on predictions for the merger rate and chirp mass distribution of merging binary black holes, aiming to identify possible degeneracies between model parameters. In many of our models, a large fraction (more than 70 per cent of detectable binary black holes) arise from the chemically homogeneous evolution scenario; these models tend to overpredict the binary black hole merger rate and produce systems that are on average too massive. Our preferred models favour enhanced mass-loss rates for helium rich Wolf–Rayet stars, in tension with recent theoretical and observational developments. We identify correlations between the impact of the mass-loss rates of Wolf–Rayet stars and the metallicity evolution of the Universe on the rates and properties of merging binary black holes. Based on the observed mass distribution, we argue that the $\sim 10{{\ \rm per\ cent}}$ of binary black holes with chirp masses greater than 40 M⊙ (the maximum predicted by our models) are unlikely to have formed through isolated binary evolution, implying a significant contribution (&amp;gt;10 per cent) from other formation channels such as dense star clusters or active galactic nuclei. Our models will enable inference on the uncertain parameters governing binary evolution in the near future.

No Evidence that the Majority of Black Holes in Binaries Have Zero Spin

The spin properties of merging black holes observed with gravitational waves can offer novel information about the origin of these systems. The magnitudes and orientations of black hole spins offer a record of binaries’ evolutionary history, encoding information about massive stellar evolution and the astrophysical environments in which binary black holes are assembled. Recent analyses of the binary black hole population have yielded conflicting portraits of the black hole spin distribution. Some works suggest that black hole spins are small but nonzero and exhibit a wide range of misalignment angles relative to binaries’ orbital angular momenta. Other works conclude that the majority of black holes are nonspinning while the remainder are rapidly rotating and primarily aligned with their orbits. We revisit these conflicting conclusions, employing a variety of complementary methods to measure the distribution of spin magnitudes and orientations among binary black hole mergers. We find that the existence of a subpopulation of black holes with vanishing spins is not required by current data. Should such a subpopulation exist, we conclude that it must contain ≲60% of binaries. Additionally, we find evidence for significant spin–orbit misalignment among the binary black hole population, with some systems exhibiting misalignment angles greater than 90°, and see no evidence for an approximately spin-aligned subpopulation.

Current and future constraints on cosmology and modified gravitational wave friction from binary black holes

Gravitational wave (GW) standard sirens are well-established probes with which one can measure cosmological parameters, and are complementary to other probes like the cosmic microwave background (CMB) or supernovae standard candles. Here we focus on dark GW sirens, specifically binary black holes (BBHs) for which there is only GW data. Our approach relies on the assumption of a source frame mass model for the BBH distribution, and we consider four models that are representative of the BBH population observed so far. In addition to inferring cosmological and mass model parameters, we use dark sirens to test modified gravity theories. These theories often predict different GW propagation equations on cosmological scales, leading to a different GW luminosity distance which in some cases can be parametrized by variables Ξ0 and n. General relativity (GR) corresponds to Ξ0 = 1. We perform a joint estimate of the population parameters governing mass, redshift, the variables characterizing the cosmology, and the modified GW luminosity distance. We use data from the third LIGO-Virgo-KAGRA observation run (O3) and find — for the four mass models and for three signal-to-noise ratio (SNR) cuts of 10, 11, 12 — that GR is consistently the preferred model to describe all observed BBH GW signals to date. Furthermore, all modified gravity parameters have posteriors that are compatible with the values predicted by GR at the 90% confidence interval (CI). We then focus on future observation runs O4 and O5, and for simplicity consider one specific mass model. We show that there are strong correlations between cosmological, astrophysical and modified gravity parameters. If GR is the correct theory of gravity, and assuming narrow priors on the cosmological parameters, we forecast an uncertainty of the modified gravity parameter Ξ0 of 51% with ∼ 90 detections at O4-like sensitivities, and Ξ0 of 20% with an additional ∼ 400 detections at O5-like sensitivity. We also consider how these forecasts depend on the current uncertainties of BBHs population distributions.

The χeff − z correlation of field binary black hole mergers and how 3G gravitational-wave detectors can constrain it

Understanding the origin of merging binary black holes is currently one of the most pressing quests in astrophysics. We show that if isolated binary evolution dominates the formation mechanism of merging binary black holes, one should expect a correlation between the effective spin parameter, χeff, and the redshift of the merger, z, of binary black holes. This correlation comes from tidal spin-up systems preferentially forming and merging at higher redshifts due to the combination of weaker orbital expansion from low metallicity stars given their reduced wind mass loss rate, delayed expansion and have smaller maximal radii during the supergiant phase compared to stars at higher metallicity. As a result, these tightly bound systems merge with short inspiral times. Given our fiducial model of isolated binary evolution, we show that the origin of a χeff − z correlation in the detectable LIGO–Virgo binary black hole population is different from the intrinsic population, which will become accessible only in the future by third-generation gravitational-wave detectors such as Einstein Telescope and Cosmic Explorer. Given the limited horizon of current gravitational-wave detectors, z ≲ 1, highly rotating black hole mergers in the LIGO–Virgo observed χeff − z correlation are dominated by those formed through chemically homogeneous evolution. This is in contrast to the subpopulation of highly rotating black holes in the intrinsic population, which is dominated by tidal spin up following a common evolve event. The different subchannel mixture in the intrinsic and detected population is a direct consequence of detector selection effects, which allows for the typically more massive black holes formed through chemically homogeneous evolution to be observable at larger redshifts and dominate the LIGO–Virgo sample of spinning binary black holes from isolated evolution at z &gt; 0.4. Finally, we compare our model predictions with population predictions based on the current catalog of binary black hole mergers and find that current data favor a positive correlation of χeff − z as predicted by our model of isolated binary evolution.

Cosmology with Gravitational Waves: A Review

AbstractStandard sirens have been the central paradigm in gravitational‐wave cosmology so far. From the gravitational wave signature of compact star binaries, it is possible to measure the luminosity distance of the source directly, and if additional information on the source redshift is provided, a measurement of the cosmological expansion can be performed. This review article discusses several methodologies that have been proposed to use gravitational waves for cosmological studies. Methods that use only gravitational‐wave signals and methods that use gravitational waves in conjunction with additional observations such as electromagnetic counterparts and galaxy catalogs will be discussed. The review also discusses the most recent results on gravitational‐wave cosmology, starting from the binary neutron star merger GW170817 and its electromagnetic counterpart and finishing with the population of binary black holes, observed with the third Gravitational‐wave Transient Catalog GWTC–3.

Limits on Hierarchical Black Hole Mergers from the Most Negative χ eff Systems

It has been proposed that some black holes (BHs) in binary black hole (BBH) systems are born from “hierarchical mergers” (HMs), i.e., earlier mergers of smaller BHs. These HM products have spin magnitudes χ ∼ 0.7, and, if they are dynamically assembled into BBH systems, their spin orientations will sometimes be antialigned with the binary orbital angular momentum. In fact, as Baibhav et al. showed, ∼16% of BBH systems that include HM products will have an effective inspiral spin parameter, χ eff < −0.3. Nevertheless, the LIGO–Virgo–KAGRA (LVK) gravitational-wave (GW) detectors have yet to observe a BBH system with χ eff ≲ −0.2, leading to upper limits on the fraction of HM products in the population. We fit the astrophysical mass and spin distribution of BBH systems and measure the fraction of BBH systems with χ eff < −0.3, which implies an upper limit on the HM fraction. We find that fewer than 26% of systems in the underlying BBH population include HM products (90% credibility). Even among BBH systems with primary masses m 1 = 60 M ⊙, the HM fraction is less than 69%, which may constrain the location of the pair-instability mass gap. With 300 GW events (to be expected in the LVK’s next observing run), if we fail to observe a BBH with χ eff < −0.3, we can conclude that the HM fraction is smaller than .

The Gravitational Wave Universe Toolbox

Context:TheGW-Universe Toolboxis a software package that simulates observations of the gravitational wave (GW) Universe with different types of GW detectors, including Earth-based and space-borne laser interferometers and pulsar timing arrays. It is accessible as a website, and can also be imported and run locally as a Python package.Methods:We employ the method used by theGW-Universe Toolboxto generate a synthetic catalogue of detection of stellar-mass binary black hole (BBH) mergers. As an example of its scientific application, we study how GW observations of BBHs can be used to constrain the merger rate as a function of redshift and masses. We study advanced LIGO (aLIGO) and theEinsteinTelescope (ET) as two representatives of the second and third generation GW observatories, respectively. We also simulate the observations from a detector that is half as sensitive as the ET at its nominal designed sensitivity, which represents an early phase of the ET. We used two methods to obtain the constraints on the source population properties from the catalogues: the first uses a parameteric differential merger rate model and applies a Bayesian inference on the parameters; the other is non-parameteric and uses weighted Kernel density estimators.Results:Our results show the overwhelming advantages of the third generation detector over those of the second generation for the study of BBH population properties, especially at redshifts higher than ∼2, where the merger rate is believed to peak. With the simulated aLIGO catalogue, the parameteric Bayesian method can still give some constraints on the merger rate density and mass function beyond its detecting horizon, while the non-parametric method loses the constraining ability completely there. The difference is due to the extra information placed by assuming a specific parameterisation of the population model in the Bayesian method. In the non-parameteric method, no assumption of the general shape of the merger rate density and mass function are placed, not even the assumption of its smoothness. These two methods represent the two extreme situations of general population reconstruction. We also find that, despite the numbers of detected events of the half ET can easily be compatible with full ET after a longer observation duration, and the catalogue from the full ET can still give much better constraints on the population properties due to its smaller uncertainties on the physical parameters of the GW events.

Suspicious Siblings: The Distribution of Mass and Spin across Component Black Holes in Isolated Binary Evolution

The LIGO and Virgo gravitational-wave detectors have uncovered binary black hole systems with definitively nonzero spins, as well as systems with significant spin residing in the more massive black hole of the pair. We investigate the ability of isolated binary evolution in forming such highly spinning, asymmetric-mass systems through both accretion onto the first-born black hole and tidal spin-up of the second-born black hole using a rapid population synthesis approach with detailed considerations of spin-up through tidal interactions. Even with the most optimistic assumptions regarding the efficiency at which an accreting star receives material from a donor, we find that it is difficult to form systems with significant mass asymmetry and moderate or high spins in the primary black hole component. Assuming efficient angular momentum transport within massive stars and Eddington-limited accretion onto black holes, we find that >1.5% of systems in the underlying binary black hole population have a primary black hole spin greater than 0.2 and a mass asymmetry of greater than 2:1 in our most optimistic models, with most models finding that this criteria is only met in ∼0.01% of systems. The production of systems with significant mass asymmetries and spin in the primary black hole component is thus an unlikely byproduct of isolated evolution unless highly super-Eddington accretion is invoked or angular momentum transport in massive stars is less efficient than typically assumed.

The Binary Black Hole Spin Distribution Likely Broadens with Redshift

The population-level distributions of the masses, spins, and redshifts of binary black holes (BBHs) observed using gravitational waves can shed light on how these systems form and evolve. Because of the complex astrophysical processes shaping the inferred BBH population, models allowing for correlations among these parameters will be necessary to fully characterize these sources. We hierarchically analyze the BBH population detected by LIGO and Virgo with a model allowing for correlations between the effective aligned spin and the primary mass and redshift. We find that the width of the effective spin distribution grows with redshift at 98.6% credibility. We determine this trend to be robust under the application of several alternative models and additionally verify that such a correlation is unlikely to be spuriously introduced using a simulated population. We discuss the possibility that this correlation could be due to a change in the natal black hole spin distribution with redshift.

Gravitational background from dynamical binaries and detectability with 2G detectors

We study the impact of young clusters on the gravitational wave background from compact binary coalescence. We simulate a catalog of sources from population I/II isolated binary stars and stars born in young clusters, corresponding to one year of observations with second-generation (2G) detectors. Taking into account uncertainties on the fraction of dynamical binaries and star formation parameters, we find that the background is dominated by the population of binary black holes, and we obtain a value of $\Omega_{gw}(25 \rm{Hz}) = 1.2^{+1.38}_{-0.65} \times 10^{-9}$ for the energy density, in agreement with the actual upper limits derived from the latest observation run of LIGO--Virgo. We demonstrate that a large number of sources in a specific corrected mass range yields to a bump in the background. This background could be detected with 8 years of coincident data by a network of 2G detectors.

Population inference of spin-induced quadrupole moments as a probe for nonblack hole compact binaries

Gravitational wave (GW) measurements of physical effects such as spin-induced quadrupole moments can distinguish binaries consisting of black holes from nonblack hole binaries. While these effects may be poorly constrained for single-event inferences with the second-generation detectors, combining information from multiple detections can help uncover features of nonblack hole binaries. The spin-induced quadrupole moment has specific predictions for different types of compact objects, and a generalized formalism must consider a population where different types of compact objects co-exist. In this study, we introduce a hierarchical mixture-likelihood formalism to estimate the fraction of nonbinary black holes in the population. We demonstrate the applicability of this method using simulated GW signals injected into Gaussian noise following the design sensitivities of the Advanced LIGO Advanced Virgo detectors. We compare the performance of this method with a traditionally-followed hierarchical inference approach. Both the methods are equally effective to hint at inhomogeneous populations, however, we find the mixture-likelihood approach to be more natural for mixture populations comprising compact objects of diverse classes. We also discuss the possible systematics in the mixture-likelihood approach, caused by several reasons, including the limited sensitivity of the second-generation detectors, specific features of the astrophysical population distributions, and the limitations posed by the waveform models employed. Finally, we apply this method to the LIGO-Virgo detections published in the second GW transient catalog (GWTC-2) and find them consistent with a binary black hole population with ${f}_{\mathrm{nbh}}$ estimated to be $\ensuremath{\le}0.29$ at 90% credibility.

Exploring Features in the Binary Black Hole Population

Abstract Vamana is a mixture model framework that infers the astrophysical distribution of chirp mass, mass ratio, and spin component aligned with the orbital angular momentum for the binary black holes (BBH) population. We extend the mixing components in this framework to also model the redshift evolution of merger rate and report all the major one- and two-dimensional features in the BBH population using the 69 gravitational-wave signals detected with a false alarm rate &lt;1 yr−1 in the third Gravitational-Wave Transient Catalog (GWTC-3). Endorsing our previous report and a recent corroborating report from LIGO Scientific, Virgo, and KAGRA Collaborations, we observe the chirp mass distribution has multiple peaks and a lack of mergers with chirp masses 10–12 M ⊙. In addition, we observe that aligned spins show mass dependence with heavier binaries exhibiting larger spins, the mass ratio shows a dependence on the chirp mass but not on the aligned spin, and the redshift evolution of the merger rate for the peaks in the mass distribution is disparate. These features possibly reflect the astrophysics associated with the BBH formation channels. However, additional observations are needed to improve our limited confidence in them.

Apples and Oranges: Comparing Black Holes in X-Ray Binaries and Gravitational-wave Sources

The component black holes (BHs) observed in gravitational-wave (GW) binary black hole (BBH) events tend to be more massive and slower spinning than those observed in black hole X-ray binaries (BH-XRBs). Without modeling their evolutionary histories, we investigate whether these apparent tensions in the BH populations can be explained by GW observational selection effects alone. We find that this is indeed the case for the discrepancy between BH masses in BBHs and the observed high-mass X-ray binaries (HMXBs), when we account for statistical uncertainty from the small sample size of just three HMXBs. On the other hand, the BHs in observed low-mass X-ray binaries (LMXBs) are significantly lighter than the astrophysical BBH population, but this may just be due to a correlation between component masses in a binary system. Given their light stellar companions, we expect light BHs in LMXBs. The observed spins in HMXBs and LMXBs, however, are in tension with the inferred BBH spin distribution at the >99.9% level. We discuss possible scenarios behind the significantly larger spins in observed BH-XRBs. One possibility is that a small subpopulation (conservatively <30%) of BBHs have rapidly spinning primary components, indicating that they may have followed a similar evolutionary pathway to the observed HMXBs. In LMXBs, it has been suggested that BHs can spin up by accretion. If LMXB natal spins follow the BBH spin distribution, we find LMXBs must gain an average dimensionless spin of , but if their natal spins follow the observed HMXB spins, the average spin-up must be <0.03.