Population Of Binary Black Holes Research Articles

Probing correlations in the binary black hole population with flexible models

Probing correlations in the binary black hole population with flexible models

The Redshift Evolution of the Binary Black Hole Mass Distribution from Dense Star Clusters

Gravitational-wave detectors are unveiling a population of binary black hole (BBH) mergers out to redshifts z ≈ 1, and are starting to constrain how the BBH population evolves with redshift. We present predictions for the redshift evolution of the BBH mass and spin distributions for systems originating from dense star clusters. Utilizing a grid of 144 state-of-the-art dynamical models for globular clusters, we demonstrate that BBH merger rates peak at higher redshifts for larger black hole primary masses M 1. Specifically, for M 1 ≳ 40 M ⊙, the BBH merger rate reaches its peak at redshift z ≈ 2.1, while for M 1 ≲ 20 M ⊙, the peak occurs at z ≈ 1.1, assuming that the cluster formation rate peaks at z = 2.2. The average BBH primary mass also increases from ∼10 M ⊙ at z = 0 to ∼30 M ⊙ at z = 10. We show that ∼20% BBHs contain massive remnants from next-generation mergers, with this fraction increasing (decreasing) for larger (smaller) primary masses. This difference is not large enough to significantly alter the effective spins of the BBH population originating from globular clusters, and we find that their effective spin distribution does not evolve across cosmic time. These findings can be used to distinguish BBHs from dense star clusters by future gravitational-wave observations.

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.

Eccentricity-induced systematic error on parametrized tests of general relativity: Hierarchical Bayesian inference applied to a binary black hole population

Eccentricity-induced systematic error on parametrized tests of general relativity: Hierarchical Bayesian inference applied to a binary black hole population

Cosmology and Astrophysics with Standard Sirens and Galaxy Catalogs in View of Future Gravitational Wave Observations

With the growing number of gravitational wave (GW) detections and the advent of large galaxy redshift surveys, a new era in cosmology is emerging. This study explores the synergies between GWs and galaxy surveys to jointly constrain cosmological and GW population parameters. We introduce CHIMERA, a novel code for GW cosmology combining information from the population properties of compact binary mergers and galaxy catalogs. We study constraints for scenarios representative of the LIGO-Virgo-KAGRA O4 and O5 observing runs, assuming to have a complete catalog of potential host galaxies with either spectroscopic or photometric redshift measurements. We find that a percent-level measurement of H 0 could be achieved with the best 100 binary black holes (BBHs) in O5 using a spectroscopic galaxy catalog. In this case, the intrinsic correlation that exists between H 0 and the BBH population mass scales is broken. Instead, by using a photometric catalog the accuracy is degraded up to a factor of ∼9, leaving a significant correlation between H 0 and the mass scales that must be carefully modeled to avoid bias. Interestingly, we find that using spectroscopic redshift measurements in the O4 configuration yields a better constraint on H 0 compared to the O5 configuration with photometric measurements. In view of the wealth of GW data that will be available in the future, we argue the importance of obtaining spectroscopic galaxy catalogs to maximize the scientific return of GW cosmology.

Two of a Kind: Comparing Big and Small Black Holes in Binaries with Gravitational Waves

When modeling the population of merging binary black holes, analyses have generally focused on characterizing the distribution of primary (i.e., more massive) black holes in the binary, while using simplistic prescriptions for the distribution of secondary masses. However, the secondary mass distribution and its relationship to the primary mass distribution provide a fundamental observational constraint on the formation history of coalescing binary black holes. If both black holes experience similar stellar evolutionary processes prior to collapse, as might be expected in dynamical formation channels, the primary and secondary mass distributions would show similar features. If they follow distinct evolutionary pathways (for example, due to binary interactions that break symmetry between the initially more massive and less massive stars), their mass distributions may differ. We present the first analysis of the binary black hole population that explicitly fits for the secondary mass distribution. We find that the data is consistent with a ∼30 M ⊙ peak existing only in the distribution of secondary rather than primary masses. This would have major implications for our understanding of the formation of these binaries. Alternatively, the data is consistent with the peak existing in both component mass distributions, a possibility not included in most previous studies. In either case, the peak is observed at 31.4−2.6+2.3M⊙ , which is shifted lower than the value obtained in previous analyses of the marginal primary mass distribution, placing this feature in further tension with expectations from a pulsational pair-instability supernova pileup.

Importance of stable mass transfer and stellar winds for the formation of gravitational wave sources

ABSTRACT The large number of gravitational wave (GW) detections have revealed the properties of the merging black hole binary population, but how such systems are formed is still heavily debated. Understanding the imprint of stellar physics on the observable GW population will shed light on how we can use the GW data, along with other observations, to constrain the poorly understood evolution of massive binaries. We perform a parameter study on the classical isolated binary formation channel with the population synthesis code seba to investigate how sensitive the properties of the coalescing binary black hole population are on the uncertainties related to first phase of mass transfer and stellar winds. We vary five assumptions: (1) and (2) the mass transfer efficiency and the angular momentum loss during the first mass transfer phase, (3) the mass transfer stability criteria for giant donors with radiative envelopes, (4) the effective temperature at which an evolved star develops a deep convective envelope, and (5) the mass-loss rates of stellar winds. We find that current uncertainties related to first phase of mass transfer have a huge impact on the relative importance of different dominant channels, while the observable demographics of GW sources are not significantly affected. Our varied parameters have a complex, interrelated effect on the population properties of GW sources. Therefore, inference of massive binary physics from GW data alone remains extremely challenging, given the large uncertainties in our current models.

Resolving the eccentricity of stellar mass binary black holes with next generation ground-based gravitational wave detectors

ABSTRACT Next generation ground-based gravitational wave (GW) detectors are expected to detect ∼104–105 binary black holes (BBHs) per year. Understanding the formation pathways of these binaries is an open question. Orbital eccentricity can be used to distinguish between the formation channels of compact binaries, as different formation channels are expected to yield distinct eccentricity distributions. Due to the rapid decay of eccentricity caused by the emission of GWs, measuring smaller values of eccentricity poses a challenge for current GW detectors due to their limited sensitivity. In this study, we explore the potential of next generation GW detectors such as Voyager, Cosmic Explorer (CE), and Einstein Telescope (ET) to resolve the eccentricity of BBH systems. Considering a GWTC-3 like population of BBHs and assuming some fiducial eccentricity distributions as well as an astrophysically motivated eccentricity distribution (Zevin et al. 2021), we calculate the fraction of detected binaries that can be confidently distinguished as eccentric. We find that for Zevin eccentricity distribution, Voyager, CE, and ET can confidently measure the non-zero eccentricity for ${\sim} 3\%$, 9%, and 13% of the detected BBHs, respectively. In addition to the fraction of resolvable eccentric binaries, our findings indicate that Voyager, CE, and ET require typical minimum eccentricities ≳0.02, 5 × 10−3, and 10−3 at 10 Hz GW frequency, respectively, to identify a BBH system as eccentric. The better low-frequency sensitivity of ET significantly enhances its capacity to accurately measure eccentricity.

Connecting core galaxy properties to the massive black hole binary population

ABSTRACT We investigate how the properties of massive black hole binaries influence the observed properties of core galaxies. We compare the observed trend in stellar mass deficit as a function of total stellar mass in the core galaxy with predicted trends in IllustrisTNG. We calculate mass deficits in simulated galaxies by applying subgrid, post-processing physics based on the results of literature N-body experiments. We find that the median value of the posterior distribution for the minimum binary mass ratio capable of creating a core is 0.7. For the gas mass fraction above which a core is erased, we find a median value of 0.6. Thus, low mass ratio binaries do not contribute to core formation and gas-rich mergers must lead to star formation within the nucleus, ultimately erasing the core. Such constraints have important implications for the overall massive black hole binary population, black hole–galaxy co-evolution, and the origin of the gravitational wave background.

Non-stationary astrophysical stochastic gravitational-wave background: a new probe to the high-redshift population of binary black holes

ABSTRACT The astrophysical stochastic gravitational-wave background (SGWB) originates from the mergers of compact binary objects that are otherwise undetected as individual events, along with other sources such as supernovae, magnetars, etc. The individual gravitational-wave (GW) signal is time-varying over a time-scale that depends on the chirp mass of the coalescing binaries. Another time-scale that plays a role is the time-scale at which the sources repeat, which depends on the merger rate. The combined effect of these two leads to a breakdown of the time translation symmetry of the observed SGWB and a correlation between different frequency modes in the signal covariance matrix of the SGWB. Using an ensemble of SGWB due to binary black hole coalescence, calculated using simulations of different black hole mass distributions and merger rates, we show how the structure of the signal covariance matrix varies. This structure in the signal covariance matrix brings additional information about the sources on top of the power spectrum. We show that there is a significant improvement in the figure of merit by using this additional information in comparison to only power spectrum estimation for the LIGO–Virgo–KAGRA (LVK) network of detectors with the design sensitivity noise with 2 yr of observation. The inclusion of the off-diagonal correlation in the covariance of the SGWB in the data analysis pipelines will be beneficial in the quest for the SGWB signal in LVK frequency bands as well as in lower frequencies and in getting an insight into its origin.

Evidence for a Correlation between Binary Black Hole Mass Ratio and Black Hole Spins

The astrophysical origins of the binary black hole systems seen with gravitational waves are still not well understood. However, features in the distribution of black hole masses, spins, redshifts, and eccentricities provide clues into how these systems form. Much has been learned by investigating these distributions one parameter at a time. However, we can extract additional information by studying the covariance between pairs of parameters. Previous work has shown preliminary support for an anticorrelation between mass ratio q ≡ m 2/m 1 and effective inspiral spin χ eff in the binary black hole population. In this study, we test for the existence of this anticorrelation using updated data from the third gravitational-wave transient catalog and improve our copula-based framework to employ a more robust model for black hole spins. We find evidence for an anticorrelation in (q, χ eff) with 99.7% credibility. This may imply high common-envelope efficiencies, stages of super-Eddington accretion, or a tendency for binary black hole systems to undergo mass-ratio reversal during isolated evolution. Covariance in (q, χ eff) may also be used to investigate the physics of tidal spinup as well as the properties of binary black hole–forming active galactic nuclei.

Nonparametric Inference of the Population of Compact Binaries from Gravitational-wave Observations Using Binned Gaussian Processes

The observation of gravitational waves from multiple compact binary coalescences by the LIGO–Virgo–KAGRA detector networks has enabled us to infer the underlying distribution of compact binaries across a wide range of masses, spins, and redshifts. In light of the new features found in the mass spectrum of binary black holes and the uncertainty regarding binary formation models, nonparametric population inference has become increasingly popular. In this work, we develop a data-driven clustering framework that can identify features in the component mass distribution of compact binaries simultaneously with those in the corresponding redshift distribution, from gravitational-wave data in the presence of significant measurement uncertainties, while making very few assumptions about the functional form of these distributions. Our generalized model is capable of inferring correlations among various population properties, such as the redshift evolution of the shape of the mass distribution itself, in contrast to most existing nonparametric inference schemes. We test our model on simulated data and demonstrate the accuracy with which it can reconstruct the underlying distributions of component masses and redshifts. We also reanalyze public LIGO–Virgo–KAGRA data from events in GWTC-3 using our model and compare our results with those from some alternative parametric and nonparametric population inference approaches. Finally, we investigate the potential presence of correlations between mass and redshift in the population of binary black holes in GWTC-3 (those observed by the LIGO–Virgo–KAGRA detector network in their first three observing runs), without making any assumptions about the specific nature of these correlations.

Pulsar Timing Array Detections of Supermassive Binary Black Holes: Implications from the Detected Common Process Signal and Beyond

Pulsar timing arrays (PTAs) are anticipated to detect the stochastic gravitational-wave background (GWB) from supermassive binary black holes (BBHs) as well as the gravitational waves from individual BBHs. Recently, a common process signal was reported by several PTAs. In this paper, we investigate the constraints on the BBH population model(s) by current PTA observations and further study the detections of both the GWB and individual BBHs by current and future PTAs. We find that the massive black hole–host galaxy scaling relation, an important ingredient of the BBH population model, is required to either evolve significantly with redshift or have a normalization ∼0.86–1.1 dex higher than the empirical ones if the GWB is the same as the common process signal. For both cases, the estimated detection probability for individual BBHs is too small for a positive detection by current PTAs. By involving either the constrained scaling relations or those empirical ones into the BBH population models, we estimate that the GWB may be detected with a signal-to-noise ratio ≳3 by the China Five-hundred-meter Aperture Spherical radio Telescope PTA (CPTA) and the Square Kilometre Array PTA (SKAPTA) after ∼2–3 (or ∼6–11) yr observation if it is the same as (or 1 order of magnitude lower than) the common process signal. The detection time of individual BBHs by CPTA and SKAPTA is close to that of the GWB detection. We show that the BBH population model can be strongly constrained by the number and property distributions of BBHs to be detected by future PTAs.

Symmetry Breaking in Merging Binary Black Holes from Young Massive Clusters and Isolated Binaries

Properties of the to-date observed binary black hole (BBH) merger events suggest a preference toward spin–orbit aligned mergers. Naturally, this has caused widespread interest and speculations regarding implications on various merger formation channels. Here we show that (i) not only the BBH merger population from isolated binaries but also (ii) BBH population formed in young massive clusters (YMCs) would possess an asymmetry in favor of aligned mergers, in the distribution of the events’ effective spin parameter (χ eff). In our analysis, we utilize BBH merger outcomes from state-of-the-art N-body evolutionary models of YMCs and isolated binary population synthesis. We incorporate, for the first time in such an analysis, misalignments due to both natal kicks and dynamical encounters. The YMC χ eff distribution has a mean (an antialigned merger fraction) of 〈χ eff〉 ≤ 0.04 (f X − ≈ 40%), which is smaller (larger) than but consistent with the observed asymmetry of 〈χ eff〉 ≈ 0.06 (f X − ≈ 28%) as obtained from the population analysis by the LIGO–Virgo–KAGRA collaboration. In contrast, isolated binaries alone tend to produce a much stronger asymmetry; for the tested physical models, 〈χ eff〉 ≈ 0.25 and f X − ≲ 7%. Although the YMC χ eff distribution is more similar to the observed counterpart, none of the channels correctly reproduce the observed distribution. Our results suggest that further extensive model explorations for both isolated binary and dynamical channels as well as better observational constraints are necessary to understand the physics of “the symmetry breaking” of the BBH merger population.

Binary black holes population and cosmology in new lights: signature of PISN mass and formation channel in GWTC-3

ABSTRACT The mass, spin, and merger rate distribution of the binary black holes (BBHs) across cosmic redshifts provide a unique way to shed light on their formation channel. Along with the redshift dependence of the BBH merger rate, the mass distribution of BBHs can also exhibit redshift dependence due to different formation channels and dependence on the metallicity of the parent stars. We explore the redshift dependence of the BBH mass distribution jointly with the merger rate evolution from the third gravitational wave (GW) catalogue GWTC-3 of the LIGO–Virgo–KAGRA collaboration. We study possible connections between peak-like features in the mass spectrum of BBHs and processes related to supernovae physics and time delay distributions. We obtain a preference for short-time delays between star formation and BBH mergers. Using a power-law form for the time delay distribution ($(t^{\rm min}_d)^{d}$), we find d < −0.7 credible at 90 per cent interval. The mass distribution of the BBHs could be fitted with a power-law form with a redshift-dependent peak feature that can be linked to the pair instability supernovae (PISN) mass-scale MPISN(Z*) at a stellar metallicity Z*. For a fiducial value of the stellar metallicity Z* = 10−4, we find the $\rm M_{\rm PISN}(Z_*)=44.4^{+7.9}_{-6.3}$$\rm M_\odot$. This is in accordance with the theoretical prediction of the lower edge of the PISN mass-scale and differs from previous analyses. Although we find a strong dependence of the PISN value on metallicity, the model that we explored is not strongly favoured over those that do not account for metallicity as the Bayes factors are inconclusive. In the future with more data, evidence towards metallicity dependence of the PISN will have a significant impact on our understanding of stellar physics.

Constraints on the Cosmic Expansion History from GWTC–3

We use 47 gravitational wave sources from the Third LIGO–Virgo–Kamioka Gravitational Wave Detector Gravitational Wave Transient Catalog (GWTC–3) to estimate the Hubble parameter H(z), including its current value, the Hubble constant H 0. Each gravitational wave (GW) signal provides the luminosity distance to the source, and we estimate the corresponding redshift using two methods: the redshifted masses and a galaxy catalog. Using the binary black hole (BBH) redshifted masses, we simultaneously infer the source mass distribution and H(z). The source mass distribution displays a peak around 34 M ⊙, followed by a drop-off. Assuming this mass scale does not evolve with the redshift results in a H(z) measurement, yielding H0=68−8+12kms−1Mpc−1 (68% credible interval) when combined with the H 0 measurement from GW170817 and its electromagnetic counterpart. This represents an improvement of 17% with respect to the H 0 estimate from GWTC–1. The second method associates each GW event with its probable host galaxy in the catalog GLADE+, statistically marginalizing over the redshifts of each event’s potential hosts. Assuming a fixed BBH population, we estimate a value of H0=68−6+8kms−1Mpc−1 with the galaxy catalog method, an improvement of 42% with respect to our GWTC–1 result and 20% with respect to recent H 0 studies using GWTC–2 events. However, we show that this result is strongly impacted by assumptions about the BBH source mass distribution; the only event which is not strongly impacted by such assumptions (and is thus informative about H 0) is the well-localized event GW190814.

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.