In this work, we investigate the black hole (BH) population of globular clusters (GCs) in Milky Way- (MW) and Andromeda- (M31) like galaxies. We combine the population synthesis code MASinGa and the MOCCA-Survey Database I to infer the properties of GCs harbouring a BH subsystem (BHS), an IMBH, or neither of those. We find that the typical number of GCs with a BHS, an IMBH, or none become comparable in the galactic outskirts, whilst the inner galactic regions are dominated by GCs without a significant dark component. Our models suggest that GCs harbouring a BHS are slightly heavier and with larger half-mass radii compared to the overall population. We retrieve the properties of binary BHs (BBHs) that have either merged in the last 3 Gyr or survived in their parent cluster until present-day. We find that around 80\% of the merging BBHs form due to dynamical interactions while the remaining originate from evolution of primordial binaries. We infer a merger rate for BBHs in the local Universe of $1.0-23\,\,\rm{yr^{-1}\,Gpc^{-3}}$, depending on the adopted assumptions. We find around 100-240 BBHs survive until present-day and are mostly concentrated in the inner few kpc of the galaxy. We estimate also the number of BHs transported into the galactic nucleus by infalling star clusters, finding around 1,000-3,000 BHs and 100-200 BBHs are transported over a time span of 12 Gyr. This enables us to constrains the total amount of BHs and BBHs binaries lurking in nuclear star cluster, i.e. $N_{BHs}=(1.4-2.2)\times10^4$ and $N_{BBHs}=700-1,100$.
Definitive evidence that globular clusters (GCs) host intermediate-mass black holes (IMBHs) is elusive. Machine learning (ML) models trained on GC simulations can in principle predict IMBH host candidates based on observable features. This approach has two limitations: first, an accurate ML model is expected to be a black box due to complexity; second, despite our efforts to realistically simulate GCs, the simulation physics or initial conditions may fail to fully reflect reality. Therefore our training data may be biased, leading to a failure in generalization on observational data. Both the first issue -- explainability/interpretability -- and the second -- out of distribution generalization and fairness -- are active areas of research in ML. Here we employ techniques from these fields to address them: we use the anchors method to explain an XGBoost classifier; we also independently train a natively interpretable model using Certifiably Optimal RulE ListS (CORELS). The resulting model has a clear physical meaning, but loses some performance with respect to XGBoost. We evaluate potential candidates in real data based not only on classifier predictions but also on their similarity to the training data, measured by the likelihood of a kernel density estimation model. This measures the realism of our simulated data and mitigates the risk that our models may produce biased predictions by working in extrapolation. We apply our classifiers to real GCs, obtaining a predicted classification, a measure of the confidence of the prediction, an out-of-distribution flag, a local rule explaining the prediction of XGBoost and a global rule from CORELS.
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.
Abstract Sizeable 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.
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 analyse 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 centre. The mock observations are modelled 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 an IMBH of considerable mass (3 per cent of the total GC mass), the analysis does not yield conclusive results in one out of five cases, because of shot noise due to bright stars close to the IMBH line of sight. This stochastic variability in the modelling outcome grows with decreasing BH mass, with approximately three failures out of four for IMBHs with 0.1 per cent of total GC mass. Finally, we find that our analysis is generally unable to exclude at 68 per cent confidence an IMBH with mass of 103 M⊙ in snapshots without a central BH. Interestingly, our results are not sensitive to GC distance within 5–20 kpc, nor to misidentification of the GC centre by less than 2 arcsec (<20 per cent 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.
There could be a significant population of double white dwarf binaries (DWDs) inside globular clusters (GCs), however, these are often too faint to be individually observed. We have utilized a large number GC models evolved with the Monte Carlo Cluster Simulator (MOCCA) code, to create a large statistical dataset of DWDs. These models include multiple-stellar populations, resulting in two distinct initial populations: one dense and another less dense. Due to the lower density of one population, a large number of objects escape during the early GC evolution, leading to a high mass-loss rate. In this dataset we have analysed three main groups of DWDs, namely in-cluster binaries, escaped binaries, and isolated evolution of primordial binaries. We compared the properties of these groups to observations of close and wide binaries. We find that the number of escaping DWDs is significantly larger than the number of in-cluster binaries and those that form via the isolated evolution of all promiridial binaries in our GC models. This suggests that dynamics play an important role in the formation of DWDs. For close binaries, we found a good agreement in the separations of escaped binaries and isolated binaries, but in-cluster binaries showed slight differences. We could not reproduce the observed extremely low mass WDs due to the limitations of our stellar and binary evolution prescriptions. For wide binaries, we also found a good agreement in the separations and masses, after accounting for observational selection effects. We conclude that, even though the current observational samples of DWDs are extremely biased and incomplete, our results compare reasonably well with observations.
We estimate the population of eccentric gravitational wave (GW) binary black hole (BBH) mergers forming during binary-single interactions in globular clusters (GCs), using ~ 800 GC models that were evolved using the MOCCA code for star cluster simulations as part of the MOCCA-Survey Database I project. By re-simulating binary-single interactions (only involving 3 BHs) extracted from this set of GC models using an N-body code that includes GW emission at the 2.5 post-Newtonian level, we find that ~ 10% of all the BBHs assembled in our GC models that merge at present time form during chaotic binary-single interactions, and that about half of this sample have an eccentricity > 0.1 at 10 Hz. We explicitly show that this derived rate of eccentric mergers is ~ 100 times higher than one would find with a purely Newtonian N-body code. Furthermore, we demonstrate that the eccentric fraction can be accurately estimated using a simple analytical formalism when the interacting BHs are of similar mass; a result that serves as the first successful analytical description of eccentric GW mergers forming during three-body interactions in realistic GCs.
The first neutron star-neutron star (NS-NS) merger was discovered on August 17, 2017 through gravitational waves (GW170817) and followed with electromagnetic observations. This merger was detected in an old elliptical galaxy with no recent star formation. We perform a suite of numerical calculations to understand the formation mechanism of this merger. We probe three leading formation mechanisms of double compact objects: classical isolated binary star evolution, dynamical evolution in globular clusters, and nuclear cluster formation to test whether they are likely to produce NS-NS mergers in old host galaxies. Our simulations with optimistic assumptions show current NS-NS merger rates at the level of 10 −2 yr −1 from binary stars, 5 × 10 −5 yr −1 from globular clusters, and 10 −5 yr −1 from nuclear clusters for all local elliptical galaxies (within 100 Mpc 3 ). These models are thus in tension with the detection of GW170817 with an observed rate of 1.5 −1.2 +3.2 yr −1 (per 100 Mpc 3 ; LIGO/Virgo 90% credible limits). Our results imply that either the detection of GW170817 by LIGO/Virgo at their current sensitivity in an elliptical galaxy is a statistical coincidence; that physics in at least one of our three models is incomplete in the context of the evolution of stars that can form NS-NS mergers; or that another very efficient (unknown) formation channel with a long delay time between star formation and merger is at play.
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