The photometric properties that we could observe for Extra-Galactic Globular Clusters (EGGCs) are the integrated light of the system and for nearby EGGCs it also is possible to measure both half-light radii and the color spatial distribution, e.g. for areas smaller and larger than the half-light radius. No information about the internal dynamical state of the system could be directly obtained from observations. On the other hand, simulations of Globular Clusters (GCs) can provide detailed information about the dynamical evolution of the system. We present a preliminary study of EGGCs' photometric properties for different dynamical evolutionary stages. We apply this study to 12 Gyr old GCs simulated as part of the MOCCA Survey Database. We determine the magnitudes in different bands from their projected snapshots using the Flexible Stellar Population Synthesis (FSPS) code and we measure the half-light radii from the surface brightness.
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…
Using a Monte Carlo code, we construct a dynamic evolutionary model of the Galactic globular cluster M22 (NGC6656). The initial conditions are chosen so that, after about 12Gyr of stellar and dynamical evolution, the model is an approximate fit to the surface brightness and velocity dispersion profiles of the cluster, to its mass function, and to the current binary fraction. Depending on the distribution of black hole natal kicks, we predict that the present-day population of stellar-mass black holes ranges from about 40 (no kicks) down to essentially zero (kicks distributed like those of neut…
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 late…
Over the last few decades, exhaustive surveys of extra Galactic globular clusters (EGGCs) have become feasible. Only recently, kinematical information of globular clusters (GCs) were available through Gaia DR2 spectroscopy and also proper motions. On the other hand, simulations of GCs can provide detailed information about the dynamical evolution of the system. We present a preliminary study of EGGCs' properties for different dynamical evolutionary stages. We apply this study to 12 Gyr-old GCs simulated as part of the MOCCA Survey Database. Mimicking observational limits, we consider only a su…
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 Kroup…
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 abund…
A comprehensive study of the co-evolution of globular cluster systems (GCS) in galaxies requires the ability to model both the large scale dynamics (0.01 - 10 kpc) regulating their orbital evolution, and the small scale dynamics (sub-pc - AU) regulating the internal dynamics of each globular cluster (GC). In this work we present a novel method that combine semi-analytic models of GCS with fully self-consistent Monte Carlo models to simultaneously evolve large GCSs. We use the population synthesis code MASinGa and the MOCCA-Survey Database I to create synthetic GC populations aimed at represent…
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 ra…
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 d…
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 predomina…
Anisotropy of gravitational wave (GW) emission results in a net momentum gained by the black hole (BH) merger product, leading to a recoil velocity up to $\sim10^3\text{ km s}^{-1}$, which may kick it out of a globular cluster (GC). We estimate GW kick retention fractions of merger products assuming different models for BH spin magnitude and orientation (MS0 - random, MS1 - spin as a function of mass and metalicity, MS2 - constant value of $0.5$). We check how they depend on BH-BH merger time and properties of the cluster. We analyze the implications of GW kick retention fractions on intermedi…
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 bin…
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 la…
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 fr…
We introduce a new prescription for the evolution of globular clusters (GCs) during the initial embedded gas phase into a Monte Carlo method. With a simplified version of the Monte Carlo MOCCA code embedded in the AMUSE framework, we study the survival of GCs after the removal of primordial gas. We first test our code and show that our results for the evolution of mass and Lagrangian radii are in good agreement with those obtained with N-body simulations. The Monte Carlo code enables a more rapid exploration of the evolution of systems with a larger number of stars than N-body simulations. We …
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 …
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 …
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 f…
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 …
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 lea…
The paper presents an analysis of formation mechanism and properties of spatial distributions of blue stragglers in evolving globular clusters, based on numerical simulations done with the MOCCA code. First, there are presented N-body and MOCCA simulations which try to reproduce the simulations presented by Ferraro (2012). Then, the agreement between N-body and the MOCCA code is shown. Finally, we discuss the formation process of the bimodal distribution. We report that so-called bimodal spatial distribution of blue stragglers is a very transient feature. It is formed for one snapshot in time …
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.
The paper presents an analysis of properties of populations of blue stragglers (BSs) in evolving globular clusters, based on numerical simulations done with the MOCCA code for various initial globular clusters conditions. We find that various populations of BSs strongly depend on the initial semi-major axes distributions. With a significant number of compact binaries, the number of evolutionary BSs can be also significant. In turn, for semi-major axes distributions preferring binaries with wider orbits, dynamical BSs are the dominant ones. Their formation scenario is very distinct: for wide bi…
We will discuss the evolution of star clusters with an large initial binary fraction, up to 95%. The initial binary population is chosen to follow the invariant orbital-parameter distributions suggested by Kroupa (1995). The Monte Carlo MOCCA simulations of star cluster evolution are compared to the observations of Milone et al. (2012) for photometric binaries. It is demonstrated that the observed dependence on cluster mass of both the binary fraction and the ratio of the binary fractions inside and outside of the half mass radius are well recovered by the MOCCA simulations. This is due to a r…
Is the overconcentration of pristine populations in Galactic globular clusters real? An N-body approach to the problem
Main Astronomical Observatory, National Academy of Sciences of Ukraine（乌克兰国家科学院主天文台）；Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天体物理中心）；Fesenkov Astrophysical Institute（费森可夫天体物理研究所）；Department of Physics, New York University Abu Dhabi（阿布扎比纽约大学物理系）；Center for Astrophysics and Space Science (CASS), New York University Abu Dhabi（阿布扎比纽约大学天体物理学与空间科学中心）；Dipartimento di Fisica, Sapienza, Universitá di Roma（罗马智慧大学物理系）
Optimised population synthesis provides an empirical method to extract the relative mix of stellar evolutionary stages and the distribution of atmospheric parameters within unresolved stellar systems, yet a robust validation of this method is still lacking. We here provide a calibration of population synthesis via non-linear bound-constrained optimisation of stellar populations based upon optical spectra of mock stellar systems and observed Galactic Globular Clusters (GGCs). The MILES stellar library is used as a basis for mock spectra as well as templates for the synthesis of deep GGC spectra…
As we enter a golden age for studies of internal kinematics and dynamics of Galactic globular clusters (GCs), it is timely to assess the performance of modelling techniques in recovering the mass, mass profile, and other dynamical properties of GCs. Here, we compare different mass-modelling techniques (distribution-function (DF)-based models, Jeans models, and a grid of N-body models) by applying them to mock observations from a star-by-star N-body simulation of the GC M 4 by Heggie. The mocks mimic existing and anticipated data for GCs: surface brightness or number density profiles, local ste…
The mass evaporation rate of globular clusters evolving in a strong Galactic tidal field is derived through the analysis of large, multi-mass $N$-body simulations. For comparison, we also study the same evaporation rates using MOCCA Monte Carlo models for globular cluster evolution. Our results show that the mass evaporation rate is a dynamical value; that is, far from a constant single number found in earlier analytical work and commonly used in the literature. Moreover, the evaporation rate derived with these simulations is higher than values previously published. These models also show that…
We created artificial color-magnitude diagrams of Monte Carlo dynamical models of globular clusters, and then used observational methods to determine the number of blue stragglers in those clusters. We compared these blue stragglers to various cluster properties, mimicking work that has been done for blue stragglers in Milky Way globular clusters to determine the dominant formation mechanism(s) of this unusual stellar population. We find that a mass-based prescription for selecting blue stragglers will choose approximately twice as many blue stragglers than a selection criterion that was devel…
Stellar halos and globular cluster (GC) systems contain valuable information regarding the assembly history of their host galaxies. Motivated by the detection of a significant rotation signal in the outer halo GC system of M31, we investigate the likelihood of detecting such a rotation signal in projection, using cosmological simulations. To this end we select subsets of tagged particles in the halos of the Aquarius simulations to represent mock GC systems, and analyse their kinematics. We find that GC systems can exhibit a non-negligible rotation signal provided the associated stellar halo al…
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).…
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…
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 simulate…
Context. Several dynamically cold streams have been associated with certain globular clusters (GCs) based on orbital energies and angular momenta. Some of these streams are surprisingly far apart from their progenitors and one such pair is Triangulum and NGC 5824. Triangulum can be considered as a piece of NGC 5824 leading tail since the cluster's future orbit matches with the stream's track well. The existence of the leading tail for NGC 5824 is the motivation behind the search for its trailing tail. Aims. Our goal is to confirm the connection between Triangulum and NGC 5824 and seek the trai…
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…
In this paper, we discuss the origin of the observed correlation between cluster concentration c and present-day mass function (PDMF) slope α reported by De Marchi, Paresce & Pulone. This relation can either be reproduced from universal initial conditions combined with some dynamical mechanism(s) that alter(s) the cluster structure and mass function over time, or it must arise early on in the cluster lifetime, such as during the gas-embedded phase of cluster formation. Using a combination of Monte Carlo and N-body models for globular cluster evolution performed with the MOCCA and NBODY6 codes,…
Exploring the dynamical evolution of binary stars in multiple-population globular clusters
Indiana University（印第安纳大学）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；Dipartimento di Fisica e Astronomia "Galileo Galilei", Univ. di Padova（帕多瓦大学伽利略·伽利莱物理与天文系）；Korea Astronomy and Space Science Institute（韩国天文学与空间科学研究所）；A. Mickiewicz University（亚当·密茨凯维奇大学）；Istituto Nazionale di Astrofisica - Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）
Even though plenty of symbiotic stars (SySts) have been found in the Galactic field and nearby galaxies, not a single one has ever been confirmed in a Galactic globular cluster (GC). We investigate the lack of such systems in GCs for the first time by analysing 144 GC models evolved with the MOCCA code, which have different initial properties and are roughly representative of the Galactic GC population. We focus here on SySts formed through the wind-accretion channel, which can be consistently modelled in binary population synthesis codes. We found that the orbital periods of the majority of s…
We present a Bayesian inference approach to estimating the cumulative mass profile and mean squared velocity profile of a globular cluster given the spatial and kinematic information of its stars. Mock globular clusters with a range of sizes and concentrations are generated from lowered isothermal dynamical models, from which we test the reliability of the Bayesian method to estimate model parameters through repeated statistical simulation. We find that given unbiased star samples, we are able to reconstruct the cluster parameters used to generate the mock cluster and the cluster's cumulative …
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 fo…
We introduce a multi-component chemo-dynamical method for splitting the Galactic population of Globular Clusters (GCs) into three distinct constituents: bulge, disc, and stellar halo. The latter is further decomposed into the individual large accretion events that built up the Galactic stellar halo: the Gaia-Enceladus-Sausage, Kraken and Sequoia structures, and the Sagittarius and Helmi streams. Our modelling is extensively tested using mock GC samples constructed from the AURIGA suite of hydrodynamical simulations of Milky Way (MW)-like galaxies. We find that, on average, a proportion of the …
The detection of intermediate mass black holes in the centres of globular clusters is highly controversial, as complementary observational methods often deliver significantly different results. In order to understand these discrepancies, we develop a procedure to simulate integral field unit (IFU) observations of globular clusters: Simulating IFU Star Cluster Observations (SISCO). The input of our software are realistic dynamical models of globular clusters that are then converted in a spectral data cube. We apply SISCO to Monte Carlo cluster simulations from Downing et al. (2010), with a real…
We present the first application of the made-to-measure method for modelling dynamical systems to globular clusters. Through the made-to-measure algorithm, the masses of individual particles within a model cluster are adjusted while the system evolves forward in time via a gravitational $N$-body code until the model cluster is able to reproduce select properties of an observed cluster. The method is first applied to observations of mock isotropic and anisotropic clusters while fitting against the cluster's three dimensional or projected density profile, density weighted mean-squared velocity p…
Using action-based distribution function for the dynamical model of the Milky Way we have estimated its total mass and its density profile. Constraints are coming from the globular cluster proper motions from Gaia EDR3, from the rotation curve based on Gaia DR2 data, and from the vertical force data. We use Bayesian Markov chain Monte Carlo method to explore the parameters, for which the globular cluster distribution function and the Galactic potential are fully constrained. Numerical simulations are used to study the uncertainties on the potential constraint if considering a possible massive …
Dynamical mass estimates of simple systems such globular clusters (GCs) still suffer from up to a factor of 2 uncertainty. This is primarily due to the oversimplifications of standard dynamical models that often neglect the effects of the long-term evolution of GCs. Here, we introduce a new approach to measure the dynamical properties of GCs, based on the combination of a deep-learning framework and the large amount of data from direct $N$-body simulations. Our algorithm, $\texttt{$π$-DOC}$ ($\textit{Predicting Images for the Dynamics Of stellar Clusters}$) is composed of two convolutional net…
We present BALRoGO: Bayesian Astrometric Likelihood Recovery of Galactic Objects, a public code to measure the centers, effective radii, and bulk proper motions of Milky Way globular clusters and Local Group dwarf spheroidals, whose data are mixed with Milky Way field stars. Our approach presents innovative methods such as surface density fits allowing for strong interloper contamination and proper motion fits using a Pearson VII distribution for interlopers, instead of classic Gaussian-mixture recipes. We also use non-parametric approaches to represent the color-magnitude diagram of such stel…
The detection of intermediate mass black holes (IMBHs) in globular clusters has been hotly debated, with different observational methods delivering different outcomes for the same object. In order to understand these discrepancies, we construct detailed mock integral field spectroscopy (IFU) observations of globular clusters, starting from realistic Monte Carlo cluster simulations. The output is a data cube of spectra in a given field-of-view that can be analyzed in the same manner as real observations and compared to other (resolved) kinematic measurement methods. We show that the main discre…
