arXiv subjects

Maya Fishbach

Publications and source records attributed to Maya Fishbach.

At least 37 records · Page 2Linked to original sources

arXiv2025

Gravitational-wave dark siren cosmology systematics from galaxy weighting

The detection of GW170817 and the measurement of its redshift from the associated electromagnetic counterpart provided the first gravitational wave determination of the Hubble constant ($H_0$), demonstrating the potential power of standard-siren cosmology. In contrast to this bright siren approach, the dark siren approach can be utilized for gravitational-wave sources in the absence of an electromagnetic counterpart: one considers all galaxies contained within the localization volume as potential hosts. When statistically averaging over the potential host galaxies, weighting them by physically-motivated properties (e.g., tracing star formation or stellar mass) could improve convergence. Using mock galaxy catalogs, we explore the impact of these weightings on the measurement of $H_0$. We find that incorrect weighting schemes can lead to significant biases due to two effects: the assumption of an incorrect galaxy redshift distribution, and preferentially weighting incorrect host galaxies during the inference. The magnitudes of these biases are influenced by the number of galaxies along each line of sight, the measurement uncertainty in the gravitational-wave luminosity distance, and correlations in the parameter space of galaxies. We show that the bias may be overcome from improved localization constraints in future GW detectors, a strategic choice of priors or weighting prescription, and by restricting the analysis to a subset of high-SNR events. We propose the use of hierarchical inference as a diagnostic of incorrectly-weighted prescriptions. Such approaches can simultaneously infer the correct weighting scheme and the values of the cosmological parameters, thereby mitigating the bias in dark siren cosmology due to incorrect host-galaxy weighting.

astro-ph.CO↗

arXiv2025

Transdimensional inference for gravitational-wave astronomy with Bilby

It has become increasingly useful to answer questions in gravitational-wave astronomy using transdimensional models where the number of free parameters can be varied depending on the complexity required to fit the data. Given the growing interest in transdimensional inference, we introduce a new package for the Bayesian inference Library (Bilby) called tBilby. The tBilby package allows users to set up transdimensional inference calculations using the existing Bilby architecture with off-the-shelf nested samplers and/or Markov Chain Monte Carlo algorithms. Transdimensional models are particularly helpful when we seek to test theoretically uncertain predictions described by phenomenological models. For example, bursts of gravitational waves can be modelled using a superposition of N wavelets where N is itself a free parameter. Short pulses are modelled with small values of N whereas longer, more complicated signals are represented with a large number of wavelets stitched together. Other transdimensional models have found use describing instrumental noise and the population properties of gravitational-wave sources. We provide a few demonstrations of tBilby, including fitting the gravitational-wave signal GW150914 with a superposition of N sine-Gaussian wavelets. We outline our plans to further develop the tbilby code suite for a broader range of transdimensional problems.

gr-qc↗

arXiv2024

Are long gamma-ray bursts progenitors to merging binary black holes?

The distribution of delay times between the formation of binary black hole (BBH) progenitors and their gravitational-wave (GW) merger provides important clues about their unknown formation histories. When inferring the delay time distribution, it is typically assumed that BBH progenitor formation traces the star formation rate (SFR). In this work, we consider the rate of long gamma-ray bursts (LGRBs) instead of the SFR. LGRBs are thought to correspond to the formation of (possibly spinning) black holes, and may therefore be related to the BBH progenitor population. By comparing the redshift evolution of the LGRB rate as inferred by Ghirlanda & Salvaterra (2022) and the BBH merger rate inferred by LIGO-Virgo-KAGRA (LVK) observations, we find that the delay time distribution between LGRBs and BBH mergers is well-described by a power law with minimum delay time $10$ Myr and slope $α={-0.96}^{+0.64}_{-0.76}$ (90% credibility). This matches theoretical expectations for the BBH delay time distribution, which in turn lends support to the hypothesis that LGRBs trace BBH progenitor formation. However, comparing the absolute rates of these two populations, we find that at most $f = {4}^{+10}_{-2}\%$ of LGRBs may evolve into merging BBH. We also consider the possibility that LGRBs only produce BBH systems with large aligned spins (with effective inspiral spin $χ_\mathrm{eff} > 0.2$). In this case, we find $f = 0.3^{+1.0}_{-0.2}\%$ and the delay time distribution favors the steepest power-law slopes we consider ($α= -2$). We argue that asynchronous observations of LGRBs and GWs provide a powerful multimessenger probe of black hole lifecycles across cosmic history.

astro-ph.HE↗

arXiv2024

Things that might go bump in the night: Assessing structure in the binary black hole mass spectrum

Several features in the mass spectrum of merging binary black holes (BBHs) have been identified using data from the Third Gravitational Wave Transient Catalog (GWTC-3). These features are of particular interest as they may encode the uncertain mechanism of BBH formation. We assess if the features are statistically significant or the result of Poisson noise due to the finite number of observed events. We simulate catalogs of BBHs whose underlying distribution does not have the features of interest, apply the analysis previously performed on GWTC-3, and determine how often such features are spuriously found. We find that one of the features found in GWTC-3, the peak at $\sim35\,M_{\odot}$, cannot be explained by Poisson noise alone: peaks as significant occur in $1.7\%$ of catalogs generated from a featureless population. This peak is therefore likely to be of astrophysical origin. The data is suggestive of an additional significant peak at $\sim10\,M_{\odot}$, though the exact location of this feature is not resolvable with current observations. Additional structure beyond a power law, such as the purported dip at $\sim14\,M_{\odot}$, can be explained by Poisson noise. We also provide a publicly-available package, \texttt{GWMockCat}, that creates simulated catalogs of BBH events with correlated measurement uncertainty and selection effects according to user-specified underlying distributions and detector sensitivities.

astro-ph.HE↗

arXiv2024

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 simplistic prescriptions are used 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 star), 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 $\sim30\,M_{\odot}$ peak existing only in the distribution of \emph{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 other previous studies. In either case, the peak is observed at $31.4_{-2.6}^{+2.3}\,M_{\odot}$, 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.

astro-ph.HE↗

arXiv2024

Inferring host-galaxy properties of LIGO-Virgo-KAGRA's black holes

Observations of gravitational waves from binary black hole (BBH) mergers have measured the redshift evolution of the BBH merger rate. The number density of galaxies in the Universe evolves differently with redshift based on their physical properties, such as their stellar masses and star formation rates. In this work we show that the measured population-level redshift distribution of BBHs sheds light on the properties of their probable host-galaxies. We first assume that the hosts of BBHs can be described by a mixture model of galaxies weighted by stellar mass or star formation rate, and find that we can place upper limits on the fraction of mergers coming from a stellar mass weighted sample of galaxies. We then constrain parameters of a physically motivated power-law delay-time distribution using GWTC-3 data, and self-consistently track galaxies in the \textsc{UniverseMachine} simulations with this delay-time model to infer the probable host-galaxies of BBHs over a range of redshifts. We find that the inferred host-galaxy distribution at redshift $z=0.21$ has a median star formation rate $\sim 0.9\,M_\odot\mathrm{yr}^{-1}$ and a median stellar mass of $\sim 1.9 \times 10^{10}\,M_\odot$. We also provide distributions for the mean stellar age, halo mass, halo radius, peculiar velocity, and large scale bias associated with the host-galaxies, as well as their absolute magnitudes in the B- and ${ \rm K_s}$-bands. Our results can be used to design optimal electromagnetic follow-up strategies for BBHs, and also to aid the measurement of cosmological parameters using the statistical dark siren method.

astro-ph.HE↗

arXiv2024

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 $z \approx 1$, 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 $M_1\gtrsim40\,M_{\odot}$, the BBH merger rate reaches its peak at redshift $z\approx2.1$, while for $M_1\lesssim20\,M_{\odot}$, the peak occurs at $z\approx1.1$, assuming that the cluster formation rate peaks at $z=2.2$. The average BBH primary mass also increases from $\sim 10\,M_{\odot}$ at $z=0$ to $\sim 30\,M_{\odot}$ at $z=10$. We show that $\sim 20\%$ 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.

astro-ph.HE↗

arXiv2024

The Mass Density of Merging Binary Black Holes Over Cosmic Time

The connection between the binary black hole (BBH) mergers observed by LIGO-Virgo-KAGRA (LVK) and their stellar progenitors remains uncertain. Specifically, the fraction $ε$ of stellar mass that ends up in BBH mergers and the delay time $τ$ between star formation and BBH merger carry information about the astrophysical processes that give rise to merging BBHs. We model the BBH merger rate in terms of the cosmic star formation history, coupled with a metallicity-dependent efficiency $ε$ and a distribution of delay times $τ$, and infer these parameters with data from the Third Gravitational-Wave Transient Catalog (GWTC-3). We find that the progenitors to merging BBHs preferentially form in low metallicity environments with a low metallicity efficiency of $\log_{10}ε_{ 10\,M_\odot$) progenitors. However, because massive stars are so short-lived, there may be more mass in merging BBHs than in living massive stars as early as $\sim 2.5$ Gyr ago. We also compare to the mass in supermassive BHs, finding that the mass densities were comparable $\sim 12.5$ Gyr ago, but the mass density in SMBHs quickly increased to $\sim 75$ times the mass density in merging stellar mass BBHs by $z\sim 1$.

astro-ph.HE↗

arXiv2023

LIGO-Virgo-KAGRA's Oldest Black Holes: Probing star formation at cosmic noon with GWTC-3

In their third observing run, the LIGO-Virgo-KAGRA gravitational-wave (GW) observatory was sensitive to binary black hole (BBH) mergers out to redshifts $z_\mathrm{merge}\approx1$. Because GWs are inefficient at shrinking the binary orbit, some of these BBH systems likely experienced long delay times $τ$ between the formation of their progenitor stars at $z_\mathrm{form}$ and their GW merger at $z_\mathrm{merge}$. In fact, the distribution of delay times predicted by isolated binary evolution resembles a power law $p(τ)\proptoτ^{α_τ}$ with slope $-1\lesssimα_τ\lesssim-0.35$ and a minimum delay time of $τ_\mathrm{min}=10$ Myr. We use these predicted delay time distributions to infer the formation redshifts of the $\sim70$ BBH events reported in the third GW transient catalog GWTC-3 and the formation rate of BBH progenitors. For our default $α_τ=-1$ delay time distribution, we find that GWTC-3 contains at least one system (with 90\% credibility) that formed earlier than $z_\mathrm{form}>4.4$. Comparing our inferred BBH progenitor formation rate to the star formation rate (SFR), we find that at $z_\mathrm{form}=4$, the number of BBH progenitor systems formed per stellar mass was $6.4^{+9.4}_{-5.5}\times10^{-6}\,M_\odot^{-1}$ and this yield dropped to $0.134^{+1.6}_{-0.127}\times10^{-6}\,M_\odot^{-1}$ by $z_\mathrm{form}=0$. We discuss implications of this measurement for the cosmic metallicity evolution, finding that for typical assumptions about the metallicity-dependence of the BBH yield, the average metallicity at $z_\mathrm{form}=4$ was $\langle\log_{10}(Z/Z_\odot)\rangle=-0.3^{+0.3}_{-0.4}$, although the inferred metallicity can vary by a factor of $\approx3$ for different assumptions about the BBH yield. Our results highlight the promise of current GW observatories to probe high-redshift star formation.

astro-ph.GA↗

arXiv2023

DAGnabbit! Ensuring Consistency between Noise and Detection in Hierarchical Bayesian Inference

Hierarchical Bayesian inference can simultaneously account for both measurement uncertainty and selection effects within astronomical catalogs. In particular, the hierarchy imposed encodes beliefs about the interdependence of the physical processes that generate the observed data. We show that several proposed approximations within the literature actually correspond to inferences that are incompatible with any physical detection process, which can be described by a directed acyclic graph (DAG). This generically leads to biases and is associated with the assumption that detectability is independent of the observed data given the true source parameters. We show several examples of how this error can affect astrophysical inferences based on catalogs of coalescing binaries observed through gravitational waves, including misestimating the redshift evolution of the merger rate as well as incorrectly inferring that General Relativity is the correct theory of gravity when it is not. In general, one cannot directly fit for the ``detected distribution'' and ``divide out'' the selection effects in post-processing. Similarly, when comparing theoretical predictions to observations, it is better to simulate detected data (including both measurement noise and selection effects) rather than comparing estimates of the detected distributions of event parameters (which include only selection effects). While the biases introduced by model misspecification from incorrect assumptions may be smaller than statistical uncertainty for moderate catalog sizes (O(100) events), they will nevertheless pose a significant barrier to precision measurements of astrophysical populations.

gr-qc↗

arXiv2023

The role of natal kicks in forming asymmetric compact binary mergers

In their most recent observing run, the LIGO-Virgo-KAGRA (LVK) Collaboration observed gravitational waves (GWs) from compact binary mergers with highly asymmetric mass ratios, including both binary black holes (BBHs) and neutron star--black holes (NSBHs). It appears that NSBHs with mass ratios $q\simeq0.2$ are more common than equally asymmetric BBHs, but the reason for this remains unclear. We use the binary population synthesis code COSMIC to investigate the evolutionary pathways leading to the formation and merger of asymmetric compact binaries. We find that within the context of isolated binary stellar evolution, most asymmetric mergers start off as asymmetric stellar binaries. Because of the initial asymmetry, these systems tend to first undergo a dynamically unstable mass transfer phase. However, after the first star collapses to a compact object, the mass ratio is close to unity and the second phase of mass transfer is usually stable. According to our simulations, this stable mass transfer fails to shrink the orbit enough on its own for the system to merge. Instead, the natal kick received by the second-born compact object during its collapse is key in determining how many of these systems can merge. For the most asymmetric systems with mass ratios $q\leq0.1$, the merging systems in our models receive an average kick magnitude of 255 km s$^{-1}$ during the second collapse, while the average kick for non-merging systems is 59 km s$^{-1}$. Because lower mass compact objects, like NSs, are expected to receive larger natal kicks than higher mass BHs, this may explain why asymmetric NSBH systems merge more frequently than asymmetric BBH systems.

astro-ph.HE↗

arXiv2023

Roman CCS White Paper: Characterizing the Galactic population of isolated black holes

Although there are estimated to be 100 million isolated black holes (BHs) in the Milky Way, only one has been found so far, resulting in significant uncertainty about their properties. The Galactic Bulge Time Domain Survey provides the only opportunity in the coming decades to grow this catalog by order(s) of magnitude. This can be achieved if 1) Roman's astrometric potential is fully realized in the observation strategy and software pipelines, 2) Roman's observational gaps of the Bulge are minimized, and 3) observations with ground-based facilities are taken of the Bulge to fill in gaps during non-Bulge seasons. A large sample of isolated BHs will enable a broad range of astrophysical questions to be answered, such as massive stellar evolution, origin of gravitational wave sources, supernova physics, and the growth of supermassive BHs, maximizing Roman's scientific return.

astro-ph.IM↗

arXiv2023

Globular cluster formation histories, masses and radii inferred from gravitational waves

Globular clusters (GCs) are found in all types of galaxies and harbor some of the most extreme stellar systems, including black holes that may dynamically assemble into merging binaries (BBHs). Uncertain GC properties, including when they formed, their initial masses and sizes, affect their production rate of BBH mergers. Using the gravitational-wave catalog GWTC-3, we measure that dynamically-assembled BBHs -- those that are consistent with isotropic spin directions -- make up ${61^{+29}_{-44}\%}$ of the total merger rate, with a local merger rate of ${10.9^{+16.8}_{-9.3}}$ Gpc$^{-3}$ yr$^{-1}$ rising to ${58.9^{+149.4}_{-46.0}}$ Gpc$^{-3}$ yr$^{-1}$ at $z = 1$. We assume this inferred rate describes the contribution from GCs and compare it against the Cluster Monte Carlo (CMC) simulation catalog to directly fit for the GC initial mass function, virial radius distribution, and formation history. We find that GC initial masses are consistent with a Schechter function with slope ${β_m = -1.9^{+0.8}_{-0.8}}$. Assuming a mass function slope of $β_m = -2$ and a mass range between $10^4$--$10^8\,M_\odot$, we infer a GC formation rate at $z = 2$ of ${5.0^{+9.4}_{-4.0}}$ Gpc$^{-3}$ yr$^{-1}$, or ${2.1^{+3.9}_{-1.7}}\times 10^6\,M_\odot$ Gpc$^{-3}$ yr$^{-1}$ in terms of mass density. We find that the GC formation rate probably rises more steeply than the global star formation rate between $z = 0$ and $z = 3$ ({82\%} credibility) and implies a local number density that is ${f_\mathrm{ev} = 22.6^{+29.9}_{-16.2}}$ times higher than the observed density of survived GCs. This is consistent with expectations for cluster evaporation, but may suggest that other environments contribute to the rate of BBH mergers with significantly tilted spins.

astro-ph.GA↗

arXiv2022

Unveiling the Universe with Emerging Cosmological Probes

The detection of the accelerated expansion of the Universe has been one of the major breakthroughs in modern cosmology. Several cosmological probes (CMB, SNe Ia, BAO) have been studied in depth to better understand the nature of the mechanism driving this acceleration, and they are being currently pushed to their limits, obtaining remarkable constraints that allowed us to shape the standard cosmological model. In parallel to that, however, the percent precision achieved has recently revealed apparent tensions between measurements obtained from different methods. These are either indicating some unaccounted systematic effects, or are pointing toward new physics. Following the development of CMB, SNe, and BAO cosmology, it is critical to extend our selection of cosmological probes. Novel probes can be exploited to validate results, control or mitigate systematic effects, and, most importantly, to increase the accuracy and robustness of our results. This review is meant to provide a state-of-art benchmark of the latest advances in emerging beyond-standard cosmological probes. We present how several different methods can become a key resource for observational cosmology. In particular, we review cosmic chronometers, quasars, gamma-ray bursts, standard sirens, lensing time-delay with galaxies and clusters, cosmic voids, neutral hydrogen intensity mapping, surface brightness fluctuations, stellar ages of the oldest objects, secular redshift drift, and clustering of standard candles. The review describes the method, systematics, and results of each probe in a homogeneous way, giving the reader a clear picture of the available innovative methods that have been introduced in recent years and how to apply them. The review also discusses the potential synergies and complementarities between the various probes, exploring how they will contribute to the future of modern cosmology.

astro-ph.CO↗

arXiv2022

The Hitchhiker's guide to the galaxy catalog approach for gravitational wave cosmology

We outline the ``dark siren'' galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz (1986), one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Hunterer 2021 recently claimed that this approach results in a biased estimate of the Hubble constant, $H_0$, when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias.

gr-qc↗

arXiv2022

Do high-spin high-mass X-ray binaries contribute to the population of merging binary black holes?

Gravitational-wave observations of binary black hole (BBH) systems point to black hole spin magnitudes being relatively low. These measurements appear in tension with high spin measurements for high-mass X-ray binaries (HMXBs). We use grids of MESA simulations combined with the rapid population-synthesis code COSMIC to examine the origin of these two binary populations. It has been suggested that Case-A mass transfer while both stars are on the main sequence can form high-spin BHs in HMXBs. Assuming this formation channel, we show that depending on critical mass ratios for the stability of mass transfer, 48-100% of these Case-A HMXBs merge during the common-envelope phase and up to 42% result in binaries too wide to merge within a Hubble time. Both MESA and COSMIC show that high-spin HMXBs formed through Case-A mass transfer can only form merging BBHs within a small parameter space where mass transfer can lead to enough orbital shrinkage to merge within a Hubble time. We find that only up to 11% of these Case-A HMXBs result in BBH mergers, and at most 20% of BBH mergers came from Case-A HMXBs. Therefore, it is not surprising that these two spin distributions are observed to be different.

astro-ph.HE↗

arXiv2022

Inferring the neutron star maximum mass and lower mass gap in neutron star-black hole systems with spin

Gravitational-wave (GW) detections of merging neutron star-black hole (NSBH) systems probe astrophysical neutron star (NS) and black hole (BH) mass distributions, especially at the transition between NS and BH masses. Of particular interest are the maximum NS mass, minimum BH mass, and potential mass gap between them. While previous GW population analyses assumed all NSs obey the same maximum mass, if rapidly spinning NSs exist, they can extend to larger maximum masses than nonspinning NSs. In fact, several authors have proposed that the $\sim2.6\,M_\odot$ object in the event GW190814 -- either the most massive NS or least massive BH observed to date -- is a rapidly spinning NS. We therefore infer the NSBH mass distribution jointly with the NS spin distribution, modeling the NS maximum mass as a function of spin. Using 4 LIGO-Virgo NSBH events including GW190814, if we assume that the NS spin distribution is uniformly distributed up to the maximum (breakup) spin, we infer the maximum non-spinning NS mass is $2.7^{+0.5}_{-0.4}\,M_\odot$ (90\% credibility), while assuming only nonspinning NSs, the NS maximum mass must be $>2.53 M_\odot$ (90\% credibility). The data support the mass gap's existence, with a minimum BH mass at $5.4^{+0.7}_{-1.0} M_\odot$. With future observations, under simplified assumptions, 150 NSBH events may constrain the maximum nonspinning NS mass to $\pm0.02\,M_\odot$, and we may even measure the relation between the NS spin and maximum mass entirely from GW data. If rapidly rotating NSs exist, their spins and masses must be modeled simultaneously to avoid biasing the NS maximum mass.

astro-ph.HE↗

arXiv2022

Limits on hierarchical black hole mergers from the most negative $χ_\mathrm{eff}$ systems

It has been proposed that some black holes (BHs) in binary black hole (BBH) systems are born from "hierarchical mergers" (HM); i.e. earlier mergers of smaller BHs. These HM products have spin magnitudes $χ\sim 0.7$, and, if they are dynamically assembled into BBH systems, their spin orientations will be sometimes anti-aligned with the binary orbital angular momentum. In fact, as Baibhav et al. (2020) showed, $\sim16\%$ of BBH systems that include HM products will have an effective inspiral spin parameter, $χ_\mathrm{eff} < -0.3$. Nevertheless, the LIGO-Virgo-Kagra (LVK) gravitational-wave (GW) detectors have yet to observe a BBH system with $χ_\mathrm{eff} \lesssim -0.2$, leading to upper limits on the fraction of HM products in the population. We fit the astrophysical mass and spin distribution of BBH systems and measure the fraction of BBH systems with $χ_\mathrm{eff} < -0.3$, which implies an upper limit on the HM fraction. We find that fewer than $26\%$ of systems in the underlying BBH population include HM products (90\%. credibility). Even among BBH systems with primary masses $m_1=60\,M_\odot$, the HM fraction is less than 69\%, which may constrain the location of the pair-instability mass gap. With 300 GW events (to be expected in the LVK's next observing run), if we fail to observe a BBH with $χ_\mathrm{eff} < -0.3$, we can conclude that the HM fraction is smaller than $2.5^{+9.1}_{-2.2}\%$.

astro-ph.HE↗