Black Holes In Star Clusters Research Articles

Demographics of three-body binary black holes in star clusters: implications for gravitational waves

ABSTRACT To explain both the dynamics of a globular cluster and its production of gravitational waves from coalescing binary black holes, it is necessary to understand its population of dynamically formed (or, ‘three-body’) binaries. We provide a theoretical understanding of this population, benchmarked by direct N-body models. We find that N-body models of clusters on average have only one three-body binary at any given time. This is different from theoretical expectations and models of binary populations, which predict a larger number of binaries (∼5), especially for low-N clusters (∼100), or in the case of two-mass models, low number of black holes. We argue that the presence of multiple binaries is suppressed by a high rate of binary–binary interactions, which efficiently ionize one of the binaries involved. These also lead to triple formation and potentially gravitational wave captures, which may provide an explanation for the recently reported high efficiency of in-cluster mergers in models of low-mass clusters ($\lesssim 10^5\, {\rm M}_\odot)$.

The dragon-II simulations – II. Formation mechanisms, mass, and spin of intermediate-mass black holes in star clusters with up to 1 million stars

ABSTRACT The processes that govern the formation of intermediate-mass black holes (IMBHs) in dense stellar clusters are still unclear. Here, we discuss the role of stellar mergers, star–BH interactions, and accretion, as well as BH binary (BBH) mergers in seeding and growing IMBHs in the Dragon-II simulation database, a suite of 19 direct N-body models representing dense clusters with up to 106 stars. Dragon-II IMBHs have typical masses of mIMBH = (100–380) M⊙ and relatively large spins χIMBH > 0.6. We find a link between the IMBH formation mechanism and the cluster structure. In clusters denser than 3 × 105 M⊙ pc−3, the collapse of massive star collision products represents the dominant IMBH formation process, leading to the formation of heavy IMBHs (mIMBH > 200 M⊙), possibly slowly rotating, that form over times <5 Myr and grow further via stellar accretion and mergers in just <30 Myr. BBH mergers are the dominant IMBH formation channel in less dense clusters, for which we find that the looser the cluster, the longer the formation time (10–300 Myr) and the larger the IMBH mass, although remaining within 200 M⊙. Strong dynamical scatterings and relativistic recoil efficiently eject all IMBHs in Dragon-II clusters, suggesting that IMBHs in this type of cluster are unlikely to grow beyond a few 102 M⊙.

Properties and Astrophysical Implications of the 150 M⊙ Binary Black Hole Merger GW190521

Abstract The gravitational-wave signal GW190521 is consistent with a binary black hole (BBH) merger source at redshift 0.8 with unusually high component masses, 85 − 14 + 21 M ⊙ and 66 − 18 + 17 M ⊙, compared to previously reported events, and shows mild evidence for spin-induced orbital precession. The primary falls in the mass gap predicted by (pulsational) pair-instability supernova theory, in the approximate range 65–120 M ⊙. The probability that at least one of the black holes in GW190521 is in that range is 99.0%. The final mass of the merger ( 142 − 16 + 28 M ⊙) classifies it as an intermediate-mass black hole. Under the assumption of a quasi-circular BBH coalescence, we detail the physical properties of GW190521’s source binary and its post-merger remnant, including component masses and spin vectors. Three different waveform models, as well as direct comparison to numerical solutions of general relativity, yield consistent estimates of these properties. Tests of strong-field general relativity targeting the merger-ringdown stages of the coalescence indicate consistency of the observed signal with theoretical predictions. We estimate the merger rate of similar systems to be 0.13 − 0.11 + 0.30 Gpc − 3 yr − 1 . We discuss the astrophysical implications of GW190521 for stellar collapse and for the possible formation of black holes in the pair-instability mass gap through various channels: via (multiple) stellar coalescences, or via hierarchical mergers of lower-mass black holes in star clusters or in active galactic nuclei. We find it to be unlikely that GW190521 is a strongly lensed signal of a lower-mass black hole binary merger. We also discuss more exotic possible sources for GW190521, including a highly eccentric black hole binary, or a primordial black hole binary.

Formation of binary black holes in star clusters as gravitational wave sources

Direct detections of gravitational wave suggest that ~ 30 solar mass binary black holes (BBHs) commonly exist in the Universe. One possible formation scenario of such BBHs is dynamical three-body encounters in a dense core of globular clusters, which consist of millions of stars. Compared to globular clusters, open clusters are less dense and less massive but more populous. Because of their shallow potential, they have not been considered to be a formation site of merging BBHs. However, we found a new channel for the formation of BBHs, which is dominant in open clusters. We performed direct N-body simulations of open clusters with a mass of 2500 solar mass for metallicity of Z/Z ⊙ = 0.1. The core-collapse time of open clusters is much shorter than that of globular clusters. Therefore, massive main-sequence stars can form binaries before they evolve to BHs. These main-sequence binaries experience mass transfer evolution, and some of them evolve to BBHs merging within the Hubble time. From our simulations, we estimated the merger rates of BBHs originated from open clusters.

Amplification of superkicks in black-hole binaries through orbital eccentricity

We present new numerical-relativity simulations of eccentric merging black holes with initially antiparallel spins lying in the orbital plane (the so-called \emph{superkick} configuration). Binary eccentricity boosts the recoil of the merger remnant by up to $25\%$. The increase in the energy flux is much more modest, and therefore this kick enhancement is mainly due to asymmetry in the binary dynamics. Our findings might have important consequences for the retention of stellar-mass black holes in star clusters and supermassive black holes in galactic hosts.

Constraining primordial black holes in dark matter with kinematics of dwarf galaxies

We propose that the kinematical observations of dwarf galaxies can be used to constrain the primordial black hole's (PBH) abundance in dark matter since the presence of primordial black holes in star clusters will lead to the radial velocity dispersion of the system. For instance, using the velocity dispersion observations from Leo I we show that the primordial black hole fraction $f_{\rm PBH}\gtrsim 2.0\times(1~M_{\odot}/m_{\rm PBH})^2$ is ruled out at a 99.99\% confidence level. This method yields the most stringent limits on the PBH abundance at the mass scales $\sim (1-10^3)~M_{\odot}$ and tightly constrains the primordial origin of gravitational wave events observed by the LIGO experiments.

Black hole mergers from quadruples

With the hundreds of merging binary black hole (BH) signals expected to be detected by LIGO/Virgo, LISA and other instruments in the next few years, the modeling of astrophysical channels that lead to the formation of compact-object binaries has become of fundamental importance. In this paper, we carry out a systematic statistical study of quadruple BHs consisting of two binaries in orbit around their center of mass, by means of high-precision direct $N$-body simulations including Post-Newtonian (PN) terms up to 2.5PN order. We found that most merging systems have high initial inclinations and the distributions peak at $\sim 90^\circ$ as for triples, but with a more prominent broad distribution tail. We show that BHs merging through this channel have a significant eccentricity in the LIGO band, typically much larger than BHs merging in isolated binaries and in binaries ejected from star clusters, but comparable to that of merging binaries formed via the GW capture scenario in clusters, mergers in hierarchical triples, or BH binaries orbiting intermediate-mass black holes in star clusters. We show that the merger fraction can be up to $\sim 3$--$4\times$ higher for quadruples than for triples. Thus even if the number of quadruples is $20\%$--$25\%$ of the number of triples, the quadruple scenario can represent an important contribution to the events observed by LIGO/VIRGO.

The black hole retention fraction in star clusters

Context. Recent research has been constraining the retention fraction of black holes (BHs) in globular clusters by comparing the degree of mass segregation with N-body simulations. They are consistent with an upper limit of the retention fraction being 50% or less. Aims. In this work, we focus on direct simulations of the dynamics of BHs in star clusters. We aim to constrain the effective distribution of natal kicks that BHs receive during supernova (SN) explosions and to estimate the BH retention fraction.Methods. We used the collisional N-body code nbody6 to measure the retention fraction of BHs for a given set of parameters, which are: the initial mass of a star cluster, the initial half-mass radius, and σBH, which sets the effective Maxwellian BH velocity kick distribution. We compare these direct N-body models with our analytic estimates and newest observational constraints. Results. The numerical simulations show that for the one-dimensional velocity kick dispersion σBH < 50 km s−1, clusters with radii of 2 pc and that are initially more massive than 5 × 103 M⊙ retain more than 20% of BHs within their half-mass radii. Our simple analytic model yields a number of retained BHs that is in good agreement with the N-body models. Furthermore, the analytic estimates show that ultra-compact dwarf galaxies should have retained more than 80% of their BHs for σBH ≤ 190 km s−1. Although our models do not contain primordial binaries, in the most compact clusters with 103 stars, we have found evidence of delayed SN explosions producing a surplus of BHs compared to the IMF due to dynamically formed binary stars. These cases do not occur in the more populous or expanded clusters.

Wandering off the centre: a characterization of the random motion of intermediate-mass black holes in star clusters

Despite recent observational efforts, unequivocal signs for the presence of intermediate-mass black holes (IMBHs) in globular clusters (GCs) have not been found yet. Especially when the presence of IMBHs is constrained through dynamical modeling of stellar kinematics, it is fundamental to account for the displacement that the IMBH might have with respect to the GC centre. In this paper we analyse the IMBH wandering around the stellar density centre using a set of realistic direct N-body simulations of star cluster evolution. Guided by the simulation results, we develop a basic yet accurate model that can be used to estimate the average IMBH radial displacement ($\left<r_\mathrm{bh}\right>$) in terms of structural quantities as the core radius ($r_\mathrm{c}$), mass ($M_\mathrm{c}$), and velocity dispersion ($\sigma_\mathrm{c}$), in addition to the average stellar mass ($m_\mathrm{c}$) and the IMBH mass ($M_\mathrm{bh}$). The model can be expressed by the equation $\left<r_\mathrm{bh}\right>/r_\mathrm{c}=A(m_\mathrm{c}/M_\mathrm{bh})^\alpha[\sigma_\mathrm{c}^2r_\mathrm{c}/(GM_\mathrm{c})]^\beta$, in which the free parameters $A,\alpha,\beta$ are calculated through comparison with the numerical results on the IMBH displacement. The model is then applied to Galactic GCs, finding that for an IMBH mass equal to 0.1% of the GC mass, the typical expected displacement of a putative IMBH is around $1''$ for most Galactic GCs, but IMBHs can wander to larger angular distances in some objects, including a prediction of a $2.5''$ displacement for NGC 5139 ($\omega$ Cen), and $>10''$ for NGC 5053, NGC 6366 and ARP2.

Dynamical Evolution of Stellar Systems

Dynamical simulations have become a powerful tool to study the evolution of star clusters due to hardware and software progresses in recent years. Here, I review the state of the art of N-body and other simulation techniques and show what we have learned from these simulations about the dynamical evolution of star clusters. Special attention is given to the results on the lifetimes of star clusters as a function of their environment, the internal changes of the mass functions, the influence of primordial gas expulsion on the ratio of first to second generation stars in globular clusters, and the possible presence of intermediate-mass black holes in star clusters.

Investigating the retention of intermediate-mass black holes in star clusters usingN-body simulations

Contrary to supermassive and stellar-mass black holes (SBHs), the existence of intermediate-mass black holes (IMBHs) with masses ranging between 10^{2-5} Msun has not yet been confirmed. The main problem in the detection is that the innermost stellar kinematics of globular clusters (GCs) or small galaxies, the possible natural loci to IMBHs, are very difficult to resolve. However, if IMBHs reside in the centre of GCs, a possibility is that they interact dynamically with their environment. A binary formed with the IMBH and a compact object of the GC would naturally lead to a prominent source of gravitational radiation, detectable with future observatories. We use N-body simulations to study the evolution of GCs containing an IMBH and calculate the gravitational radiation emitted from dynamically formed IMBH-SBH binaries and the possibility that the IMBH escapes the GC after an IMBH-SBH merger. We run for the first time direct-summation integrations of GCs with an IMBH including the dynamical evolution of the IMBH with the stellar system and relativistic effects, such as energy loss in gravitational waves (GWs) and periapsis shift, and gravitational recoil. We find in one of our models an intermediate mass-ratio inspiral (IMRI), which leads to a merger with a recoiling velocity higher than the escape velocity of the GC. The GWs emitted fall in the range of frequencies that a LISA-like observatory could detect, like the European eLISA or in mission options considered in the recent preliminary mission study conducted in China. The merger has an impact on the global dynamics of the cluster, as an important heating source is removed when the merged system leaves the GC. The detection of one IMRI would constitute a test of GR, as well as an irrefutable proof of the existence of IMBHs.

Stellar-mass black holes in star clusters: implications for gravitational wave radiation

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). We examine the properties of these BH-BH binaries through direct N-body simulations of star clusters using the GPU-enabled NBODY6 code. We perform simulations of N <= 10^5 Plummer clusters of low-mass stars with an initial population of BHs. Additionally, we do several calculations of star clusters confined within a reflective boundary mimicking only the core of a massive cluster. We find that stellar-mass BHs with masses ~ 10 solar mass segregate rapidly into the cluster core and form a sub-cluster of BHs within typically 0.2 - 0.5 pc radius, which is dense enough to form BH-BH binaries through 3-body encounters. While most BH binaries are ejected from the cluster by recoils received during super-elastic 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 $N \ga 5\times 10^4$, typically 1 - 2 BH-BH mergers occur within them during the first ~ 4 Gyr of 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 earlier. In contrast, young massive clusters are too young to produce significant number of BH-BH mergers. Our results imply significant BH-BH merger detection rates for the proposed "Advanced LIGO" GW detector. (Abridged)

Stellar-mass black holes in star clusters: implications for gravitational-wave radiation

AbstractWe study the dynamics of stellar-mass black holes (BHs) in star clusters, with particular attention to the formation of BH–BH binaries, which are interesting as sources of gravitational waves (GWs). We examine the properties of these BH–BH binaries through direct N-body simulations of Plummer clusters of N ≤ 105 low-mass stars with an initial population of stellar-mass BHs, using the nbody6 code. We find that the stellar-mass BHs segregate rapidly into the cluster core and form a dense subcluster of BHs in which BH–BH binaries form through three-body encounters. While most BH binaries are ejected from the cluster by recoils due to superelastic encounters with the single BHs, we find that for clusters with N ≳ 5 × 104, typically a few of them harden sufficiently so that they can merge via GW emission within the cluster. Also, for each of such clusters there are a few escaping BH binaries that merge within a Hubble time, with most merger times being within a few Gyr. These results imply that the intermediate-age massive clusters constitute the most important class of star cluster candidates that can produce dynamical BH–BH mergers at the present epoch. The BH–BH merger rates obtained from our computations imply a significant detection rate (~30 yr−1) for the proposed Advanced LIGO GW detector.

HST's hunt for intermediate-mass black holes in star clusters

AbstractEstablishing or ruling out, either through solid mass measurements or upper limits, the presence of intermediate-mass black holes (IMBHs; with masses of 102 − 105 M⊙) at the centers of star clusters would profoundly impact our understanding of problems ranging from the formation and long-term dynamical evolution of stellar systems, to the nature of the seeds and the growth mechanisms of supermassive black holes. While there are sound theoretical arguments both for and against their presence in today's clusters, observational studies have so far not yielded truly conclusive IMBH detections nor upper limits. We argue that the most promising approach to solving this issue is provided by the combination of measurements of the proper motions of stars at the centers of Galactic globular clusters and dynamical models able to take full advantage of this type of data set. We present a program based on HST observations and recently developed tools for dynamical analysis designed to do just that.

COMMISSION 35: STELLAR CONSTITUTION

The Commission home page &lt;iau-c35.stsci.edu&gt; is maintained by Claus Leitherer and contains general information on the Commission structure and activities, including links to stellar structure resources that were made available by the owners. The resources contain evolutionary tracks and isochrones from various groups, nuclear reaction, EOS, and opacity data as well as links to main astronomical journals. As a routine activity, the Organizing Committee has commented on and ranked proposals for several IAU sponsored meetings. Our Commission acted as one of the coordinating bodies of a Symposium held at the IAU XXVI General Assembly in Prague, August 2006, (IAU Symposium No. 239Convection in Astrophysics, and participated in the organization of the following Joint Discussions: JD05Calibrating the Top of the Stellar Mass-Luminosity Relation, JD06Neutron Stars and Black Holes in Star Clusters, JD08Solar and Stellar Activity Cycles, JD11Pre-Solar Grains as Astrophysical Tools; JD14Modelling Dense Stellar Systems; and JD17Highlights of Recent Progress in the Seismology of the Sun and Sun-like Stars.

Ratios of star cluster core and half-mass radii: a cautionary note on intermediate-mass black holes in star clusters

There is currently much interest in the possible presence of intermediate-mass black holes in the cores of globular clusters. Based on theoretical arguments and simulation results it has previously been suggested that a large core radius -- or particularly a large ratio of the core radius to half-mass radius -- is a promising indicator for finding such a black hole in a star cluster. In this study N-body models of 100000 stars with and without primordial binaries are used to investigate the long-term structural evolution of star clusters. Importantly, the simulation data is analysed using the same processes by which structural parameters are extracted from observed star clusters. This gives a ratio of the core and half-mass (or half-light) radii that is directly comparable to the Galactic globular cluster sample. As a result, it is shown that the ratios observed for the bulk of this sample can be explained without the need for an intermediate-mass black hole. Furthermore, it is possible that clusters with large core to half-light radius ratios harbour a black-hole binary (comprised of stellar mass black holes) rather than a single massive black hole. This work does not rule out the existence of intermediate-mass black holes in the cores of at least some star clusters.

Initial Populations of Black Holes in Star Clusters

Using an updated population synthesis code we study the formation and evolution of black holes (BHs) in young star clusters following a massive starburst. This study continues and improves on the initial work described by Belczynski, Sadowski & Rasio (2004). In our new calculations we account for the possible ejections of BHs and their progenitors from clusters because of natal kicks imparted by supernovae and recoil following binary disruptions. The results indicate that the properties of both retained BHs in clusters and ejected BHs (forming a field population) depend sensitively on the depth of the cluster potential. In particular, most BHs ejected from binaries are also ejected from clusters with central escape speeds Vesc 50 km/s. BHs from single star evolution are also affected significantly: about half of the BHs originating from primordial single stars are ejected from clusters with Vesc < 50 km/s. Our results lay a foundation for theoretical studies of the formation of BH X-ray binaries in and around star clusters, including possible ultra-luminous sources, as well as merging BH--BH binaries detectable with future gravitational-wave observatories.

Joint Discussion 6 Neutron stars and black holes in star clusters

This article was co-authored by all invited speakers at Joint Discussion 6 onNeutron Stars and Black Holes in Star Clusters, which took place during the IAU General Assembly in Prague, Czech Republic, on August 17 and 18, 2006. Each section presents a short summary of recent developments in a key area of research, incorporating the main ideas expressed during the corresponding panel discussion at the meeting.

Formation and Evolution of Massive Black Holes in Star Clusters

AbstractWe present results of N-body simulations on the formation of massive black holes by run-away merging in young star clusters and the later dynamical evolution of star clusters containing massive black holes. We determine the initial conditions necessary for run-away merging to form a massive black hole and study the equilibrium profile that is established in the cluster center as a result of the interaction of stars with the central black hole. Our results show that star clusters which contain black holes have projected luminosity profiles that can be fitted by standard King models. The presence of massive black holes in (post-)core collapse clusters is therefore ruled out by our simulations.

Massive Black Holes in Star Clusters. I. Equal‐Mass Clusters

In this paper we report results of collisional N-body simulations of the dynamical evolution of equal-mass star clusters containing a massive central black hole. Each cluster is composed of between 5,000 to 180,000 stars together with a central black hole which contains between 0.2% to 10% of the total cluster mass. We find that for large enough black hole masses, the central density follows a power-law distribution with slope \rho \sim r^{-1.75} inside the radius of influence of the black hole, in agreement with predictions from earlier Fokker Planck and Monte Carlo models. The tidal disruption rate of stars is within a factor of two of that derived in previous studies. It seems impossible to grow an intermediate-mass black hole (IMBH) from a M \le 100 Msun progenitor in a globular cluster by the tidal disruption of stars, although M = 10^3 Msun IMBHs can double their mass within a Hubble time in dense globular clusters. The same is true for the supermassive black hole at the centre of the Milky Way. Black holes in star clusters will feed mainly on stars tightly bound to them and the re-population of these stars causes the clusters to expand, reversing core-collapse without the need for dynamically active binaries. Close encounters of stars in the central cusp also lead to an increased mass loss rate in the form of high-velocity stars escaping from the cluster. A companion paper will extend these results to the multi-mass case.