Dense Star Clusters Research Articles

Population synthesis of black hole binary mergers from star clusters

ABSTRACT Black hole (BH) binary mergers formed through dynamical interactions in dense star clusters are believed to be one of the main sources of gravitational waves (GWs) for Advanced LIGO and Virgo. Here, we present a fast numerical method for simulating the evolution of star clusters with BHs, including a model for the dynamical formation and merger of BH binaries. Our method is based on Hénon’s principle of balanced evolution, according to which the flow of energy within a cluster must be balanced by the energy production inside its core. Because the heat production in the core is powered by the BHs, one can then link the evolution of the cluster to the evolution of its BH population. This allows us to construct evolutionary tracks of the cluster properties including its BH population and its effect on the cluster and, at the same time, determine the merger rate of BH binaries as well as their eccentricity distributions. The model is publicly available and includes the effects of a BH mass spectrum, mass-loss due to stellar evolution, the ejection of BHs due to natal and dynamical kicks, and relativistic corrections during binary–single encounters. We validate our method using direct N-body simulations, and find it to be in excellent agreement with results from recent Monte Carlo models of globular clusters. This establishes our new method as a robust tool for the study of BH dynamics in star clusters and the modelling of GW sources produced in these systems. Finally, we compute the rate and eccentricity distributions of merging BH binaries for a wide range of cluster initial conditions, spanning more than two orders of magnitude in mass and radius.

Dynamically formed black hole binaries: In-cluster versus ejected mergers

AbstractThe growing number of black hole binary (BHB) mergers detected by the Laser Interferometer Gravitational-Wave Observatory have the potential to enable an unprecedented characterisation of the physical processes and astrophysical conditions that govern the formation of compact binaries. In this paper, we focus on investigating the dynamical formation of BHBs in dense star clusters through a state-of-the-art set of 58 direct N-body simulations with N$\leqslant200\,000$particles which include stellar evolution, gravitational braking, orbital decay through gravitational radiation, and galactic tidal interactions. The simulations encompass a range of initial conditions representing typical young globular clusters, including the presence of primordial binaries. The systems are simulated for$\sim 12$Gyr. The dataset yields 117 BHB gravitational wave (GW) events, with 97 binaries merging within their host cluster and 20 merging after having been ejected. Only 8% of all ejected BHBs merge within the age of the Universe. Systems in this merging subset tend to have smaller separations and larger eccentricities, as this combination of parameters results in greater emission of gravitational radiation. We confirm known trends from Monte Carlo simulations, such as the anti-correlation between the mass of the binary and age of the cluster. In addition, we highlight for the first time a difference at low values of the mass ratio distribution between in-cluster and ejected mergers. However, the results depend on assumptions on the strength of GW recoils, thus in-cluster mergers cannot be ruled out at a significant level of confidence. A more substantial catalogue of BHB mergers and a more extensive library of N-body simulations are needed to constrain the origin of the observed events.

Order-disorder phase transition in black-hole star clusters. II. A scale-free cluster

Abstract The supermassive black holes found at the centres of galaxies are often surrounded by dense star clusters. The ages of these clusters are generally longer than the resonant-relaxation time and shorter than the two-body relaxation time over a wide range of radii. We explore the thermodynamic equilibria of such clusters using a simple self-similar model. We find that the cluster exhibits a phase transition between a high-temperature spherical equilibrium and a low-temperature equilibrium in which the stars are on high-eccentricity orbits with nearly the same orientation. In the absence of relativistic precession, the spherical equilibrium is metastable below the critical temperature and the phase transition is first-order. When relativistic effects are important, the spherical equilibrium is linearly unstable below the critical temperature and the phase transition is continuous. A similar phase transition has recently been found in a model cluster composed of stars with a single semimajor axis. The presence of the same phenomenon in two quite different cluster models suggests that lopsided equilibria may form naturally in a wide variety of black-hole star clusters.

Probing the Survival of Planetary Systems in Globular Clusters with Tidal Disruption Events

Abstract Among the growing list of confirmed exoplanets, the number of planets identified in dense star clusters remains sparse. Previous analyses have suggested that this may be due in part to dynamical interactions that can unbind planets from their host stars, limiting the survival of planetary systems in clusters. Thus, alternative detection strategies may be necessary to study planets in clusters that may no longer be bound to a host. Here, we use N-body models to explore the evolution of planetary systems in dense star clusters. Depending on various initial conditions, we show that 10%–50% of primordial planetary systems are broken through dynamical encounters over a cluster’s full lifetime, populating clusters with “free-floating” planets. Furthermore, a large number (30%–80%) of planets are ejected from their host cluster through strong dynamical encounters and/or tidal loss. Additionally, we show that planets naturally mix with stellar-mass black holes (BHs) in the cores of their host cluster. As a consequence, up to a few hundred planets will be tidally disrupted through close passages of BHs. We show that these BH–planet tidal disruption events (TDEs) occur in clusters at a rate of up to 10−5 yr−1 in a Milky-Way-type galaxy. In principle, these BH–planet TDEs may be detected by upcoming transient surveys such as the Large Synoptic Survey Telescope at a rate of a few events per year, although identification of these events may prove challenging. The observed rate of BH–planet TDEs could place new constraints upon the formation and survival of planetary systems and BHs in dense star clusters.

Black holes: The next generation—repeated mergers in dense star clusters and their gravitational-wave properties

When two black holes merge in a dense star cluster, they form a new black hole with a well-defined mass and spin. If that "second-generation" black hole remains in the cluster, it will continue to participate in dynamical encounters, form binaries, and potentially merge again. Using a grid of 96 dynamical models of dense star clusters and a cosmological model of cluster formation, we explore the production of binary black hole mergers where at least one component of the binary was forged in a previous merger. We create four hypothetical universes where every black hole born in the collapse of a massive star has a dimensionless Kerr spin parameter, $\chi_{\rm birth}$, of 0.0, 0.1, 0.2, or 0.5. We show that if all stellar-born black holes are non-spinning ($\chi_{\rm birth} = 0.0$), then more than 10% of merging binary black holes from clusters have components formed from previous mergers, accounting for more than 20% of the mergers from globular clusters detectable by LIGO/Virgo. Furthermore, nearly 7% of detectable mergers would have a component with a mass $\gtrsim 55M_{\odot}$, placing them clearly in the mass "gap" region where black holes cannot form from isolated collapsing stars due to the pulsational-pair instability mechanism. On the other hand, if black holes are born spinning, then the contribution from these second-generation mergers decreases, making up as little as 1% of all detections from globular clusters when $\chi_{\rm birth} = 0.5$. We make quantitative predictions for the detected masses, mass ratios, and spin properties of first- and second-generation mergers from dense star clusters, and show how these distributions are highly sensitive to the birth spins of black holes.

Ionizing the intergalactic medium by star clusters: the first empirical evidence

ABSTRACT We present a VLT/X-Shooter spectroscopy of the Lyman continuum (LyC) emitting galaxy Ion2 at z = 3.2121 and compare it to that of the recently discovered strongly lensed LyC emitter at z = 2.37, known as the Sunburst arc. Three main results emerge from the X-Shooter spectrum: (a) the Ly α has three distinct peaks with the central one at the systemic redshift, indicating a ionized tunnel through which both Ly α and LyC radiation escape; (b) the large O32 oxygen index ([O iii] λλ4959, 5007/[O ii] λλ3727, 3729) of $9.18_{-1.32}^{+1.82}$ is compatible to those measured in local (z ∼0.4) LyC leakers; (c) there are narrow nebular high-ionization metal lines with σv < 20 km s−1, which confirms the presence of young hot, massive stars. The He iiλ1640 appears broad, consistent with a young stellar component including Wolf–Rayet stars. Similarly, the Sunburst LyC emitter shows a triple-peaked Ly α profile and from VLT/MUSE spectroscopy the presence of spectral features arising from young hot and massive stars. The strong lensing magnification, (μ > 20), suggests that this exceptional object is a gravitationally bound star cluster observed at a cosmological distance, with a stellar mass M ≲ 107 M⊙ and an effective radius smaller than 20 pc. Intriguingly, sources like Sunburst but without lensing magnification might appear as Ion2-like galaxies, in which unresolved massive star clusters dominate the ultraviolet emission. This work supports the idea that dense young star clusters can contribute to the ionization of the IGM through holes created by stellar feedback.

Probing the black hole merger history in clusters using stellar tidal disruptions

The dynamical assembly of binary black holes (BBHs) in dense star clusters (SCs) is one of the most promising pathways for producing observable gravitational wave (GW) sources, however several other formation scenarios likely operate as well. One of the current outstanding questions is how these different pathways may be distinguished apart. In this paper we suggest a new multi-messenger observable that can be used to constrain the formation of BBH mergers originating from SCs: the electromagnetic signal from tidal disruptions (TDs) of stars by BBHs. Such TDs will show variability in their light curve from the orbital motion of the disruptive BBHs, and can therefore be used to map the BBH orbital period distribution, and thereby also the dynamical mechanisms that eventually drive the BBHs to merger. Using an analytical approach including General Relativistic effects, we find that the orbital period distribution of BBHs within globular clusters peaks on timescales of days, which we argue is unique to this assembly pathway. We propose that the search for variable TDs in current and future EM transient surveys might be used to constrain the merger history of BBHs in SCs.

Tidal Disruptions of Stars by Black Hole Remnants in Dense Star Clusters

Abstract In a dense stellar environment, such as the core of a globular cluster (GC), dynamical interactions with black holes (BHs) are expected to lead to a variety of astrophysical transients. Here we explore tidal disruption events (TDEs) of stars by stellar-mass BHs through collisions and close encounters. Using state-of-the-art cluster simulations, we show that these TDEs occur at significant rates throughout the evolution of typical GCs and we study how their relative rates relate to cluster parameters such as mass and size. By incorporating a realistic cosmological model of GC formation, we predict a BH–main-sequence-star TDE rate of approximately 3 Gpc−3 yr−1 in the local universe (z < 0.1) and a cosmological rate that peaks at roughly 25 Gpc−3 yr−1 for redshift 3. Furthermore, we show that the ejected mass associated with these TDEs could produce optical transients of luminosity ∼1041−1044 erg s−1 with timescales of about a day to a month. These should be readily detectable by optical transient surveys such as the Zwicky Transient Facility. Finally, we comment briefly on BH–giant encounters and discuss how these events may contribute to the formation of BH–white-dwarf binaries.

TESS Reveals that the Nearby Pisces–Eridanus Stellar Stream is only 120 Myr Old

Abstract Pisces–Eridanus (Psc–Eri), a nearby (d ≃ 80–226 pc) stellar stream stretching across ≈120° of the sky, was recently discovered with Gaia data. The stream was claimed to be ≈1 Gyr old, which would make it an exceptional discovery for stellar astrophysics, as star clusters of that age are rare and tend to be distant, limiting their utility as benchmark samples. We test this old age for Psc–Eri in two ways. First, we compare the rotation periods for 101 low-mass members (measured using time-series photometry from the Transiting Exoplanet Survey Satellite) to those of well-studied open clusters. Second, we identify 34 new high-mass candidate members, including the notable stars λ Tauri (an Algol-type eclipsing binary) and HD 1160 (host to a directly imaged object near the hydrogen-burning limit). We conduct an isochronal analysis of the color–magnitude data for these highest-mass members, again comparing our results to those for open clusters. Both analyses show that the stream has an age consistent with that of the Pleiades, i.e., ≈120 Myr. This makes the Psc–Eri stream an exciting source of young benchmarkable stars and, potentially, exoplanets located in a more diffuse environment that is distinct from that of the Pleiades and of other dense star clusters.

Order-Disorder Phase Transition in Black-Hole Star Clusters.

The centers of most galaxies contain massive black holes surrounded by dense star clusters. The structure of these clusters determines the rate and properties of observable transient events, such as flares from tidally disrupted stars and gravitational-wave signals from stars spiraling into the black hole. Most estimates of these rates enforce spherical symmetry on the cluster. Here we show that, in the course of generic evolutionary processes, a star cluster surrounding a black hole can undergo a robust phase transition from a spherical thermal equilibrium to a lopsided equilibrium, in which most stars are on high-eccentricity orbits with aligned orientations. The rate of transient events is expected to be much higher in the ordered phase. Better models of cluster formation and evolution are needed to determine whether clusters should be found in the ordered or disordered phase.

Black hole mergers induced by tidal encounters with a galactic centre black hole

We discuss the properties of stellar mass black hole (BH) mergers induced by tidal encounters with a massive BH at galactic centres or potentially in dense star clusters. The tidal disruption of stellar binaries by a massive BH is known to produce hypervelocity stars. However, such a tidal encounter does not always lead to the break-up of binaries. Since surviving binaries tend to become hard and eccentric, this process can produce BH mergers in principle. For initially circular binaries, we show that the gravitational wave (GW) merger times become shorter by a factor of more than $10^{2}$ ($10^5$) in $10\%$ ($1\%$) of the surviving cases. This reduction is primarily due to the growth in binary's eccentricity at the tidal encounter. We also investigate the effective spins of the survivors, assuming that BH spins are initially aligned with the binary orbital angular momentum. We find that binary orientations can flip in the opposite direction at the tidal encounter. For the survivors with large merger time reduction factors, the effective spin distribution is rather flat. We estimate the merger rate due to the tidal encounter channel to be $\sim 0.6\ \textrm{Gpc}^{-3}\textrm{yr}^{-1}$. This mechanism is unlikely to be the dominant formation channel of BH mergers. However, the current and near-future GW observatories are expected to detect an enormous number of BH mergers. If mergers are found in the vicinity of massive BHs (e.g. the detection of GW lensing echoes or preceding extreme-mass-ratio bursts), this mechanism would provide a possible explanation for their origin.

Black hole growth through hierarchical black hole mergers in dense star clusters: implications for gravitational wave detections

In a star cluster with a sufficiently large escape velocity, black holes (BHs) that are produced by BH mergers can be retained, dynamically form new BH binaries, and merge again. This process can repeat several times and lead to significant mass growth. In this paper, we calculate the mass of the largest BH that can be formed through repeated mergers of stellar seed BHs and determine how its value depends on the physical properties of the host cluster. We adopt an analytical model in which the energy generated by the black hole binaries in the cluster core is assumed to be regulated by the process of two-body relaxation in the bulk of the system. This principle is used to compute the hardening rate of the binaries and to relate this to the time-dependent global properties of the parent cluster. We demonstrate that in clusters with initial escape velocity $\gtrsim 300\rm km\ s^{-1}$ in the core and density $\gtrsim 10^5\ M_\odot\rm pc^{-3}$, repeated mergers lead to the formation of BHs in the mass range $100-10^5 \,M_\odot$, populating any upper mass gap created by pair-instability supernovae. This result is independent of cluster metallicity and the initial BH spin distribution. We show that about $10\%$ of the present-day nuclear star clusters meet these extreme conditions, and estimate that BH binary mergers with total mass $\gtrsim 100\,M _\odot$ should be produced in these systems at a maximum rate $\approx 0.05 \,\rm Gpc^{-3} yr^{-1}$, corresponding to one detectable event every few years with Advanced LIGO/VIRGO at design sensitivity. The contribution of globular clusters is likely to be negligible instead because the first BH merger remnant escapes following the relativistic kick. A possible connection of our results to the formation of massive BH seeds in galaxy nuclei and globular clusters is discussed.

The Role of “black hole burning” in the evolution of dense star clusters

AbstractAs self-gravitating systems, dense star clusters exhibit a natural diffusion of energy from their innermost to outermost regions, leading to a slow and steady contraction of the core until it ultimately collapses under gravity. However, in spite of the natural tendency toward “core collapse,” the globular clusters (GCs) in the Milky Way exhibit a well-observed bimodal distribution in core radii separating the core-collapsed and non-core-collapsed clusters. This suggests an internal energy source is at work, delaying the onset of core collapse in many clusters. Over the past decade, a large amount of work has suggested that stellar black holes (BHs) play a dynamically-significant role in clusters throughout their entire lifetimes. Here we review our latest understanding of BH populations in GCs and demonstrate that, through their dynamical interaction with their host cluster, BHs can naturally explain the distinction between core-collapsed and non-core-collapsed clusters through a process we call “black hole burning.”

Unexpectedly high formation rate of merging binary black holes in open clusters

AbstractGravitational wave direct detections suggest that 30 M⊙ binary black holes (BBHs) commonly exist in the universe. One possible formation scenario of such BBHs is dynamical three-body encounters in dense star clusters. We performed a series of direct N-body simulations with a mass of 2500 and 10000 M⊙ and found a new channel for the formation of BBHs which is dominant in open clusters. In open clusters, the core-collapse time is shorter than in globular clusters, and therefore massive main-sequence (MS) binaries can form before they evolve to BHs. These MS binaries experience common envelope evolution and evolve to hard BBHs, which can merge within the Hubble time. The number of BBH mergers per unit mass obtained from our simulations reached 20–50 % of that for globular clusters, assuming an initial cluster mass function. Thus, open clusters can be a dominant formation site of hard BBHs.

Survivability of planetary systems in young and dense star clusters

Aims.We perform a simulation using the Astrophysical Multipurpose Software Environment of the Orion Trapezium star cluster in which the evolution of the stars and the dynamics of planetary systems are taken into account.Methods.The initial conditions from earlier simulations were selected in which the size and mass distributions of the observed circumstellar disks in this cluster are satisfactorily reproduced. Four, five, or size planets per star were introduced in orbit around the 500 solar-like stars with a maximum orbital separation of 400 au.Results.Our study focuses on the production of free-floating planets. A total of 357 become unbound from a total of 2522 planets in the initial conditions of the simulation. Of these, 281 leave the cluster within the crossing timescale of the star cluster; the others remain bound to the cluster as free-floating intra-cluster planets. Five of these free-floating intra-cluster planets are captured at a later time by another star.Conclusions.The two main mechanisms by which planets are lost from their host star, ejection upon a strong encounter with another star or internal planetary scattering, drive the evaporation independent of planet mass of orbital separation at birth. The effect of small perturbations due to slow changes in the cluster potential are important for the evolution of planetary systems. In addition, the probability of a star to lose a planet is independent of the planet mass and independent of its initial orbital separation. As a consequence, the mass distribution of free-floating planets is indistinguishable from the mass distribution of planets bound to their host star.

Post-Newtonian dynamics in dense star clusters: Binary black holes in the LISA band

The dynamical processing of black holes in the dense cores of globular clusters (GCs), makes them efficient factories for producing binary black holes (BBHs). Here we explore the population of BBHs that form dynamically in GCs and may be observable at mHz frequencies or higher with LISA. We use our Monte Carlo stellar dynamics code, which includes gravitational radiation reaction effects for all BH encounters. By creating a representative local universe of GCs, we show that up to dozens of these systems may be resolvable by LISA with signal-to-noise ratios of at least 5. Approximately one third of these binaries will have measurable eccentricities ($e > 10^{-3}$) in the LISA band and a small number ($\lesssim 5$) may evolve from the LISA band to the LIGO band during the LISA mission.

The Star Clusters That Make Black Hole Binaries across Cosmic Time

Abstract We explore the properties of dense star clusters that are likely to be nurseries of stellar black holes pairing in close binaries. We combine a cosmological model of globular cluster formation with analytic prescriptions for the dynamical assembly and evolution of black hole binaries (BHBs) to constrain which types of clusters are most likely to form binaries tight enough to coalesce within a Hubble time. We find that BHBs that are ejected and later merge ex situ form in clusters of a characteristic mass , whereas binaries that merge in situ form in more massive clusters, . The clusters that dominate the production of BHBs are similar in age and metallicity to the entire population. Finally, we estimate an approximate cosmic black hole merger rate of dynamically assembled binaries using the mean black hole mass for each cluster, given its metallicity. We find an intrinsic rate of at z = 0, a weakly increasing merger rate out to z = 1.5, and then a decrease out to z = 4. Our results can be used to provide a cosmological context and choose initial conditions in numerical studies of BHBs assembled in star clusters.

Frustrated supercritical collapse in tunable charge arrays on graphene

The photon-like behavior of electrons in graphene causes unusual confinement properties that depend strongly on the geometry and strength of the surrounding potential. We report bottom-up synthesis of atomically-precise one-dimensional (1D) arrays of point charges on graphene that allow exploration of a new type of supercritical confinement of graphene carriers. The arrays were synthesized by arranging F4TCNQ molecules into a 1D lattice on back-gated graphene, allowing precise tuning of both the molecular charge and the array periodicity. While dilute arrays of ionized F4TCNQ molecules are seen to behave like isolated subcritical charges, dense arrays show emergent supercriticality. In contrast to compact supercritical clusters, these extended arrays display both supercritical and subcritical characteristics and belong to a new physical regime termed “frustrated supercritical collapse”. Here carriers in the far-field are attracted by a supercritical charge distribution, but their fall to the center is frustrated by subcritical potentials in the near-field, similar to trapping of light by a dense cluster of stars in general relativity.

Eccentric Black Hole Mergers in Dense Star Clusters: The Role of Binary–Binary Encounters

Abstract We present the first systematic study of strong binary–single and binary–binary black hole (BH) interactions with the inclusion of general relativity. By including general relativistic effects in the equations of motion during strong encounters, the dissipation of orbital energy from the emission of gravitational waves (GWs) can lead to captures and subsequent inspirals with appreciable eccentricities when entering the sensitive frequency ranges of the LIGO and Virgo GW detectors. It has been shown that binary–single interactions significantly contribute to the rate of eccentric mergers, but no studies have looked exclusively into the contribution from binary–binary interactions. To this end, we perform binary–binary and binary–single scattering experiments with general relativistic dynamics up through the 2.5 post-Newtonian order included, both in a controlled setting to gauge the importance of non-dissipative post-Newtonian terms and derive scaling relations for the cross section of GW captures, as well as experiments tuned to the strong interactions from state-of-the art globular cluster (GC) models to assess the relative importance of the binary–binary channel in facilitating GW captures and the resultant eccentricity distributions of inspiral from channel. Although binary–binary interactions are 10–100 times less frequent in GCs than binary–single interactions, their longer lifetime and more complex dynamics leads to a higher probability for GW captures to occur during the encounter. We find that binary–binary interactions contribute 25%–45% of the eccentric mergers that occur during strong BH encounters in GCs, regardless of the properties of the cluster environment. The inclusion of higher multiplicity encounters in dense star clusters therefore have major implications on the predicted rates of highly eccentric binaries potentially detectable by the LIGO/Virgo network. Because gravitational waveforms of eccentric inspirals are distinct from those generated by merging binaries that have circularized, measurements of eccentricity in such systems would highly constrain their formation scenario.

Post-Newtonian dynamics in dense star clusters: Formation, masses, and merger rates of highly-eccentric black hole binaries

Using state-of-the-art dynamical simulations of globular clusters, including radiation reaction during black hole encounters and a cosmological model of star cluster formation, we create a realistic population of dynamically-formed binary black hole mergers across cosmic space and time. We show that in the local universe, 10% of these binaries form as the result of gravitational-wave emission between unbound black holes during chaotic resonant encounters, with roughly half of those events having eccentricities detectable by current ground-based gravitational-wave detectors. The mergers that occur inside clusters typically have lower masses than binaries that were ejected from the cluster many Gyrs ago. Gravitational-wave captures from globular clusters contribute 1-2 Gpc^-3 yr^-1 to the binary merger rate in the local universe, increasing to ~10 Gpc^-3 yr^-1 at z~3. Finally, we discuss some of the technical difficulties associated with post-Newtonian scattering encounters, and how care must be taken when measuring the binary parameters during a dynamical capture.