We study the dynamics of stellar‐mass black holes (BH) in star clusters with particular attention to the formation of BH–BH binaries, which are interesting as sources of gravitational waves (GW). In the present study, we examine the properties of these BH–BH binaries through direct N‐body simulations of star clusters using the nbody6 code on graphical processing unit platforms. We perform simulations for star clusters with ≤105 low‐mass stars starting from Plummer models with an initial population of BHs, varying the cluster mass and BH‐retention fraction. Additionally, we do several calculations of star clusters confined within a reflective boundary mimicking only the core of a massive star cluster which can be performed much faster than the corresponding full cluster integration. We find that stellar‐mass BHs with masses ∼10 M⊙ segregate rapidly (∼100 Myr time‐scale) into the cluster core and form a dense subcluster of BHs within typically 0.2–0.5 pc radius. In such a subcluster, BH–BH binaries can be formed through three‐body encounters, the rate of which can become substantial in dense enough BH cores. While most BH binaries are finally ejected from the cluster by recoils received during superelastic encounters with the single BHs, few of them harden sufficiently so that they can merge via GW emission within the cluster. We find that for clusters with N≳ 5 × 104, typically 1–2 BH–BH mergers occur per cluster within the first ∼4 Gyr of cluster evolution. Also for each of these clusters, there are a few escaping BH binaries that can merge within a Hubble time, most of the merger times being within a few Gyr. These results indicate that intermediate‐age massive clusters constitute the most important class of candidates for producing dynamical BH–BH mergers. Old globular clusters cannot contribute significantly to the present‐day BH–BH merger rate since most of the mergers from them would have occurred much earlier. On the other hand, young massive clusters with ages less that 50 Myr are too young to produce significant number of BH–BH mergers. We finally discuss the detection rate of BH–BH inspirals by the ‘Laser Interferometer Gravitational‐Wave Observatory' (LIGO) and ‘Advanced LIGO’ GW detectors. Our results indicate that dynamical BH–BH binaries constitute the dominant channel for BH–BH merger detection.

The study of stellar-remnant black holes (BH) in dense stellar clusters is now in the spotlight, especially due to their intrinsic ability to form binary black holes (BBH) through dynamical encounters, that potentially coalesce via gravitational-wave (GW) radiation. In this work, which is a continuation from a recent study (Paper I), additional models of compact stellar clusters with initial masses 10 5 M and also those with small fractions of primordial binaries ( 10%) are evolved for long term, applying the direct N-body approach, assuming state-of-the-art stellar-wind and remnantformation prescriptions. That way, a substantially broader range of computed models than that in Paper I is achieved. As in Paper I, the general-relativistic BBH mergers continue to be mostly mediated by triples that are bound to the clusters rather than happen among the ejected BBHs. In fact, the number of such in situ BBH mergers, per cluster, tend to increase significantly with the introduction of a small population of primordial binaries. Despite the presence of massive primordial binaries, the merging BBHs, especially the in situ ones, are found to be exclusively dynamically assembled and hence would be spin-orbit misaligned. The BBHs typically traverse through both the LISA's and the LIGO's detection bands, being audible to both instruments. The "dynamical heating" of the BHs keeps the Electron-Capture-Supernova (ECS) neutron stars (NS) from effectively mass segregating and participating in exchange interactions; the dynamically-active BHs would also exchange into any NS binary within 1 Gyr. Such young massive and open clusters have the potential to contribute to the dynamical BBH merger detection rate to a similar extent as their more massive globular-cluster counterparts.

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.

Stellar-remnant black holes (BH) in dense stellar clusters have always drawn attention due to their potential in a number of phenomena, especially the dynamical formation of binary black holes (BBH), which potentially coalesce via gravitational-wave (GW) radiation. This study presents a preliminary set of evolutionary models of compact stellar clusters with initial masses ranging over 1.0 × 10 4 M − 5.0 × 10 4 M , and halfmass radius of 2 or 1 pc, that is typical for young massive and starburst clusters. They have metallicities between 0.05Z − Z . Including contemporary schemes for stellar wind and remnant formation, such model clusters are evolved, for the first time, using the state-of-the-art direct N-body evolution program NBODY7 , until their dissolution or at least for 10 Gyr. That way, a self-regulatory behaviour in the effects of dynamical interactions among the BHs is demonstrated. In contrast to earlier studies, the BBH coalescences obtained in these models show a prominence in triple-mediated coalescences while being bound to the clusters, compared to those occurring among the BBHs that are dynamically ejected from the clusters. A broader mass spectrum of the BHs and lower escape velocities of the clusters explored here might cause this difference, which is yet to be fully understood. Among the BBH coalescences obtained here, there are ones that resemble the detected GW151226, LVT151012, and GW150914 events and also ones which are even more massive. A preliminary estimate suggests few 10s-100s of BBH coalescences per year, originating due to dynamics in stellar clusters, that can be detected by the LIGO at its design sensitivity.

We conduct a theoretical study on the ejection of runaway massive stars from R136 -the central massive, star-burst cluster in the 30 Doradus complex of the Large Magellanic Cloud. Specifically, we investigate the possibility of the very massive star (VMS) VFTS 682 being a runaway member of R136. Recent observations of the above VMS, by virtue of its isolated location and its moderate peculiar motion, have raised the fundamental question whether isolated massive star formation is indeed possible. We perform the first realistic N-body computations of fully mass-segregated R136-type star clusters in which all the massive stars are in primordial binary systems. These calculations confirm that the dynamical ejection of a VMS from a R136-like cluster, with kinematic properties similar to those of VFTS 682, is common. Hence the conjecture of isolated massive star formation is unnecessary to account for this VMS. Our results are also quite consistent with the ejection of 30 Dor 016, another suspected runaway VMS from R136. We further note that during the clusters' evolution, mergers of massive binaries produce a few single stars per cluster with masses significantly exceeding the canonical upper-limit of 150M ⊙ . The observations of such single super-canonical stars in R136, therefore, do not imply an IMF with an upper limit greatly exceeding the accepted canonical 150M ⊙ limit, as has been suggested recently, and they are consistent with the canonical upper limit.