Black Holes In Globular Clusters Research Articles

Searching for Intermediate-mass Black Holes in Globular Clusters through Tidal Disruption Events

Intermediate-mass black holes (IMBHs) may be the link between stellar mass holes and the supermassive variety in the nuclei of galaxies, and globular clusters (GCs) may be one of the most promising environments for their formation. Here, we carry out a pilot study of the observability of tidal disruption events (TDEs) from 103 M ⊙ < M • < 105 M ⊙ IMBHs embedded in stellar cusps at the center of GCs. We model the long super-Eddington accretion phase and ensuing optical flare, and derive the disruption rate of main-sequence stars as a function of black hole mass and GC properties with the help of a 1D Fokker–Planck approach. The photospheric emission of the adiabatically expanding outflow dominates the observable radiation and peaks in the near-ultraviolet/optical bands, outshining the brightness of the (old) stellar population of GCs in Virgo for a period of months to years. A search for TDE events in a sample of nearly 4000 GCs observed at multiple epochs by the Next Generation Virgo Cluster Survey yields null results. Given our model predictions, this sample is too small to set stringent constraints on the present-day occupation fraction of GCs hosting IMBHs. Naturally, better simulations of the properties of the cluster central stellar distribution, TDE light curves, and rates, together with larger surveys of GCs are all needed to gain deeper insights into the presence of IMBHs in GCs.

Accelerated binary black holes in globular clusters: forecasts and detectability in the era of space-based gravitational-wave detectors

ABSTRACT The motion of the centre of mass of a coalescing binary black hole (BBH) in a gravitational potential, imprints a line-of-sight acceleration (LOSA) on to the emitted gravitational-wave (GW) signal. The acceleration could be sufficiently large in dense stellar environments, such as globular clusters (GCs), to be detectable with next-generation space-based detectors. In this work, we use outputs of the cluster monte carlo (cmc) simulations of dense star clusters to forecast the distribution of detectable LOSAs in DECIGO and LISA eras. We study the effect of cluster properties – metallicity, virial and galactocentric radii – on the distribution of detectable accelerations, account for cosmologically motivated distributions of cluster formation times, masses, and metallicities, and also incorporate the delay time between the formation of BBHs and their merger in our analysis. We find that larger metallicities provide a larger fraction of detectable accelerations by virtue of a greater abundance of relatively lighter BBHs, which allow a higher number of GW cycles in the detectable frequency band. Conversely, smaller metallicities result in fewer detections, most of which come from relatively more massive BBHs with fewer cycles but larger LOSAs. We similarly find correlations between the virial radii of the clusters and the fractions of detectable accelerations. Our work, therefore, provides an important science case for space-based GW detectors in the context of probing GC properties via the detection of LOSAs of merging BBHs.

Black Holes in Globular Clusters

Black holes are the laboratory for extreme physics research in the universe, and the detection of black holes is one of the most cutting-edge international scientific goals at present. Globular clusters are old, self-gravity-bound object systems in the Milky Way that contain millions of stars with a high stellar densities inside. Hundreds of pulsar objects have been observed in globular clusters, but the existence of black holes in globular clusters remains an unsolved mystery. A globular cluster may have an intermediatemass black hole at its centre, with masses ranging from 1, 000 to 10, 000 times solar masses. At the same time, there may be a large number of stellar black holes in globular clusters, which will affect the evolution of globular clusters and form. some special objects in globular clusters, which can be observed and confirmed by astronomical observation equipment. This paper will focus on the possible observational features of the presence of black holes in globular clusters and their effects on the properties of globular clusters. Black holes are coupled with their host globular clusters through dynamics, which are important sites for the formation of black hole X-ray binaries and gravitational wave sources, and black holes change the dynamical structure and evolutionary processes of their host clusters. Therefore, searching for X-ray sources, detecting gravitational wave signals, and studying the characteristics of globular clusters are important astronomical evidence for detecting black holes in globular clusters.

Lensing of gravitational waves from tidal disruption events

ABSTRACT In this work, we investigate the effect of gravitational lensing on the gravitational wave (GW) signals of a population of tidal disruption events (TDEs). We estimate the number of lensed-magnified signals that we expect to detect with future space-based GW observatories, in particular LISA and DECIGO. We model the lens distribution using an hybrid approach that combines semi-analytic methods with numerical results from ray tracing simulations. We divide the TDE population in two classes, nuclear TDEs (main sequence stars tidally disrupted by massive black holes in the cores of galaxies) and globular TDEs (white dwarfs tidally disrupted by intermediate mass black holes in globular clusters). We find that, even considering the effect of lensing, LISA will not be able to observe any TDEs, while DECIGO could detect ∼16 strongly lensed (μ &amp;gt; 2) globular TDEs and ∼135 strongly lensed nuclear TDEs, over an observational period of 10 yr. Our results reveal the role that lensing will play in future deci-Hertz GW observatories, indicating exciting multimessenger opportunities with TDEs but at same time signalling the need to develop adequate data analysis techniques to correctly reconstruct the astrophysical properties of the source.

Dynamics of intermediate mass black holes in globular clusters

Context. We recently introduced a new method for simulating collisional gravitational N-body systems with approximately linear time scaling with N. Our method is based on the multi-particle collision (MPC) scheme, previously applied in fluid dynamics and plasma physics. We were able to simulate globular clusters with a realistic number of stellar particles (at least up to several times 106) on a standard workstation. Aims. We simulated clusters hosting an intermediate mass black hole (IMBH), probing a broad range of BH-cluster and BH–average-star mass ratios, unrestricted by the computational constraints that affect direct N-body codes. Methods. We set up a grid of hybrid particle-in-cell-MPC N-body simulations using our implementation of the MPC method, MPCDSS. We used either single mass models or models with a Salpeter mass function (a single power law with an exponent of −2.35), with the IMBH initially sitting at the centre. The force exerted by and on the IMBH was evaluated with a direct sum scheme with or without softening. For all simulations we measured the evolution of the Lagrangian radii and core density and velocity dispersion over time. In addition, we also measured the evolution of the velocity anisotropy profiles. Results. We find that models with an IMBH undergo core collapse at earlier times, the larger the IMBH mass the shallower they are, with an approximately constant central density at core collapse. The presence of an IMBH tends to lower the central velocity dispersion. These results hold independently of the mass function of the model. For the models with Salpeter MF, we observed that equipartition of kinetic energies is never achieved, even long after core collapse. Orbital anisotropy at large radii appears to be driven by energetic escapers on radial orbits, triggered by strong collisions with the IMBH in the core. We measured the wander radius, that is the distance of the IMBH from the centre of mass of the parent system over time, finding that its distribution has positive kurtosis. Conclusions. Among the results we obtained, which mostly confirm or extend previously known trends that had been established over the range of parameters accessible to direct N-body simulations, we underline that the leptokurtic nature of the IMBH wander radius distribution might lead to IMBHs presenting as off-centre more frequently than expected, with implications on observational IMBH detection.

Hunting for intermediate-mass black holes in globular clusters: an astrometric study of NGC 6441

ABSTRACT We present an astrometric study of the proper motions (PMs) in the core of the globular cluster NGC 6441. The core of this cluster has a high density and observations with current instrumentation are very challenging. We combine ground-based, high-angular-resolution NACO@VLT images with Hubble Space Telescope ACS/HRC data and measure PMs with a temporal baseline of 15 yr for about 1400 stars in the centremost 15 arcsec of the cluster. We reach a PM precision of ∼30 µas yr−1 for bright, well-measured stars. Our results for the velocity dispersion are in good agreement with other studies and extend already existing analyses of the stellar kinematics of NGC 6441 to its centremost region never probed before. In the innermost arcsecond of the cluster, we measure a velocity dispersion of (19.1 ± 2.0) km s−1 for evolved stars. Because of its high mass, NGC 6441 is a promising candidate for harbouring an intermediate-mass black hole (IMBH). We combine our measurements with additional data from the literature and compute dynamical models of the cluster. We find an upper limit of $M_{\rm IMBH} \lt 1.32 \times 10^4\, \textrm{M}_\odot$ but we can neither confirm nor rule out its presence. We also refine the dynamical distance of the cluster to $12.74^{+0.16}_{-0.15}$ kpc. Although the hunt for an IMBH in NGC 6441 is not yet concluded, our results show how future observations with extremely large telescopes will benefit from the long temporal baseline offered by existing high-angular-resolution data.

Evaluating the merger rate of binary black holes from direct captures and third-body soft interactions using the Milky Way globular clusters

The multitude of binary black hole coalescence detections in gravitational waves has renewed our interest on environments that can be the cradle of these mergers. In this work we study merger rates of binary black holes in globular clusters that are among the most dense stellar environments and a natural place for the creation of black hole binaries. To model these systems with all their variations we rely on the observational properties of the known Milky Way globular clusters. We consider direct capture events between black holes, as well as soft interactions of black hole binaries with stars as third bodies that accelerate the evolution of these binaries. We find that binary black holes from direct captures merge at an averaged rate of $0.3-5 \times 10^{-11}$ yr$^{-1}$ per cluster. Third body soft interactions are a much more prominent channel giving an averaged rate of $2-4 \times 10^{-10}$ yr$^{-1}$ per cluster. Those rates in globular clusters can lead to a cumulative merger rate of about 100 mergers per year up to redshift of 1, i.e. a significant fraction of the detectable in the near future binary black hole coalescence events. Further observations of cluster properties both in terms of their masses, profile properties, velocity dispersion of stars and their cosmological distribution, will allow us to better constrain the contribution of these environments to the detectable coalescence events rate.

Intermediate-Mass Black Holes

We describe ongoing searches for intermediate-mass black holes with MBH≈ 10–105M⊙. We review a range of search mechanisms, both dynamical and those that rely on accretion signatures. We find the following conclusions: ▪ Dynamical and accretion signatures alike point to a high fraction of 109–1010M⊙galaxies hosting black holes with MBH∼ 105M⊙. In contrast, there are no solid detections of black holes in globular clusters. ▪ There are few observational constraints on black holes in any environment with MBH≈ 100–104M⊙. ▪ Considering low-mass galaxies with dynamical black hole masses and constraining limits, we find that the MBH–σ*relation continues unbroken to MBH∼105M⊙, albeit with large scatter. We believe the scatter is at least partially driven by a broad range in black hole masses, because the occupation fraction appears to be relatively high in these galaxies. ▪ We fold the observed scaling relations with our empirical limits on occupation fraction and the galaxy mass function to put observational bounds on the black hole mass function in galaxy nuclei. ▪ We are pessimistic that local demographic observations of galaxy nuclei alone could constrain seeding mechanisms, although either high-redshift luminosity functions or robust measurements of off-nuclear black holes could begin to discriminate models.

BSE versus StarTrack: Implementations of new wind, remnant-formation, and natal-kick schemes in NBODY7 and their astrophysical consequences

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.

Single-single gravitational-wave captures in globular clusters: Eccentric deci-Hertz sources observable by DECIGO and Tian-Qin

We study the formation rate of binary black hole mergers formed through gravitational-wave emission between unbound, single black holes in globular clusters. While the formation of these binaries in very dense systems such as galactic nuclei has been well studied, we show here that this process can operate in lower-density stellar systems as well, forming binaries at a rate similar to other proposed pathways for creating eccentric mergers. Recent advances in post-Newtonian cluster dynamics indicate that a large fraction of dynamically-assembled binary black holes merge inside their host clusters during weak and strong binary-single and binary-binary interactions, and that these systems may retain measurable eccentricities as they travel through the LIGO and LISA sensitivity bands. Using an analytic approach to modeling binary black holes from globular clusters, we show that the formation of merging binaries from previously unbound black holes can operate at a similar rate to mergers forming during strong binary encounters, and that these binaries inhabit a unique region of the gravitational-wave frequency space which can be identified by proposed deci-Hertz space-based detectors.

Merging of spinning binary black holes in globular clusters

AbstractBased on our current high resolution direct N-body modelling of the Milky Way typical Star Cluster systems dynamical evolution we try to numerically estimate the influence of individual spin values and orientations on gravitational wave (GW) waveforms and observed time-frequency maps during multiple cycles for binary black hole (BBH) mergers. In our up to date N-body dynamical simulations we use the high order relativistic post-Newtonian corrections for the BH binary particles (3.5 post-Newtonian (PN) terms including spin-spin and spin-orbit terms). In the current work, we present the GW waveforms catalogue which covers the large parameter space in mass ratios 0.05 - 0.82 and extreme possible individual spin cases.

Anisotropic Mass Segregation in Rotating Globular Clusters

Abstract We investigate the internal dynamics of anisotropic, rotating globular clusters with a multimass stellar population by performing new direct N-body simulations. In addition to the well-known radial mass segregation effect, where heavy stars and stellar remnants sink toward the center of the cluster, we find a mass segregation in the distribution of orbital inclinations as well. This newly discovered anisotropic mass segregation leads to the formation of a disk-like structure of massive objects near the equatorial plane of a rotating cluster. This result has important implications on the expected spatial distribution of black holes in globular clusters.

Slow decline and rise of the broad [O iii] emission line in globular cluster black hole candidate RZ2109

ABSTRACT RZ2109 is the first of several extragalactic globular clusters shown to host an ultraluminous X-ray source. RZ2109 is particularly notable because optical spectroscopy shows it has broad, luminous [O iii] λλ4959,5007 emission, while also having no detectable hydrogen emission. The X-ray and optical characteristics of the source in RZ2109 make it a good candidate for being a stellar mass black hole accreting from a white dwarf donor (i.e. an ultracompact black hole X-ray binary). In this paper we present optical spectroscopic monitoring of the [O iii]5007 emission line from 2007 to 2018. We find that the flux of the emission line is significantly lower in recent observations from 2016 to 2018 than it was in earlier observations in 2007–2011. We also explore the behaviour of the emission line shape over time. Both the core and the wings of the emission line decline over time, with some evidence that the core declines more rapidly than the wings. However, the most recent observations (in 2019) unexpectedly show the emission line core rebrightening

Intermediate mass black holes in globular clusters: effects on jerks and jounces of millisecond pulsars

Globular clusters may host intermediate mass black holes (IMBHs) at their centres. Here we propose a new method for their identification using millisecond pulsars (MSPs) as probes. We show that measuring the first (jerk) and second (jounce) derivatives of the accelerations of an ensemble of MSPs will let us infer the presence of an IMBH in a globular cluster better than measuring the sole accelerations. We test this concept by simulating a set of star clusters with and without a central IMBH to extract the distributions of the stellar jerks and jounces. We then apply this technique to the ensemble of MSPs in the Galactic globular cluster 47 Tucanae. Current timing observations are insufficient to constrain the presence of an IMBH and can only be used to pose upper limits on its mass. But, with few more years of observations it will be possible to test for the presence of a central IMBH with mass smaller than $\sim$ 1000 M$_{\odot}$. We conclude that jerks and jounces help significantly in reducing the upper limit of the mass of IMBHs in Galactic globular clusters.

Stellar-mass Black Holes in Globular Clusters: Dynamical consequences and observational signatures

AbstractSizeable number of stellar-mass black holes (BHs) in globular clusters (GCs) can strongly influence the dynamical evolution and observational properties of their host cluster. Using results from a large set of numerical simulations, we identify the key ingredients needed to sustain a sizeable population of BHs in GCs up to a Hubble time. We find that while BH natal kick prescriptions are essential in determining the initial retention fraction of BHs in GCs, the long-term survival of BHs is determined by the size, initial central density and half-mass relaxation time of the GC. Simulated GC models that contain many BHs are characterized by relatively low central surface brightness, large half-light and core radii values. We also discuss novel ways to compare simulated results with available observational data to identify GCs that are most likely to contain many BHs.

When do star clusters become multiple star systems? II. Towards a half-life formalism with four bodies

We present a half-life formalism for describing the disruption of gravitationally-bound few-body systems, with a focus on binary-binary scattering. For negative total encounter energies, the four-body problem has three possible decay products in the point particle limit. For each decay product and a given set of initial conditions, we obtain directly from numerical scattering simulations the half-life for the distribution of disruption times. As in radioactive decay, the half-lives should provide a direct prediction for the relative fractions of each decay product. We test this prediction with simulated data and find good agreement with our hypothesis. We briefly discuss applications of this feature of the gravitational four-body problem to populations of black holes in globular clusters. This paper, the second in the series, builds on extending the remarkable similarity between gravitational chaos at the macroscopic scale and radioactive decay at the microscopic scale to larger-N systems.

Prospects for detection of intermediate-mass black holes in globular clusters using integrated-light spectroscopy

The detection of intermediate mass black holes (IMBHs) in Galactic globular clusters (GCs) has so far been controversial. In order to characterize the effectiveness of integrated-light spectroscopy through integral field units, we analyze realistic mock data generated from state-of-the-art Monte Carlo simulations of GCs with a central IMBH, considering different setups and conditions varying IMBH mass, cluster distance, and accuracy in determination of the center. The mock observations are modeled with isotropic Jeans models to assess the success rate in identifying the IMBH presence, which we find to be primarily dependent on IMBH mass. However, even for a IMBH of considerable mass (3% of the total GC mass), the analysis does not yield conclusive results in 1 out of 5 cases, because of shot noise due to bright stars close to the IMBH line-of-sight. This stochastic variability in the modeling outcome grows with decreasing BH mass, with approximately 3 failures out of 4 for IMBHs with 0.1% of total GC mass. Finally, we find that our analysis is generally unable to exclude at 68% confidence an IMBH with mass of $10^3~M_\odot$ in snapshots without a central BH. Interestingly, our results are not sensitive to GC distance within 5-20 kpc, nor to mis-identification of the GC center by less than 2'' (<20% of the core radius). These findings highlight the value of ground-based integral field spectroscopy for large GC surveys, where systematic failures can be accounted for, but stress the importance of discrete kinematic measurements that are less affected by stochasticity induced by bright stars.

BINARY BLACK HOLES IN DENSE STAR CLUSTERS: EXPLORING THE THEORETICAL UNCERTAINTIES

ABSTRACT Recent N-body simulations predict that large numbers of stellar black holes (BHs) could at present remain bound to globular clusters (GCs), and merging BH–BH binaries are produced dynamically in significant numbers. We systematically vary “standard” assumptions made by numerical simulations related to, e.g., BH formation, stellar winds, binary properties of high-mass stars, and IMF within existing uncertainties, and study the effects on the evolution of the structural properties of GCs, and the BHs in GCs. We find that variations in initial assumptions can set otherwise identical initial clusters on completely different evolutionary paths, significantly affecting their present observable properties, or even affecting the cluster’s very survival to the present. However, these changes usually do not affect the numbers or properties of local BH–BH mergers. The only exception is that variations in the assumed winds and IMF can change the masses and numbers of local BH–BH mergers, respectively. All other variations (e.g., in initial binary properties and binary fraction) leave the masses and numbers of locally merging BH–BH binaries largely unchanged. This is in contrast to binary population synthesis models for the field, where results are very sensitive to many uncertain parameters in the initial binary properties and binary stellar-evolution physics. Weak winds are required for producing GW150914-like mergers from GCs at low redshifts. LVT151012 can be produced in GCs modeled both with strong and weak winds. GW151226 is lower-mass than typical mergers from GCs modeled with weak winds, but is similar to mergers from GCs modeled with strong winds.

Searching for intermediate-mass black holes in globular clusters with gravitational microlensing

We discuss the potential of the gravitational microlensing method as a unique tool to detect unambiguous signals caused by intermediate-mass black holes in globular clusters. We select clusters near the line of sight to the Galactic Bulge and the Small Magellanic Cloud, estimate the density of background stars for each of them, and carry out simulations in order to estimate the probabilities of detecting the astrometric signatures caused by black hole lensing. We find that for several clusters, the probability of detecting such an event is significant with available archival data from the Hubble Space Telescope. Specifically, we find that M 22 is the cluster with the best chances of yielding an IMBH detection via astrometric microlensing. If M 22 hosts an IMBH of mass $10^5M_\odot$, then the probability that at least one star will yield a detectable signal over an observational baseline of 20 years is $\sim 86\%$, while the probability of a null result is around $14\%$. For an IMBH of mass $10^6M_\odot$, the detection probability rises to $>99\%$. Future observing facilities will also extend the available time baseline, improving the chance of detections for the clusters we consider.

MOCCA code for star cluster simulations – IV. A new scenario for intermediate mass black hole formation in globular clusters

We discuss a new scenario for the formation of intermediate mass black holes in dense star clusters. In this scenario, intermediate mass black holes are formed as a result of dynamical interactions of hard binaries containing a stellar mass black hole, with other stars and binaries. We discuss the necessary conditions to initiate the process of intermediate mass black hole formation and the influence of an intermediate mass black hole on the host global globular cluster properties. We discuss two scenarios for intermediate mass black hole formation. The SLOW and FAST scenarios. They occur later or earlier in the cluster evolution and require smaller or extremely large central densities, respectively. In our simulations, the formation of intermediate mass black holes is highly stochastic. In general, higher formation probabilities follow from larger cluster concentrations (i.e. central densities). We further discuss possible observational signatures of the presence of intermediate mass black holes in globular clusters that follow from our simulations. These include the spatial and kinematic structure of the host cluster, possible radio, X-ray and gravitational wave emissions due to dynamical collisions or mass-transfer and the creation of hypervelocity main sequence escapers during strong dynamical interactions between binaries and an intermediate mass black hole. All simulations discussed in this paper were performed with the MOCCA Monte Carlo code. MOCCA accurately follows most of the important physical processes that occur during the dynamical evolution of star clusters but, as with other dynamical codes, it approximates the dissipative processes connected with stellar collisions and binary mergers.