Black hole binary mergers in dense star clusters: the importance of primordial binaries

Dense stellar clusters are expected to house the ideal conditions for binary black hole (BBH) formation, both through binary stellar evolution and through dynamical encounters. We use theoretical arguments as well as $N$-body simulations to make predictions for the evolution of BBHs formed through stellar evolution inside clusters from the cluster birth (which we term $\textbf{primordial binaries}$), and for the sub-population of merging BBHs. We identify three key populations: (i) BBHs that form in the cluster, and merge before experiencing any $\textit{strong}$ dynamical interaction; (ii) binaries that are ejected from the cluster after only one dynamical interaction; and, (iii) BBHs that experience more than one strong interaction inside the cluster. We find that populations (i) and (ii) are the dominant source of all BBH mergers formed in clusters with escape velocity $v_{\mathrm{esc}}\leq 30$ $\mathrm{km\,s^{-1}}$. At higher escape velocities, dynamics are predicted to play a major role both for the formation and subsequent evolution of BBHs. Finally, we argue that for sub-Solar metallicity clusters with $v_{\mathrm{esc}}\lesssim100$ $\mathrm{km\,s^{-1}}$, the dominant form of interaction experienced by primordial BBHs (BBHs formed from primordial binaries) within the cluster is with other BBHs. The complexity of these binary-binary interactions will complicate the future evolution of the BBH and influence the total number of mergers produced.Comment: 20 pages, 12 figures. Accepted by MNRA

Coalescing black hole binaries from globular clusters: mass distributions and comparison to gravitational wave data from GWTC-3

We use our cluster population model, cBHBd, to explore the mass distribution of merging black hole binaries formed dynamically in globular clusters. We include in our models the effect of mass growth through hierarchical mergers and compare the resulting distributions to those inferred from the third gravitational wave transient catalogue. We find that none of our models can reproduce the peak at $m_1\simeq 10M_\odot$ in the primary black hole mass distribution that is inferred from the data. This disfavours a scenario where most of the detected sources are formed in globular clusters. On the other hand, a globular cluster origin can account for the inferred secondary peak at $m_1\simeq 35M_\odot$, which requires that the most massive clusters form with half-mass densities $\rho_{\rm h,0} \gtrsim 10^4 M_\odot \rm pc^{-3}$. Finally, we find that the lack of a high mass cut--off in the inferred mass distribution can be also explained by the repopulation of an initial mass gap through hierarchical mergers. Matching the inferred merger rate above $\simeq 50M_\odot$ requires both initial cluster densities $\rho_{\rm h,0} \gtrsim 10^4 M_\odot \rm pc^{-3}$, and that black holes form with nearly zero spin. A hierarchical merger scenario makes specific predictions for the appearance and position of multiple peaks in the black hole mass distribution, which can be tested against future data.Comment: Submitted to MNRAS; 10 pages, 5 figure

Black hole binary mergers in dense star clusters: the importance of primordial binaries

Dense stellar clusters are expected to house the ideal conditions for binary black hole (BBH) formation, both through binary stellar evolution and through dynamical encounters. We use theoretical arguments as well as N-body simulations to make predictions for the evolution of BBHs formed through stellar evolution inside clusters from the cluster birth (which we term primordial binaries), and for the sub-population of merging BBHs. We identify three key populations: (i) BBHs that form in the cluster, and merge before experiencing any strong dynamical interaction; (ii) binaries that are ejected from the cluster after only one dynamical interaction; and (iii) BBHs that experience more than one strong interaction inside the cluster. We find that populations (i) and (ii) are the dominant source of all BBH mergers formed in clusters with escape velocity vesc ≤ 30 ⁠. At higher escape velocities, dynamics are predicted to play a major role both for the formation and subsequent evolution of BBHs. Finally, we argue that for sub-Solar metallicity clusters with vesc ≲ 100 ⁠, the dominant form of interaction experienced by primordial BBHs (BBHs formed from primordial binaries) within the cluster is with other BBHs. The complexity of these binary–binary interactions will complicate the future evolution of the BBH and influence the total number of mergers produced

Binary black hole mergers in nuclear star clusters: eccentricities, spins, masses, and the growth of massive seeds

We investigate the formation of intermediate mass black holes (IMBHs) through hierarchical mergers of stellar origin black holes (BHs), as well as BH mergers formed dynamically in nuclear star clusters. Using a semi-analytical approach which incorporates probabilistic mass-function-dependent double BH (DBH) pairing, binary-single encounters, and a mass-ratio-dependent prescription for energy dissipation in hardening binaries, we find that IMBHs with masses of $\mathcal{O}(10^2)$~--~$\mathcal{O}(10^4)\,\rm M_\odot$ can be formed solely through hierarchical mergers in timescales of a few $100$\,Myrs to a few\,Gyrs. Clusters with escape velocities $\gtrsim400$\,km\,s$^{-1}$ inevitably form high-mass IMBHs. The spin distribution of IMBHs with masses $\gtrsim 10^3M_\odot$ is strongly clustered at $\chi\sim 0.15$; while for lower masses, it at $\chi\sim 0.7$. Eccentric mergers are more frequent for equal-mass binaries containing first- and/or second-generation BHs. Metal-rich, young, dense clusters can produce up to $20\%$ of their DBH mergers with eccentricity $\geq0.1$ at $10\,\rm Hz$, and $\sim2$~--~$9\%$ of all in-cluster mergers can form at $>10$\,Hz. Nuclear star clusters are therefore promising environments for the formation of highly-eccentric DBH mergers, detectable with current gravitational-wave detectors. Clusters of extreme mass ($\sim10^8$\,M$_\odot$) and density ($\sim10^8$\,M$_\odot$pc$^{-3}$) can have about half of all of their DBH mergers with primary masses $\geq100$\,M$_\odot$. The fraction of in-cluster mergers increases rapidly with increasing cluster escape velocity, being nearly unity for $v_{\rm esc}\gtrsim 200$\,km\,s$^{-1}$. Cosmological merger rate of DBHs from nuclear clusters varies $\approx0.01-1$\,Gpc$^{-3}$yr$^{-1}$.Comment: submitted to MNRA

Neutron star-black hole mergers in next generation gravitational-wave observatories

Observations by the current generation of gravitational-wave detectors have been pivotal in expanding our understanding of the universe. Although tens of exciting compact binary mergers have been observed, neutron star-black hole (NSBH) mergers remained elusive until they were first confidently detected in 2020. The number of NSBH detections is expected to increase with sensitivity improvements of the current detectors and the proposed construction of new observatories over the next decade. In this work, we explore the NSBH detection and measurement capabilities of these upgraded detectors and new observatories using the following metrics: network detection efficiency and detection rate as a function of redshift, distributions of the signal-to-noise ratios, the measurement accuracy of intrinsic and extrinsic parameters, the accuracy of sky position measurement, and the number of early-warning alerts that can be sent to facilitate the electromagnetic follow-up. Additionally, we evaluate the prospects of performing multi-messenger observations of NSBH systems by reporting the number of expected kilonova detections with the Vera C. Rubin Observatory and the Nancy Grace Roman Space Telescope. We find that as many as $\mathcal{O}(10)$ kilonovae can be detected by these two telescopes every year, depending on the population of the NSBH systems and the equation of state of neutron stars.Comment: 30 pages, 15 figure

Binary population synthesis with probabilistic remnant mass and kick prescriptions

We report on the impact of a probabilistic prescription for compact remnant masses and kicks on massive binary population synthesis. We find that this prescription populates the putative mass gap between neutron stars and black holes with low-mass black holes. However, evolutionary effects reduce the number of X-ray binary candidates with low-mass black holes, consistent with the dearth of such systems in the observed sample. We further find that this prescription is consistent with the formation of heavier binary neutron stars such as GW190425, but over-predicts the masses of Galactic double neutron stars. The revised natal kicks, particularly increased ultra-stripped supernova kicks, do not directly explain the observed Galactic double neutron star orbital period--eccentricity distribution. Finally, this prescription allows for the formation of systems similar to the recently discovered extreme mass ratio binary GW190814, but only if we allow for the survival of binaries in which the common envelope is initiated by a donor crossing the Hertzsprung gap, contrary to our standard model.Comment: Updated version as accepted by MNRA

Double black hole mergers in nuclear star clusters: eccentricities, spins, masses, and the growth of massive seeds

We investigate the formation of intermediate mass black holes (IMBHs) through hierarchical mergers of stellar origin black holes (BHs), as well as BH mergers formed dynamically in nuclear star clusters. Using a semi-analytical approach that incorporates probabilistic mass-function-dependent double BH (DBH) pairing, binary-single encounters, and a mass-ratio-dependent prescription for energy dissipation in hardening binaries, we find that IMBHs with masses of – can be formed solely through hierarchical mergers in time-scales of a few 100 Myrs to a few Gyrs. Clusters with escape velocities ≳400 km s−1 inevitably form high-mass IMBHs. The spin distribution of IMBHs with masses ≳ 103 M⊙ is strongly clustered at χ ∼ 0.15; while for lower masses, it peaks at χ ∼ 0.7. Eccentric mergers are more frequent for equal-mass binaries containing first- and/or second-generation BHs. Metal-rich, young, dense clusters can produce up to 20 per cent of their DBH mergers with eccentricity ≥0.1 at ⁠, and ∼2–9 per cent of all in-cluster mergers can form at >10 Hz. Nuclear star clusters are therefore promising environments for the formation of highly eccentric DBH mergers, detectable with current gravitational-wave detectors. Clusters of extreme mass (∼108 M⊙) and density (∼108 M⊙ pc−3) can have about half of all of their DBH mergers with primary masses ≥100 M⊙. The fraction of in-cluster mergers increases rapidly with increasing cluster escape velocity, being nearly unity for vesc ≳ 200 km s−1. Cosmological merger rate of DBHs from nuclear clusters varies ⪅0.01–1 Gpc−3 yr−1, where the large error bars come from uncertainties in the cluster initial conditions, number density distribution, and redshift evolution of nucleated galaxies

Linking the rates of neutron star binaries and short gamma-ray bursts

Short gamma-ray bursts are believed to be produced by both binary neutron star (BNS) and neutron star-black hole (NSBH) mergers. We use current estimates for the BNS and NSBH merger rates to calculate the fraction of observable short gamma-ray bursts produced through each channel. This allows us to constrain merger rates of BNS to $\mathcal{R}_{\rm{BNS}}=384^{+431}_{-213}{\rm{Gpc}^{-3} \rm{yr}^{-1}}$ ($90\%$ credible interval), a $16\%$ decrease in the rate uncertainties from the second LIGO--Virgo Gravitational-Wave Transient Catalog, GWTC-2. Assuming a top-hat emission profile with a large Lorentz factor, we constrain the average opening angle of gamma-ray burst jets produced in BNS mergers to $\approx 15^\circ$. We also measure the fraction of BNS and NSBH mergers that produce an observable short gamma-ray burst to be $0.02^{+0.02}_{-0.01}$ and $0.01 \pm 0.01$, respectively and find that $\gtrsim 40\%$ of BNS mergers launch jets (90\% confidence). We forecast constraints for future gravitational-wave detections given different modelling assumptions, including the possibility that BNS and NSBH jets are different. With $24$ BNS and $55$ NSBH observations, expected within six months of the LIGO-Virgo-KAGRA network operating at design sensitivity, it will be possible to constrain the fraction of BNS and NSBH mergers that launch jets with $10\%$ precision. Within a year of observations, we can determine whether the jets launched in NSBH mergers have a different structure than those launched in BNS mergers and rule out whether $\gtrsim 80\%$ of binary neutron star mergers launch jets. We discuss the implications of future constraints on understanding the physics of short gamma-ray bursts and binary evolution.Comment: Accepted in Physical Review D: 13 pages, 5 figure

Black hole–black hole total merger mass and the origin of LIGO/Virgo sources

Abstract: The LIGO–Virgo–KAGRA (LVK) Collaboration has reported nearly 100 black hole (BH)–BH mergers. LVK provides estimates of rates, masses, effective spins, and redshifts for these mergers. Yet the formation channel(s) of the mergers remains uncertain. One way to search for a formation site is to contrast the properties of detected BH–BH mergers with different models of BH–BH merger formation. Our study is designed to investigate the usefulness of the total BH–BH merger mass and its evolution with redshift in establishing the origin of gravitational-wave sources. We find that the average intrinsic BH–BH total merger mass shows exceptionally different behaviors for the models that we adopt for our analysis. In the local universe (z = 0), the average merger mass changes from M¯tot, int∼25M⊙ for the common envelope binary evolution and open cluster formation channels, to M¯tot, int∼30M⊙ for the stable Roche lobe overflow binary channel, to M¯tot, int∼45M⊙ for the globular cluster channel. These differences are even more pronounced at larger redshifts. However, these differences are diminished when considering the LVK O3 detector sensitivity. A comparison with the LVK O3 data shows that none of our adopted models can match the data, despite the large errors on BH–BH masses and redshifts. We emphasize that our conclusions are derived from a small set of six models that are subject to numerous known uncertainties. We also note that BH–BH mergers may originate from a mix of several channels, and that other (than those adopted here) BH–BH formation channels may exist