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Abstract Very massive stars (VMSs) formed via a sequence of stellar collisions in dense star clusters have been proposed as the progenitors of massive black hole seeds. VMSs could indeed collapse to form intermediate-mass black holes, which would then grow by accretion to become the supermassive black holes observed at the centers of galaxies and powering high-redshift quasars. Previous studies have investigated how different cluster initial conditions affect the formation of a VMS, including mass segregation, stellar collisions, and binaries, among others. In this study, we investigate the growth of VMSs with a new grid of Cluster Monte Carlo star cluster simulations—the most expansive to date. The simulations span a wide range of initial conditions, varying the number of stars, cluster density, stellar initial mass function (IMF), and primordial binary fraction. We find a gradual shift in the mass of the most massive collision product across the parameter space; in particular, denser clusters born with top-heavy IMFs provide strong collisional regimes that form VMSs with masses easily exceeding 1000M_⊙. Our results are used to derive a fitting formula that can predict the typical mass of a VMS formed as a function of the star cluster properties. Additionally, we study the stochasticity of this process and derive a statistical distribution for the mass of the VMS formed in one of our models, recomputing the model 50 times with different initial random seeds. 

Abstract Over 60 yr after the discovery of the first quasar, more than 275 such sources are identified in the epoch of reionization atz> 6. JWST is now exploring higher redshifts (z≳ 8) and lower-mass (≲10⁷M_⊙) ranges. The discovery of progressively farther quasars is instrumental to constraining the properties of the first population of black holes (BHs), or BH seeds, formed atz∼ 20–30. For the first time, we use Bayesian analysis of the most comprehensive catalog of quasars atz> 6 to constrain the distribution of BH seeds. We show that the mass distribution of BH seeds can be effectively described by combining a power law and a lognormal function tailored to the mass ranges associated with light and heavy seeds, assuming Eddington-limited growth and early seeding time. Our analysis reveals a power-law slope of $-{0.70}_{-0.46}^{+0.46}$and a lognormal mean of ${4.44}_{-0.30}^{+0.30}$. The inferred values of the Eddington ratio, the duty cycle, and the mean radiative efficiency are ${0.82}_{-0.10}^{+0.10}$, ${0.66}_{-0.23}^{+0.23}$, and ${0.06}_{-0.02}^{+0.02}$, respectively. Models that solely incorporate a power law or a lognormal distribution within the specific mass range corresponding to light and heavy seeds are statistically strongly disfavored, unlike models not restricted to this specific range. Our results suggest that including both components is necessary to comprehensively account for the masses of high-redshift quasars, and that both light and heavy seeds formed in the early Universe and grew to form the population of quasars we observe. 

Abstract We apply for the first time orbit-averaged Monte Carlo star cluster simulations to study tidal tail and stellar stream formation from globular clusters (GCs), assuming a circular orbit in a time-independent spherical Galactic potential. Treating energetically unbound bodies—potential escapers (PEs)—as collisionless enables this fast but spherically symmetric method to capture asymmetric extratidal phenomena with exquisite detail. Reproducing stream features such as epicyclic overdensities, we show howreturning tidal tailscan form after the stream fully circumnavigates the Galaxy, enhancing the stream's velocity dispersion by several kilometers per second in our ideal case. While a truly clumpy, asymmetric, and evolving Galactic potential would greatly diffuse such tails, they warrant scrutiny as potentially excellent constraints on the Galaxy’s history and substructure. Reexamining the escape timescale Δtof PEs, we find new behavior related to chaotic scattering in the three-body problem; the Δtdistribution features sharp plateaus corresponding to distinct locally smooth patches of the chaotic saddle separating the phase-space basins of escape. We study for the first time Δtin an evolving cluster, finding that $\mathrm{\Delta }t\sim (E_{\mathrm{J}}^{-0.1},E_{\mathrm{J}}^{-0.4})$for PEs with (low, high) Jacobi energyE_J, flatter than for a static cluster ( $E_{\mathrm{J}}^{-2}$). Accounting for cluster mass loss and internal evolution lowers the median Δtfrom ∼10 Gyr to ≲100 Myr. We finally outline potential improvements to escape in the Monte Carlo method intended to enable the first large grids of tidal tail/stellar stream models from full GC simulations and detailed comparison to stream observations. 

Abstract Intermediate-mass black holes (IMBHs) are believed to be the missing link between the supermassive black holes (BHs) found at the centers of massive galaxies and BHs formed through stellar core collapse. One of the proposed mechanisms for their formation is a collisional runaway process in high-density young star clusters, where an unusually massive object forms through repeated stellar collisions and mergers, eventually collapsing to form an IMBH. This seed IMBH could then grow further through binary mergers with other stellar-mass BHs. Here we investigate the gravitational-wave (GW) signals produced during these later IMBH–BH mergers. We use a state-of-the-art semi-analytic approach to study the stellar dynamics and to characterize the rates and properties of IMBH–BH mergers. We also study the prospects for detection of these mergers by current and future GW observatories, both space-based (LISA) and ground-based (LIGO Voyager, Einstein Telescope, and Cosmic Explorer). We find that most of the merger signals could be detected, with some of them being multiband sources. Therefore, GWs represent a unique tool to test the collisional runaway scenario and to constrain the population of dynamically assembled IMBHs. 

Abstract With about one hundred mergers of binary black holes (BBHs) detected via gravitational waves by the LIGO-Virgo-KAGRA (LVK) Collaboration, our understanding of the darkest objects in the universe has taken unparalleled steps forward. While most of the events are expected to consist of black holes (BHs) directly formed from the collapse of massive stars, some may contain the remnants of previous BBH mergers. In the most massive globular clusters and in nuclear star clusters, successive mergers can produce second- (2G) or higher-generation BHs, and even form intermediate-mass BHs (IMBHs). Overall, we predict that up to ∼10%, ∼1%, or ∼0.1% of the BBH mergers have one component being a 2G, 3G, or 4G BH, respectively. Assuming that ∼500 BBH mergers will be detected in O4 by LVK, this means that ∼50, ∼5, or ∼0.5 events, respectively, will involve a 2G, 3G, or 4G BH, if most sources are produced dynamically in dense star clusters. With their distinctive signatures of higher masses and spins, such hierarchical mergers offer an unprecedented opportunity to learn about the BH populations in the densest stellar systems and to shed light on the elusive IMBHs that may form therein. 

Abstract With the growing number of binary black hole (BBH) mergers detected by LIGO/Virgo/KAGRA, several systems have become difficult to explain via isolated binary evolution, having components in the pair-instability mass gap, high orbital eccentricities, and/or spin–orbit misalignment. Here we focus on GW191109_010717, a BBH merger with component masses of 65 − 11 + 11 and 47 − 13 + 15 M ⊙ and an effective spin of − 0.29 − 0.31 + 0.42 , which could imply a spin–orbit misalignment of more than π /2 rad for at least one of its components. Besides its component masses being in the pair-instability mass gap, we show that isolated binary evolution is unlikely to reproduce the proposed spin–orbit misalignment of GW191109 with high confidence. On the other hand, we demonstrate that BBHs dynamically assembled in dense star clusters would naturally reproduce the spin–orbit misalignment and masses of GW191109 and the rates of GW191109-like events if at least one of the components were to be a second-generation BH. Finally, we generalize our results to all events with a measured negative effective spin, arguing that GW200225 also has a likely dynamical origin. 

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. 

ABSTRACT Galactic nuclei are potential hosts for intermediate-mass black holes (IMBHs), whose gravitational field can affect the motion of stars and compact objects. The absence of observable perturbations in our own Galactic Centre has resulted in a few constraints on the mass and orbit of a putative IMBH. Here, we show that the Laser Interferometer Space Antenna (LISA) can further constrain these parameters if the IMBH forms a binary with a compact remnant (a white dwarf, a neutron star, or a stellar-mass black hole), as the gravitational-wave signal from the binary will exhibit Doppler-shift variations as it orbits around Sgr A*. We argue that this method is the most effective for IMBHs with masses $$10^3\, \mathrm{ M}_\odot \lesssim M_{\rm IMBH}\lesssim 10^5\, \mathrm{ M}_\odot$$ and distances of 0.1–2 mpc with respect to the supermassive black hole, a region of the parameter space partially unconstrained by other methods. We show that in this region the Doppler shift is most likely measurable whenever the binary is detected in the LISA band, and it can help constrain the mass and orbit of a putative IMBH in the centre of our Galaxy. We also discuss possible ways for an IMBH to form a binary in the Galactic Centre, showing that gravitational-wave captures of stellar-mass black holes and neutron stars are the most efficient channel. 

ABSTRACT It has been argued that heavy binaries composed of neutron stars (NSs) and millisecond pulsars (MSPs) can end up in the outskirts of star clusters via an interaction with a massive black hole (BH) binary expelling them from the core. We argue here, however, that this mechanism will rarely account for such observed objects. Only for primary masses ≲100 M⊙ and a narrow range of orbital separations should a BH–BH binary be both dynamically hard and produce a sufficiently low recoil velocity to retain the NS binary in the cluster. Hence, BH binaries are in general likely to eject NSs from clusters. We explore several alternative mechanisms that would cause NS/MSP binaries to be observed in the outskirts of their host clusters after a Hubble time. The most likely mechanism is a three-body interaction involving the NS/MSP binary and a normal star. We compare to Monte Carlo simulations of cluster evolution for the globular clusters NGC 6752 and 47 Tuc, and show that the models not only confirm that normal three-body interactions involving all stellar-mass objects are the dominant mechanism for putting NS/MSP binaries into the cluster outskirts, but also reproduce the observed NS/MSP binary radial distributions without needing to invoke the presence of a massive BH binary. Higher central densities and an episode of core collapse can broaden the radial distributions of NSs/MSPs and NS/MSP binaries due to three-body interactions, making these clusters more likely to host NSs in the cluster outskirts.