Black Hole Binaries Research Articles

Impact of higher derivative corrections to general relativity on black hole mergers

Impact of higher derivative corrections to general relativity on black hole mergers

Development of convective envelopes in massive stars. Implications for gravitational wave sources

The structure of stellar envelopes strongly influences the course and outcome of binary mass transfer, in particular of common-envelope (CE) evolution. Convective envelopes can most easily be ejected during CE events, leading to short-period binaries and, potentially, gravitational-wave (GW) sources. Conversely, radiative envelopes are thought to lead to CE mergers and Thorne-\.Zytkow objects (T\.ZOs) or quasi-stars (QSs). Rapid binary models based on Hurley et al. (2000) often assume that any CE event with a Hertzsprung gap donor results in a CE merger, in tension with the literature. We improve on this assumption with a more self-consistent criterion based on the presence of a convective envelope. Using 1D stellar models ( MESA ), we systematically investigated the development of convective envelopes in massive stars. We provided fitting formulae for rapid binary codes and implemented them into the StarTrack population synthesis code to refine the CE treatment and examined the impact on GW sources, T\.ZOs, and QSs. We show that convective envelopes in massive stars are highly sensitive to the treatment of superadiabacity and the mixing length. Our revised CE model significantly reduces (by a factor sim 20) the predicted merger rate of binary black hole (BH-BH) mergers with total masses between sim 20 and 50 $M_ This leads to a bimodal mass distribution with a strong metallicity dependence. We also predict that the current T\.ZO--QS formation rate in the Galaxy (up to sim $ yr$^ $), combined with their predicted lifetimes, makes their detection unlikely. Our study strongly suggests that the role of CE evolution in the formation of BH-BH mergers has been considerably overestimated for BH-BH mergers with $M_ tot $\,geq \,20 $M_ We highlight that any prediction from the CE channel for massive BH-BH mergers (>50 $M_ heavily hinges on our limited understanding of stellar structure and mass loss close to the Eddington limit.

A physically modelled selection function for compact binary mergers in the LIGO-Virgo O3 run and beyond

Abstract Despite the observation of nearly 100 compact binary coalescence (CBC) events up to the end of the Advanced gravitational-wave (GW) detectors' third observing run (O3), there remain fundamental open questions regarding their astrophysical formation mechanisms and environments. Population analysis should yield insights into these questions, but requires careful control of uncertainties and biases. GW observations have a strong selection bias: this is due first to the dependence of the signal amplitude on the source's (intrinsic and extrinsic) parameters, and second to the complicated nature of detector noise and of current detection methods. In this work, we introduce a new physically-motivated model of the sensitivity of GW searches for CBC events, aimed at enhancing the accuracy and efficiency of population reconstructions. In contrast to current methods which rely on re-weighting simulated signals (injections) via importance sampling, we model the probability of detection of binary black hole (BBH) mergers as a smooth, analytic function of source masses, orbit-aligned spins, and distance, fitted to accurately match injection results. The estimate can thus be used for population models whose signal distribution over parameter space differs significantly from the injection distribution. Our method has already been used in population studies such as reconstructing the BBH merger rate dependence on redshift.

Gravitational wave memory imprints on the CMB from populations of massive black hole mergers

Our aim is to showcase and characterise the rich phenomenology of temperature fluctuation patterns that are imprinted on the cosmic microwave background (CMB) by the gravitational wave memory (GWM) of massive black hole mergers. We analysed both individual binaries as well as populations of binaries, distributed in local cosmological boxes at a given redshift. The magnitude of the temperature fluctuations scales primarily as a function of binary total mass and pattern angular scale, and accumulates as a random-walk process when populations of mergers are considered. Fluctuations of order $ $ K are reached across scales of $ 1'$ to $ circ $ for realistic volumetric merger rates of 10$^ $ Mpc$^ $ Gyr$^ $, as is appropriate for massive galaxies at $z=1$. We determined numerically that GWM temperature fluctuations result in a universal power spectrum with a scaling of $P(k) While not detectable given the limitations of current all-sky CMB surveys, our work explicitly shows how every black hole merger in the Universe left us its unique faint signature.

The MeerKAT Pulsar Timing Array: the 4.5-yr data release and the noise and stochastic signals of the millisecond pulsar population

ABSTRACT Pulsar timing arrays (PTAs) are ensembles of regularly observed millisecond pulsars timed to high precision. Each pulsar in an array could be affected by a suite of noise processes, most of which are astrophysically motivated. Analysing them carefully can be used to understand these physical processes. However, the primary purpose of these experiments is to detect signals that are common to all pulsars, in particular signals associated with a stochastic gravitational wave background. To detect this, it is paramount to appropriately characterize other signals that may otherwise impact array sensitivity or cause a spurious detection. Here, we describe the second data release and first detailed noise analysis of the pulsars in the MeerKAT Pulsar Timing Array, comprising high-cadence and high-precision observations of 83 millisecond pulsars over 4.5 yr. We use this analysis to search for a common signal in the data, finding a process with an amplitude of $\log _{10}{A_{\mathrm{ CURN}}} = -14.25^{+0.21}_{-0.36}$ and spectral index $\gamma _\mathrm{CURN} = 3.60^{+1.31}_{-0.89}$. Fixing the spectral index at the value predicted for a background produced by the inspiral of binary supermassive black holes, we measure the amplitude to be $\log _{10}{A_{\mathrm{ CURN}}} = -14.28^{+0.21}_{-0.21}$ at a significance expressed as a Bayes factor of $\ln (\mathcal {B}) = 4.46$. Under both assumptions, the amplitude that we recover is larger than those reported by other PTA experiments. We use the results of this analysis to forecast our sensitivity to a gravitational wave background possessing the spectral properties of the common signal we have measured.

High-Energy Spectra of Black Hole and Neutron Star Low-Mass X-Ray Binaries

In the case of low-mass X-ray binaries, the companion star is often too faint for detection; therefore, there is no chance for dynamical studies to independently determine the mass of the compact object. In the absence of a mass estimate, one cannot make a distinction as to whether the binary hosts a black hole or neutron star. Therefore, the question arises whether this distinction can be made based on the X-ray data alone, even when there are no bursts or pulsations. These would automatically imply a neutron star, but they are not always present. Black hole systems are known to emit radiation with an unbroken power–law shape up to several hundred keV energies in their high/soft states. If the non-thermal Comptonization processes that are responsible for this are somehow related to the lack of a solid surface, and to the fact that more gravitational potential energy can be released for a black hole, then there would be a definite method to reliably distinguish between the two sources. This work intends to review the available observations and studies to compare how these two populations behave during their different spectral states. A conclusion can be made that high/soft-state spectra are really different for black holes and neutron stars, for the low/hard state; however, the same conclusion cannot be safely made.

The MeerKAT Pulsar Timing Array: Maps of the gravitational wave sky with the 4.5-yr data release

ABSTRACT In an accompanying publication, the MeerKAT Pulsar Timing Array (MPTA) Collaboration reports tentative evidence for the presence of a stochastic gravitational wave background, following observations of similar signals from the European and Indian Pulsar Timing Arrays, the North American Nanohertz Observatory for Gravitational Waves, the Parkes Pulsar Timing Array, and the Chinese Pulsar Timing Array. If such a gravitational wave background signal originates from a population of inspiraling supermassive black hole binaries, the signal may be anisotropically distributed in the sky. In this paper, we evaluate the anisotropy of the MPTA signal using a spherical harmonic decomposition. We discuss complications arising from the covariance between pulsar pairs and the regularization of the Fisher matrix. Applying our method to the $4.5 \hbox{-}\text{yr}$ data set, we obtain two forms of sky maps for the three most sensitive MPTA frequency bins between $7 \ {\rm and} \ 21 \, {\rm nHz}$. Our ‘clean maps’ estimate the distribution of gravitational wave strain power with minimal assumptions. Our radiometer maps answer the question: Is there a statistically significant point source? We find a noteworthy hotspot in the $7 \, \mathrm{nHz}$ clean map with a p-factor of $p=0.015$ (not including trial factors). Future observations are required to determine if this hotspot is of astrophysical origin.

Can we discern millilensed gravitational-wave signals from signals produced by precessing binary black holes with ground-based detectors?

Can we discern millilensed gravitational-wave signals from signals produced by precessing binary black holes with ground-based detectors?

The spin magnitude of stellar-mass black holes evolves with the mass

Aims. Using gravitational-wave (GW) data from the latest GW Transient Catalog (GWTC-3), we conduct a comprehensive investigation into the relationship between the masses and spin magnitudes (χ) of binary black holes (BBHs). Our focus is on identifying potential correlations between BBH masses and spin magnitudes, and exploring their astrophysical implications in terms of formation channels. Methods. We employed hierarchical Bayesian methods and new population models for spin-mass distributions to analyze the GW data. We further validated our results with several sanity checks. Results. Analyzing 59 GW signals, we find statistical evidence for an evolution of the spin magnitude of the BBHs as a function of the mass. We interpret the evolution in two ways. First, using a class of population models that parameterize the evolution of the spin distribution with mass, we observe a transition from a population of BBHs with lower spin magnitudes (χ ∼ 0.2) at lower masses to higher, but less constrained, spin magnitudes for higher masses. The transition between these two distinct distributions occurs around 45 M⊙ − 55 M⊙. Additionally, using population models built by mixing independent populations of BBHs, we find that the observed GW signals can be interpreted as consisting ∼98% of low-spin black holes with masses ≲40 M⊙ and ∼2% high-spin black holes with masses ≳40 M⊙. Conclusions. Using different prescriptions for the interplay between BBH spins and masses, we find evidence of a mass scale at 45 M⊙ − 55 M⊙, where the population distribution of spin magnitudes changes. We speculate that this result may support the hypothesis that a large fraction of low-mass, low-spin BBHs are formed through the evolution of isolated stellar binaries, whereas a smaller fraction of higher-mass, high-spin BBHs are likely formed through dynamical assembly or hierarchical mergers.

PyMerger: Detecting Binary Black Hole Mergers from the Einstein Telescope Using Deep Learning

We present PyMerger, a Python tool for detecting binary black hole (BBH) mergers from the Einstein Telescope (ET), based on a deep residual neural network (ResNet) model. ResNet was trained on data combined from all three proposed subdetectors of ET (TSDCD) to detect BBH mergers. Five different lower-frequency cutoffs (F low)—5 Hz, 10 Hz, 15 Hz, 20 Hz, and 30 Hz—with the match-filter signal-to-noise ratio (MSNR) ranges 4–5, 5–6, 6–7, 7–8, and >8 were employed in the data simulation. Compared to previous work that utilized data from a single subdetector, the detection accuracy from TSDCD has shown substantial improvements, increasing from 60%, 60.5%, 84.5%, 94.5%, and 98.5% to 78.5%, 84%, 99.5%, 100%, and 100% for sources with MSNRs of 4–5, 5–6, 6–7, 7–8, and >8, respectively. The ResNet model is evaluated on the first ET mock data challenge (ET-MDC1) data set, where the model demonstrates strong performance in detecting BBH mergers, identifying 5566 out of 6578 BBH events, with optimal SNRs starting from 1.2 and a minimum and maximum D L of 0.5 Gpc and 148.95 Gpc, respectively. Despite being trained only on BBH mergers without overlapping sources, the model achieves high BBH detection rates. Notably, even though the model was not trained on binary neutron star (BNS) and black hole-neutron star (BHNS) mergers, it successfully detected 11,477 BNS and 323BHNS mergers in ET-MDC1, with optimal SNRs starting from 0.2 and 1, respectively, indicating its potential for broader applicability.

Exploring Field-evolution and Dynamical-capture Coalescing Binary Black Holes in GWTC-3

We investigate formation channels for merging binary black holes (BBHs) in GWTC-3, with a dedicated semiparametric population model. The model first describes or excludes a high-spin (with magnitudes of ∼0.7) and high-mass (ranging in ∼20–80M ⊙) subpopulation, which was identified by previous works and can be interpreted as hierarchical mergers. We find that the rest of BBH population can be categorized into two subpopulations with different mass and mass-ratio distributions, as indicated by a Bayes factor of lnB=1.8 . One subpopulation, characterized by nearly aligned spins and consistent with isolated field formation, likely dominates the 10-solar-mass peak in the primary-mass function. The other subpopulation, with isotropic spins and consistent with the dynamical channels, shows a stronger preference for symmetric pairing, and mainly contributes to the 35-solar-mass peak in the primary-mass function. Note that the Bayes factor is not high enough with the currently available data, so that the case of a single population is still acceptable. Additionally, we compare the mass distributions between merging BBHs and black holes (BHs) in high-mass X-ray binaries (HMXBs). We find that the primary mass of the aligned subpopulation is slightly lighter than those of the HMXB BHs, while the isotropic subpopulation is consistent with the HMXB BHs, if the power-law index of its mass function is shifted by 2, as indicated by the dynamical formation channels. However, the spin magnitudes of both subpopulations are significantly smaller than those of the HMXB BHs.

Detection Rate of Galaxy Cluster-lensed Stellar Binary Black Hole Mergers by the Third-generation Gravitational-wave Detectors

Gravitational waves (GWs) from stellar binary black hole (sBBH) mergers can be strongly gravitational lensed by intervening galaxies/galaxy clusters. Only a few works have investigated cluster-lensed sBBH mergers by adopting oversimplified models, while galaxy-lensed ones have been intensively studied. In this paper, we estimate the detection rate of cluster-lensed sBBH mergers with third-generation GW detectors and its dependence on the lens models. We adopt detailed modeling of galaxy cluster lenses by using the mock clusters in the Synthetic Sky Catalog for Dark Energy Science with LSST (cosmoDC2) and/or approximations of the pseudo-Jaffe profile or an eccentric Navarro–Frenk–White dark matter halo plus a bright central galaxy with singular isothermal sphere profile. Considering that the formation of sBBH mergers is dominated by the evolution of the massive binary star (EMBS) channel, we find that the detection rate of cluster-lensed sBBHs is ∼5–84 yr−1, depending on the adopted lens model and uncertainty in the merger rate density, which is about ∼13−2.0+28 yr−1 if adopting relatively more realistic galaxy clusters with central main and member galaxies in the cosmoDC2 catalog, close to the estimated detection rate of sBBH mergers lensed by galaxies. In addition, we also consider the case in which the production of sBBH mergers is dominated by the dynamical interactions in dense stellar systems. We find that the detection rate of cluster-lensed sBBHs from the dynamical channel is about 1.5 times larger than that from the EMBS channel, and the redshift distribution of the former peaks at a higher redshift (∼3) compared with that from the latter (∼2).

Dynamical friction and the evolution of black holes in cosmological simulations: A new implementation in OpenGadget3

Aims. We introduce a novel sub-resolution prescription to correct for the unresolved dynamical friction (DF) onto black holes (BHs) in cosmological simulations, to describe BH dynamics accurately, and to overcome spurious motions induced by numerical effects. Methods. We implemented a sub-resolution prescription for the unresolved DF onto BHs in the OpenGadget3 code. We carried out cosmological simulations of a volume of (16 comoving Mpc)3 and zoomed-in simulations of a galaxy group and of a galaxy cluster. We assessed the advantages of our new technique in comparison to commonly adopted methods for hampering spurious BH displacements, namely repositioning onto a local minimum of the gravitational potential and ad hoc boosting of the BH particle dynamical mass. We inspected variations in BH demography in terms of offset from the centres of the host sub-halos, the wandering population of BHs, BH–BH merger rates, and the occupation fraction of sub-halos. We also analysed the impact of the different prescriptions on individual BH interaction events in detail. Results. The newly introduced DF correction enhances the centring of BHs on host halos, the effects of which are at least comparable with those of alternative techniques. Also, the correction becomes gradually more effective as the redshift decreases. Simulations with this correction predict half as many merger events with respect to the repositioning prescription, with the advantage of being less prone to leaving substructures without any central BH. Simulations featuring our DF prescription produce a smaller (by up to ~50% with respect to repositioning) population of wandering BHs and final BH masses that are in good agreement with observations. Regarding individual BH–BH interactions, our DF model captures the gradual inspiraling of orbits before the merger occurs. By contrast, the repositioning scheme, in its most classical renditions, describes extremely fast mergers, while the dynamical mass misrepresents the dynamics of the black holes, introducing numerical scattering between the orbiting BHs. Conclusions. The novel DF correction improves the accuracy if tracking BHs within their hosts galaxies and the pathway to BH- BH mergers. This opens up new possibilities for better modeling the evolution of BH populations in cosmological simulations across different times and different environments.

Analytical study of the merging rate of low-mass intermediate-mass black holes in preparation for the future Einstein Telescope

Context. The detection of gravitational wave (GW) signals by Advanced LIGO, Virgo, and KAGRA interferometers opened a new chapter in our understanding of the formation of compact objects. In particular, the detection of GW190521 is observational confirmation of the existence of intermediate-mass black holes (IMBHs); yet more direct observations are needed to better understand the mechanisms behind their formation. Aims. In this study, we explore the potential of the next-generation ground-based detector, the Einstein Telescope (ET), to advance our understanding of astrophysics through the detection of GWs emitted by IMBHs. To achieve this, the ET is designed to have improved sensitivity in the low-frequency range of approximately 2–10 Hz, enabling the detection of GWs originating from binary systems containing IMBHs with masses in the range of approximately 102–105 M⊙. Methods. We consider black holes (BHs) in the pair-instability form via the hierarchical merger model in galaxies, and approximate the number of events that could be observed by the ET. Results. Our findings indicate that ET could detect a binary black hole (BBH) merger rate of around 2 × 105 Gpc−3 yr−1 for BH masses ranging from 10 to 200 M⊙, with around 100 Gpc−3 yr−1 of this rate specifically attributed to BHs in the 100–200 M⊙ mass range, which we classify as low-mass IMBHs in this study. This suggests that ET could detect several dozen events similar to GW190521. The exact locations of these BBH mergers are not specified and we count our BH mergers across the entire universe up to a redshift of z ≈ 2. Conclusions. Observations made with the ET are expected to significantly enhance our comprehension of galactic BH growth, and the existence and characteristics of low-mass IMBHs.

Euclid: The rb−M* relation as a function of redshift

Core ellipticals, which are massive early-type galaxies with almost constant inner surface brightness profiles, are the result of dry mergers. During these events, a binary black hole (BBH) is formed, destroying the original cuspy central regions of the merging objects and scattering stars that are not on tangential orbits. The size of the emerging core correlates with the mass of the finally merged black hole (BH). Therefore, the determination of the size of the core of massive early-type galaxies provides key insights not only into the mass of the black hole, but also into the origin and evolution of these objects. In this work, we report the first Euclid-based dynamical mass determination of a supermassive black hole (SMBH). To this end, we study the center of NGC 1272, the second most luminous elliptical galaxy in the Perseus cluster, combining the Euclid Visible Camera (VIS) photometry coming from the Early Release Observations (EROs) of the Perseus cluster with the Visible Integral-field Replicable Unit Spectrograph (VIRUS) spectroscopic observations at the Hobby-Eberly Telescope (HET). The core of NGC 1272 is detected on the Euclid VIS image. Its size is 1.​​″29 ± 0.​​″07 or 0.45 kpc, which was determined by fitting PSF-convolved core-Sérsic and Nuker-law functions. We deproject the surface brightness profile of the galaxy, finding that the galaxy is axisymmetric and nearly spherical. The two-dimensional stellar kinematics of the galaxy is measured from the VIRUS spectra by deriving optimally regularized non-parametric line-of-sight velocity distributions. Dynamical models of the galaxy are constructed using our axisymmetric and triaxial Schwarzschild codes. We measure a BH mass of (5 ± 3)×109 M⊙, which is in line with the expectation from the MBH − rb correlation, but is eight times larger than predicted by the MBH − σ correlation (at 1.8σ significance). The core size, rather than the velocity dispersion, allows one to select galaxies harboring the most massive BHs. The spatial resolution, wide area coverage, and depth of the Euclid (Wide and Deep) surveys allow us to find cores of passive galaxies that are larger than 2 kpc at a redshift of up to 1.

Structure formation with primordial black holes: collisional dynamics, binaries, and gravitational waves

Primordial black holes (PBHs) could compose the dark matter content of the Universe. We present the first simulations of cosmological structure formation with PBH dark matter that consistently include collisional few-body effects, post-Newtonian orbit corrections, orbital decay due to gravitational wave emission, and black-hole mergers. We carefully construct initial conditions by considering the evolution during radiation domination as well as early-forming binary systems. We identify numerous dynamical effects due to the collisional nature of PBH dark matter, including evolution of the internal structures of PBH halos and the formation of a hot component of PBHs. We also study the properties of the emergent population of PBH binary systems, distinguishing those that form at primordial times from those that form during the nonlinear structure formation process. These results will be crucial to sharpen constraints on the PBH scenario derived from observational constraints on the gravitational wave background. Even under conservative assumptions, the gravitational radiation emitted over the course of the simulation appears to exceed current limits from ground-based experiments, but this depends on the evolution of the gravitational wave spectrum and PBH merger rate toward lower redshifts.

Exploring Pulsar Timing Precision: A Comparative Study of Polarization Calibration Methods for NANOGrav Data from the Green Bank Telescope

Pulsar timing array experiments have recently uncovered evidence for a nanohertz gravitational wave background by precisely timing an ensemble of millisecond pulsars. The next significant milestones for these experiments include characterizing the detected background with greater precision, identifying its source(s), and detecting continuous gravitational waves from individual supermassive black hole binaries. To achieve these objectives, generating accurate and precise times of arrival of pulses from pulsar observations is crucial. Incorrect polarization calibration of the observed pulsar profiles may introduce errors in the measured times of arrival. Further, previous studies have demonstrated that robust polarization calibration of pulsar profiles can reduce noise in the pulsar timing data and improve timing solutions. In this paper, we investigate and compare the impact of different polarization calibration methods on pulsar timing precision using three distinct calibration techniques: the Ideal Feed Assumption (IFA), Measurement Equation Modeling (MEM), and Measurement Equation Template Matching (METM). Three NANOGrav pulsars—PSRs J1643−1224, J1744−1134, and J1909−3744—observed with the 800 MHz and 1.5 GHz receivers at the Green Bank Telescope (GBT) are utilized for our analysis. Our findings reveal that all three calibration methods enhance timing precision compared to scenarios where no polarization calibration is performed. Additionally, among the three calibration methods, the IFA approach generally provides the best results for timing analysis of pulsars observed with the GBT receiver system. We attribute the comparatively poorer performance of the MEM and METM methods to potential instabilities in the reference noise diode coupled to the receiver and temporal variations in the profile of the reference pulsar, respectively.

Non-Kerr constraints using binary black hole inspirals considering phase modifications up to 4 PN order

The gravitational field around an astrophysical black hole (BH) is thought to be described by the Kerr spacetime, which is a solution of the Einstein equation. Signatures of binary black hole (BBH) coalescence in gravitational waves (GW) follow the Kerr spacetime as the theoretical foundation. Hence, any possible deviations from the Kerr spacetime around BHs serve as a test of the nature of gravity in the strong-field regime and of the predictions of General Relativity. In our study, we perform a theory-agnostic test of the Kerr hypothesis using BBH inspirals from the third Gravitational-wave Transient Catalog (GWTC-3). Considering the Johannsen metric, we compute the leading-order deviation to the emitted GW in the frequency domain. Our results provide constraints on two deformation parameters (α13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _{13}$$\\end{document} and ϵ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon _3$$\\end{document}) and demonstrate the degeneracy between these two non-Kerr parameters.

Mass Function of Stellar Black Holes as Revealed by the LIGO–Virgo–KAGRA Observations

Ninety gravitational-wave events have been detected by the LIGO–Virgo–KAGRA network and are released in the Gravitational-Wave Transient Catalog. Among these events, 83 cases are definitely binary black hole mergers, since the masses of all the objects involved significantly exceed the upper limit of neutron stars. The black holes in these merger events naturally form two interesting samples, a premerger sample that includes all the black holes before the mergers and a postmerger sample that consists of the black holes generated during the merging processes. The former represents black holes that once existed in the Universe, while the latter represents newly born black holes. Here we present a statistical analysis of these two samples. The nonparametric τ statistic method is adopted to correct for the observational selection effect. The Lynden-Bell C − method is further applied to derive the mass distribution and density function of black holes. It is found that the mass distribution can be expressed as a broken power-law function. More interestingly, the power-law index in the high-mass region is comparable for the two samples. The number density of black holes is found to depend on redshift as ρ(z) ∝ z −2.06—z −2.12 based on the two samples. The implications of these findings on the origin of black holes are discussed.

Black hole-black hole mergers with and without an electromagnetic counterpart: A model for stable tertiary mass transfer in hierarchical triple systems

Triple stars are prevalent within the population of observed stars. Their evolution compared to binary systems is notably more complex and is influenced by unique dynamical, tidal, and mass transfer processes inherent in higher order multiples. Understanding these phenomena is essential for comprehensive insight into multistar evolution and the formation of energetic transients, including gravitational wave (GW) mergers. Our study aims to probe the evolution of triple star systems when the tertiary component fills its Roche lobe and transfers mass to the inner binary. Specifically, we focus on the impact of tertiary mass transfer on the evolution of the inner orbit and investigate whether it could lead to the formation of GW sources with distinct properties. To achieve this, we developed an analytical model that describes the evolution of the inner and outer orbits of hierarchical triples undergoing stable mass transfer from the tertiary component. We have publicly released this model as a python package on Zenodo. Utilising population synthesis simulations, we investigated triples with a Roche-lobe filling tertiary star and an inner binary black hole (BBH). These systems stem from inner binaries experiencing chemically homogeneous evolution (CHE). Our analysis encompasses two distinct populations with metallicities of $Z=0.005$ and $Z=0.0005$, focusing on primary components in the inner binary with initial masses ranging from 20 to $100\ M odot $ and inner and outer orbital separations of up to $40\ R odot $ and $10^5\ R odot $, respectively, targeting the parameter space where chemically homogeneous evolution is anticipated. Our results indicate that for the systems we studied, the mass transfer phase predominantly leads to orbital shrinkage of the inner binary and evolution towards non-zero eccentricities and is accompanied by an expansion of the outer orbit. In the systems where the inner binary components evolve in a chemically homogeneous manner, 9.5<!PCT!> result in mass transfer from the tertiary onto an inner BBH. Within this subset, we predict a high formation efficiency of GW mergers ranging from 85.1<!PCT!> to 100<!PCT!> at $Z=0.005$ and 100<!PCT!> at $Z=0.0005$ with short delay times, partly attributable to the mass transfer phase. Owing to the rarity of triples with a CHE inner binary in the stellar population, we project local merger rates in the range of 0.69 to 1.74 $ Gpc^ $. Of the prospected BBH mergers that enter the LISA and aLIGO frequency band due to GW emission, a fraction is still accreting gas from the tertiary star. This could produce a strong electromagnetic (EM) counterpart to the GW source and maintain high eccentricities as the system enters the frequency range detectable by GW detectors. The occurrence of EM signals accompanying mergers varies significantly depending on model assumptions, with fractions ranging from less than 0.03<!PCT!> to as high as 46.8<!PCT!> of all mergers if the formation of a circumbinary disc is allowed.