Search

The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them., Comment: TianQin Gravitational Wave Whitepaper, 72 pages, 30 figures

We explore the evolution of various properties of multiple-population globular clusters (GCs) for a broad range of initial conditions. We simulated over 200 GC models using the MOCCA Monte Carlo code and find that present-day properties (core and half-light radii, ratio of the number of second-generation (SG) stars to the total number of stars, NSG/NTOT) of these models cover the observed values of these quantities for Milky Way GCs. Starting with a relatively small value of the SG fraction (NSG/NTOT ~ 0.25) and a SG system concentrated in the inner regions of the cluster, we find, in agreement with previous studies, that systems in which the first-generation (FG) is initially tidally filling or slightly tidally underfilling best reproduce the observed ratios of NSG/NTOT and have values of the core and half-light radii typical of those of many Galactic globular clusters. Models in which the FG is initially tidally underfilling retain values of NSG/NTOT close to their initial values. These simulations expand previous investigations and serve to further constrain the viable range of initial parameters and better understand their influence on present-day GC properties. The results of this investigation also provide the basis for our future survey aimed at building specific models to reproduce the observed trends (or lack thereof) between the properties of multiple stellar populations and other clusters properties., Comment: Accepted to Astronomy and Astrophysics (A&A)

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., Comment: 15 pages, 9 figures

We recently introduced three new parameters that describe the shape of the normalized cumulative radial distribution (nCRD) of the innermost stars in globular clusters and trace the clusters dynamical evolution. Here we extend our previous investigations to the case of a large set of Monte Carlo simulations of globular clusters, started from a broad range of initial conditions. All the models are analyzed at the same age of 13 Gyr, when they have reached different evolutionary phases. The sample of models is well representative of the structural properties of the observed population of Galactic globular clusters. We confirm that the three nCRD parameters are powerful tools to distinguish systems in early stages of dynamical evolution, from those that already experienced core collapse. They might also help disentangle clusters hosting a low-mass intermediate-mass black hole of a few hundred solar masses, from cases with large concentrations of dark remnants in their centers. With respect to other dynamical indicators, the nCRD parameters offer the advantage of being fully empirical and easier to measure from observational data., Comment: Accepted for publication in ApJ, 15 pages, 10 figures, 1 table

Black holes (BHs) with masses between 100 to 100,000 times the mass of the Sun ($\rm{M}_{\odot}$) are classified as intermediate-mass black holes (IMBHs), potentially representing a crucial link between stellar-mass and supermassive BHs. Stellar-mass BHs are endpoints of the evolution of stars initially more massive than roughly 20 $\rm{M}_{\odot}$ and generally weigh about 10 to 100 $\rm{M}_{\odot}$. Supermassive BHs are found in the centre of many galaxies and weigh between $10^{6}$ to $10^{10} \ \rm{M}_{\odot}$. The origin of supermassive BHs remains an unresolved problem in astrophysics, with many viable pathways suggesting that they undergo an intermediate-mass phase. Whether IMBHs really stand as an independent category of BHs or rather they represent the heaviest stellar mass and the lightest supermassive BHs is still unclear, mostly owing to the lack of an observational smoking gun. The first part of this chapter discusses proposed formation channels of IMBHs and focuses on their formation and growth in dense stellar environments like globular and nuclear star clusters. It also highlights how the growth of IMBHs through mergers with other BHs is important from the point of view of gravitational waves and seeding of supermassive BHs in our Universe. The second part of the chapter focuses on the multi-wavelength observational constraints on IMBHs in dense star clusters and dwarf galactic nuclei. It also examines the potential insights that future gravitational wave detectors could offer in unraveling the mystery surrounding IMBHs., Comment: To appear as Chapter 2 of the book, "Black Holes in the Era of Gravitational Wave Astronomy", ed. Arca Sedda, Bortolas, Spera, pub. Elsevier. All authors equally contributed to the chapter. A. Askar is the author of part I of the chapter. V. F. Baldassare and M. Mezcua are authors of part II. Figures from other publications have been reproduced with permission

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., Comment: ApJ accepted

We present an upgraded version of the \MOCCA code for the study of dynamical evolution of globular clusters (GCs) and its first application to the study of evolution of multiple stellar populations. We explore initial conditions spanning different structural parameters for the first (FG) and second generation of stars (SG) and we analyze their effect on the binary dynamics and survival. Here, we focus on the number ratio of FG and SG binaries, its spatial variation, and the way their abundances are affected by various cluster initial properties. We find that present-day SG stars are more abundant in clusters that were initially tidally filling. Conversely, FG stars stay more abundant in clusters that were initially tidally underfilling. We find that the ratio between binary fractions is not affected by the way we calculate these fractions (e.g. only main-sequence binaries (MS) or observational binaries, i.e. MS stars $> 0.4 M_{\odot}$ mass ratios $> 0.5$). This implies that the MS stars themselves are a very good proxy for probing entire populations of FG and SG. We also discuss how it relates to the observations of Milky Way GCs. We show that \MOCCA models are able to reproduce the observed range of SG fractions for Milky Way GCs for which we know these fractions. We show how the SG fractions depend on the initial conditions and provide some constraints for the initial conditions to have more numerous FG or SG stars at the Hubble time., Comment: Acceped to MNRAS

The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA's first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultracompact stellar-mass binaries, massive black hole binaries, and extreme or intermediate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.

In the cores of dense stellar clusters, close gravitational encounters between binary and single stars can frequently occur. Using the Tsunami code, we computed the outcome of a large number of binary-single interactions involving two black holes (BHs) and a star to check how the inclusion of orbital energy losses due to tidal dissipation can change the outcome of these chaotic interactions. Each interaction was first simulated without any dissipative processes and then we systematically added orbital energy losses due to gravitational wave emission (using post-Newtonian (PN) corrections) and dynamical tides and recomputed the interactions. We find that the inclusion of tides increases the number of BH-star mergers by up to 75 per cent but it does not affect the number of BH-BH mergers. These results highlight the importance of including orbital energy dissipation due to dynamical tides during few-body encounters and evolution of close binary systems within stellar cluster simulations. Consistent with previous studies, we find that the inclusion of PN terms increases the number of BH-BH mergers during binary-single encounters. However, BH-star mergers are largely unaffected by the inclusion of these terms., Comment: 14 pages, 6 figures, 12 tables, accepted for publication in MNRAS

The Einstein Telescope (ET), a wide-band, future third generation gravitational wave detector, is expected to have detection rates of $\sim 10^5 - 10^6$ binary black hole (BBH) detections and $\sim 7 \times 10^4$ binary neutron star (BNS) detections in one year. The coalescence of compact binaries with a total mass of 20 - 100 $M_{\odot}$, typical of BH-BH or BH-NS binaries, will be visible up to redshift $z\approx 20$ and even higher, thus facilitating the understanding of the dark era of the Universe preceding the birth of the first stars. The ET will therefore be a crucial instrument for population studies. We analysed the compact binaries originating in stars from (i) Population (Pop) I+II, (ii) Pop III, and (iii) globular clusters (GCs), with the single ET instrument, using the ET-D design sensitivity for the analysis. We estimated the constraints on the chirp mass, redshift, and merger rate as function of redshift for these classes of compact object binaries. We conclude that the ET as a single instrument is capable of detecting and distinguishing different compact binary populations separated in chirp mass - redshift space. While compact binaries originating in stars from Pop III are clearly distinguishable, owing to the separation in chirp mass - redshift space, the other two populations, Pop I+II, and GCs, can be distinguished with just 500 detections, corresponding to an observation time of $\sim 1$ hr. The mass distribution characteristics of such different compact binary populations can also be estimated with the single ET instrument., Comment: 16 pages, 10 figures, Accepted in Astronomy & Astrophysics

In this work we investigate properties of intermediate-mass black holes (IMBHs) that escape from star clusters due to dynamical interactions. The studied models were simulated as part of the preliminary second survey carried out using the MOCCA code (MOCCA-SURVEY Database II), which is based on the Monte Carlo N-body method and does not include gravitational wave recoil kick prescriptions of the binary black hole merger product. We have found that IMBHs are more likely to be formed and ejected in models where both initial central density and central escape velocities have high values. Most of our studied objects escape in a binary with another black hole (BH) as their companion and have masses between $100$ and $140\: M_{\odot}$. Escaping IMBHs tend to build-up mass most effectively through repeated mergers in a binary with BHs due to gravitational wave emission. Binaries play a key role in their ejection from the system as they allow these massive objects to gather energy needed for escape. The binaries in which IMBHs escape tend to have very high binding energy at the time of escape and the last interaction is strong but does not involve a massive intruder. These IMBHs gain energy needed to escape the cluster gradually in successive dynamical interactions. We present specific examples of the history of IMBH formation and escape from star cluster models. We also discuss the observational implications of our findings as well as the potential influence of the gravitational wave recoil kicks on the process., Comment: 11 pages, 11 figures, accepted for publish to MNRAS

The dynamical evolution of globular clusters (GCs) is tied to their binary population, as binaries segregate to the cluster centre, leading to an increased binary fraction in the core. This central overabundance of mainly hard binaries can serve as a source of energy for the cluster and has a significant effect on the observed kinematics, such as artificially increasing the observed line-of-sight velocity dispersion. We analyse the binary fractions and distributions of 95 simulated GCs, with and without an intermediate-mass black hole (IMBH) in their centre. We show that an IMBH will not only halt the segregation of binaries towards the cluster centre, but also, directly and indirectly, disrupt the binaries that segregate, thus depleting binaries in the cluster core. We illustrate this by showing that clusters with an IMBH have fewer binaries and flatter radial binary distributions than their counterparts without one. These differences in the binary fraction and distribution provide an additional indicator for the presence of a central IMBH in GCs. In addition, we analyse the effects of the binary fraction on the line-of-sight velocity dispersion in the simulated GCs and find that binaries can cause an overestimation of up to $70\%$ of the velocity dispersion within the core radius. Using recent VLT/MUSE observations of NGC 3201 by Giesers et al. (2019), we find an overestimation of $32.2\pm7.8\%$ in the velocity dispersion that is consistent with the simulations and illustrates the importance of accurately accounting for the binary population when performing kinematic or dynamical analysis., Comment: Accepted for publication in MNRAS. 14 pages, 12 figures. The main results are shown in Figures 6,7 and 10

In many galactic nuclei, a nuclear stellar cluster (NSC) co-exists with a supermassive black hole (SMBH). In this work, we explore the idea that the NSC forms before the SMBH through the merger of several stellar clusters that may contain intermediate-mass black holes (IMBHs). These IMBHs can subsequently grow by mergers and accretion to form an SMBH. To check the observable consequences of this proposed SMBH seeding mechanism, we created an observationally motivated mock population of galaxies, in which NSCs are constructed by aggregating stellar clusters that may or may not contain IMBHs. We model the growth of IMBHs in the NSCs through gravitational wave (GW) mergers with other IMBHs and gas accretion. In the case of GW mergers, the merged BH can either be retained or ejected depending on the GW recoil kick it receives. The likelihood of retaining the merged BH increases if we consider growth of IMBHs in the NSC through gas accretion. We find that nucleated lower-mass galaxies ($\rm M_{\star} \lesssim 10^{9} \ M_{\odot}$; e.g. M33) have an SMBH seed occupation fraction of about 0.3 to 0.5. This occupation fraction increases with galaxy stellar mass and for more massive galaxies ($\rm 10^{9} \ M_{\odot} \lesssim \rm M_{\star} \lesssim 10^{11} \ M_{\odot}$), it is between 0.5 and 0.8, depending on how BH growth is modelled. These occupation fractions are consistent with observational constraints. Furthermore, allowing for BH growth also allows us to reproduce the observed diversity in the mass range of SMBHs in the $\rm M_{\rm NSC} - M_{\rm BH}$ plane., Comment: 17 pages, 20 figures, 2 tables, accepted for publication in MNRAS

The presence or absence of intermediate-mass black holes (IMBHs) at the centre of Milky Way globular clusters (GCs) is still an open question. This is either due to observational restrictions or limitations in the dynamical modelling method; in this work, we explore the latter. Using a sample of high-end Monte Carlo simulations of GCs, with and without a central IMBH, we study the limitations of spherically symmetric Jeans models assuming constant velocity anisotropy and mass-to-light ratio. This dynamical method is one of the most widely used modelling approaches to identify a central IMBH in observations. With these models, we are able to robustly identify and recover the mass of the central IMBH in our simulation with a high-mass IMBH ($M_{\rm IMBH}/M_{\rm GC}\sim4\%$). Simultaneously, we show that it is challenging to confirm the existence of a low-mass IMBH ($M_{\rm IMBH}/M_{\rm GC}\sim0.3\%$), as both solutions with and without an IMBH are possible within our adopted error bars. For simulations without an IMBH we do not find any certain false detection of an IMBH. However, we obtain upper limits which still allow for the presence of a central IMBH. We conclude that while our modelling approach is reliable for the high-mass IMBH and does not seem to lead towards a false detection of a central IMBH, it lacks the sensitivity to robustly identify a low-mass IMBH and to definitely rule out the presence of an IMBH when it is not there., Comment: Accepted for publication in MNRAS. 21 pages, 20 figures. The main results can be seen in figures 9 and 10. Figures 4, 14 and A2 bring interesting points for discussion

The dynamical formation of black hole binaries in globular clusters that merge due to gravitational waves occurs more frequently in higher stellar density. Meanwhile, the probability to form intermediate mass black holes (IMBHs) also increases with the density. To explore the impact of the formation and growth of IMBHs on the population of stellar mass black hole binaries from globular clusters, we analyze the existing large survey of Monte-Carlo globular cluster simulation data (MOCCA SURVEY Database I). We show that the number of binary black hole mergers agrees with the prediction based on clusters' initial properties when the IMBH mass is not massive enough or the IMBH seed forms at a later time. However, binary black hole formation and subsequent merger events are significantly reduced compared to the prediction when the present-day IMBH mass is more massive than $\sim10^4 \rm M_{\odot}$ or the present-day IMBH mass exceeds about 1 per cent of cluster's initial total mass. By examining the maximum black hole mass in the system at the moment of black hole binary escaping, we find that $\sim$ 90 per cent of the merging binary black holes escape before the formation and growth of the IMBH. Furthermore, large fraction of stellar mass black holes are merged into the IMBH or escape as single black holes from globular clusters in cases of massive IMBHs, which can lead to the significant under-population of binary black holes merging with gravitational waves by a factor of 2 depending on the clusters' initial distributions., Comment: 9 pages, 8 figures, Accepted for publication in MNRAS

Supermassive black holes (SMBHs) are found in most galactic nuclei. A significant fraction of these nuclei also contain a nuclear stellar cluster (NSC) surrounding the SMBH. In this paper, we consider the idea that the NSC forms first, from the merger of several stellar clusters that may contain intermediate-mass black holes (IMBHs). These IMBHs can subsequently grow in the NSC and form an SMBH. We carry out $N$-body simulations of the simultaneous merger of three stellar clusters to form an NSC, and investigate the outcome of simulated runs containing zero, one, two and three IMBHs. We find that IMBHs can efficiently sink to the centre of the merged cluster. If multiple merging clusters contain an IMBH, we find that an IMBH binary is likely to form and subsequently merge by gravitational wave emission. We show that these mergers are catalyzed by dynamical interactions with surrounding stars, which systematically harden the binary and increase its orbital eccentricity. The seed SMBH will be ejected from the NSC by the recoil kick produced when two IMBHs merge, if their mass ratio $q\gtrsim 0.15$. If the seed is ejected then no SMBH will form in the NSC. This is a natural pathway to explain those galactic nuclei that contain an NSC but apparently lack an SMBH, such as M33. However, if an IMBH is retained then it can seed the growth of an SMBH through gas accretion and tidal disruption of stars., Comment: 19 pages, 17 figures, 6 tables, accepted for publication in MNRAS

We utilize multi-epoch MUSE spectroscopy to study binaries in the core of NGC 3201. Our sample consists of 3553 stars with 54883 spectra in total comprising 3200 main-sequence stars up to 4 magnitudes below the turn-off. Each star in our sample has between 3 and 63 (with a median of 14) reliable radial velocity (RV) measurements within five years of observations. We introduce a statistical method to determine the probability of a star showing RV variations based on the whole inhomogeneous RV sample. Using HST photometry and an advanced dynamical MOCCA simulation of this specific GC we overcome observational biases that previous spectroscopic studies had to deal with. This allows us to infer a binary frequency in the MUSE FoV and enables us to deduce the underlying true binary frequency of (6.75+-0.72) % in NGC 3201. The comparison of the MUSE observations with the MOCCA simulation suggests a significant fraction of primordial binaries. We can also confirm a radial increase of the binary fraction towards the GC centre due to mass segregation. We discovered that in our sample at least (57.5+-7.9) % of blue straggler stars (BSS) are in a binary system. For the first time in a study of GCs, we were able to fit Keplerian orbits to a significant sample of 95 binaries. We present the binary system properties of eleven BSS and show evidence that two BSS formation scenarios, the mass transfer in binary (or triple) star systems and the coalescence due to binary-binary interactions, are present in our data. We also describe the binary and spectroscopic properties of four sub-subgiant (or red straggler) stars. Furthermore, we discovered two new black hole (BH) candidates with minimum masses (Msini) of (7.68+-0.50) M_sun, (4.4+-2.8) M_sun, and refine the minimum mass estimate on the already published BH to (4.53+-0.21) M_sun. These BHs are consistent with an extensive BH subsystem hosted by NGC 3201.

We investigate the dissolution process of star clusters embedded in an external tidal field and harboring a subsystem of stellar-mass black hole. For this purpose we analyzed the MOCCA models of real star clusters contained in the Mocca Survey Database I. We showed that the presence of a stellar-mass black hole subsystem in tidally filling star cluster can lead to abrupt cluster dissolution connected with the loss of cluster dynamical equilibrium. Such cluster dissolution can be regarded as a third type of cluster dissolution mechanism. We additionally argue that such a mechanism should also work for tidally under-filling clusters with a top-heavy initial mass function., Comment: 4 pages, 1 figure. Contribution to the proceedings of the IAU Symposium No. 351: "Star Clusters: from the Milky Way to the Early Universe"

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., Comment: 4 pages, 2 figures, 1 table. Contribution to the proceedings of the IAU Symposium No. 351: "Star Clusters: from the Milky Way to the Early Universe"

Supermassive black holes are found in most galactic nuclei. A large fraction of these nuclei also contain a nuclear stellar cluster surrounding the black hole. Here we consider the idea that the nuclear stellar cluster formed first and that the supermassive black hole grew later. In particular we consider the merger of three stellar clusters to form a nuclear stellar cluster, where some of these clusters contain a single intermediate-mass black hole (IMBH). In the cases where multiple clusters contain IMBHs, we discuss whether the black holes are likely to merge and whether such mergers are likely to result in the ejection of the merged black hole from the nuclear stellar cluster. In some cases, no supermassive black hole will form as any merger product is not retained. This is a natural pathway to explain those galactic nuclei that contain a nuclear stellar cluster but apparently lack a supermassive black hole; M33 being a nearby example. Alternatively, if an IMBH merger product is retained within the nuclear stellar cluster, it may subsequently grow, e.g. via the tidal disruption of stars, to form a supermassive black hole., Comment: 4 pages, 3 figures, 1 table. Contribution to the proceedings of the IAU Symposium No. 351: "Star Clusters: from the Milky Way to the Early Universe"

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., Comment: 16 pages, 5 figures. Accepted version (PRD)

We have been investigating populations of cataclysmic variables (CVs) in a set of more than 300 globular cluster (GC) models evolved with the MOCCA code. One of the main questions we have intended to answer is whether most CVs in GCs are dynamically formed or not. Contrary to what has been argued for a long time, we found that dynamical destruction of primordial CV progenitors is much stronger in GCs than dynamical formation of CVs. In particular, we found that, on average, the detectable CV population is predominantly composed of CVs formed via a typical common envelope phase (> 70 per cent). However, core-collapsed models tend to have higher fractions of bright CVs than non-core-collapsed ones, which suggests then that the formation of CVs is indeed slightly favoured through strong dynamical interactions in core-collapsed GCs, due to the high stellar densities in their cores., Comment: 4 pages, 1 figures, contribution to the proceedings of the IAU Symposium No. 351, 2019, "Star Clusters: from the Milky Way to the Early Universe"

In this paper we explore the interplay between intermediate-mass black holes (IMBHs) and their nursing globular clusters (GCs), taking advantage of over 2000 Monte Carlo GC models. We find that the average density of IMBHs sphere of influence can be uniquely connected to the host GCs luminosity and half-light radius via a fundamental plane. We propose a statistical approach to systematically identify potential Galactic GCs harbouring either an IMBH or a massive subsystem comprised of stellar BHs. Our models show that the IMBH is often bound to a stellar companion or a stellar BH, which can lead to tidal disruption events or to low-frequency gravitational waves. We show that GCs orbiting close to the Galactic Centre have a larger probability to witness IMBH formation during their early evolution. These low-orbit GCs can deliver several IMBHs into the galaxy innermost regions, with potential impact on both electromagnetic and GW emission. We discuss potential connections between IMBHs and SMBHs inhabiting galactic nuclei, exploring the possibility that in some cases they share similar formation pathways., Comment: 19 pages, 1 appendix, 3 tables, 16 figures. MNRAS submitted. Comments welcome

We briefly describe and discuss the set-up of the project MOCCA Survey Database I. The database contains more than 2000 Monte Carlo models of evolution of real star cluster performed with the MOCCA code. Then, we very briefly discuss results of analysis of the database regarding the following projects: formation of intermediate mass black holes, abrupt cluster dissolution harboring black hole subsystems, retention fraction of black hole - black hole mergers, and tidal disruption events with intermediate mass black holes., Comment: 10 pages, 4 figures. MG15 Proceedings

We investigate the dissolution process for dynamically evolving star clusters embedded in an external tidal field by exploring the MOCCA Survey Database I, with focus on the presence and evolution of a stellar-mass black hole subsystem. We argue that the presence of a black hole subsystem can lead to the dissolution of tidally filling star clusters and this can be regarded as a third type of cluster dissolution mechanism (in addition to well-known mechanisms connected with strong mass loss due to stellar evolution and mass loss connected with the relaxation process). This third process is characterized by abrupt cluster dissolution connected with the loss of dynamical equilibrium. The abrupt dissolution is powered by strong energy generation from a stellar-mass black hole subsystem accompanied by tidal stripping. Additionally, we argue that such a mechanism should also work for even tidally under-filling clusters with top-heavy initial mass function. Observationally, star clusters which undergo dissolution powered by the third mechanism would look as a 'dark cluster' i.e. composed of stellar mass black holes surrounded by an expanding halo of luminous stars (Banerjee & Kroupa 2011), and they should be different from 'dark clusters' harbouring intermediate mass black holes as discussed by Askar et al. (2017a). An additional observational consequence of an operation of the third dissolution mechanism should be a larger than expected abundance of free floating black holes in the Galactic halo., Comment: 14 pages, 14 figures, accepted to MNRAS

Machine learning is a powerful technique, becoming increasingly popular in astrophysics. In this paper, we apply machine learning to more than a thousand globular cluster (GC) models simulated as part of the 'MOCCA-Survey Database I' project in order to correlate present-day observable properties with the presence of a subsystem of stellar mass black holes (BHs). The machine learning model is then applied to available observed parameters for Galactic GCs to identify which of them that are most likely to be hosting a sizeable number of BHs and reveal insights into what properties lead to the formation of BH subsystems. With our machine learning model, we were able to shortlist 21 Galactic GCs that are most likely to contain a BH subsystem. We show that the clusters shortlisted by the machine learning classifier include those in which BH candidates have been observed (M22, M10 and NGC 3201) and that our results line up well with independent simulations and previous studies that manually compared simulated GC models with observed properties of Galactic GCs. These results can be useful for observers searching for elusive stellar mass BH candidates in GCs and further our understanding of the role BHs play in GC evolution. In addition, we have released an online tool that allows one to get predictions from our model after they input observable properties., Comment: 20 pages, 9 figures, 7 tables. Accepted for publication in MNRAS. Source code available at https://github.com/ammaraskar/black-holes-black-boxes

We investigate here populations of cataclysmic variables (CVs) in a set of 288 globular cluster (GC) models evolved with the MOCCA code. This is by far the largest sample of GC models ever analysed with respect to CVs. Contrary to what has been argued for a long time, we found that dynamical destruction of primordial CV progenitors is much stronger in GCs than dynamical formation of CVs, and that dynamically formed CVs and CVs formed under no/weak influence of dynamics have similar white dwarf mass distributions. In addition, we found that, on average, the detectable CV population is predominantly composed of CVs formed via typical common envelope phase (CEP) ($\gtrsim70$ per cent), that only $\approx2-4$ per cent of all CVs in a GC is likely to be detectable, and that core-collapsed models tend to have higher fractions of bright CVs than non-core-collapsed ones. We also consistently show, for the first time, that the properties of bright and faint CVs can be understood by means of the pre-CV and CV formation rates, their properties at their formation times and cluster half-mass relaxation times. Finally, we show that models following the initial binary population proposed by Kroupa and set with low CEP efficiency better reproduce the observed amount of CVs and CV candidates in NGC 6397, NGC 6752 and 47 Tuc. To progress with comparisons, the essential next step is to properly characterize the candidates as CVs (e.g. by obtaining orbital periods and mass ratios)., Comment: 18 pages, 13 figures; accepted for publication in MNRAS

The dense environment of globular clusters (GCs) can facilitate the formation of binary black holes (BBHs), some of which can merge with gravitational waves (GW) within the age of the Universe. We have performed a survey of Monte-Carlo simulations following the dynamical evolution of GCs with different masses, sizes and binary fractions and explored the impact of the host GC properties on the formation of BBH mergers. We find that the number of BBH mergers from GCs is determined by the GC's initial mass, size and primordial binary fraction. We identify two groups of BBH mergers: a primordial group whose formation does not depend on cluster's dynamics and a dynamical group whose formation is driven by the cluster's dynamical evolution. We show how the BBH origin affects the BBH mergers' main properties such as the chirp mass and merging time distributions. We provide analytic expressions for the dependence of the number of BBH mergers from individual GCs on the main cluster's structural properties and the time evolution of the merger rates of these BBHs. These expressions provide an essential ingredient for a general framework allowing to estimate the merger rate density. Using the relations found in our study, we find a local merger rate density of 0.18$-$1.8 ${\rm Gpc}^{-3}{\rm yr}^{-1}$ for primordial BBH mergers and 0.6$-$18 ${\rm Gpc}^{-3}{\rm yr}^{-1}$ for dynamical BBH mergers, depending on the GC mass and size distributions, initial binary fraction and the number density of GCs in the Universe., Comment: 12 pages, 12 figures, 2 tables, accepted for publication in MNRAS

The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress., Comment: White Paper for the COST action "Gravitational Waves, Black Holes, and Fundamental Physics", 272 pages, 12 figures; v4: updated references and author list. Overall improvements and corrections. To appear in Classical and Quantum Gravity

We study the gravitational wave (GW) frequency and chirp mass distribution of binary black hole (BBH) mergers assembled through three-body interactions in globular clusters (GCs), when GW emission at the 2.5 post-Newtonian (PN) level is included in the $N$-body equation-of-motion (EOM). From performing $\sim 2.5\times10^{6}$ PN binary-single interactions based on GC data from the `MOCCA-Survey Database I' project, and by the use of analytical methods, we find that $5-10\%$ of all the three-body assembled GC BBH mergers have a GW frequency at formation that is $\gtrsim 10^{-1}$ Hz, implying they enter the LIGO band without having drifted through the LISA band first. If PN terms are not included in the EOM, one finds instead that all BBH mergers drifts through both LISA and LIGO. As the fraction of BBH mergers that only show up in LIGO is expected to be $\sim 0\%$ for standard field binary BBH mergers, future joint measurements with LISA and LIGO can be used to gain insight into the formation of BBH mergers., Comment: 7 pages, 2 figures. comments welcome

There have been increasing theoretical speculations and observational indications that certain globular clusters (GCs) could contain a sizeable population of stellar mass black holes (BHs). In this paper, we shortlist at least 29 Galactic GCs that could be hosting a subsystem of BHs (BHS). In a companion paper, we analysed results from a wide array of GC models (simulated with the MOCCA code for cluster simulations) that retained few tens to several hundreds of BHs at 12 Gyr and showed that the properties of the BHS in those GCs correlate with the GC's observable properties. Building on those results, we use available observational properties of 140 Galactic GCs to identify 29 GCs that could potentially be harbouring up to a few hundreds of BHs. Utilizing observational properties and theoretical scaling relations, we estimate the density, size and mass of the BHS in these GCs. We also calculate the total number of BHs and the fraction of BHs contained in a binary system for our shortlisted Galactic GCs. Additionally, we mention other Galactic GCs that could also contain significant number of single BHs or BHs in binary systems., Comment: 13 pages, 5 figures, 3 tables, accepted for publication in MNRAS. Revised manuscript includes minor corrections and a new subsection (2.5)

In this paper, we discuss how globular clusters (GCs) structural and observational properties can be used to infer the presence of a black hole system (BHS) inhabiting their inner regions. We propose a novel way to identify the BHS size, defined as the GC radius containing a mass contributed equally from stars and stellar BHs. Using this definition, similar to the well-known concept of "influence radius", we found a "fundamental plane" connecting the BHS typical density with the GC central surface density profile, total luminosity and observational half-mass radius. Our approach allows us to define a unique way to connect the observational GCs parameters with their dark content. Comparing our results with observed Milky Way GCs, we found that many of them likely host, at the present time, as many as several hundreds of BHs. These BHS are characterized by a relatively low typical density, $\rho_\bhs \sim 10-10^5\Ms$ pc$^{-3}$ and composed of relatively massive BHs, with average masses in the range $m_\bhs = 14-22\Ms$. We also show that a similar approach can be used to find Milky Way GCs potentially hosting an intermediate-mass black hole., Comment: 14 pages, 12 figures, resubmitted to MNRAS after requested revision

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., Comment: 5 pages, 1 figure, revised manuscript has been accepted for publication in ApJ

Numerical simulations were carried out to study the origin of multiple stellar populations in the intermediate-age clusters NGC 411 and NGC 1806 in the Magellanic Clouds. We performed NBODY6++ simulations based on two different formation scenarios, an ad hoc formation model where second-generation (SG) stars are formed inside a cluster of first-generation (FG) stars using the gas accumulated from the external intergalactic medium and a minor merger model of unequal mass ($M_{SG}$/$M_{FG}$ ~5-10%) clusters with an age difference of a few hundred million years. We compared our results such as the radial profile of the SG-to-FG number ratio with observations on the assumption that the SG stars in the observations are composed of cluster members, and confirmed that both the ad hoc formation and merger scenarios reproduce the observed radial trend of the SG-to-FG number ratio which shows less centrally concentrated SG than FG stars. It is difficult to constrain the formation scenario for the multiple populations by only using the spatial distribution of the SG stars. SG stars originating from the merger scenario show a significant velocity anisotropy and rotational features compared to those from the ad hoc formation scenario. Thus, observations aimed at kinematic properties like velocity anisotropy or rotational velocities for SG stars should be obtained to better understand the formation of the multiple populations in these clusters. This is, however, beyond current instrumentation capabilities., Comment: 11 pages, 8 figures, 1 table; accepted for publication in MNRAS

Colour-magnitude diagrams (CMDs) are powerful tools that might be used to infer stellar properties in globular clusters (GCs), for example, the binary fraction and their mass ratio ($q$) distribution. In the past few years, observations have revealed that q distributions of GC main-sequence (MS) binaries are generally flat, and a distribution characterized by a strong increase towards q $\approx$ 1 is not typical in GCs. In numerical simulations of GC evolution with the initial binary population (IBP) described by Kroupa, synthetic CMD colour distributions exhibit a peak associated with binaries that have q $\approx$ 1. While the Kroupa IBP reproduces binary properties in star-forming regions, clusters and the Galactic field, the peak in the q distribution towards q $\approx$ 1 observed for GC simulations is not consistent with distributions derived from observations. The objective of this paper is to refine and further improve the physical formulation of pre-main-sequence eigenevolution proposed by Kroupa in order to achieve CMD colour distributions of simulated GC models similar to those observed in real GCs, and to get a similarly good agreement with binary properties for late-type binaries in the Galactic field. We present in this paper a modified Kroupa IBP, in which early-type stars follow observational distributions, and late-type stars are generated according to slightly modified pre-main-sequence eigenevolution prescriptions. Our modifications not only lead to a qualitatively good agreement with respect to long-term observations of late-type binaries in the Galactic field, but also resolve the above-mentioned problem related to binary distributions in GC models., Comment: 18 pages, 10 figures, 4 tables; accepted for publication in MNRAS

We introduce and present results from the COCOA (Cluster simulatiOn Comparison with ObservAtions) code that has been developed to create idealized mock photometric observations using results from numerical simulations of star cluster evolution. COCOA is able to present the output of realistic numerical simulations of star clusters carried out using Monte Carlo or \textit{N}-body codes in a way that is useful for direct comparison with photometric observations. In this paper, we describe the COCOA code and demonstrate its different applications by utilizing globular cluster (GC) models simulated with the MOCCA (MOnte Carlo Cluster simulAtor) code. COCOA is used to synthetically observe these different GC models with optical telescopes, perform PSF photometry and subsequently produce observed colour magnitude diagrams. We also use COCOA to compare the results from synthetic observations of a cluster model that has the same age and metallicity as the Galactic GC NGC 2808 with observations of the same cluster carried out with a 2.2 meter optical telescope. We find that COCOA can effectively simulate realistic observations and recover photometric data. COCOA has numerous scientific applications that maybe be helpful for both theoreticians and observers that work on star clusters. Plans for further improving and developing the code are also discussed in this paper., Comment: 18 pages, 12 figures, accepted for publication in MNRAS. Revised manuscript has a new title, better quality figures and many other improvements. COCOA can be downloaded from: https://github.com/abs2k12/COCOA (comments are welcome)

In this third of a series of papers related to cataclysmic variables (CVs) and related objects, we analyse the population of CVs in a set of 12 globular cluster models evolved with the MOCCA Monte Carlo code, for two initial binary populations (IBPs), two choices of common-envelope phase (CEP) parameters, and three different models for the evolution of CVs and the treatment of angular momentum loss. When more realistic models and parameters are considered, we find that present-day cluster CV duty cycles are extremely-low ($\lesssim 0.1$ per cent) which makes their detection during outbursts rather difficult. Additionally, the IBP plays a significant role in shaping the CV population properties, and models that follow the Kroupa IBP are less affected by enhanced angular momentum loss. We also predict from our simulations that CVs formed dynamically in the past few Gyr (massive CVs) correspond to bright CVs (as expected), and that faint CVs formed several Gyr ago (dynamically or not) represent the overwhelming majority. Regarding the CV formation rate, we rule out the notion that it is similar irrespective of the cluster properties. Finally, we discuss the differences in the present-day CV properties related to the IBPs, the initial cluster conditions, the CEP parameters, formation channels, the CV evolution models, and the angular momentum loss treatments., Comment: 18 pages, 7 figures, 2 tables; accepted for publication in MNRAS

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., Comment: 10 pages, 8 figures; Accepted for publication in MNRAS

This is the second in a series of papers associated with cataclysmic variables (CVs) and related objects, formed in a suite of simulations for globular cluster evolution performed with the MOCCA Monte Carlo code. We study the properties of our simulated CV populations throughout the entire cluster evolution. We find that dynamics extends the range of binary CV progenitor properties, causing CV formation from binary progenitors that would otherwise not become CVs. The CV formation rate in our simulations can be separated into two regimes: an initial burst ($\lesssim$ 1 Gyr) connected with the formation of the most massive white dwarfs, followed by a nearly constant formation rate. This result holds for all models regardless of the adopted initial conditions, even when most CVs form dynamically. Given the cluster age-dependence of CV properties, we argue that direct comparisons to observed Galactic field CVs could be misleading, since cluster CVs can be up to 4 times older than their field counterparts. Our results also illustrate that, due mainly to unstable mass transfer, some CVs that form in our simulations are destroyed before the present-day. Finally, some field CVs might have originated from globular clusters, as found in our simulations, although the fraction of such escapers should be small relative to the entire Galactic field CV population., Comment: 19 pages, 7 figures, 2 tables; minor changes made to the text, accepted for publication in MNRAS

In this first of a series of papers, we utilize results for around two thousand star cluster models simulated using the MOCCA code for star cluster evolution (Survey Database I) to determine the astrophysical properties and local merger rate densities for coalescing binary black holes (BBHs) originating from globular clusters (GCs). We extracted information for all coalescing BBHs that escape the cluster models and subsequently merge within a Hubble time along with BBHs that are retained in our GC models and merge inside the cluster via gravitational wave (GW) emission. By obtaining results from a substantial number of realistic star cluster models that cover different initial parameters, we have an extremely large statistical sample of BBHs with stellar mass and massive stellar BH ($\lesssim 100M_{\odot}$) components that merge within a Hubble time. Using this data, we estimate local merger rate densities for these BBHs originating from GCs to be at least 5.4 ${\rm Gpc}^{-3}\,{\rm yr}^{-1}$, Comment: 5 pages, 4 figures, 1 table, accepted for publication in MNRAS Letters

We very briefly discuss proposed in the literature possible scenarios for intermediate mass black holes (IMBH) formation in globular clusters. We also discuss the results of the MOCCA simulations of about 2000 models (BigSurvey) regarding the distribution of events connected with electromagnetic and gravitational radiations, namely: mass transfer on IMBH, collisions and mergers with IMBH and mergers with IMBH due to gravitational radiation. The rates of these events are very small, so their observation is very improbable., Comment: 4 pages, 1 figure

We describe the dynamical evolution of a unique type of dark star cluster model in which the majority of the cluster mass at Hubble time is dominated by an intermediate-mass black hole (IMBH). We analyzed results from about 2000 star cluster models (Survey Database I) simulated using the Monte-Carlo code MOCCA and identified these dark star cluster models. Taking one of these models, we apply the method of simulating realistic "mock observations" by utilizing the COCOA and SISCO codes to obtain the photometric and kinematic observational properties of the dark star cluster model at 12 Gyr. We find that the perplexing Galactic globular cluster NGC 6535 closely matches the observational photometric and kinematic properties of the dark star cluster model presented in this paper. Based on our analysis and currently observed properties of NGC 6535, we suggest that this globular cluster could potentially harbour an IMBH. If it exists, the presence of this IMBH can be detected robustly with proposed kinematic observations of NGC 6535., Comment: 11 pages, 10 figures, 5 tables, Accepted for publication in MNRAS

In this first investigation of the MOCCA database with respect to cataclysmic variables, we found that for models with Kroupa initial distributions, considering the standard value of the efficiency of the common-envelope phase adopted in BSE, no single cataclysmic variable was formed only via binary stellar evolution, i. e., in order to form them, strong dynamical interactions have to take place. Our results also indicate that the population of cataclysmic variables in globular clusters are, mainly, in the last stage of their evolution and observational selection effects can change drastically the expected number and properties of observed cataclysmic variables., Comment: 4 pages, 3 figures. Presented at the MODEST 16/Cosmic Lab conference in Bologna, Italy, April 18-22 2016. To be pusblished in Mem. S. A. It. Conference Series

In this paper, which is the first in a series of papers associated with cataclysmic variables and related objects, we introduce the CATUABA code, a numerical machinery written for analysis of the MOCCA simulations, and show some first results by investigating the present-day population of cataclysmic variables in globular clusters. Emphasis was given on their properties and the observational selection effects when observing and detecting them. In this work we analysed in this work six models, including three with Kroupa distributions of the initial binaries. We found that for models with Kroupa initial distributions, considering the standard value of the efficiency of the common envelope phase adopted in BSE, no single cataclysmic variable was formed only via binary stellar evolution, i. e., in order to form them, strong dynamical interactions have to take place. We show and explain why this is inconsistent with observational and theoretical results. Our results indicate that the population of cataclysmic variables in globular clusters is, mainly, in the last stage of their evolution and observational selection effects can drastically change the expected number of observed cataclysmic variables. We show that the probability of observing them during the outbursts is extremely small and conclude that the best way of looking for cataclysmic variables in globular clusters is by searching for variabilities during quiescence, instead of during outbursts. For that, one would need a very deep observation which could reach magnitudes $\gtrsim$ 27 mag. Finally, we argue that cataclysmic variables in globular clusters are not necessarily magnetic., Comment: 21 pages, 5 figures, 2 tables; minor changes made to the text, accepted for publication in MNRAS

Introducing the DRAGON simulation project, we present direct $N$-body simulations of four massive globular clusters (GCs) with $10^6$ stars and 5$\%$ primordial binaries at a high level of accuracy and realism. The GC evolution is computed with NBODY6++GPU and follows the dynamical and stellar evolution of individual stars and binaries, kicks of neutron stars and black holes, and the effect of a tidal field. We investigate the evolution of the luminous (stellar) and dark (faint stars and stellar remnants) GC components and create mock observations of the simulations (i.e. photometry, color-magnitude diagrams, surface brightness and velocity dispersion profiles). By connecting internal processes to observable features we highlight the formation of a long-lived 'dark' nuclear subsystem made of black holes (BHs), which results in a two-component structure. The inner core is dominated by the BH subsystem and experiences a core collapse phase within the first Gyr. It can be detected in the stellar (luminous) line-of-sight velocity dispersion profiles. The outer extended core - commonly observed in the (luminous) surface brightness profiles - shows no collapse features and is continuously expanding. We demonstrate how a King (1966) model fit to observed clusters might help identify the presence of post core-collapse BH subsystems. For global observables like core and half-mass radii the direct simulations agree well with Monte-Carlo models. Variations in the initial mass function can result in significantly different GC properties (e.g. density distributions) driven by varying amounts of early mass loss and the number of forming BHs., Comment: 18 pages, 8 figures, MNRAS accepted

We introduce and present preliminary results from COCOA (Cluster simulatiOn Comparison with ObservAtions) code for a star cluster after 12 Gyrs of evolution simulated using the MOCCA code. The COCOA code is being developed to quickly compare results of numerical simulations of star clusters with observational data. We use COCOA to obtain parameters of the projected cluster model. For comparison, a FITS file of the projected cluster was provided to observers so that they could use their observational methods and techniques to obtain cluster parameters. The results show that the similarity of cluster parameters obtained through numerical simulations and observations depends significantly on the quality of observational data and photometric accuracy., Comment: 2 pages, 1 figure, Conference proceedings for poster presented at IAUS 312