Dense Stellar Clusters Research Articles

Segregation and Collisions in Galactic Nuclei: Rates of Destructive Events Near a Supermassive Black Hole

The centers of galaxies host a supermassive black hole (SMBH) surrounded by a dense stellar cluster. The cluster is expected to develop mass segregation, in which gravitational scatterings among the stars cause heavier objects to sink closer to the central black hole, while lighter objects will tend to be overconcentrated in the outer regions. This work focuses on the implications of mass segregation on the different channels for violent destruction of stars in the cluster: tidal disruptions, gravitational-wave-driven inspirals and high-velocity destructive collisions between stars. All such events occur close to the central black hole, where the heavier objects congregate. The analysis is based on a simplified Monte Carlo simulation, which evolves a two-mass population in a cluster surrounding a Milky Way–like SMBH. The simulation is based on the single-mass scheme used by Sari & Fragione and Balberg & Yassur, which has been extended to allow for the dynamical friction effects typical of unequal-mass populations. The effects of mass segregation on the rates of the different destruction channels are analyzed self-consistently in the overall evolution of the cluster. Also considered are stars which are injected into the cluster after being disrupted from a binary system by the SMBH. Such stars are captured in the inner regions of the cluster, and so their orbital evolution, as well as their destruction rate, are therefore influenced by heavy objects that might be abundant in the vicinity of the SMBH.

Stellar Collisions in Galactic Nuclei: Impact on Destructive Events Near a Supermassive Black Hole

The centers of galaxies host both a supermassive black hole and a dense stellar cluster. Such an environment should lead to stellar collisions, possibly at very high velocities so that the total energy involved is of the same order as supernova explosions. We present a simplified numerical analysis of the destructive stellar collision rate in a cluster similar to that of the Milky Way. The analysis includes an effective average two-body relaxation Monte Carlo scheme and general relativistic effects, as used by Sari & Fargione, to which we added explicit tracking of local probabilities for stellar collisions. We also consider stars which are injected into the stellar cluster after being disrupted from a binary system by the supermassive black hole. Such stars are captured in the vicinity of the black hole and enhance the expected collision rate. In our results we examine the rate and energetic distribution function of high-velocity stellar collisions, and compare them self-consistently with the other destructive processes which occur in the galactic center, namely tidal disruptions and extreme mass ratio inspirals.

Nitrogen enhancements 440 Myr after the big bang: supersolar N/O, a tidal disruption event, or a dense stellar cluster in GN-z11?

ABSTRACT Recent observations of GN-z11 with JWST/NIRSpec revealed numerous oxygen, carbon, nitrogen, and helium emission lines at z = 10.6. Using the measured line fluxes, we derive abundance ratios of individual elements within the interstellar medium (ISM) of this superluminous galaxy. Driven by the unusually-bright N iii] λ1750 and N iv] λ1486 emission lines (and by comparison, faint O iii] λλ1660, 1666 lines), our fiducial model prefers log (N/O) > −0.25, greater than four times solar and in stark contrast to lower-redshift star-forming galaxies. The derived log (C/O) > −0.78, (≈30 per cent solar) is also elevated with respect to galaxies of similar metallicity (12 + log (O/H) ≈ 7.82), although less at odds with lower-redshift measurements. We explore the feasibility of achieving these abundance ratios via several enrichment mechanisms using metal yields available in the literature. Given the long time-scale typically expected to enrich nitrogen with stellar winds, traditional scenarios require a very fine-tuned formation history to reproduce such an elevated N/O. We find no compelling evidence that nitrogen enhancement in GN-z11 can be explained by enrichment from metal-free Population III stars. Interestingly, yields from runaway stellar collisions in a dense stellar cluster or a tidal disruption event provide promising solutions to give rise to these unusual emission lines at z = 10.6, and explain the resemblance between GN-z11 and a nitrogen-loud quasar. These recent observations showcase the new frontier opened by JWST to constrain galactic enrichment and stellar evolution within 440 Myr of the big bang.

Transient Stellar Collisions as Multimessenger Probes: Nonthermal, Gravitational-wave Emission and the Cosmic Ladder Argument

In dense stellar clusters like galactic nuclei and globular clusters, stellar densities are so high that stars might physically collide with each other. In galactic nuclei the energy and power output can be close to, and even exceed, those from supernovae events. We address the event rate and the electromagnetic characteristics of collisions of main-sequence stars (MS) and red giants (RGs). We also investigate the case in which the cores form a binary and emit gravitational waves. In the case of RGs, this is particularly interesting because the cores are degenerate. We find that MS event rate can be as high as tens per year, and that of RGs 1 order of magnitude larger. The collisions are powerful enough to mimic supernovae or tidal disruptions events. We find Zwicky Transient Facility observational data that seem to exhibit the features we describe. The cores embedded in the gaseous debris experience a friction force that has an impact on the chirping mass of the gravitational wave. As a consequence, the two small cores in principle mimic two supermassive black holes merging. However, their evolution in frequency along with the precedent electromagnetic burst and the ulterior afterglow are efficient tools to reveal the impostors. In the particular case of RGs, we derive the properties of the degenerate He cores and their H-burning shells to analyze the formation of the binaries. The merger is such that it can be misclassified with SN Ia events. Because the masses and densities of the cores are so dissimilar in values depending on their evolutionary stage, the argument about standard candles and cosmic ladder should be reevaluated.

Searching for clues of past binary supermassive black hole mergers in nuclear star clusters

ABSTRACTGalaxy mergers are common processes in the Universe. As a large fraction of galaxies hosts at their centres a central supermassive black hole (SMBH), mergers can lead to the formation of a supermassive black hole binary (SMBHB). The formation of such a binary is more efficient when the SMBHs are embedded in a nuclear star cluster (NSC). NSCs are dense and massive stellar clusters present in the majority of the observed galaxies. Their central densities can reach up to $10^7\, {\rm M_{\odot }}\,{\rm pc^{-3}}$ and their masses can be as large as a few $10^7\, {\rm M_{\odot }}$. The direct detection of an SMBHB is observationally challenging. In this work, we illustrate how the large-scale structural and dynamical properties of an NSC can help to identify nucleated galaxies that recently went through a merger that possibly led to the formation of a central SMBHB. Our models show that the merger can imprint signatures on the shape, density profile, rotation, and velocity structure of the NSC. The strength of the signatures depends on the mass ratio between the SMBHs and on the orbital initial conditions of the merger. In addition, the number of hypervelocity stars produced in the mergers is linked to the SMBHB properties. The merger can also contribute to the formation of the nuclear stellar disc of the galaxy.

Influence of tidal dissipation on outcomes of binary–single encounters between stars and black holes in stellar clusters

ABSTRACT In the cores of dense stellar clusters, close gravitational encounters between binary and single stars can frequently occur. Using the tsunami code, we computed the outcome of a large number of binary–single interactions involving two black holes (BHs) and a star to check how the inclusion of orbital energy losses due to tidal dissipation can change the outcome of these chaotic interactions. Each interaction was first simulated without any dissipative processes and then we systematically added orbital energy losses due to gravitational wave emission [using post-Newtonian (PN) corrections] and dynamical tides and recomputed the interactions. We find that the inclusion of tides increases the number of BH–star mergers by up to 75 per cent; however, it does not affect the number of BH–BH mergers. These results highlight the importance of including orbital energy dissipation due to dynamical tides during few-body encounters and evolution of close binary systems within stellar cluster simulations. Consistent with previous studies, we find that the inclusion of PN terms increases the number of BH–BH mergers during binary–single encounters. However, BH–star mergers are largely unaffected by the inclusion of these terms.

On the Mass Ratio Distribution of Black Hole Mergers in Triple Systems

Observations have shown that the majority of massive stars, the progenitors of black holes (BHs), have on average more than one stellar companion. In triple systems, wide inner binaries can be driven to a merger by a third body due to long-term secular interactions, most notably by the eccentric Lidov–Kozai effect. In this study, we explore the properties of BH mergers in triple systems and compare their population properties to those of binaries produced in isolation and assembled in dense star clusters. Using the same stellar physics and identical assumptions for the initial populations of binaries and triples, we show that stellar triples yield a significantly flatter mass ratio distribution from q = 1 down to q ∼ 0.3 than either binary stars or dense stellar clusters, similar to the population properties inferred from the most recent catalog of gravitational-wave events, though we do not claim that all the observed events can be accounted for with triples. While hierarchical mergers in clusters can also produce asymmetric mass ratios, the unique spins of such mergers can be used to distinguish them from those produced from stellar triples. All three channels occupy distinct regions in the total mass–mass ratio space, which may allow them to be disentangled as more BH mergers are detected by LIGO, Virgo, and KAGRA.

The discovery of the oldest supermassive black hole

<p indent="0mm">On December 20, 2021, the website of <italic>Science News</italic> summarized “6 surprising records science set in 2021”, including the oldest black hole discovered by astronomers. These new findings extend the limits of scientific research and the imagination of human beings. Here we present a brief introduction to the discovery of the oldest black hole in the early Universe and its importance in science, and give some prospects of the related studies in the future. Quasars are luminous active galactic nuclei with supermassive black holes (SMBHs) in their centers, accreting the surrounding gas and emitting huge power. Distant quasars are unique tracers to study the formation of the earliest SMBHs and the history of cosmic reionization. On January 14, 2021, in a paper appeared in the <italic>Astrophysical Journal Letters</italic>, an international team led by Dr. Feige Wang, Dr. Jinyi Yang and Prof. Xiaohui Fan at University of Arizona reported the discovery of a luminous quasar J0313-1806 at redshift 7.64. This discovery breaks the former redshift record, 7.54 for the quasar J1342+0928, making J0313-1806 the most distant quasar discovered so far, with a distance of about 13 billion light years from us. The near-infrared spectra taken with several largest ground based telescopes reveal the existence of a black hole of 1.6 billion solar masses in the center of J0313-1806. It becomes the oldest black hole in the early Universe, with the age of only 670 million years after the Big Bang. How can a black hole grow to 1.6 billion solar masses within 670 million years (only about 5% of the universe’s current age)? The discovery of the oldest black hole provides the most serious challenge to the current understanding of the black hole formation and growth. SMBHs are thought to grow from smaller seed black holes that accrete the surrounding matter. The popular idea is that the seed black holes formed through the collapse of the first generation massive stars (or population III stars), but this can only make the seed black holes up to a few hundred solar masses in most cases, or up to a few thousand solar masses for the extreme cases in the dense stellar clusters. However, even if we assume that J0313-1806’s seed black hole grew as fast as possible, it would have needed a starting mass of at least 10000 solar masses at redshift 30. Among the theoretical models currently known, only the direct collapse black hole (DCBH) model involving the vast amounts of primordial cold hydrogen gas can provide a possible explanation. In addition, J0313-1806 also shows many important features. The rest-frame UV spectrum exhibits broad absorption troughs, which are thought to be produced by the extremely high-velocity outflows launched from the accretion disk around the central black hole. These outflows have a maximum velocity up to 20% of the speed of light, and can provide strong feedbacks to affect the star formation in the quasar host galaxy due to the extremely high kinetic power. J0313-1806’s host galaxy has a very rapid star formation process, with the star formation rate 200 times higher than the Milky Way. Together with its huge luminosity of 36 trillion times higher than the Sun, J0313-1806 has become one of the most important targets to study the formation and growth of the supermassive black holes, as well as their influences on the host galaxies in the early Universe. There will be more observations on the oldest black hole in the near future. The James Webb Space Telescope (JWST) was successfully launched on December 25, 2021. The team who discovered the oldest black hole has been awarded the JWST time of more than two hundred hours. More surprising discoveries are expected to be revealed by the future JWST observations on the most distant black holes, galaxies and quasars in the epoch of cosmic reionization.

Can Thorne-Żytkow objects source GW190814-type events?

The LIGO-Virgo collaboration reported in their third run the coalescence event GW190814 involving a 2.6 $M_{\odot}$ object with a 23 $M_{\odot}$ black hole. In this letter we study the conditions under which Thorne-$\dot{\textrm{Z}}$ytkow objects (T$\dot{\textrm{Z}}$Os) can be connected to that type of events. We evaluate first the rate of appearance of T$\dot{\textrm{Z}}$Os in the local Universe. Under the assumption that T$\dot{\textrm{Z}}$Os eventually become low mass gap black holes we evaluate how those black holes end up in binaries with other stellar mass black holes and compare to the reported rate for GW190814-type of events (1-23 $\textrm{Gpc}^{-3} \textrm{yr}^{-1}$). We find that T$\dot{\textrm{Z}}$Os in dense stellar clusters can not explain the LIGO-Virgo rate without a T$\dot{\textrm{Z}}$Os population in the field providing a dominant contribution. We also find that T$\dot{\textrm{Z}}$Os formed within hierarchical triple systems in the field with the third more distant star being the progenitor of a stellar mass black hole, may be able to give a rate comparable to that of GW190814-type events. In that case, future observations should discover mergers between stellar mass and low mass gap black holes, with the lower mass spanning the entire low mass gap range.

The Imprint of Superradiance on Hierarchical Black Hole Mergers

Ultralight bosons are a proposed solution to outstanding problems in cosmology and particle physics: they provide a dark-matter candidate while potentially explaining the strong charge-parity problem. If they exist, ultralight bosons can interact with black holes through the superradiant instability. In this work we explore the consequences of this instability on the evolution of hierarchical black holes within dense stellar clusters. By reducing the spin of individual black holes, superradiance reduces the recoil velocity of merging binary black holes, which, in turn, increases the retention fraction of hierarchical merger remnants. We show that the existence of ultralight bosons with mass 2 × 10−14 ≲ μ/eV ≲ 2 × 10−13 would lead to an increased rate of hierarchical black hole mergers in nuclear star clusters. An ultralight boson in this energy range would result in up to ≈60% more present-day nuclear star clusters supporting hierarchical growth. The presence of an ultralight boson can also double the rate of intermediate-mass black hole mergers to ≈0.08 Gpc−3 yr−1 in the local universe. These results imply that a select range of ultralight boson masses can have far-reaching consequences for the population of black holes in dense stellar environments. Future studies into black hole cluster populations and the spin distribution of hierarchically formed black holes will test this scenario.

Contribution to the extragalactic neutrino background from dense environment of GRB jets

Long gamma-ray bursts (GRBs) are at present well confirmed sites of acceleration of particles to relativistic energies due to observations of gamma-ray emission in the GeV-TeV energy range. We consider a scenario in which the mechanism accelerating electrons is also responsible for acceleration of hadrons in the GRB jets to multi-PeV energies. Since progenitors of long GRBs are massive stars still immersed in dense stellar clusters, these hadrons can efficiently interact with the matter after escaping from the jet. We calculate the spectra of neutrinos from the interaction of those hadrons with the matter of a huge cloud surrounding GRB. Those neutrinos form an afterglow on a time scale determined by their diffusion time scale in the cloud. Due to this long delay, their identification with any specific GRB is not possible. We estimate contribution of neutrinos from such afterglows to the extragalactic neutrino background recently reported by the IceCube Observatory.

Infrared study of the star-forming region associated with the UC HII regions G45.07+0.13 and G45.12+0.13

AbstractUltra-compact Hii(UC HII) regions are an important phase in the formation and early evolution of massive stars and a key component of the interstellar medium (ISM). The main objectives of this work are to study the young stellar population associated with the G45.07+0.13 and G45.12+0.13 UC HII regions, as well as the ISM in which they are embedded. We determined the distribution of the hydrogen column density (N($\mathrm{H}_2$)) and dust temperature ($T_d$) in the molecular cloud using Modified blackbody fitting onHerschelimages obtained in four bands: 160, 250, 350, and$500\,\unicode{x03BC}\mathrm{m}$. We used near-, mid-, and far-infrared photometric data to identify and classify the young stellar objects (YSOs). Their main parameters were determined by the radiation transfer models. We also constructed a colour-magnitude diagram and K luminosity functions (KLFs) to compare the parameters of stellar objects with the results of the radiative transfer models. We found that N($\mathrm{H}_2$) varies from${\sim}3.0 \times 10^{23}$to$5.5 \times 10^{23}\,\mathrm{cm}^{-2}$within the G45.07+0.13 and G45.12+0.13 regions, respectively. The maximum$T_d$value is 35 K in G45.12+0.13 and 42 K in G45.07+0.13.$T_d$then drops significantly from the centre to the periphery, reaching about 18–20 K at distances of${\sim}2.6$and${\sim}3.7\,\mathrm{pc}$from InfraRed Astronomical Satellite (IRAS) 19110+1045 (G45.07+0.13) and IRAS 19111+1048 (G45.12+0.13), respectively. The gas plus dust mass value included in G45.12+0.13 is${\sim}3.4 \times 10^5\,\mathrm{M}_\odot$and${\sim}1.7 \times 10^5\,\mathrm{M}_\odot$in G45.07+0.13. The UC HII regions are connected through a cold ($T_d = 19\,\mathrm{K}$) bridge. The radial surface density distribution of the identified 518 YSOs exhibits dense clusters in the vicinity of both IRAS sources. The parameters of YSOs in the IRAS clusters (124 objects) and 394 non-cluster objects surrounding them show some differences. About 75% of the YSOs belonging to the IRAS clusters have an evolutionary age greater than$10^6$yr. Their slope$\alpha$of the KLF agrees well with a Salpeter-type initial mass function (IMF) ($\gamma = 1.35$) for a high mass range (O–F stars,$\beta \sim 2$) at 1 Myr. The non-cluster objects are uniformly distributed in the molecular cloud, 80% of which are located to the right of the 0.1 Myr isochrone. The slope$\alpha$of the KLF of non-cluster objects is$0.55\,\pm\,0.09$, corresponding better to a Salpeter-type IMF for low-mass objects (G–M stars,$\beta \sim 1$). Our results show that two dense stellar clusters are embedded in these two physically connected UC HII regions. The clusters include several high- and intermediate-mass zero-age main sequence stellar objects. Based on the small age spread of the stellar objects, we suggest that the clusters originate from a single triggering shock. The extended emission observed in both UC HII regions is likely due to the stellar clusters.

The Uncertain Future of Massive Binaries Obscures the Origin of LIGO/Virgo Sources

Abstract The LIGO/Virgo gravitational-wave observatories have detected at least 50 double black hole (BH) coalescences. This sample is large enough to have allowed several recent studies to draw conclusions about the implied branching ratios between isolated binaries versus dense stellar clusters as the origin of double BHs. It has also led to the exciting suggestion that the population is highly likely to contain primordial BHs. Here we demonstrate that such conclusions cannot yet be robust because of the large current uncertainties in several key aspects of binary stellar evolution. These include the development and survival of a common envelope, the mass and angular-momentum loss during binary interactions, mixing in stellar interiors, pair-instability mass loss, and supernova outbursts. Using standard tools such as the rapid population synthesis codes StarTrack and COMPAS and the detailed stellar evolution code MESA, we examine as a case study the possible future evolution of Melnick 34, the most massive known binary star system (with initial component masses of 144 M ⊙ and 131 M ⊙). We show that, despite its fairly well-known orbital architecture, various assumptions regarding stellar and binary physics predict a wide variety of outcomes: from a close BH–BH binary (which would lead to a potentially detectable coalescence), through a wide BH–BH binary (which might be seen in microlensing observations), or a Thorne–Żytkow object, to a complete disruption of both objects by a pair-instability supernova. Thus, because the future of massive binaries is inherently uncertain, sound predictions about the properties of BH–BH systems formed in the isolated binary evolution scenario are highly challenging at this time. Consequently, it is premature to draw conclusions about the formation channel branching ratios that involve isolated binary evolution for the LIGO/Virgo BH–BH merger population.

Accelerating NBODY6 with a graphics processing unit-enabled Particle-Particle Particle-Tree scheme

ABSTRACTWe describe a modified version of the nbody6 code for simulating star clusters which greatly improves computational efficiency while sacrificing little in the way of accuracy. The distant force calculator is replaced by a graphics processing unit-enabled Barnes–Hut code, and integration is done with a standard leap frog scheme. Short-range forces continue to use the CPU-based fourth-order Hermite predictor-corrector scheme of nbody6. Our code outperforms nbody6 for systems with more than 3 × 105 particles and runs more than a factor 2 faster for systems of 106 particles with similar energy conservation. Our code should be useful for simulating realistic dense stellar clusters, such as globular clusters or galactic nuclei.

The impact of stellar clustering on the observed multiplicity of super-earth systems: outside–in cascade of orbital misalignments initiated by stellar flybys

ABSTRACT A recent study suggests that the observed multiplicity of super-Earth (SE) systems is correlated with stellar overdensities: field stars in high phase-space density environments have an excess of single-planet systems compared to stars in low-density fields. This correlation is puzzling as stellar clustering is expected to influence mostly the outer part of planetary systems. Here, we examine the possibility that stellar flybys indirectly excite the mutual inclinations of initially coplanar SEs, breaking their co-transiting geometry. We propose that flybys excite the inclinations of exterior substellar companions, which then propagate the perturbation to the inner SEs. Using analytical calculations of the secular coupling between SEs and companions, together with numerical simulations of stellar encounters, we estimate the expected number of ‘effective’ flybys per planetary system that lead to the destruction of the SE co-transiting geometry. Our analytical results can be rescaled easily for various SE and companion properties (masses and semimajor axes) and stellar cluster parameters (density, velocity dispersion, and lifetime). We show that for a given SE system, there exists an optimal companion architecture that leads to the maximum number of effective flybys; this results from the trade-off between the flyby cross-section and the companion’s impact on the inner system. Subject to uncertainties in the cluster parameters, we conclude that this mechanism is inefficient if the SE system has a single exterior companion, but may play an important role in ‘SE + two companions’ systems that were born in dense stellar clusters. Whether this effect causes the observed correlation between planet multiplicity and stellar overdensities remains to be confirmed.

State of the Field: Binary Black Hole Natal Kicks and Prospects for Isolated Field Formation after GWTC-2

Abstract Advanced LIGO and Advanced Virgo’s newly released GWTC-2 catalog of gravitational-wave detections offers unprecedented information about the spin magnitudes and orientations of merging binary black holes (BBHs). Notably, analysis of the BBH population suggests the presence of binaries whose component spins are significantly misaligned with respect to their orbital angular momenta. Significantly misaligned spins are typically predicted to be at odds with isolated field formation via standard common envelope (CE) evolution, and hence a “smoking gun” signature of dynamical binary formation inside dense stellar clusters. Here, we explore whether the LIGO/Virgo observation of spin–orbit misalignment indeed rules out the possibility that BBHs are formed entirely in the field via standard CE evolution. In particular, we seek to understand whether, by varying the natal kicks black holes receive upon formation, we can invoke the CE scenario to self-consistently explain both the observed spin distribution and merger rate of BBHs. We find that, if isolated black holes are born with small natal spins, then BBHs formed through CE require extreme natal kicks to match the observed BBH population, with a velocity dispersion σ = 9.7 − 5.9 + 26.7 × 10 2 km s − 1 and σ &gt; 260 km s−1 at 99% credibility. To avoid the need for extreme kicks, we argue that it is necessary to assume that isolated black holes are born with nonvanishing natal spins, that one or more alternative channels contribute to the observed BBH population, and/or that other unforeseen mechanisms serve to yield large spin–orbit misalignment in the field.

Adding eccentricity to quasicircular binary-black-hole waveform models

The detection of gravitational-wave signals from coalescing eccentric binary black holes would yield unprecedented information about the formation and evolution of compact binaries in specific scenarios, such as dynamical formation in dense stellar clusters and three-body interactions. The gravitational-wave searches by the ground-based interferometers, LIGO and Virgo, rely on analytical waveform models for binaries on quasicircular orbits. Eccentric merger waveform models are less developed, and only few numerical simulations of eccentric mergers are publicly available, but several eccentric inspiral models have been developed from the post-Newtonian expansion. Here we present a novel method to convert the dominant quadrupolar mode of any circular analytical binary-black-hole model into an eccentric model. First, using numerical simulations, we examine the additional amplitude and frequency modulations of eccentric signals that are not present in their circular counterparts. Subsequently, we identify suitable analytical descriptions of those modulations and interpolate key parameters from twelve numerical simulations designated as our training dataset. This allows us to reconstruct the modulated amplitude and phase of any waveform up to mass ratio 3 and eccentricity 0.2. We find that the minimum overlap of the new model with numerical simulations is around 0.98 over all of our test dataset that are scaled to a 50M$_\odot$ black-hole binary starting at 35 Hz with aLIGO A+ design sensitivity. A Python package \pyrex easily carries out the computation of this method.

Stellar collisions in flattened and rotating Population III star clusters

Fragmentation often occurs in disk-like structures, both in the early Universe and in the context of present-day star formation. Supermassive black holes (SMBHs) are astrophysical objects whose origin is not well understood; they weigh millions of solar masses and reside in the centers of galaxies. An important formation scenario for SMBHs is based on collisions and mergers of stars in a massive cluster with a high stellar density, in which the most massive star moves to the center of the cluster due to dynamical friction. This increases the rate of collisions and mergers since massive stars have larger collisional cross sections. This can lead to a runaway growth of a very massive star which may collapse to become an intermediate-mass black hole. Here we investigate the dynamical evolution of Miyamoto-Nagai models that allow us to describe dense stellar clusters, including flattening and different degrees of rotation. We find that the collisions in these clusters depend mostly on the number of stars and the initial stellar radii for a given radial size of the cluster. By comparison, rotation seems to affect the collision rate by at most 20%. For flatness, we compared spherical models with systems that have a scale height of about 10% of their radial extent, in this case finding a change in the collision rate of less than 25%. Overall, we conclude that the parameters only have a minor effect on the number of collisions. Our results also suggest that rotation helps to retain more stars in the system, reducing the number of escapers by a factor of 2−3 depending on the model and the specific realization. After two million years, a typical lifetime of a very massive star, we find that about 630 collisions occur in a typical models withN = 104,R = 100R⊙and a half-mass radius of 0.1 pc, leading to a mass of about 6.3 × 103 M⊙for the most massive object. We note that our simulations do not include mass loss during mergers or due to stellar winds. On the other hand, the growth of the most massive object may subsequently continue, depending on the lifetime of the most massive object.

Joint constraints on the field-cluster mixing fraction, common envelope efficiency, and globular cluster radii from a population of binary hole mergers via deep learning

The recent release of the second Gravitational-Wave Transient Catalog (GWTC-2) has increased significantly the number of known GW events, enabling unprecedented constraints on formation models of compact binaries. One pressing question is to understand the fraction of binaries originating from different formation channels, such as isolated field formation versus dynamical formation in dense stellar clusters. In this paper, we combine the $\texttt{COSMIC}$ binary population synthesis suite and the $\texttt{CMC}$ code for globular cluster evolution to create a mixture model for black hole binary formation under both formation scenarios. For the first time, these code bodies are combined self-consistently, with $\texttt{CMC}$ itself employing $\texttt{COSMIC}$ to track stellar evolution. We then use a deep-learning enhanced hierarchical Bayesian analysis to constrain the mixture fraction $f$ between formation models, while simultaneously constraining the common envelope efficiency $\alpha$ assumed in $\texttt{COSMIC}$ and the initial cluster virial radius $r_v$ assumed in $\texttt{CMC}$. Under specific assumptions about other uncertain aspects of isolated binary and globular cluster evolution, we report the median and $90\%$ confidence interval of three physical parameters $(f,\alpha,r_v)=(0.20^{+0.32}_{-0.18},2.26^{+2.65}_{-1.84},2.71^{+0.83}_{-1.17})$. This simultaneous constraint agrees with observed properties of globular clusters in the Milky Way and is an important first step in the pathway toward learning astrophysics of compact binary formation from GW observations.

Stellar-mass black holes in young massive and open stellar clusters – IV. Updated stellar-evolutionary and black hole spin models and comparisons with the LIGO-Virgo O1/O2 merger-event data

ABSTRACT I present a set of long-term, direct, relativistic many-body computations of model dense stellar clusters with up-to-date stellar-evolutionary, supernova (SN), and remnant natal-kick models, including pair instability and pulsation pair instability supernova (PSN and PPSN), using an updated version of ${\rm{\small NBODY7}}$ N-body simulation program. The N-body model also includes stellar evolution-based natal spins of black holes (BHs) and treatments of binary black hole (BBH) mergers based on numerical relativity. These, for the first time in a direct N-body simulation, allow for second-generation BBH mergers. The set of 65 evolutionary models have initial masses $10^4{\!-\!}10^5\, \mathrm{M}_{\odot }$, sizes 1–3 pc, metallicity 0.0001–0.02, with the massive stars in primordial binaries and they represent young massive clusters (YMC) and moderately massive open clusters (OC). Such models produce dynamically paired BBH mergers that agree well with the observed masses, mass ratios, effective spin parameters, and final spins of the LVC O1/O2 merger events, provided BHs are born with low or no spin but spin-up after undergoing a BBH merger or matter accretion on to it. In particular, the distinctly higher mass, effective spin parameter, and final spin of GW170729 merger event is naturally reproduced, as also the mass asymmetry of the O3 event GW190412. The computed models produce intermediate-mass, $\sim 100\, \mathrm{M}_{\odot }$ BBH mergers with primary mass within the ‘PSN gap’ and also yield mergers involving remnants in the ‘mass gap’. They also suggest that YMCs and OCs produce persistent, Local-Universe GW sources detectable by LISA. Such clusters are also capable of producing eccentric LIGO-Virgo mergers.