Dynamical Evolution Of Globular Clusters Research Articles

Dynamical state of the globular clusters Rup 106 and IC 4499

The dynamical evolution of globular clusters is theoretically described by a series of well-known events typical of N-body systems. Still, the identification of observational signatures able to empirically describe the stage of dynamical evolution of a stellar system with a density typical of a globular cluster represents a challenge. In this paper, we study the dynamical age of the globular clusters Rup 106 and IC 4499. To this aim, we study the radial distribution of the blue straggler stars (BSSs) via the A+ parameter and of the slope of the main sequence mass function. Both tracers show that Rup 106 and IC 4499 are dynamically young clusters where dynamical friction has just started to segregate massive stars towards their respective centres. Furthermore, we observe that the BSSs are more centrally concentrated in both clusters than the reference population. Similarly, we find that in both cases the slope of the mass function significantly decreases as a function of the cluster-centric distance. This result provides additional support for the use of the radial distribution of the BSSs as a powerful and observationally convenient indicator of the cluster dynamical age.

Investigating dynamical properties of globular clusters through a family of lowered isothermal models

ABSTRACT To investigate the dynamical properties of globular clusters, surface brightness and kinematic data were collected and fitted to a family of lowered isothermal models called limepy models. For the 18 globular clusters studied, the amounts of concentration, truncation, and anisotropy were determined. In addition, the cluster mass, half-mass radius, distance, and mass-to-light ratio were also obtained. In general, limepy models can describe these clusters well. Among these 18 clusters, NGC 5139, 6388, and 7078 have been claimed to be candidates for hosting intermediate-mass black holes in the literature. The models could not appropriately fit the central proper-motion velocity dispersion of NGC 5139, nor the slope of the proper-motion velocity dispersion profile of NGC 6388. Thus, more dedicated models with intermediate-mass black holes or a group of stellar-mass black holes at cluster centres may need to be considered. Regarding NGC 7078, our model with some degree of anisotropy can fit the data. Finally, a strong concentration–truncation anticorrelation and a truncation–semimajor-axis correlation were revealed, which could be the observational imprint of the dynamical evolution of globular clusters.

Mocca: dynamics and evolution of single and binary stars of multiple stellar populations in tidally filling and underfilling globular star clusters

ABSTRACT 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 analyse their effect on the binary dynamics and survival. Here, we focus on the number ratio of FG and SG binaries, their 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⊙ 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.

Using binaries in globular clusters to catch sight of intermediate-mass black holes

ABSTRACT 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 $70 \rm {per \, cent}$ 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 $32.2\pm 7.8 \rm {per \, cent}$ 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.

The possible role of stellar mergers for the formation of multiple stellar populations in globular clusters

ABSTRACTMany possible scenarios for the formation of multiple stellar populations (MSPs) in globular clusters (GCs) have been discussed so far, including the involvement of asymptotic giant branch stars, fast-rotating main-sequence stars, very massive main-sequence stars and mass-transferring massive binaries based on stellar evolution modelling. But self-consistent, dynamical simulations of very young GCs are usually not considered. In this work, we perform direct N-body modelling of such systems with total masses up to 3.2 × 105 M⊙, taking into account the observationally constrained primordial binary properties, and discuss the stellar mergers driven both by binary stellar evolution and dynamical evolution of GCs. The occurrence of stellar mergers is enhanced significantly in binary-rich clusters such that stars forming from the gas polluted by merger-driven ejection/winds would appear as MSPs. We thus emphasize that stellar mergers can be an important process that connects MSP formation with star cluster dynamics, and that multiple MSP formation channels can naturally work together. The scenario studied here, also in view of a possible top-heavy initial mass function, may be particularly relevant for explaining the high mass fraction of MSPs (the mass budget problem) and the absence of MSPs in young and low-mass star clusters.

Intermediate-Mass Black Holes in binary rich star clusters

AbstractThree-body interactions of stellar-mass binaries with intermediate mass black holes (IMBHs) in nuclei of globular clusters may produce specific features that may serve as an independent indicator of existence of the IMBHs. By means of direct N-body integrations we follow the dynamical evolution of globular clusters of moderate extension and mass with 50% binary population over a time span of ≍ 0.8 Gyr and compare the cases with and without the primordial binaries as well as with and without the IMBH. We show that (i) presence of the IMBH leads to rapid formation of a density cusp regardless of the initial binary fraction, (ii) binary rich clusters with the IMBH produce high velocity escapers at a rate of ≍ 0.1 Myr−1 and (iii) clusters hosting an IMBH together with high number of binaries form a denser halo of marginally unbound stars than clusters that lack either the IMBH or the binary population.

The blue straggler population of the old open cluster Berkeley 17

Context. Blue straggler stars (BSSs) are observed in Galactic globular clusters and old open clusters. The radial distribution of BSSs has been used to diagnose the dynamical evolution of globular clusters. For the first time, with a reliable sample of BSSs identified with Gaia DR2, we conduct such an analysis for an open cluster. Aims. We aim to identify members, including BSSs, of the oldest known Galactic open cluster Berkeley 17 with the Gaia DR2 proper motions and parallaxes. We study the radial distribution of the BSS population to understand the dynamical evolution of the cluster. Methods. We selected cluster members to populate the colour magnitude diagram in the Gaia filters. Cluster parameters are derived using the brightest members. The BSSs and giant branch stars are identified, and their radial distributions are compared. The segregation of BSSs is also evaluated with respect to the giant branch stars using the minimum spanning tree (MST) analysis. Results. We determine Berkeley 17 to be at 3138.6−352.9+285.5 pc. We find 23 BSS cluster members, only two of which were previously identified. We find a bimodal radial distribution of BSSs supported by findings from the MST method. Conclusions. The bimodal radial distribution of BSSs in Berkeley 17 indicates that they have just started to sink towards the cluster centre, placing Berkeley 17 with globular clusters of intermediate dynamical age. This is the first such determination for an open cluster.

Binary black hole mergers from globular clusters: the impact of globular cluster properties

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.

Dynamical evolution of globular clusters: Recent developments

We analyze structural parameters of the globular clusters belonging to the Milky Way system which were listed in the latest edition of the Harris Catalogue. We search for observational evidences of the effect of tidal forces induced by the Galaxy on the dynamical and thermodynamical evolution of a globular cluster. The behavior for the [Formula: see text] distribution exhibited by the globular cluster population seems to be in contrast with theoretical results in literature about gravothermal instability, and suggest a new limit value smaller than the previous one.

Inverting the dynamical evolution of globular clusters: clues to their origin

AbstractScaling relations for globular clusters (GC) differ from the scaling relations for pressure supported (elliptical) galaxies. In this contribution we discuss the relative importance of nature and nurture in the establishment of the scaling between cluster density (or radius), mass and Galactocentric distance for the Milky Way GCs. We show that energy diffusion by stellar encounters (i.e. two-body relaxation) is the dominant mechanism in shaping the bivariate dependence of density on mass and Galactocentric distance for GCs with masses ≲ 106M⊙, and it can not be excluded that GCs formed with similar scaling relations as the more massive ultra-compact dwarf galaxies (UCDs). To explore the initial properties that give rise to the distributions of these quantities, we developed a fast cluster evolution model (Evolve Me A Cluster of StarS, emacss) and use it in a hierarchical Bayesian framework to fit a parameterised model for the initial properties of Milky Way GCs to the observed present-day properties. The best-fit cluster initial mass function is substantially flatter (power-law with index − 0.6 ± 0.2) than what is observed for young massive clusters (YMCs) forming in the nearby Universe (power-law with index − 2). This result is driven by the metal-poor GCs, a slightly steeper CIMF is allowed when considering the metal-rich GCs separately (α ≃ −1.2 ± 0.4). If stellar mass loss and two-body relaxation in the Milky Way tidal field are the dominant disruption mechanisms, then GCs formed differently from YMCs.

Destruction of Globular Clusters in the Galactic Gravitational Field

Abstract We present some results of numerical simulation of a dynamical evolution of globular clusters in the tidal field of the Galaxy. An analytical description of tidal destruction of such clusters and simple estimate of their lifetimes are proposed.

THE DYNAMICAL EVOLUTION OF STELLAR BLACK HOLES IN GLOBULAR CLUSTERS

Our current understanding of the stellar initial mass function and massive star evolution suggests that young globular clusters may have formed hundreds to thousands of stellar-mass black holes, the remnants of stars with initial masses from $\sim 20 - 100\, M_\odot$. Birth kicks from supernova explosions may eject some black holes from their birth clusters, but most should be retained. Using a Monte Carlo method we investigate the long-term dynamical evolution of globular clusters containing large numbers of stellar black holes. We describe numerical results for 42 models, covering a range of realistic initial conditions, including up to $1.6\times10^6$ stars. In almost all models we find that significant numbers of black holes (up to $\sim10^3$) are retained all the way to the present. This is in contrast to previous theoretical expectations that most black holes should be ejected dynamically within a few Gyr. The main reason for this difference is that core collapse driven by black holes (through the Spitzer "mass segregation instability") is easily reverted through three-body processes, and involves only a small number of the most massive black holes, while lower-mass black holes remain well-mixed with ordinary stars far from the central cusp. Thus the rapid segregation of stellar black holes does not lead to a long-term physical separation of most black holes into a dynamically decoupled inner core, as often assumed previously. Combined with the recent detections of several black hole X-ray binary candidates in Galactic globular clusters, our results suggest that stellar black holes could still be present in large numbers in many globular clusters today, and that they may play a significant role in shaping the long-term dynamical evolution and the present-day dynamical structure of many clusters.

Galactic globular cluster 47 Tucanae: new ties between the chemical and dynamical evolution of globular clusters?

It is generally accepted today that Galactic globular clusters (GGCs) consist of at least two generations of stars that are different in their chemical composition and perhaps age. However, knowledge about the kinematical properties of these stellar generations, which may provide important information for constraining evolutionary scenarios of the GGCs, is still limited. We therefore study the connections between chemical and kinematical properties of different stellar generations in the Galactic globular cluster 47 Tuc. To achieve this goal, we used abundances of Li, O, and Na determined in 101 main sequence turn-off (TO) stars with the aid of 3D hydrodynamical model atmospheres and NLTE abundance analysis methodology. We divided our sample TO stars into three groups according to their position in the [Li/Na]-[Na/O] plane to study their spatial distribution and kinematical properties. We find that there are statistically significant radial dependencies of lithium and oxygen abundances, A(Li) and A(O), as well as that of [Li/Na] abundance ratio. Our results show that first-generation stars are less centrally concentrated and dynamically hotter than stars belonging to subsequent generations. We also find a significant correlation between the velocity dispersion and O and Na abundance, and between the velocity dispersion and the [Na/O] abundance ratio.

Understanding the dynamical state of globular clusters: core-collapsed versus non-core-collapsed

We study the dynamical evolution of globular clusters using our H\'enon-type Monte Carlo code for stellar dynamics including all relevant physics such as two-body relaxation, single and binary stellar evolution, Galactic tidal stripping, and strong interactions such as physical collisions and binary mediated scattering. We compute a large database of several hundred models starting from broad ranges of initial conditions guided by observations of young and massive star clusters. We show that these initial conditions very naturally lead to present day clusters with properties including the central density, core radius, half-light radius, half-mass relaxation time, and cluster mass, that match well with those of the old Galactic globular clusters. In particular, we can naturally reproduce the bimodal distribution in observed core radii separating the "core-collapsed" vs the "non core-collapsed" clusters. We see that the core-collapsed clusters are those that have reached or are about to reach the equilibrium "binary burning" phase. The non core-collapsed clusters are still undergoing gravo-thermal contraction.

NUMERICAL MODELING OF GLOBULAR CLUSTERS TIDAL DISSOLUTION

Numerical model of dynamical evolution of globular clusters(GCs) is described, with an emphasis of the mass loss rate in tidal interactions with the Galaxy. On a set of models dependence of the tidal destruction on cluster parameter sand initial conditions, such as: the initial cluster mass, its initial position in the Galaxy, the eccentricity of the orbit–are studied. An analytical description of tidal destruction of GCs and simple estimate of their life times is proposed.

INITIAL SIZE DISTRIBUTION OF THE GALACTIC GLOBULAR CLUSTER SYSTEM

Despite the importance of their size evolution in understanding the dynamical evolution of globular clusters (GCs) of the Milky Way, studies are rare that focus specifically on this issue. Based on the advanced, realistic Fokker-Planck (FP) approach, we predict theoretically the initial size distribution (SD) of the Galactic GCs along with their initial mass function and radial distribution. Over one thousand FP calculations in a wide parameter space have pinpointed the best-fit initial conditions for the SD, mass function, and radial distribution. Our best-fit model shows that the initial SD of the Galactic GCs is of larger dispersion than today's SD, and that typical projected half-light radius of the initial GCs is ~4.6 pc, which is 1.8 times larger than that of the present-day GCs (~2.5 pc). Their large size signifies greater susceptibility to the Galactic tides: the total mass of destroyed GCs reaches 3-5x10^8 M_sun$, several times larger than the previous estimates. Our result challenges a recent view that the Milky Way GCs were born compact on the sub-pc scale, and rather implies that (1) the initial GCs are generally larger than the typical size of the present-day GCs, (2) the initially large GCs mostly shrink and/or disrupt as a result of the galactic tides, and (3) the initially small GCs expand by two-body relaxation, and later shrink by the galactic tides.

The origins of blue stragglers and binarity in globular clusters

(abridged) We use newly available empirical binary fractions for globular clusters to carry out a direct test of the binary evolution hypothesis, and of collisional channels that involve binary stars. More specifically, using the previously reported correlation between blue straggler numbers and core mass as a benchmark, we test for correlations with the number of binary stars, as well as with the rates of single-single, single-binary, and binary-binary encounters. Surprisingly, we find that the simple correlation with core mass remains by far the strongest predictor of blue straggler population size, even in our joint models. This is despite the fact that the binary fractions themselves strongly anti-correlate with core mass, just as expected in the binary evolution model. At first sight, these results do not fit neatly with either binary evolution or collisional models in their simplest forms. Arguably the simplest and most intriguing possibility to explain this unexpected result is that observational errors on the core binary fractions are larger than the true intrinsic dispersion associated with their dependence on core mass. In the context of the binary evolution model, this would explain why the combination of binary fraction and core mass is a poorer predictor of blue straggler numbers than core mass alone. It would also imply that core mass is a remarkably clean predictor of core binary fractions. This would be of considerable importance for the dynamical evolution of globular clusters, and provides an important benchmark for models attempting to understand their present-day properties.

Outer density profiles of 19 Galactic globular clusters from deep and wide-field imaging

Using deep photometric data from WFC@INT and WFI@ESO2.2m we measure the outer number density profiles of 19 stellar clusters located in the inner region of the Milky Way halo (within a Galactocentric distance range of 10-30 kpc) in order to assess the impact of internal and external dynamical processes on the spatial distribution of stars. Adopting power-law fitting templates, with index $-\gamma$ in the outer region, we find that the clusters in our sample can be divided in two groups: a group of massive clusters ($ \ge 10^5 $ M_sun) that has relatively flat profiles with $2.5 < \gamma < 4$ and a group of low-mass clusters ($ \le 10^5 $ M_sun), with steep profiles ($\gamma > 4$) and clear signatures of interaction with the Galactic tidal field. We refer to these two groups as 'tidally unaffected' and 'tidally affected', respectively. Our results also show a clear trend between the slope of the outer parts and the half-mass density of these systems, which suggests that the outer density profiles may retain key information on the dominant processes driving the dynamical evolution of Globular Clusters.

Ground- and space-based study of two globular cluster cataclysmic variables: M22 CV1 and M5 V101

As a class of compact binaries with large binding energy, cataclysmic variables formed through close encounters play an important role in the dynamical evolution of globular clusters. As part of a systematic search for CVs undergoing dwarf nova eruptions in globular clusters, our 2004 monitoring programme of M22 detected an outburst of the dwarf nova candidate CV1 during May. We implement the ISIS image subtraction routine to obtain a light curve for an outburst of CV1. We present the outburst light curve as well as HST/WFPC2 photometry in the V, U and near ultra-violet (nUV) bands and a Chandra/ACIS-S spectrum of the object. Our results confirm the DN nature of the outburst and the CV status of the object. We also present the results of a ground-based study of another globular cluster CV, M5 V101 - including quiescent medium-resolution WHT/ISIS spectroscopy in the B and R bands, displaying prominent Balmer and HeI emission, and R-band photometry.

MONTE CARLO SIMULATIONS OF GLOBULAR CLUSTER EVOLUTION. V. BINARY STELLAR EVOLUTION

We study the dynamical evolution of globular clusters containing primordial binaries, including full single and binary stellar evolution using our Monte Carlo cluster evolution code updated with an adaptation of the single and binary stellar evolution codes SSE/BSE from Hurley et. al (2000, 2002). We describe the modifications we have made to the code. We present several test calculations and comparisons with existing studies to illustrate the validity of the code. We show that our code finds very good agreement with direct N-body simulations including primordial binaries and stellar evolution. We find significant differences in the evolution of the global properties of the simulated clusters using stellar evolution compared to simulations without any stellar evolution. In particular, we find that the mass loss from stellar evolution acts as a significant energy production channel simply by reducing the total gravitational binding energy and can significantly prolong the initial core contraction phase before reaching the binary-burning quasi steady state of the cluster evolution as noticed in Paper IV. We simulate a large grid of clusters varying the initial cluster mass, binary fraction, and concentration and compare properties of the simulated clusters with those of the observed Galactic globular clusters (GGCs). We find that our simulated cluster properties agree well with the observed GGC properties. We explore in some detail qualitatively different clusters in different phases of their evolution, and construct synthetic Hertzprung-Russell diagrams for these clusters.