Binary Black Hole Merger Events Research Articles

On the detection and precise localization of merging black holes events through strong gravitational lensing

ABSTRACT To unlock the full spectrum of astrophysical and cosmological applications of gravitational-wave detections, it is essential to localize the associated black hole mergers to high precision inside their host galaxies. One possible method to achieve this is to compare the properties of multiple detections of gravitationally lensed binary black hole merger events with the properties of strong gravitational lens systems located in the joint sky localization of the gravitational-wave detections. In this work, we simulate the population of binary black hole mergers lensed by galaxy-scale lenses and detectable by LIGO-Virgo-Kagra in the coming decade and the population of galaxy-scale strong lenses that will be detected by Euclid. We use these simulations to investigate the prospects for localizing strongly lensed binary black hole mergers inside the lensed galaxies of ‘Euclid-like’ galaxy-scale strong lenses. We find that for 20–$50\, \rm \%$ of strongly lensed gravitational-wave events the lens system is detectable with Euclid, if the event falls in its survey footprint. Of these, we expect to correctly identify the strongly lensed host galaxy as likely (with posterior probability) host galaxy – based on Bayesian evidence ranking of candidate hosts – for 34.6–$21.9\,\mathrm{ per\,cent}$ of quadruply lensed gravitational-wave events when given an a priori 1–5 $\deg ^{2}$ gravitational-wave-only sky localization. For triply and doubly lensed gravitational-wave events, this becomes 29.8–$14.9\,\mathrm{ per\,cent}$ and 16.4–$6.6\,\mathrm{ per\,cent}$ respectively. If successfully identified, however, the localization can be better than a fraction of the host-galaxy size, i.e. of order milli-arcseconds. A first detection in the coming decade, however, probably requires dedicated deep and high-resolution follow-ups and continued upgrades in the current and planned gravitational-wave detectors.

Binary Black Hole Spins: Model Selection with GWTC-3

The origin of the spins of stellar-mass black holes is still controversial, and angular momentum transport inside massive stars is one of the main sources of uncertainty. Here, we apply hierarchical Bayesian inference to derive constraints on spin models from the 59 most confident binary black hole merger events in the third gravitational-wave transient catalogue (GWTC-3). We consider up to five parameters: chirp mass, mass ratio, redshift, effective spin, and precessing spin. For the model selection, we use a set of binary population synthesis simulations spanning drastically different assumptions for black hole spins and natal kicks. In particular, our spin models range from the maximal to minimal efficiency of angular momentum transport in stars. We find that if we include the precessing spin parameter into our analysis, models predicting only vanishingly small spins are in tension with GWTC-3 data. On the other hand, models in which most spins are vanishingly small but that also include a subpopulation of tidally spun-up black holes are a good match to the data. Our results show that the precessing spin parameter has a crucial impact on model selection.

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.

Reconstruction of power spectrum of primordial curvature perturbations on small scales from primordial black hole binaries scenario of LIGO/VIRGO detection

As a candidate bound for the Binary Black Hole (BBH) merger events detected by LIGO/Virgo, Primordial Black Holes (PBHs) provide a useful tool to investigate the primordial curvature perturbations on small scales. Using the GWTC-1 to GWTC-3 catalogs, under the scenario that PBHs originate from large primordial curvature perturbations on small scales during inflationary epoch, we for the first time reconstruct the power spectrum of primordial curvature perturbations on small scales. It is found that the value of the amplitude of the primordial power spectrum is enhanced to $\mathcal{O}(10^{-2})$ on scales $\mathcal{O}(1)$ pc. This may imply the validity of PBH as a possible BBH merger candidate.

Contracting and Expanding Binary Black Holes in 3D Low-mass AGN Disks: The Importance of Separation

LIGO/Virgo has detected several binary black hole (BBH) merger events that may have originated in the accretion disks of active galactic nuclei (AGNs). These events require individual black hole masses that fall within the pair instability supernova mass gap, and therefore these black holes may have been grown from hierarchical mergers. AGN disks are a prime environment for hierarchical mergers and thus a potential location for the progenitors of BBH gravitational wave events. Understanding how a BBH embedded in an AGN disk interacts with the surrounding environment is thus crucial for determining whether this interaction can lead to its merger. However, there are few high-fidelity simulations of this process, and almost all are two-dimensional. We present the results from 3D, high-resolution, local shearing-box simulations of an embedded BBH interacting with an AGN disk. In these first simulations of their kind, we focus on determining the mass accretion rate and the orbital evolution rate at different BBH separations. We find that circular, equal-mass BBHs with separations greater than 10% of their Hill radius contract while accreting at a super-Eddington rate. At smaller separations, however, our 3D simulations find that BBHs expand their orbits. This result suggests that it may be difficult for an AGN disk to push a BBH to merger, but we discuss several mechanisms, including MHD turbulence and radiative and mechanical feedback, which could alleviate this difficulty.

Impact of gravitational lensing on black hole mass function inference with third-generation gravitational wave detectors

ABSTRACT The recent rapid growth of the black hole (BH) catalogue from gravitational waves (GWs) has allowed us to study the substructure of black hole mass function (BHMF) beyond the simplest power–law distribution. However, the BH masses inferred from binary BH merger events, may be systematically ‘brightened’ or ‘dimmed’ by the gravitational lensing effect. In this work, we investigate the impact of gravitational lensing on the BHMF inference considering the detection of the third-generation GW detector – the Einstein Telescope (ET). We focus on high redshift, z = 10 in order to obtain the upper limits of this effect. We use Monte Carlo (MC) method to simulate the data adopting three original BHMFs under Un-Lensed and Lensed scenarios, then recover the parameters of BHMFs from the mock data, and compare the difference of results, respectively. We found that all the parameters are well recovered within one standard deviation(std., 1σ), and all three BHMF models are reconstructed within 68 per cent credible interval, suggesting that lensing would not change the main structure drastically, even at very high redshifts and with high precision of ET. And the modest influence beyond 50M⊙, depends on the modeling of the high mass tail or substructure of BHMF. We conclude that the impact of lensing on BHMF inference with ET can be safely ignored in the foreseeable future. Careful handling of lensing effects is required only when focusing on an accurate estimation of the high mass end of BHMF at high redshifts.

Binary black hole mergers from young massive clusters in the pair-instability supernova mass gap

Context. The recent discovery of the binary black hole (BBH) merger event GW190521, between two black holes (BHs) of ≈100 Msamp, in addition to other massive BBH merger events involving BHs within the pair-instability supernova (PSN) mass gap have sparked widespread debate on the origin of such extreme gravitational-wave (GW) events. GW190521 simultaneously triggers two critical questions: how BHs can appear within the ‘forbidden’ PSN gap and, if they do, how they get to participate in general-relativistic (GR) mergers. Aims. In this study, I investigate whether dynamical interactions in young massive clusters (YMCs) serve as a viable scenario for assembling PSN-gap BBH mergers. Methods. To that end, I explore a grid of 40 new evolutionary models of a representative YMC of initial mass and size Mcl = 7.5 × 104 Msamp (N ≈ 1.28 × 105) and rh = 2 pc, respectively. The model grid ranges over metallicity 0.0002 ≤ Z ≤ 0.02 and comprises initial cluster configurations of King central concentration parameters W0 = 7 and 9. In each model, all BH progenitor stars are initially in primordial binaries following observationally motivated distributions. All cluster models are evolved with the direct, relativistic N-body code NBODY7, incorporating up-to-date remnant formation, BH natal spin, and GR merger recoil schemes. Results. Binary black hole mergers from these model cluster computations agree well with the masses and effective spin parameters, χeff, of the events from the latest gravitational-wave transient catalogue (GWTC). In particular, GW190521-like, that is to say ≈200 Msamp, low χeff events are produced via a dynamical merger among BHs derived from star-star merger products. GW190403_051519-like, that is PSN-gap, highly asymmetric, high χeff events result from mergers involving BHs that are spun up via matter accretion or a binary interaction. The resulting present-day, differential intrinsic merger rate density, within the PSN gap, accommodates that from GWTC well. Conclusions. This study demonstrates that, subject to model uncertainties, the tandem of massive binary evolution and dynamical interactions in ≲100 Myr-old, low metallicity YMCs in the Universe can plausibly produce GR mergers involving PSN-gap BHs and in rates consistent with that from up-to-date GW observations. Such clusters can produce extreme events similar to GW190521 and GW190403_051519. The upper limit of the models’ GW190521-type event rate is within the corresponding LIGO-Virgo-KAGRA (LVK)-estimated rate limits, although the typical model rate lies below LVK’s lower limit. The present YMC models yield a merger rate density of 0−3.8 × 10−2 yr−1 Gpc−3 for GW190521-type events. They produce GW190403_051519-like events at a rate within 0−1.6 × 10−1 yr−1 Gpc−3 and their total BBH-merger yield within the PSN gap is 0−8.4 × 10−1 yr−1 Gpc−3.

Nonorthogonal wavelet transformation for reconstructing gravitational wave signals

Detections of gravitational-wave signals from compact binary coalescences have enabled us to study extreme astrophysical phenomena and explore fundamental physics. A crucial requisite for these studies is to have accurate signal models with characteristic morphologies, which have been challenging for many decades, and researchers are still endeavoring to incorporate important physics. Therefore, morphology-independent methods have been developed for identifying a signal and its reconstruction. The reconstructed signal allows us to test the agreement between the observed signal and the waveform posterior samples from parameter estimation. These methods model observed signals using a nearly orthogonal wavelet basis in the frame of continuous wavelet transformation. Here, we propose log-uniform scales to construct the wavelets, which are are highly redundant (nonorthogonal) compared to the conventional octave scales but more efficient for reconstructing the signals at high frequencies. And we introduce a semi-model-dependent reconstruction method using the posterior samples of the events, where we model the signal using Gabor-Morlet wavelets with log-uniform scales. We demonstrate the ability to detect deviation using a numerical simulation of an eccentric binary black hole merger, where the signal in the data does not belong to the search template waveform manifold. Finally, we apply this method to each binary black hole merger event in GWTC-1. We have found that the signal produced by the GW150914 event has 96% agreement with the waveform posterior samples. As the detector sensitivity improves and the detected population of black hole mergers grows, we expect the proposed method will provide even stronger tests.

Ensemble of deep convolutional neural networks for real-time gravitational wave signal recognition

With the rapid development of deep learning technology, more and more researchers apply it to gravitational wave (GW) data analysis. Previous studies focused on a single deep learning model. In this paper we design an ensemble algorithm combining a set of convolutional neural networks (CNN) for GW signal recognition. The whole ensemble model consists of two sub-ensemble models. Each sub-ensemble model is also an ensemble model of deep learning. The two sub-ensemble models treat data of Hanford and Livinston detectors respectively. Proper voting scheme is adopted to combine the two sub-ensemble models to form the whole ensemble model. We apply this ensemble model to all reported GW events in the first observation and second observation runs (O1/O2) by LIGO-VIRGO Scientific Collaboration. We find that the ensemble algorithm can clearly identify all binary black hole merger events except GW170818. We also apply the ensemble model to one month (August 2017) data of O2. There is no false trigger happens although only O1 data are used for training. Our test results indicate that the ensemble learning algorithms can be used in real-time GW data analysis.

Deep learning for estimating parameters of gravitational waves

ABSTRACT In recent years, improvements in deep learning (DL) techniques towards gravitational wave (GW) astronomy have led to a significant rise in the development of various classification algorithms that have been successfully employed to extract GWs of binary black hole merger events from noisy time-series data. However, the success of these models is constrained by the length of time sample and the class of GW source: black hole binaries and neutron star binaries to some extent. In this work, we intended to advance the boundaries of DL techniques using convolutional neural networks, to go beyond binary classification and predict the physical parameters of the events. We aim to propose an alternative method that can be employed for real-time detection and parameter prediction. The DL model we present has been trained on 12s of data to predict the GW source parameters if detected. During training, the maximum accuracy attained was 90.93 per cent, with a validation accuracy of 89.97 per cent.

Constrains on the electric charges of the binary black holes with GWTC-1 events

Testing black hole’s charged property is a fascinating topic in modified gravity and black hole astrophysics. In the first Gravitational-Wave Transient Catalog (GWTC-1), ten binary black hole merger events have been formally reported, and these gravitational wave signals have significantly enhanced our understanding of the black hole. In this paper, we try to constrain the amount of electric charge with the parameterized post-Einsteinian framework by treating the electric charge as a small perturbation in a Bayesian way. We find that the current limits in our work are consistent with the result of Fisher information matrix method in previous works. We also develop a waveform model considering a leading order charge effect for binary black hole inspiral.

GECKO Optical Follow-up Observation of Three Binary Black Hole Merger Events: GW190408_181802, GW190412, and GW190503_185404

Abstract We present optical follow-up observation results of three binary black hole merger (BBH) events, GW190408_181802, GW190412, and GW190503_185404, which were detected by the Advanced LIGO and Virgo gravitational wave (GW) detectors. Electromagnetic (EM) counterparts are generally not expected for BBH merger events. However, some theoretical models suggest that EM counterparts of BBH can possibly arise in special environments, prompting motivation to search for EM counterparts for such events. We observed high-credibility regions of the sky for the three BBH merger events with telescopes of the Gravitational-wave EM Counterpart Korean Observatory (GECKO), including the KMTNet. Our observation started as soon as 100 minutes after the GW event alerts and covered 29–63 deg2 for each event with a depth of ∼22.5 mag in the R band within hours of observation. No plausible EM counterparts were found for these events, but based on there being no detection of the GW190503_185404 event, for which we covered the 69% credibility region, we place the BBH merger EM counterpart signal to be M g > − 18.0 AB mag within about one day of the GW event. The comparison of our detection limits with light curves of several kilonova models suggests that a kilonova event could have been identified within hours of the GW alert with GECKO observations if the compact merger happened at <400 Mpc and the localization accuracy was on the order of 50 deg2. Our result shows great promise for the GECKO facilities to find EM counterparts within a few hours from GW detection in future GW observation runs.

The Emergence of Structure in the Binary Black Hole Mass Distribution

Abstract We use the gravitational wave signals from binary black hole merger events observed by LIGO and Virgo to reconstruct the underlying mass and spin distributions of the population of merging black holes. We reconstruct the population using the mixture model framework VAMANA using observations in GWTC-2 occurring during the first two observing runs and the first half of the third run (O1, O2, and O3a). Our analysis identifies a structure in the chirp mass distribution of the observed population. Specifically, we identify peaks in the chirp mass distribution at 8, 14, 26, and 45 M ⊙ and a complementary structure in the component mass distribution with an excess of black holes at masses of 9, 16, 45, and 57 M ⊙. Intriguingly, for both the distributions, the location of subsequent peaks are separated by a factor of around two and there is a lack of mergers with chirp masses of 10–12 M ⊙. The appearance of multiple peaks is a feature of a hierarchical merger scenario when, due to a gap in the black hole mass spectrum, a pile-up occurs at the first peak followed by mergers of lower mass black holes to hierarchically produce higher mass black holes. However, cross-generation merger peaks and observations with high spins are also predicted to occur in such a scenario that we are not currently observing. The results presented are limited in measurement accuracy due to small numbers of observations but if corroborated by future gravitational wave observations these features have far-reaching implications.

Unveiling the spectrum of inspiralling binary black holes

The higher-multipoles of gravitational wave signals from coalescing compact binaries play a vital role in the accurate reconstruction of source properties, bringing about a deeper and nuanced understanding of fundamental physics and astrophysics. Their effect is most pronounced in systems with asymmetric masses having an orbital geometry that is not face-on. The detection of higher-multipoles of GW signals from any single, isolated merger event is challenging, as there is much less power in comparison to the dominant quadrupole mode. In this paper, we present a new method for their detection by combining multiple events observed in interferometric gravitational wave detectors. Sub-dominant modes present in (the inspiral part of) the signal from separate events are stacked using time-frequency spectrogram of the data. We demonstrate that this procedure enhances the signal-to-noise ratio of the higher-multipole components and thereby leads to increased chances of their detection. From Monte-Carlo simulations, we estimate that a combination of $\sim 100$ events observed in two-detector coincidence can lead to the detection of the higher-multipole components with a $\geq$ 95\% detection probability. The advanced-LIGO detectors are expected to record these many binary black hole merger events within a month of operation at design sensitivity. We also present results from the analysis of data from O1 and O2 science runs containing previously detected events using our new method.

Inferring the gravitational wave memory for binary coalescence events

Full, non-linear general relativity predicts a memory effect for gravitational waves. For compact binary coalescence, the total gravitational memory serves as an inferred observable, conceptually on the same footing as the mass and the spin of the final black hole. Given candidate waveforms for any LIGO event, then, one can calculate the posterior probability distribution functions for the total gravitational memory, and use them to compare and contrast the waveforms. In this paper we present these posterior distributions for the binary black hole merger events reported in the first Gravitational Wave Transient Catalog (GWTC-1), using the Phenomenological and Effective-One-Body waveforms. On the whole, the two sets of posterior distributions agree with each other quite well though we find larger discrepancies for the $\ell=2, m=1$ mode of the memory. This signals a possible source of systematic errors that was not captured by the posterior distributions of other inferred observables. Thus, the posterior distributions of various angular modes of total memory can serve as diagnostic tools to further improve the waveforms. Analyses such as this would be valuable especially for future events as the sensitivity of ground based detectors improves, and for LISA which could measure the total gravitational memory directly.

Modified gravity and the black hole mass gap

We pioneer the black hole mass gap as a powerful new tool for constraining modified gravity theories. These theories predict fifth forces that alter the structure and evolution of population-III stars, exacerbating the pair-instability. This results in the formation of lighter astrophysical black holes and lowers both the upper and lower edges of the mass gap. These effects are explored using detailed numerical simulations to derive quantitative predictions that can be used as theoretical inputs for Bayesian data analysis. We discuss detection strategies in light of current and upcoming data as well as complications that may arise due to environmental screening. To demonstrate the constraining power of the mass gap, we present a novel test of the strong equivalence principle where we apply our results to an analysis of the first ten LIGO/Virgo binary black hole merger events to obtain a 7% bound on the relative difference between the gravitational constant experienced by baryonic matter, and that experienced by black holes, $\mathrm{\ensuremath{\Delta}}G/G$. The recent GW190521 event resulting from two black holes with masses in the canonical mass gap can be explained by modified gravity if the event originated from an unscreened galaxy where the strength of gravity is either enhanced or reduced by $\ensuremath{\sim}30%$ relative to its strength in the Solar System.

Gravitational-wave astronomy with an uncertain noise power spectral density

In order to extract information about the properties of compact binaries, we must estimate the noise power spectral density of gravitational-wave data, which depends on the properties of the gravitational-wave detector. In practice, it is not possible to know this perfectly, only to estimate it from the data. Multiple estimation methods are commonly used and each has a corresponding statistical uncertainty. However, this uncertainty is widely ignored when measuring the physical parameters describing compact binary coalescences, and the appropriate likelihoods which account for the uncertainty are not well known. In order to perform increasingly precise astrophysical inference and model selection, it will be essential to account for this uncertainty. In this work, we derive the correct likelihood for one of the most widely used estimation methods in gravitational-wave transient analysis, the median average. We demonstrate that simulated Gaussian noise follows the predicted distributions. We then examine real gravitational-wave data at and around the time of GW151012, a relatively low-significance binary black hole merger event. We show that the data are well described by stationary-Gaussian noise and explore the impact of different noise power spectral density estimation methods on the astrophysical inferences we draw about GW151012.

Source properties of the lowest signal-to-noise-ratio binary black hole detections

We perform a detailed parameter estimation study of binary black hole merger events reported in Zackay et al. and Venumadhav et al.. These are some of the faintest signals reported so far, and hence, relative to the loud events in the GWTC-1 catalog, the data should have lesser constraining power on their intrinsic parameters. Hence we examine the robustness of parameter inference to choices made in the analysis, as well as any potential systematics. We check the impact of different methods of estimating the noise power spectral density, different waveform models, and different priors for the compact object spins. For most of the events, the resulting differences in the inferred values of the parameters are much smaller than their statistical uncertainties. The estimation of the effective spin parameter $\chi_{\mathrm{eff}}$, i.e. the projection of the mass-weighted total spin along the angular momentum, can be sensitive to analysis choices for two of the sources with the largest effective spin magnitudes, GW151216 and GW170403. The primary differences arise from using a 3D isotropic spin prior: the tails of the posterior distributions should be interpreted with care and due consideration of the other data analysis choices.

Probing noncommutative gravity with gravitational wave and binary pulsar observations

Noncommutative gravity is a natural method of quantizing spacetime by promoting the spacetime coordinates themselves to operators which do not commute. This approach is motivated, for example, from a quantum gravity perspective, among others. Noncommutative gravity has been tested against the binary black hole merger event GW150914. Here, we extend and improve upon such a previous analysis by (i) relaxing an assumption made on the preferred direction due to noncommutativity, (ii) using posterior samples produced by the LIGO/Virgo Collaborations, (iii) consider other gravitational wave events, namely GW151226, GW170608, GW170814 and GW170817, and (iv) consider binary pulsar observations. Using Kepler's law that contains the noncommutative effect at second post-Newtonian order, we derive corrections to the gravitational waveform phase and the pericenter precession. Using the gravitational wave and double pulsar binary observations, we find bounds on a space-time noncommutative tensor $\theta^{0i}$ in terms of the preferred frame direction with respect to the orientation of each binary. We find that the gravitational wave bounds are stronger than the binary pulsar one by an order of magnitude and the noncommutative tensor normalized by the Planck length and time is constrained to be of order unity.

BSE versus StarTrack: Implementations of new wind, remnant-formation, and natal-kick schemes in NBODY7 and their astrophysical consequences

Context. As a result of their formation via massive single and binary stellar evolution, the masses of stellar-remnant black holes (BH) are subjects of great interest in this era of gravitational-wave detection from binary black hole (BBH) and binary neutron star merger events. Aims. In this work, we present new developments in the stellar-remnant formation and related schemes of the current N-body evolution program NBODY7. We demonstrate that the newly implemented stellar-wind and remnant-formation schemes in the stellar-evolutionary sector or BSE of the NBODY7 code, such as the “rapid” and the “delayed” supernova (SN) schemes along with an implementation of pulsational-pair-instability and pair-instability supernova (PPSN/PSN), now produce neutron star (NS) and BH masses that agree nearly perfectly, over large ranges of zero-age-main-sequence (ZAMS) mass and metallicity, with those from the widely recognised StarTrack population-synthesis program. We also demonstrate the new, recipe-based implementations of various widely debated mechanisms of natal kicks on NSs and BHs, such as “convection-asymmetry-driven”, “collapse-asymmetry-driven”, and “neutrino-emission-driven” kicks, in addition to a fully consistent implementation of the standard, fallback-dependent, momentum-conserving natal kick. Methods. All the above newly implemented schemes are also shared with the standalone versions of SSE and BSE. All these demonstrations are performed with both the updated standalone BSE and the updated NBODY7/BSE. Results. When convolved with stellar and primordial-binary populations as observed in young massive clusters, such remnant-formation and natal-kick mechanisms crucially determine the accumulated number, mass, and mass distribution of the BHs retained in young massive, open, and globular clusters (GCs); these BHs would eventually become available for long-term dynamical processing. Conclusions. Among other conclusions, we find that although the newer, delayed SN remnant formation model gives birth to the largest number (mass) of BHs, the older remnant-formation schemes cause the largest number (mass) of BHs to survive in clusters, when incorporating SN material fallback onto the BHs. The SN material fallback also causes the convection-asymmetry-driven SN kick to effectively retain similar numbers and masses of BHs in clusters as for the standard, momentum-conserving kick. The collapse-asymmetry-driven SN kick would cause nearly all BHs to be retained in clusters irrespective of their mass, remnant-formation model, and metallicity, whereas the inference of a large population of BHs in GCs would potentially rule out the neutrino-driven SN kick mechanism. Pre-SN mergers of massive primordial binaries would potentially cause BH masses to deviate from the theoretical, single-star ZAMS to mass-remnant mass relation unless a substantial of the total merging stellar mass of up to ≈40% is lost during a merger process. In particular, such mergers, at low metallicities, have the potential to produce low-spinning BHs within the PSN mass gap that can be retained in a stellar cluster and be available for subsequent dynamical interactions. As recent studies indicate, the new remnant-formation modelling reassures us that young massive and open clusters would potentially contribute to the dynamical BBH merger detection rate to a similar extent as their more massive GC counterparts.