Dense Star Clusters Research Articles

Intermediate mass black hole formation in compact young massive star clusters

ABSTRACT Young dense massive star clusters are promising environments for the formation of intermediate mass black holes (IMBHs) through collisions. We present a set of 80 simulations carried out with nbody6++gpu of 10 models of compact $\sim 7 \times 10^4 \, \mathrm{M}_{\odot }$ star clusters with half-mass radii Rh ≲ 1 pc, central densities $\rho _\mathrm{core} \gtrsim 10^5 \, \mathrm{M}_\odot \, \mathrm{pc}^{-3}$, and resolved stellar populations with 10 per cent primordial binaries. Very massive stars (VMSs) up to $\sim 400 \, \mathrm{M}_\odot$ grow rapidly by binary exchange and three-body scattering with stars in hard binaries. Assuming that in VMS–stellar black hole (BH) collisions all stellar material is accreted on to the BH, IMBHs with masses up to $M_\mathrm{BH} \sim 350 \, \mathrm{M}_\odot$ can form on time-scales of ≲15 Myr, as qualitatively predicted from Monte Carlo mocca simulations. One model forms an IMBH of 140 $\mathrm{M_{\odot }}$ by three BH mergers with masses of 17:28, 25:45, and 68:70 $\mathrm{M_{\odot }}$ within ∼90 Myr. Despite the stochastic nature of the process, formation efficiencies are higher in more compact clusters. Lower accretion fractions of 0.5 also result in IMBH formation. The process might fail for values as low as 0.1. The IMBHs can merge with stellar mass BHs in intermediate mass ratio inspiral events on a 100 Myr time-scale. With 105 stars, 10 per cent binaries, stellar evolution, all relevant dynamical processes, and 300 Myr simulation time, our large suite of 80 simulations indicate another rapid IMBH formation channel in young and compact massive star clusters.

Black Holes and the Supermassive Compact Object at the Galactic Center: Multi-arts of Thought and Nature

Black Holes and the Supermassive Compact Object at the Galactic Center: Multi-arts of Thought and Nature

Black Hole Mergers from Hierarchical Triples in Dense Star Clusters

Abstract Hierarchical triples are expected to be produced by the frequent binary-mediated interactions in the cores of globular clusters. In some of these triples, the tertiary companion can drive the inner binary to merger following large eccentricity oscillations, as a result of the eccentric Kozai–Lidov mechanism. In this paper, we study the dynamics and merger rates of black hole (BH) hierarchical triples, formed via binary–binary encounters in the CMC Cluster Catalog, a suite of cluster simulations with present-day properties representative of the Milky Way’s globular clusters. We compare the properties of the mergers from triples to the other merger channels in dense star clusters, and show that triple systems do not produce significant differences in terms of mass and effective spin distribution. However, they represent an important pathway for forming eccentric mergers, which could be detected by LIGO–Virgo/KAGRA (LVK), and future missions such as LISA and the DECi-hertz Interferometer Gravitational wave Observatory. We derive a conservative lower limit for the merger rate from this channel of 0.35 Gpc−3 yr−1 in the local universe and up to ∼ 9 % of these events may have a detectable eccentricity at LVK design sensitivity. Additionally, we find that triple systems could play an important role in retaining second-generation BHs, which can later merge again in the core of the host cluster.

Populating the Upper Black Hole Mass Gap through Stellar Collisions in Young Star Clusters

Abstract Theoretical modeling of massive stars predicts a gap in the black hole (BH) mass function above ∼40–50 M ⊙ for BHs formed through single star evolution, arising from (pulsational) pair-instability supernovae (PISNe). However, in dense star clusters, dynamical channels may exist that allow construction of BHs with masses in excess of those allowed from single star evolution. The detection of BHs in this so-called “upper-mass gap” would provide strong evidence for the dynamical processing of BHs prior to their eventual merger. Here, we explore in detail the formation of BHs with masses within or above the pair-instability gap through collisions of young massive stars in dense star clusters. We run a suite of 68 independent cluster simulations, exploring a variety of physical assumptions pertaining to growth through stellar collisions, including primordial cluster mass segregation and the efficiency of envelope stripping during collisions. We find that as many as ∼20% of all BH progenitors undergo one or more collisions prior to stellar collapse and up to ∼1% of all BHs reside within or above the pair-instability gap through the effects of these collisions. We show that these BHs readily go on to merge with other BHs in the cluster, creating a population of massive BH mergers at a rate that may compete with the “multiple-generation” merger channel described in other analyses. This has clear relevance for the formation of very massive BH binaries as recently detected by the Laser Interferometer Gravitational-Wave Observatory/Virgo in GW190521. Finally, we describe how stellar collisions in clusters may provide a unique pathway to PISNe and briefly discuss the expected rate of these events and other electromagnetic transients.

On the Origin of GW190521-like Events from Repeated Black Hole Mergers in Star Clusters

Abstract LIGO and Virgo have reported the detection of GW190521, from the merger of a binary black hole (BBH) with a total mass around 150 M ⊙. While current stellar models limit the mass of any black hole (BH) remnant to about 40–50 M ⊙, more massive BHs can be produced dynamically through repeated mergers in the core of a dense star cluster. The process is limited by the recoil kick (due to anisotropic emission of gravitational radiation) imparted to merger remnants, which can escape the parent cluster, thereby terminating growth. We study the role of the host cluster metallicity and escape speed in the buildup of massive BHs through repeated mergers. Almost independent of host metallicity, we find that a BBH of about 150 M ⊙ could be formed dynamically in any star cluster with escape speed ≳200 km s−1, as found in galactic nuclear star clusters as well as the most massive globular clusters and super star clusters. Using an inspiral-only waveform, we compute the detection probability for different primary masses (≥60 M ⊙) as a function of secondary mass and find that the detection probability increases with secondary mass and decreases for larger primary mass and redshift. Future additional detections of massive BBH mergers will be of fundamental importance for understanding the growth of massive BHs through dynamics and the formation of intermediate-mass BHs.

Demographics of Triple Systems in Dense Star Clusters

Abstract Depending on the stellar type, more than 15% of stars in the field have at least two stellar companions. Hierarchical triple systems can be assembled dynamically in dense star clusters, as a result of few-body encounters among stars and/or compact remnants in the cluster core. In this paper, we present the demographics of stellar and compact-object triples formed via binary–binary encounters in the CMC Cluster Catalog, a suite of cluster simulations with present-day properties representative of the globular clusters (GCs) observed in the Milky Way. We show how the initial properties of the host cluster set the typical orbital parameters and formation times of the formed triples. We find that a cluster typically assembles hundreds of triples with at least one black hole (BH) in the inner binary, while only clusters with sufficiently small virial radii are efficient in producing triples with no BHs. We show that a typical GC is expected to host tens of triples with at least one luminous component at present. We discuss how the Lidov–Kozai mechanism can drive the inner binary of these dynamically formed triples to high eccentricities, whenever it takes place before the triple is dynamically reprocessed by encountering another cluster member. Some of these systems can reach sufficiently large eccentricities to form a variety of transients and merger products, such as blue stragglers, X-ray binaries, Type Ia supernovae, Thorne–Zytkow objects, and gravitational wave sources.

Self-similar orbit-averaged Fokker-Planck equation for isotropic spherical dense star clusters (i) accurate pre-collapse solution

This is the first paper of a series of our works on the self-similar orbit-averaged Fokker-Planck (OAFP) equation to model distribution function for stars in isotropic dense spherical star clusters. At the late stage of the relaxation evolution of the clusters, standard stellar dynamics predicts that the clusters evolve in a self-similar fashion forming collapsing cores. However, the corresponding mathematical model, the self-similar OAFP equation, has never been solved on the whole energy domain (−1<E<0). Existing works based on kinds of finite difference methods provide solutions only on the truncated domain −1<E⪅−0.2. To broaden the range of the truncated domain, the present work resorts to a (highly accurate and efficient) Gauss-Chebyshev pseudo-spectral method. We provide a spectral solution accurate to four significant figures on the whole domain. The solution can reduce to a semi-analytical form whose degree of polynomials is only eighteen holding three significant figures. We also provide the new eigenvalues c1=9.0925×10−4,c2=1.1118×10−4,c3=7.1975×10−2 , and c4=3.303×10−2, corresponding to the core-collapse rate ξ=3.64×10−3, scaled escape energy ,χesc=13.881 and power-law exponent α=2.2305. Since the solution is unstable against the degree of Chebyshev polynomials on the whole domain, we also provide spectral solutions on truncated domains (−1<E<Emax, where −0.35≤Emax≤−0.03) to explain how to handle the instability. By reformulating the self-similar OAFP equation in several ways, we improve the accuracies of the spectral solutions and reproduce an existing self-similar solution, which infers that the existing solutions are accurate up to only one significant figure.

Binary black holes in young star clusters: the impact of metallicity

ABSTRACT Young star clusters are the most common birthplace of massive stars and are dynamically active environments. Here, we study the formation of black holes (BHs) and binary black holes (BBHs) in young star clusters, by means of 6000 N-body simulations coupled with binary population synthesis. We probe three different stellar metallicities (Z = 0.02, 0.002, and 0.0002) and two initial-density regimes (density at the half-mass radius ρh ≥ 3.4 × 104 and ≥1.5 × 102 M⊙ pc−3 in dense and loose star clusters, respectively). Metal-poor clusters tend to form more massive BHs than metal-rich ones. We find ∼6, ∼2, and &amp;lt;1 per cent of BHs with mass mBH &amp;gt; 60 M⊙ at Z = 0.0002, 0.002, and 0.02, respectively. In metal-poor clusters, we form intermediate-mass BHs with mass up to ∼320 M⊙. BBH mergers born via dynamical exchanges (exchanged BBHs) can be more massive than BBH mergers formed from binary evolution: the former (latter) reach total mass up to ∼140 M⊙ (∼80 M⊙). The most massive BBH merger in our simulations has primary mass ∼88 M⊙, inside the pair-instability mass gap, and a mass ratio of ∼0.5. Only BBHs born in young star clusters from metal-poor progenitors can match the masses of GW 170729, the most massive event in first and second observing run (O1 and O2), and those of GW 190412, the first unequal-mass merger. We estimate a local BBH merger rate density ∼110 and ∼55 Gpc−3 yr−1, if we assume that all stars form in loose and dense star clusters, respectively.

Planetary systems in a star cluster II: intermediate-mass black holes and planetary systems

ABSTRACT Most stars form in dense stellar environments. It is speculated that some dense star clusters may host intermediate-mass black holes (IMBHs), which may have formed from runaway collisions between high-mass stars, or from the mergers of less massive black holes. Here, we numerically explore the evolution of populations of planets in star clusters with an IMBH. We study the dynamical evolution of single-planet systems and free-floating planets, over a period of 100 Myr, in star clusters without an IMBH, and in clusters with a central IMBH of mass $100\, \mathrm{M}_\odot$ or $200\, \mathrm{M}_\odot$. In the central region ($r\lesssim 0.2$ pc), the IMBH’s tidal influence on planetary systems is typically 10 times stronger than the average neighbour star. For a star cluster with a $200\, \mathrm{M}_\odot$ IMBH, the region in which the IMBH’s influence is stronger within the virial radius (∼1 pc). The IMBH quenches mass segregation, and the stars in the core tend to move towards intermediate regions. The ejection rate of both stars and planets is higher when an IMBH is present. The rate at which planets are expelled from their host star rate is higher for clusters with higher IMBH masses, for t &amp;lt; 0.5trh, while remains mostly constant while the star cluster fills its Roche lobe, similar to a star cluster without an IMBH. The disruption rate of planetary systems is higher in initially denser clusters, and for wider planetary orbits, but this rate is substantially enhanced by the presence of a central IMBH.

Binary Black Hole Mergers: Formation and Populations

We review the main physical processes that lead to the formation of stellar binary black holes (BBHs) and to their merger. BBHs can form from the isolated evolution of massive binary stars. The physics of core-collapse supernovae and the process of common envelope are two of the main sources of uncertainty about this formation channel. Alternatively, two black holes can form a binary by dynamical encounters in a dense star cluster. The dynamical formation channel leaves several imprints on the mass, spin and orbital properties of BBHs.

Formation and Evolution of Compact-object Binaries in AGN Disks

Abstract The astrophysical origin of gravitational wave (GW) events discovered by LIGO/VIRGO remains an outstanding puzzle. In active galactic nuclei (AGNs), compact-object binaries form, evolve, and interact with a dense star cluster and a gas disk. An important question is whether and how binaries merge in these environments. To address this question, we have performed one-dimensional N-body simulations combined with a semianalytical model that includes the formation, disruption, and evolution of binaries self-consistently. We point out that binaries can form in single–single interactions through the dissipation of kinetic energy in a gaseous medium. This “gas-capture” binary formation channel contributes up to 97% of gas-driven mergers and leads to a high merger rate in AGN disks even without preexisting binaries. We find the merger rate to be in the range of ∼0.02–60 Gpc−3 yr−1. The results are insensitive to the assumptions on the gaseous hardening processes: we find that once they are formed, binaries merge efficiently via binary–single interactions even if these gaseous processes are ignored. We find that the average number of mergers per black hole (BH) is 0.4, and the probability for repeated mergers in 30 Myr is ∼0.21–0.45. High BH masses due to repeated mergers, high eccentricities, and a significant Doppler drift of GWs are promising signatures that distinguish this merger channel from others. Furthermore, we find that gas-capture binaries reproduce the distribution of low-mass X-ray binaries in the Galactic center, including an outer cutoff at ∼1 pc due to the competition between migration and hardening by gas torques.

The effects of a background potential in star cluster evolution

Runaway stellar collisions in dense star clusters are invoked to explain the presence of very massive stars or blue stragglers in the center of those systems. This process has also been explored for the first star clusters in the Universe and shown to yield stars that may collapse at some points into an intermediate mass black hole. Although the early evolution of star clusters requires the explicit modeling of the gas out of which the stars form, these calculations would be extremely time-consuming and often the effects of the gas can be accurately treated by including a background potential to account for the extra gravitational force. We apply this approximation to model the early evolution of the first dense star clusters formed in the Universe by performingN-body simulations, our goal is to understand how the additional gravitational force affects the growth of a very massive star through stellar mergers in the central parts of the star cluster. Our results show that the background potential increases the velocities of the stars, causing an overall delay in the evolution of the clusters and in the runaway growth of a massive star at the center. The population of binary stars is lower due to the increased kinetic energy of the stars, initially reducing the number of stellar collisions, and we show that relaxation processes are also affected. Despite these effects, the external potential enhances the mass of the merger product by a factor ∼2 if the collisions are maintained for long times.

GW190412 as a Third-generation Black Hole Merger from a Super Star Cluster

Abstract We explore the possibility that GW190412, a binary black hole merger with a non-equal-mass ratio and significantly spinning primary, was formed through repeated black hole mergers in a dense super star cluster. Using a combination of semianalytic prescriptions for the remnant spin and recoil kick of black hole mergers, we show that the mass ratio and spin of GW190412 are consistent with a binary black hole whose primary component has undergone two successive mergers from a population of black holes in a high-metallicity environment. We then explore the production of GW190412-like analogs in the CMC Cluster Catalog, a grid of 148 N-body star cluster models, as well as a new model, behemoth, with nearly 107 particles and initial conditions taken from a cosmological MHD simulation of galaxy formation. We show that, if the spins of black holes born from stars are small, the production of binaries with GW190412-like masses and spins is dominated by massive super star clusters with high metallicities and large central escape speeds. While many are observed in the local universe, our results suggest that a careful treatment of these massive clusters, many of which may have been disrupted before the present day, is necessary to characterize the production of unique gravitational-wave events produced through dynamics.

Merger rate density of binary black holes formed in open clusters

ABSTRACT Several binary black holes (BBHs) have been observed using gravitational wave detectors. For the formation mechanism of BBHs, two main mechanisms, isolated binary evolution and dynamical formation in dense star clusters, have been suggested. Future observations are expected to provide more information about BBH distributions, and it will help us to distinguish the two formation mechanisms. For the star cluster channel, globular clusters have mainly been investigated. However, recent simulations have suggested that BBH formation in open clusters is not negligible. We estimate a local merger rate density of BBHs originated from open clusters using the results of our N-body simulations of open clusters with four different metallicities. We find that the merger rate per cluster is the highest for our 0.1 solar metallicity model. Assuming a cosmic star formation history and a metallicity evolution with dispersion, we estimate the local merger rate density of BBHs originated from open clusters to be ∼70 yr−1 Gpc−3. This value is comparable to the merger rate density expected from the first and second observation runs of LIGO and Virgo. In addition, we find that BBH mergers obtained from our simulations can reproduce the distribution of primary mass and mass ratio of merging BBHs estimated from the LIGO and Virgo observations.

Fingerprints of Binary Black Hole Formation Channels Encoded in the Mass and Spin of Merger Remnants

Abstract Binary black holes (BBHs) are thought to form in different environments, including the galactic field and (globular, nuclear, young, and open) star clusters. Here, we propose a method to estimate the fingerprints of the main BBH formation channels associated with these different environments. We show that the metallicity distribution of galaxies in the local universe along with the relative amount of mergers forming in the field or in star clusters determine the main properties of the BBH population. Our fiducial model predicts that the heaviest merger to date, GW170729, originated from a progenitor that underwent 2–3 merger events in a dense star cluster, possibly a galactic nucleus. The model predicts that at least one merger remnant out of a hundred BBH mergers in the local universe has mass , and one in a thousand can reach a mass as large as . Such massive black holes would bridge the gap between stellar-mass and intermediate-mass black holes. The relative number of low- and high-mass BBHs can help us unravel the fingerprints of different formation channels. Based on the assumptions of our model, we expect that isolated binaries are the main channel of BBH merger formation if of the whole BBH population has remnants with masses , whereas % of remnants having masses points to a significant subpopulation of dynamically formed BBH binaries.

Newton versus the machine: solving the chaotic three-body problem using deep neural networks

ABSTRACT Since its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the solution for a given initialization can only be found by performing laborious iterative calculations that have unpredictable and potentially infinite computational cost, due to the system’s chaotic nature. We show that an ensemble of converged solutions for the planar chaotic three-body problem obtained using an arbitrarily precise numerical integrator can be used to train a deep artificial neural network (ANN) that, over a bounded time interval, provides accurate solutions at a fixed computational cost and up to 100 million times faster than the numerical integrator. In addition, we demonstrate the importance of training an ANN using converged solutions from an arbitrary precise integrator, relative to solutions computed by a conventional fixed precision integrator, which can introduce errors in the training data, due to numerical round-off and time discretization, that are learned by the ANN. Our results provide evidence that, for computationally challenging regions of phase space, a trained ANN can replace existing numerical solvers, enabling fast and scalable simulations of many-body systems to shed light on outstanding phenomena such as the formation of black hole binary systems or the origin of the core collapse in dense star clusters.

Deep into the core of dense star clusters: an astrometric and photometric test case for ELT

ABSTRACT We present a novel analysis of a young star cluster in the Large Magellanic cloud, R136-like, as seen by the Extremely Large Telescope (ELT). The main aim of this study is to quantify precision and accuracy of stellar proper motion measurements in crowded field when using an ELT working at its diffraction limit. This can serve as a reference study for future development of ELT scientific cases. In particular, we investigate our future ability to detect the dynamical signature of intermediate-mass black holes (IMBHs) with mass ∼104 M⊙ through detailed measurements of stellar proper motions. We have simulated two N-body dynamical cluster models with and without an IMBH. For each model, we have chosen two snapshots temporally spaced by 5 yr. Stellar fluxes in IJHK filters and star positions have been used to create ELT mock images for both single- and multiconjugate adaptive optics observing modes following the requierements given by ESO technical specifications for the first light imager. These images have been analysed using a classical software for seeing-limited data reduction, daophot/allstar. We make accurate photometry till the very faint pre-main-sequence stars, i.e. depending on the adaptive optics (AO) mode, magnitudes down to K ∼ 24 mag (single-conjugate AO) or K ∼ 22 mag (multiconjugate AO) in a total integration time of 20 min on target. Although daophot suite of programs is not devoted to precise astrometry, the astrometric accuracy is impressive, reaching few μas yr−1 or km s−1. In these assumptions, we are able to detect the IMBH signature at the centre of the cluster.

Dissecting the properties of neutron star\u2013black hole mergers originating in dense star clusters

The detection of gravitational waves emitted during a neutron star–black hole merger and the associated electromagnetic counterpart will provide a wealth of information about stellar evolution nuclear matter, and general relativity. While the theoretical framework about neutron star–black hole binaries formed in isolation is well established, the picture is loosely constrained for those forming via dynamical interactions. Here, we use N-body simulations to show that mergers forming in globular and nuclear clusters could display distinctive marks compared to isolated mergers, namely larger masses, heavier black holes, and the tendency to have no associated electromagnetic counterpart. These features could represent a useful tool to interpreting forthcoming observations. In the local Universe, gravitational waves emitted from dynamical mergers could be unraveled by detectors sensitive in the decihertz frequency band, while those occurring at the distance range of Andromeda and the Virgo Cluster could be accessible to lower-frequency detectors like LISA.

Towards studying hierarchical assembly in real time: a Milky Way progenitor galaxy at z = 2.36 under the microscope

ABSTRACT We use Hubble Space Telescope (HST) imaging and near-infrared spectroscopy from Keck/Multi-Object Spectrometer For Infra-Red Exploration (MOSFIRE) to study the substructure around the progenitor of a Milky Way-mass galaxy in the Hubble Frontier Fields (HFF). Specifically, we study an $r_\mathrm{ e} = 40^{+70}_{-30}$ pc, $M_{\star } \sim 10^{8.2} \, \mathrm{M}_{\odot }$ rest-frame ultraviolet luminous ‘clump’ at a projected distance of ∼100 pc from a M⋆ ∼ 109.8 M⊙ galaxy at z = 2.36 with a magnification μ = 5.21. We measure the star formation history of the clump and galaxy by jointly modelling the broad-band spectral energy distribution from HST photometry and Hα from MOSFIRE spectroscopy. Given our inferred properties (e.g. mass, metallicity, dust) of the clump and galaxy, we explore scenarios in which the clump formed in situ (e.g. a star-forming complex) or ex situ (e.g. a dwarf galaxy being accreted). If it formed in situ, we conclude that the clump is likely a single entity as opposed to a aggregation of smaller star clusters, making it one of the most dense star clusters catalogued. If it formed ex situ, then we are witnessing an accretion event with a 1:40 stellar mass ratio. However, our data alone are not informative enough to distinguish between in situ and ex situ scenarios to a high level of significance. We posit that the addition of high-fidelity metallicity information, such as [O iii] 4363 Å, which can be detected at modest signal-to-noise ratio with only a few hours of James Webb Space Telescope(JWST)/Near-Infrared Spectrograph (NIRSpec) time, may be a powerful discriminant. We suggest that studying larger samples of moderately lensed substructures across cosmic time can provide unique insight into the hierarchical formation of galaxies like the Milky Way.

Order–disorder phase transition in black hole star clusters – III. A mono-energetic cluster

ABSTRACT Supermassive black holes at the centres of galaxies are often surrounded by dense star clusters. For a wide range of cluster properties and orbital radii the resonant relaxation times in these clusters are much shorter than the Hubble time. Since resonant relaxation conserves semimajor axes, these clusters should be in the maximum-entropy state consistent with the given semimajor axis distribution. We determine these maximum-entropy equilibria in a simplified model in which all of the stars have the same semimajor axes. We find that the cluster exhibits a phase transition from a disordered, spherical, high-temperature equilibrium to an ordered low-temperature equilibrium in which the stellar orbits have a preferred orientation or line of apsides. Here ‘temperature’ is a measure of the non-Keplerian or self-gravitational energy of the cluster; in the spherical state, temperature is a function of the rms eccentricity of the stars. We explore a simple two-parameter model of black hole star clusters – the two parameters are semimajor axis and black hole mass – and find that clusters are susceptible to the lopsided phase transition over a range of ∼102 in semimajor axis, mostly for black hole masses $\lesssim 10^{7.5}\, \mathrm{M}_{\odot }$.